The God Problem: How a Godless Cosmos Creates 

by Howard Bloom

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Last annotated on October 25, 2016

The God Problem: How a Godless Cosmos Creates 

FORWARD

An autodidact, he has no graduate degrees and no cozy university or institute to house him. He refuses to specialize or take on modest byte-size projects, instead hopping around between physics and space travel, war and the nature of human community.  Read more at location 192

his unaccountability to any scientific or intellectual establishment often puts him ahead of the curve, where he can pinpoint issues and trends that are barely discernible from the mainstream. That was the case with his 2000 book, Global Brain, on the emergence of a collective human consciousness, and even more so with this audacious volume, which challenges the philosophical underpinnings of science and shows how they will have to evolve to keep up with empirical reality.  Read more at location 195

the assumption of Western science has been that the universe, or physical world, is dead, meaning that anything that goes on it can be ultimately reduced to the interactions of inert bits of matter. An amoeba, for example, doesn't move because it “wants” to, but because of attractions and repulsions between molecules on its surface and chemicals within its environment. In practice, this has meant that science is on a mission to crush all forms of agency  Read more at location 199

The hummingbird's speed and grace is explained by the density of mitochondria in its wing muscles, leading to an abundant flow of ATP to the myosin. All notions of play or agency or will are banished. As for humans, individual scientists usually hedge on the subject of whether humans possess, but the long-term trend has been to extinguish it to an occasional flicker.  Read more at location 214

However grudgingly, the scientific worldview is being reanimated, which is not to say the world is being re-“enchanted.”  Read more at location 235

Agency, meaning also desire and will, is, in some form, everywhere, from inchworms to electrons, and it is time for science to recognize that everything is, in some not merely metaphorical sense, alive.  Read more at location 238

PREFACE: ADVENTURE THAT TAKES YOUR BREATH AWAY

Researching The God Problem was one of the greatest intellectual adventures of my life. Nearly every discovery came as a shock.  Read more at location 254

all the standard sources on the history of math from Bertrand Russell's History of Western Philosophy to the Encyclopædia Britannica agreed on one thing: The Mesopotamians had invented angles and the 360-degree way of measuring them.  Read more at location 279

Maybe I couldn't find even the slightest hint of a Mesopotamian protractor because—are you ready for this—there was no such thing. And maybe there was no such thing as a Mesopotamian protractor because all the books and reference sources were wrong.  Read more at location 288

thus began an adventure into the origin of ideas that you and I take for granted every day. Ideas at the very foundations of logic and reason. Your logic and reason and mine. Thus began an adventure that led to heresies. Five heresies, to be precise. Heresies that seem outrageous.  Read more at location 290

One more tiny confession: This is a book about metaphysics.  Read more at location 293

CHAPTER 1: APPETIZERS, CANAPES, AND SNACKS

INTRODUCTION: I DARE YOU—THE WEIRDEST RIDE IN THE UNIVERSE

How does the universe invent astonishments? And why does a material universe, a universe of mere forces, things, and laws, have creativity at all? That, too, is the God Problem, the problem that the creationists and the intelligent design advocates are trying to rub our noses in. It's the problem that scientific atheists like Richard Dawkins, Daniel Dennett, Christopher Hitchens, and Sam Harris have all too often dodged. How does a cosmos of elementary particles and gravity turn the impossible into the real, the real into the ordinary, and the ordinary into the raw material of new inventions, new breakthroughs, new astonishments, and new impossibilities? How does the cosmos pull off the act of genesis over and over again? Without a creator?  Read more at location 328

How old are you? If you gave a figure under 150, you're wrong. Why? For the answer, try another question: Why didn't your finger go through your palm and come out on the other side of your hand? It's because you're solid, right? And what makes you solid? The answer is protons. How old are those protons? They're 13.73 billion years old.  Read more at location 361

THE CAFÉ TABLE AT THE BEGINNING OF THE UNIVERSE

nothing comes from nothing. Zero plus zero equals zero. The idea that this basic fact could ever change is wild-eyed fantasy. And it defies the first law of thermodynamics, the law of the conservation of matter and energy, a law so basic that every respectable twenty-first-century scientist will someday declare it thoroughly and completely right.  Read more at location 383

that pinprick blows up so fast that it makes me dizzy. And sure enough, it has three properties that have never existed before. Three properties that, if common sense prevailed, should not exist. Those properties are time, space, and speed—time, space, and energy.  Read more at location 388

space and time, you say, is about to produce something called “things.” And those things are going to precipitate from the sheet of space, time, and speed the way that raindrops precipitate from a storm cloud.  Read more at location 395

This peculiar rule-breaking and massively innovating cosmos that you and I have been watching from our café table will churn out galaxies, stars, molecules, cells, and DNA. Not to mention thinkers, talkers, lollypops, common sense, croissants, cannibals, café tables, and you and me. But how? That is the God Problem.  Read more at location 405

THE PROBLEM WITH GOD: THE TALE OF A TWISTED CONFESSION

the first two rules of science are: The truth at any price including the price of your life. Look at things right under your nose as if you've never seen them before, then proceed from there.  Read more at location 424

God, in Russell's opinion, is a silly idea. If it took a God to create a universe, then a thing as complex and as powerful as a God would need a creator, too. And who or what created God?  Read more at location 434

When you and I were born, only one thing was certain about the rest of our lives: that you and I would someday die. Just as billions of humans and over a trillion, trillion, trillion (1036) microorganisms, animals, and plants have died before us. Yes, God kills creatures by the trillions of trillions of trillions. In fact, trillions of trillions of trillions is an undercount. A God who slaughters is no God at all.  Read more at location 470

And if God is not the creator and the controller of violence, then God is not omnipotent. He is not all powerful. He is not God.  Read more at location 476

But take God out of the skies, put him in the minds, guts, and gonads of human beings, and you're left with a massive question. How does a Godless cosmos pull off the tricks that every genesis myth tries to grasp?  Read more at location 508

From that no thing came the first some thing, the big bang. And it wasn't just any something. It wasn't just an undifferentiated mass like a black hole. It was a speed rush of time and space that had within it the seeds of an entire universe. The seeds of atoms, suns, planets, and galactic superclusters. The seeds of algae, cabbages, flamingos, termites, and trees. The seeds of you and me. That's a colossal act of creativity, a stupendous act of genesis and invention. How did it happen?  Read more at location 511

How does the cosmos create? That's not just any question, it's THE question. It's the God Problem.  Read more at location 527

CHAPTER 2: A TASTE OF SIN

BRACE YOURSELF: THE FIVE HERESIES

here are five assumptions conveniently overturned for your edification and delight.  Read more at location 533

************  A does not equal A. One plus one does not equal two. The second law of thermodynamics, that all things tend toward disorder, that all things tend toward entropy, is wrong. The concept of randomness is a mistake. These days randomness goes under the fancy name of stochasticity. But no matter how it slicks itself up with arcane terminology, there is far less randomness in this universe than today's science believes. And far less randomness than you and I often think. Information theory is not really about information. Its equations cover only a tiny sliver of what the theory claims. The real core of communication is what information theory's founder Claude Shannon calls “meaning.” And “meaning,” believe it or not, is not covered in information theory. Why is that a big mistake? Meaning is central to the cosmos. Central to quarks, protons, photons, galaxies, stars, lizards, lobsters, puppies, bees, and human beings.  Read more at location 534

concepts we'll use to probe the implications of the five heresies:  Read more at location 542

Ur patterns, deep structures of the cosmos, patterns the cosmos repeats over and over again.  Read more at location 543

Repetition.

Which leads to the concept of translation.

Corollary generator theory.

Implicit versus explicit realities.

Opposites are joined at the hip.

The bottom line? Sociality.

HERESY NUMBER ONE: WHY A DOES NOT EQUAL A

Logic, reason, algebra, calculus, and trigonometry are based on the notion that A is A.  Read more at location 559

(Note: **** a != a)  Barry Mazur, the Gerhard Gade University Professor of Mathematics at Harvard University, asks, “When is one thing equal to some other thing?” The answer should be simple, right? Not really. In fact, Mazur says that, “One can't do mathematics for more than ten minutes without grappling, in some way or other, with the slippery notion of equality.” Why slippery? Because each A, each “thing,” is presented to us in a different context, says Mazur. Each A is at the heart of a different network of relationships. And the very quality of A-ness is the result of an act of distortion. A violent act of reality abuse. An act of abstraction.  Read more at location 578

Mazur wrote a twenty-four-page paper on the problems with A = A. But Terence Parsons, professor of philosophy and linguistics at UCLA, was even more bugged about A = A. He wrote an entire book on the subject, Indeterminate Identity: Metaphysics and Semantics.  Read more at location 588

Parsons puts the problem of A is A like this: Suppose a ship sets sail, and while at sea it is completely rebuilt, plank by plank; is the resulting ship with new parts the ship that originally set sail? What if the discarded pieces of the original ship are assembled into a ship; is that the ship that originally set sail?  Read more at location 590

***********  abstractions may be indispensable. But they don't accurately reflect reality.  Read more at location 615

Bertrand Russell, the man whose writings helped shoehorn you into atheism, was tortured by the paradoxes of A is A in his 1903 book The Principles of Mathematics. He puzzled over whether the relationships called “=” and “is” even exist.  Read more at location 616

****  Russell said, “It may be said, identity cannot be a relation.”16 It can't represent something that exists in the real world. But we have to use it. Why? It's handy as all get out.  Read more at location 619

why in the world does one A not equal another A? If we clone you and get an identical copy, why are you not your clone? Location, location, location. Location in time. Location in space. Location in a big picture. And your place in many smaller pictures nested within that big picture.  Read more at location 631

WHEN IS A FROG A RIVER? ARISTOTLE WRESTLES HERACLITUS

Aristotle developed his ideas in opposition to Heraclitus, the founder of the school of perpetual transformation.  Read more at location 646

another Athenian philosopher, Cratylus, took Heraclitus's notion of perpetual, second-by-second change a step further.23 According to University of Pennsylvania philosopher Charles H. Kahn, “Cratylus denied that you could even step in the river once, since you are changing too.”24 The result, says Aristotle, was that the “most extreme”25 followers of Heraclitus said it was impossible to fix a name to anything.  Read more at location 658

Cratylus reduced all philosophy to helpless hand waving. Or, as Aristotle put it, the change-obsessives’ argument meant that you couldn't even consider things “as existing.”  Read more at location 669

Aristotle put forth a principle that would remain fundamental to philosophy, mathematics, and logic for the next 2,300 years. Formally it's called “the law of noncontradiction.”29 Here's how Aristotle put it in his Metaphysics: “The same attribute cannot at the same time belong and not belong to the same subject and in the same respect.”  Read more at location 673

Leibniz put it a bit more clearly. He came up with “A is A.”  Read more at location 687

Aristotle says that A is A, the law of noncontradiction, is the most fundamental of all the propositions in philosophy and in daily life. It is “the starting point even for all the other axioms.”  Read more at location 706

****  (Note:   exactly)  A = A is fundamental to logic. It is fundamental to mathematics. It is fundamental to science. And it is fundamental to the care and feeding of frogs. But I have sorry news to report. A = A is false. It is sometimes a good approximation. But in the end, it's not 100 percent true. Why? Because Aristotle was right. But so was Heraclitus. Opposites can be true simultaneously. In fact, they usually are. It all goes back to location, location, location. It all goes back to differentiation.  Read more at location 715

All these things—neurons, synapses, synaptic senders, synaptic receivers, and the facets of culture in the cloud of your mind, a cloud that shifts from second to second—change between the reading of one A and another. Your mind is like Heraclitus's river.  Read more at location 732

Take a look at just this super-short phrase, a phrase with two a's in very different contexts doing very different jobs: all alone Small as this phrase is, large-scale structure, big-picture structure, gives each a a radically different role. And large-scale structure makes each a a part of a very different team. The three-letter all team makes a very different sound and meaning than the five letter team of alone. Let's shift A = A to physics for a second. A proton = a proton, right? Two protons are identical, n’est-ce pas? Not quite. Like the letter a in a Shakespearean sonnet, every proton has a unique place in big-picture structures. And that place in the big picture changes the proton's role in the cosmos. Protons are participants in social processes. And those social processes help generate the radical differences between the swatches of space and the clumps of matter in this universe.  Read more at location 748

Big-picture structure counts. Your unique place in the social mesh changes your role. So does mine. And big-picture structure and positioning in the social mesh are location. Or, to put it in real estate terms, big-picture structure and positioning are location, location, location. And in the end, location, location, location gives every fleck and fiber of this cosmos a different role in a massive weave, a massively shifting, changing, and self-upgrading tapestry.  Read more at location 780

****  A = A is a generalization. It is not precise. It is half a truth. The whole truth? A is A. But each A is different. Aristotle was right. And so was Heraclitus. Opposites are joined at the hip.  Read more at location 788

A = A is a simplification, one so radical that it sometimes utterly distorts reality. It skins reality alive. Is A = A useful? Does logic come in handy? Is math a magnificent symbolic system with which to comprehend what's around us? And is math based on A = A? Yes. Absolutely. But math and logic are just that—very, very simplified representations. Symbolic systems with massive powers. But symbolic systems that sometimes do enormous injustice to the richness of that which they attempt to represent.  Read more at location 800

What happens if you introduce two up quarks to one down quark? Do you get just three quarks?  Read more at location 820

it's called a neutron. That's like putting three pats of butter on a bread plate and ending up with a dancing whale. What the hell is going on here? Cosmic creativity. Raw and unadorned cosmic creativity. A creativity in which A does not equal A and one plus one does not equal two. The creativity at the heart and soul of the God Problem.  Read more at location 832

HERESY NUMBER THREE: PREPARE TO BE BURNED AT THE STAKE (THE SECOND LAW OF THERMODYNAMICS—WHY ENTROPY IS AN OUTRAGE)

The central issue…is whether the surprising—one might even say unreasonable—propensity for matter and energy to self-organize “against the odds” can be explained using the known laws of physics, or whether completely new fundamental principles are required. In practice, attempts to explain complexity and self-organization using the basic laws of physics have met with little success.47 —Paul Davies  Read more at location 836

Where did the second law of thermodynamics come from? A central metaphor. The steam engine. And that's one reason it is wrong. The cosmos is not a steam engine.  Read more at location 842

What is the second law? All things tend toward disorder.  Read more at location 844

Are form and structure steadily stumbling down the stairway of form into the chaos of a wispy gas? No. In fact, the very opposite is true. The universe is steadily climbing up. It is steadily becoming more form filled and more structure rich. Huh? How could that possibly be true? Everyone knows that the second law of thermodynamics is gospel. Including everybody who is anybody in the world of physics, chemistry, and even complexity theory.  Read more at location 868

At first, all I see is a mixed up, random flurry of protons and neutrons jittering maniacally in the scalding soup of a plasma. All I see is elementary particles slamming and smashing into each other, then ricocheting away at speeds that make the collision of bullets slamming head-on look like gentle slow-motion kisses. And I'm about to tell you that what's in front of my nose has proven you radically wrong. But then I take in the macroscale. And something very different is happening. These gazillions of crashing particles are cooperating in the formation of waves and troughs. Waves and troughs that ripple from one end of the cosmos to the other. The slam-banging, bump-em-car particles are collaborating the way that molecules of water in ocean waves work together. They are rippling as coherently as ropes of clay, ropes that stretch across the cosmos for hundreds of light-years, waves that roll protons and neutrons in tight synchrony, waves that retain their identity until they reach distant corners of the cosmos hundreds of thousands of light-years from the point where they began.  Read more at location 892

In other words, the plasma shows a form of coordinated social behavior that defies belief. Any rational, logical thinker would know that a cosmos of elementary particles descended from nothing would swish and swivel at random. But randomness, a concept whose gaffs, gaps, and gashes we'll soon see, fails to materialize. Thanks to large-scale structure, big-picture structure, and social behavior, the particles of this cosmos rock and roll to their own self-generated beat. They defy the rules of arithmetic. Protons plus neutrons does not just equal protons plus neutrons.  Read more at location 905

HERESY NUMBER FOUR: RANDOMNESS IS WRONG—THE SIX MONKEYS AT SIX TYPEWRITERS ERROR

The chances that merely by chance they [DNA molecules] should have become arranged in the meaningful ways in which they are arranged are beyond much doubt less than the chances that a pile of rocks rolling down a hillside will arrange themselves by chance on a railway embankment in such a way as to spell out in English the name of the town where the embankment is. —Michael Polanyi, Fellow of the Royal Society  Read more at location 922

a proton is more than 1,837 times more massive than an electron. So any rational and sober thinker can see that there is no way in hell that protons and electrons are going to develop electromagnetic lusts.  Read more at location 944

Roughly 380,000 years after the big bang, electrons discover that their needs fit the longings of protons perfectly. No matter where the electron is and no matter what its life history, pick any proton in this universe at random, flip it an electron from anywhere you please, and they embrace. What's more, their fit is more precise than anything that even the makers of the ultimate high-precision scientific device, CERN's Large Hadron Collider,60 have ever been able to achieve. If this were a truly random universe, this fit simply should not be.  Read more at location 950

Instead of a random mix of permutations and combinations, elementary particles have astonishing uniformity. The total number of different kinds of elementary particles in the cosmos comes to less than four hundred.61 Only four hundred kinds of nanobits in a cosmos of 1087 particles. And the kinds of teams these particles make when they first mingle and mate are even smaller. That is utterly shocking.  Read more at location 966

when electrons discover how naturally they fit around protons, the result is a radically new set of properties. Radically new, but radically few. It's the handful of properties we call an atom: hardness, durability, and the ability to play with others in the sandbox of space, to team up in ways this cosmos has never seen before. How many kinds of atoms does a cosmos of zillions of particles sliding into each other's arms produce? If things were really random, the species of newly born atoms should be wacky, crazed, and without end. But our universe does not blat out more than a zillion to the zillionth power new forms of atoms, as the probabilistic equations of randomness would imply. Far from it. It produces just three rigidly constrained species of atoms. One is called hydrogen. One is called helium. And the third is called lithium.  Read more at location 971

A BRIEF HISTORY OF THE GOD PROBLEM: WERE KEPLER, GALILEO, AND NEWTON CREATIONISTS?

Kepler, Galileo, and Newton believed in God. They believed in an intelligent designer.  Read more at location 986

****  In the beginning, said Kepler, there was nothing but God. And God had geometry at his heart. God had curves, straight lines, triangles, squares, and circles in every inch of his immeasurable consciousness. “Why waste words,” wrote Kepler in his 1619 Harmonices Mundi, his Harmony of the World, “Geometry, which was before the origin of things was coeternal with the divine mind and is God himself.”67  Read more at location 1005

So geometry, said Kepler, “passed over to Man along with the image of God.”71 The result? Said Kepler, the ability to grasp mathematics and geometry was built into the very foundation of the human mind. Or, to put it in Kepler's words, man's math skill, “the recognition of quantities…is innate in the mind.”  Read more at location 1017

****  Every scientist who makes breakthroughs does it with the use of a tool, a central metaphor. What was Kepler's central metaphor? Circles, triangles, and the five Platonic solids. Geometry.  Read more at location 1032

The mystery of metaphor will prove vital to the secret heart of the God Problem. So will deep structures. But we'll save the role of metaphor for later.  Read more at location 1036

GALILEO'S NATURE FETISH: POKING THE POPE

in Galileo's opinion, the problem of cosmic creativity did not exist. Why? Because “God placed the sun at the center of heaven and…therefore He brings about the ordered motions of the moon and the other wandering stars by making it turn around itself like a wheel.”79 It's very simple. God put together a cosmos. He crafted it the way a wheelwright crafts a wagon wheel. There is no further question. No mystery. There is no God Problem.  Read more at location 1048

Galileo argued for ignoring holy books. Why? There was a better way to get to God. The writers of the Bible, Galileo said, had manipulated the details to produce mass appeal. Explained Galileo, “To accommodate the understanding of the common people it is appropriate for Scripture to say many things that are different (in appearance and in regard to the literal meaning of the words) from the absolute truth.” To understand God, he said, don't be fooled by the creator's propaganda. Don't look at holy writ. Look at the world God has created. Nature, said Galileo, is the real holy deal.  Read more at location 1059

Galileo explained, “the Holy Scripture and nature derive equally from the Godhead.”  Read more at location 1068

Galileo, too, relied on a central metaphor, one that had been used for close to three thousand years—laws. Laws dictated by a central authority, a Lord. And Galileo used a second metaphor. He imagined that if he carried out what he called an “experiment”83 on a table top, his strangely limited test could reveal the principles underlying the motions  Read more at location 1077

The “grand book [of] the Universe,” Galileo said, “is written in the language of mathematics.”90 But Galileo's mathematics had very few numbers. And it had no formulae, no equations.91 What did it have? Explained Galileo, “Triangles, circles, and other geometrical figures.”92 Things you could picture. Things you could draw. Why geometrical figures? Because the only respectable math among intellectuals in Galileo's day was geometry. Geometry and simple ratios between numbers.  Read more at location 1090

“The language of mathematics,” Galileo explained, is written in characters, and those characters are “triangles, circles, and other geometrical figures.” Without those “geometrical figures,” he warned, “it is impossible to understand a single word of it.”94 A single word of what? A single word of the “grand book [of the] universe.”95 That's a lot of metaphors. A lot of comparisons. The universe is a book. The cosmos is written in a language. The characters of that language are the triangles, circles, and other figures of geometry.  Read more at location 1096

Three peculiar assumptions were Galileo's contribution to the God Problem: (1) That the universe is governed by laws like the laws that governed Galileo's three hometowns, Padua, Pisa, and Florence.96 (2) That an experiment in a home workroom could say something meaningful about the strangest and most distant of things, things whose size might dwarf that of the balls Galileo experimented on.97 And (3) That the essence of the experiment could be caught in geometry. In other words, that mathematical scratches of ink on pieces of mashed tree pulp—paper—could express the essence both of tabletop experiments and of heavenly things.  Read more at location 1102

Isaac Newton started his scientific career thirty-five years after Kepler and Galileo. And, like Kepler and Galileo, Newton was a creationist and a believer in intelligent design.  Read more at location 1110

Newton declared in his culture-changing masterpiece, his 1687 Philosophiae Naturalis Principia Mathematica, better known as the Principia, that “this most beautiful system of the Sun, planets, and comets, could only proceed, from the counsel and dominion of an intelligent and powerful Being.”  Read more at location 1120

To Newton, the cosmos is as it is because of the biggest jack-in-the-box in history. The ultimate deus ex machina—God.109 God said it, so it was so. Yes, Newton used the God Copout. But Newton also contributed a more down-to-earth metaphor  Read more at location 1135

Newton gave us God the contriver. God the engineer in chief. God the maker of machines. Why was the cosmos such an astonishing place? Because it was an invention. An incredibly precise gadget fitted together by God.  Read more at location 1139

Let's inch back to what Newton imagined God the Contriver might be. What other gadgets were fresh in Newton's mind when he wrote his central book, the Principia? Newton used the example of the pendulum clock,115 of yet another pendulum-powered gizmo, a pendulum hung over a ruler,116 and of “machines.” What machines did Newton have in mind? We all know about Newton's interest in the inner workings of “clocks and such like instruments.” But Newton did not see clocks the way that you and I do. The word “gear” for a wheel with teeth had not yet been invented.117 So Newton perceived clocks as machines “made up from a combination of wheels.” More important to Newton were devices that amplified the power of your arms and hands:  Read more at location 1158

What's the trick to the pulley, the screw, the drill, and the wedge? For example, what's the secret to the wedge that's used to split a tree trunk into planks? Translation. All of them translate one kind of movement into another, one kind of force into another. Says Newton, “The power and use of machines consist only in this, that by diminishing the velocity we may augment the force.”  Read more at location 1167

****  Newton's metaphor of the machine maker and of the contrivance crafter's creation—a mechanism—would stick like glue. Today, scientists are obsessed with finding an explanatory “mechanism” to open the mysteries they are trying to pierce. Without a mechanism, they often won't accept a new idea.  Read more at location 1174

But the concept of mechanism is a metaphor. It's based on Newton's pulleys, wedges, windmills, and clocks. And it involves a huge stretch—imagining that the patterns of our tools and of our contraptions can tell us something profound about the stars in the skies and about the workings of our minds and eyes.  Read more at location 1179

To Newton, the problem of cosmic creativity had a simple solution: God. God was the great contriver in the sky. God was the heavenly mechanic crafting a universe that worked like a machine.  Read more at location 1182

there is a list of people who would come up with clues to cosmic creativity: Gottfried Leibniz, Georg Hegel, Karl Ernst von Baer, George Boole, Hans Driesch, and Herbert Spencer. Not to mention George Henry Lewes, Bertrand Russell, and Giuseppe Peano. Each of these men (and, alas, they are all men, not women) would come at the God Problem from a different point of view. But like the five blind men trying to figure out the elephant, each of them would be right.  Read more at location 1189

GAMOW VERSUS HOYLE: THE WAR BETWEEN BIG BANG AND STEADY STATE

The battle between George Gamow and Fred Hoyle.  Read more at location 1246

From the late 1940s to the mid-1960s, the battle of big bang versus steady state was the biggest slamdown in the physics community. It was a mud wrestling match between two competing stories.  Read more at location 1247

Fred Hoyle's steady state theory said that the cosmos churned out new matter constantly. Hoyle's steady state also declared that aside from a cycle of expansion and contraction, the universe had remained pretty much the same forever. And it would stay pretty much the same in an infinite future. Big bang theory was very different. It said the cosmos was limited. It had a beginning. It had been spat from nothing in an all-powerful whomp. Then the newborn universe had evolved. It had coughed out particles, plasmas, atoms, gasses, galaxies, stars, and human beings. It had self-assembled. It had pulled off an act of secular genesis.  Read more at location 1250

The battle between Hoyle and Gamow, the battle between the steady state and big bang theories, was not restricted to science. Religion would hover just out of sight. The struggle would eventually turn Hoyle from a staunch atheist into a believer in God. And it would bring a strange ally to the side of Gamow, a man who hovered between agnosticism and atheism.133 That unexpected supporter was, of all people, the pope.  Read more at location 1280

And what is steady state theory? The universe has no beginning and no end. It just keeps chugging along, expanding and contracting, then expanding again.138 OK, if the universe is in a holding pattern, in a loop, then why is it expanding? Because, says Hoyle's steady state theory, the cosmos is continuously churning out new matter.  Read more at location 1302

How does the cosmos create new matter from mere emptiness? Hoyle never really answers that question. In his last book, written in 2000 and titled A Different Approach to Cosmology, a book that emerged the year before Hoyle died, Sir Fred confronts the question and answers it like this: “Where do new particles come from if not from some previously existing particle? Our answer conceptually is from the basic fabric of space time.”142 But how is space-time twisted into knots of matter? Hoyle basically takes a pass. He says, “Everything is made out of nothing, despite the saying attributed to Lucretius that only nothing can be created out of nothing.”  Read more at location 1317

Meanwhile, in the United States, George Gamow was developing the theory of the big bang. Here's where the redshift and radio astronomy came in. Steady state theory said that the redshift came from the exhaustion of geriatric light. Big bang theory said that the redshift came from the expansion of a universe that had begun as an exploding pinprick and had been whuffling outward ever since. And there was no way these two views would ever meet. Gamow was the uncontested leader of the big bang crowd.  Read more at location 1353

Nine years later, that microwave background whose temperature Hoyle and Gamow debated would demolish steady state theory. Shatter it and bury it. Despite the fact that, ironically, Fred Hoyle's prediction of the temperature of that background radiation would prove to be on target and George Gamow's would not. The background radiation, one source of radio astronomy's hiss, would be interpreted as leftover energy from the big bang. Certain evidence that, indeed, a big bang had taken place.  Read more at location 1376

THE TALE OF THE TERMITES

****  (Note:   fascinating!)  The termite itch for cleanliness results in an architectural masterpiece—a termite hive eighteen feet high with a basement six feet deep. A termite hive 972 times the height of the average termite—the equivalent of a 640-story human building over a mile and a half high and four miles wide. A hive topped with spires or domes. A hive with air conditioning that ups the level of moisture in the room the workers use to farm the fungus they feed on. A hive whose air ducts tweak the level of carbon dioxide and keep the temperature at a steady eighty-six degrees in the chamber of the queen and in the brood chambers no matter what the outside conditions might be. A hive whose airshafts process one thousand liters of air each day. A hive that houses two million inhabitants. From tiny obsessions and trivial fixations great things can grow. Is there a termite blueprint for this intricate structure? No. So how does this spectacular termite city arise? From the simple rule of termite obsession—pick up the mess and stack it neatly on the biggest pile around. From another basic rule: attraction and repulsion. From repulsion against mess and from attraction toward the tallest pile in the neighborhood. From iteration—from the repetition of a rule upon itself. From the repetition of a rule with obsessive persistence. From the repetition of a rule twenty-six billion times or more.  Read more at location 1420

****  Think of it this way: the termite's simple rule is an assumption. And the termite's assumption turns out to map onto reality. A reality that does not exist until the termite makes it. A reality no single termite can make. A reality that only tens of thousands of termites can build. A reality that pulls an impossibility into existence.  Read more at location 1430

CHAPTER 3: THE SAGA OF THE SCRATCH MARK  

THE MYSTERY OF THE MAGIC BEANS: WHAT THE HELL IS AN AXIOM?

Different collections of mathematical equations are different universes. —Brian Greene  Read more at location 1437

what came spilling from Peano's axioms was amazing: addition, subtraction, multiplication, division, squares, square roots, and rational numbers. The entire mathematical system that it had taken you eight years of grammar school and more than eight math textbooks to learn. All the complex and powerful twists of arithmetic and more were present from the beginning in the half page of Peano's axioms.  Read more at location 1446

What are Peano's axioms?

Peano 1: There is a nonempty set with a distinguished element 1. The set will be henceforth denoted N. Peano 2: For each x ϵ N there exists one and only one element x’. The element x’ will be from now on called the successor of x. Peano 3: x’ ≠ 1 for every x ϵ N. Peano 4: If x’ = y’ then x = y. Peano 5: If M is a subset of N with the following properties (i) 1 ϵ M, and (ii) n ϵ M → (n + 1) ϵ M for every n ϵ M, then M = N.3 Wikipedia, which often does a far better job of summarizing than it's given credit for, puts Peano's axioms in easier words. But even this is close to impossible to understand. There is a natural number 0. Every natural number a has a successor, denoted by S(a). There is no natural number whose successor is 0. Distinct natural numbers have distinct successors: if a ≠ b, then S(a) ≠ S(b). If a property is possessed by 0 and also by the successor of every natural number it is possessed by, then it is possessed by all natural numbers.  Read more at location 1451

***** ****  (Note:   author's premise)   Corollary generator theory is very simple. It says that perhaps this universe started with a handful of rules, a handful of axioms, just like you did at Reed. And just like the termite. And perhaps the universe has been doing her homework ever since. Perhaps she has been yanking the implications of those simple rules from their hiding place. Perhaps she has been extracting the starting rules’ corollaries. Perhaps she has been figuring out what new forms and functions are consistent with those starting rules. And perhaps she has been holding on to what fits and tossing out what does not.  Read more at location 1475

Russell declared the year 1900 to be “the most important year of my intellectual life.”15 Why? In part, because Giuseppe Peano had pulled off the ultimate in axiomatization.  Read more at location 1512

BARLEY, BRICKS, AND BABYLONIANS: THE BIRTH OF MATH

like the citizens of Jericho, the builders of Catalhöyük did and did not give us the plane, the straight line, and the right angle. Why? They inserted lines and planes into our daily lives, but did not insert them into our minds. And, indeed, the circle and the line would remain implicit for a very long time. It would take thousands of years before we humans would turn the circle and the line into concepts, into mental tools, into explicit realities.  Read more at location 1547

In his definitive book, The History of Western Philosophy, Bertrand Russell says about one group of Mesopotamians, namely the Babylonians, that “we owe to the Babylonians the division of the right angle into ninety degrees, and of the degree into sixty minutes”22 This claim is repeated wherever you look, from popular online educational sources like the Internet's WonderQuest23 to the Notes and Queries section of Britain's newspaper the Guardian.24 Not to mention books like Graham Faiella's The Technology of Mesopotamia.25 But it's wrong. Dead wrong.26 And the real story is even more interesting. The Babylonians never invented the concept of the angle.27 They had no word at all for a right angle. And they never divided a circle into 360 degrees. The way they did think is utterly alien to us.  Read more at location 1560

What mind tools did the Sumerians and the Babylonians really invent? Massive breakthroughs.28 Breakthroughs that laid the groundwork for math, for modern science, and for axioms. In roughly 2600 BCE the priests of the city of Sumer,29 the city that introduced irrigation and monocropping, came up with a brand-new way of counting things,30 a mathematical system  Read more at location 1569

all of these things had to be translated into scratch marks on clay. Yes, translated. And all of them had to be reduced to some sort of common unit of measure. No matter how artificial and distorted that unit of measure might be. In other words, all of them had to be homogenized with an equal sign. All of them had to be expressed in some form of A equals A.  Read more at location 1674

A equals A. A scratch is a scratch is a scratch. Frazer would tell you to watch out for the pitfall of “sympathetic magic.” Watch out for “the mistake of assuming that things which resemble each other are the same.”  Read more at location 1680

You've just translated barleycorns into fingers; now you translate fingers into arms. You use the width of a finger of your right hand to measure your left arm from your elbow to your fingertips. When the Babylonians did this, they got twenty-four. So twenty-four finger-widths equal one forearm, one cubit, one “kus.” You are now set up to translate forearms into, brace yourself, barleycorns. Since one arm is twenty four finger-widths, and one finger-width equals seven barleycorns, one arm length equals 168 barleycorns. You get that figure by using one of your new inventions: the multiplication table.  Read more at location 1692

in Mesopotamia, the brick is at the bottom of everything. One reed-strip is one hundred and eighty bricks. If I accuse you of nonsense, we can get a load of bricks, use your measuring reed to lay out one reed-strip, cover it with bricks, and count them. But I will simply have to trust you. So you tell me that the “field” of my dad's property—the area—is thirty-six thousand bricks. And using your table of reciprocals, each of us brothers gets nine thousand bricks of land. In another real-life example from ancient Babylon, the land shown in a Babylonian field plan called BM 47437 comes to “4 reeds 4 cubits 4 small cubits + I cubit 18 fingers 4 1/2 barley-corns.”58 Yes, barleycorns, bricks, land, fingers, forearms, ropes, scratches on clay, and numbers all equal each other in some radically peculiar way. No wonder the world calls you Mesopotamian math priests Magi—the original magicians.59 How have you Babylonians done all of this? By probing the nothingness for implicit opportunities, for implicit realities, for what twentieth-century physicist David Bohm will someday call “implicate properties.”  Read more at location 1767

You've achieved the impossible. How? By turning what's merely implicit into the explicit. By turning your technologies into ideas. Into new thought tools. Into metaphors. By acts of iteration and translation, acts of translation from one medium to another. By turning a brick from building material and a barleycorn from gruel, transforming them into standard measuring devices. And by turning those standard measuring devices into numbers. By turning mere wisps and imaginings into something hard and fast. By turning everyday things into ideas, concepts, metaphors, and mind tools. By being innovative as all hell. By translating patterns from one medium to another. By translating absurdities—scratch marks—into something that matches your everyday reality…and mine. Something that allows you to predict new solidities. Something that gives you instant shortcuts to counting up a million barleycorns.  Read more at location 1781

Take a look at one of the ideas that the Babylonians did not get. Thanks to bricks and to the straight walls that bricks make, the Babylonians had walls that met at what we call “right angles.” But, despite the protestations of Bertrand Russell, the Babylonians had no concept of the angle.61 No concept of any form of angle. Not to mention no concept of the right angle. And this was despite the fact that every room they sat in had corners. And despite the fact that the solidity of their buildings depended on getting right angles, well, umm, right. Get the angles wrong and your building might collapse.62 Angles are measured with circles. And the Mesopotamians had no idea that a circle could be defined by a radius sweeping out an arc from a center point. No idea that every point on a circle is an equal distance from the circle's center. They had no idea that a circle was a special sort of mathematical entity.  Read more at location 1790

Angles, circles, and hemispheres, things that seem to us obvious, did not exist in their vocabulary. Despite the fact that they drew circles. With compasses. And despite the fact that they used tables of reciprocals to “break” things apart, they didn't invent division. Each of these things would have been a breakthrough. Each was implicit in what the Babylonians had already invented—the brick, the compass, math, and astronomy. And each was obvious. Or was it? If it was so obvious, why did 180 generations of Babylonians working their way through millions of calculations and billions of words and numbers not get it? More important, if the Babylonians didn't get these simple concepts, what concepts are hovering just outside our grasp, outside your grasp and mine,  Read more at location 1798

In Turkey's Archaeological Museum of Istanbul there's a roughly four-foot-long copper rod shaped like a walking stick. It's called the Nippur Ell. What is it? A tool of translation. A tool for transforming length into words. A tool for translating length into cuneiform markings on clay. A tool for transforming length into numbers. It's a standard that gives the length of eight elementary Sumerian distance markers.  Read more at location 1809

The copper rod is not yet a measuring stick or a number line. It is not a modern ruler. It has no number markings. It has no small units that subdivide the rod so you can use it to measure with precision. Again, it's simply a device for translating length into words.  Read more at location 1815

SCRATCH MUD AND YOU GET MIND: THE RISE OF A VIRTUAL REALITY 

***********  Us moderns forget that an inch, a foot, and a yard are based on metaphor and radical abstraction. We forget that they are based on a fantastical relationship between arms, fingers, and ink on paper. We forget that they make an impossible claim—that squiggles on pulped tree stuff or on a computer screen equal farm fields and food. We forget the bizarre claims of the equal sign. The bizarre claims of “equation.”  Read more at location 1837

The Mesopotamians will also use the math of barleycorns and silver, the math of shekels, to invent loans and interest. And they will make tables calculating just how much I'll owe you on a loan after a day, a week, a month, a year, two years, three years, and more.  Read more at location 1858

Most important, the Mesopotamians will use math to invent one of the most potent forms of magic humankind has ever seen: science. The Sumerians and the Babylonians will keep records for hundreds of years and examine those records to look for repeating patterns, number patterns, the sort of patterns that show up on grids and tables of numbers, tables of symbols for bricks and barleycorns laid out on hand-sized slabs of clay.66 They will hunt for patterns in the past from which they can predict patterns in the future, patterns from which they can predict things to come.  Read more at location 1863

And they will find patterns. They will find what experts on Babylonian math call “zigzag” patterns. What we would call “oscillating patterns.” Patterns that go back and forth on a table over and over again. Patterns that jerk from side to side. And after seventeen hundred years of math,70 they will start something new—keeping detailed records of the movements of the sun, the moon, the planets, and the stars. They will invent libraries and will compile hundreds of years of records of the heavens.  Read more at location 1872

The Mesopotamians will find that the positions of stars and planets on the horizon change in recurring patterns as the seasons change and as the years roll by. Patterns that repeat. Patterns that iterate. The Mesopotamians will invent astronomy, market analysis, weather prediction, and a mathematical form of political science based on the stars. Their market predictions, their political predictions, and their math-and-star-based guidance for the personal life of the average Mesopotamian citizen will not quite work out. They will miss the mark in “the real world.” But they will fit our emotional needs so precisely that they will remain alive today in the practice of astrology.  Read more at location 1881

THE SORCERY OF CORNERS 

They will unfold a pattern that's mistakenly named for a Greek—Pythagoras. It's called the pattern of Pythagorean triples. But Pythagorean triples are Mesopotamian through and through. And like multiplication, the powers of these triples are so close to summoning spirits from the ether that it's ridiculous.  Read more at location 1897

The year is 1781 BCE, nearly four thousand years ago. It's close to a thousand years before the founding of Rome, and there's a political catastrophe. Shamshi-Adad, an Assyrian king who has pulled together an empire that holds much of Mesopotamia, Syria, and Asia Minor in its fist, dies. His death is a disaster. To quote historian William James Hamblin, “Six rival kings jockeyed for position, aiding, betraying, and attacking each other in dizzying turnabouts.”  Read more at location 1900

He takes control of twenty-four of the cities of the Land of the Lords of Brightness.73 He is Hammurabi, ruler of Babylon. And he turns all of Mesopotamia into one of those things that's implicit in the invention of the city, an empire: the Babylonian Empire. One of Hammurabi's most important technologies is the scratch mark in a hand tablet of clay. But Hammurabi translates that scratch mark to a new medium, stone. Then using the scratch mark on a stone monument or two, Hammurabi standardizes something far more elusive than measurements. He standardizes human behavior. He translates human actions and punishments into units of their own kind. He puts together one of the first written codes of law. And under Hammurabi's laws, Mesopotamian city life flourishes.  Read more at location 1905

There are two creation myths in the Bible. In one, God is a wind whuffling over the sea and the open landscape, a god who makes grass as his very first life-form.75 He is a god of nomadic sheep herders. Nomadic sheep herders like the man Abraham, the father of the Jews. In that first creation myth, God is a wind, a breath, who speaks things into existence. Language is his central technology. Language—a human invention—is the first creation myth's central metaphor. Language is something a nomad constantly moving his tent to a new location, a nomad who has to avoid heavy burdens, can carry with ease. God says four words, “Let there be light,”76 and there is light. Words have power.  Read more at location 1913

Abraham was originally a townie, not a wanderer. He was born in roughly 1812 BCE in Ur,77 a sister city to Babylon.  Read more at location 1919

much like the owner of a house in a city, a city of the “elohim”—a city of “the gods.” God's technology in this second biblical myth is based on mud, the source of Babylon's bricks and of its kitchen pottery.78 Not to mention the source of its writing pads.  Read more at location 1920

Why does the city god of one creation myth in the Hebrew Bible use something Mesopotamian, mud, and in the other use the ultimate portable technology, the word? The Jews believed that their founding father, Abraham, had left the city life of Ur in roughly 1782 BCE and had become a shepherd, a wanderer. So in one creation myth, God is a “roo-ach,” a drifting wind. And in the other, God has a Mesopotamian lifestyle.  Read more at location 1927

Height was apparently one of the few things that allowed the gods to lord it over humankind. The Semitic word for a god, “al”—as in “elohim” and “Allah”—is associated with height and the sky. And the Babylonians were about to break the gods’ monopoly on altitude. So the Lord got the other gods on his block together and said let's stop those pesky humans before they become as mighty as we are. Why? Because, said God, “now nothing will be restrained from them, which they have imagined to do.”85 So together the mighty ones of heaven—the elohim, the gods—toppled the Babylonians’ tower and split men into separate language groups, forcing them to babble incomprehensibly so they would never have the power to unite and threaten the sky giants again.  Read more at location 1947

Translation and repetition of old rules in a new medium, iteration, are tools of genesis, tools of creation?  Read more at location 1955

Structures so astonishing that they will attract gawkers like the Greek historian Herodotus from 1,220 miles away. Structures that will express the majesty of Babylon. To fashion amazements, you, the architect, will have to extract new implicit meanings from brickwork, new implicit possibilities from the iteration of old rules in brand-new ways. Your job will be to do what termites do. To create buildings that grab attention. How do you get a termite's attention? With the trick of the gods. With height.  Read more at location 1959

you will have to make sure that your walls are straight. And you will have to make sure that your walls meet at something you don't have a word for—perfect right angles.  Read more at location 1979

But you don't have the concept of an angle. Any kind of angle. And you don't have a word for a “right angle.” What's more, you are over fourteen hundred years away from the notion of ninety degrees.87 So how do you make sure that you've got your corner angle, your right angle right?  Read more at location 1982

Extend the lines of the wannabe right angle of bricks at your feet. Make one line of bricks three bricks long. Make the other line four bricks long. Now use a string of gut to measure the diagonal between the farthest tips of your two lines of bricks. And move your lines of bricks until the diagonal is precisely five bricks long.  Read more at location 1988

Babylonians have discovered that this 3:4:5 relationship is just the beginning of a series of magic number relationships that match up with perfect right angles. Even though you don't have a word for right angles. In Columbia University's Plimpton collection is a Babylonian tablet from 1700 BCE. On its face is a table of fifteen numbers,89 fifteen of what we today call Pythagorean triples. They should really be called Babylonian triples. Pythagoras would not appear on the scene for another 1,130 years. The peculiar trios of numbers are triples like these: 3:4:5 5:12:13 8:15:17 All of these numbers match up with perfect right angles.  Read more at location 1998

CELEBRITIES IN THE HEAVENS: HOW TO INVENT ASTRONOMY 

The human brain is a pattern recognition machine. And one key tool in our arsenal of pattern recognition devices is the story.  Read more at location 2029

You watch the heavenly bodies’ social relationships. You watch carefully to see when two stars, planets, or constellations come together or separate as they rise or fall on the horizon.  Read more at location 2035

You never come up with the clincher that makes the measurement of angles possible—the circular precision measuring device marked out in 360 equal units. Instead, you use a pattern recognition tool far more compelling than numbers—you use myth.  Read more at location 2043

in the words of Rupert Gleadow, a mid-twentieth-century sidereal astrologer who wrote a history of something vital in his field, The Origin of the Zodiac, the scribes of Babylon engineered a crisis. A sea monsteress arose and threatened creation. That monsteress of bitter waves and of salt water flooding, that monsteress of the tsunami, was Tiamut. So terrifying was Tiamut, says Gleadow, that “even Anu, the original creator, fled before her.”93 One brave petty god volunteered to do battle with this female Mesopotamian Godzilla. He was Marduk, the god of the Babylonians. But Marduk wanted something in exchange. If he battled Tiamut and won, he wanted a promotion. He wanted to be counted among the big guys of the sky, the great gods. Marduk did more than challenge and stop the encroaching bitter water monster. He tore Tiamut, the monsteress, in half.  Read more at location 2048

The monsters of Tiamut were accompanied in the heaven by a ragged handful of other constellations—Tiamut herself, “her husband Kingu, and the constellation Hydra, representing an unfortunate dragon.”95 Eventually eighteen constellations would be whittled down to twelve. The twelve constellations of what the Greeks would later organize in a very different way and would call the zodiac. So when it came to the Babylonians’ first attempts to understand the sky, anthropomorphism ruled. The early pattern recognition tool was the story. The myth. Math came next.  Read more at location 2057

The Babylonians did not have what we call geometry. The sphere was not in the tool kit of the Babylonian mind. The circle was not a standard tool of Babylonian math. It seldom if ever appeared in the Babylonian mathematical and astronomical vocabulary. To the Babylonians, the sky was not a circle. It was not a part of a sphere. It was not a hemisphere. It was a roof.  Read more at location 2063

day the sun rises in a slightly different place. And each night the sky is different. Why? Roughly once a month a new constellation rises on the horizon. In fact, a new constellation rises in a very significant spot on the horizon—it surrounds the swatch of sky from which the sun will rise roughly twelve hours later. It  Read more at location 2087

Every month another constellation takes possession of that key line of the eastern sky from which roughly twelve hours later the sun will push forth like a bull bolting from the gate of a pen or like a chariot charging from a gate. The Babylonians coupled these shifts in the constellations with changes in the phases of the moon. And they used those changes of the moon to cut their year into twelve parts—twelve moon-ths, twelve months.  Read more at location 2107

This is where math and mythology cross paths. What did the Babylonians find using their clay charts and tables? Ways to figure out the time of night. Ways to predict eclipses of the moon. Ways to predict the month, the day of the month, and the part of the moon that would be eclipsed.  Read more at location 2150

You could use your charts of the sun, moon, planets, and stars to give your ruler a heads up on the sorts of cyclical patterns that Shakespeare would someday characterize with a metaphor of another chartable pattern that links heaven and earth, another chartable up-and-down that couples the moon and the sea: “There is a tide in the affairs of men.”  Read more at location 2155

WHAT'S THE ANGLE? BLINDNESS IN BABYLON 

All of this was an act of translation from one medium to another. From sky to clay to mind. It was an attempt to interpret recurring regularities, an attempt to uncover iterative rules and deep structures of the sky, using the pattern-recognition tool of anthropomorphism. We don't know if any of its human predictions came true. But there was a spinoff in another realm. In the realm of math.  Read more at location 2169

They discovered what those who study Mesopotamian clay tablets on astronomy and astrology call “zigzag” patterns.124 Without circles the Babylonians discovered something we only see in terms of circular things—cycles.  Read more at location 2173

A Babylonian water clock was a jar with carefully calibrated markings on the inside and a hole in the bottom.128 You measured time by the weight of the water that had run from the hole. What unit did you use for your measurements? The “mina.”129 You measured time in units of, of all things, weight. Weight—the heft you can feel in your hands, arms, and shoulders when you pick up something.  Read more at location 2204

Why do central metaphors work? Why does math work? There is a giant equal sign at the core of our logic. But why?  Read more at location 2224

WHY KNOT? THE EGYPTIAN ROPE TRICK 

The Egyptians would invent the first precision tool of measurement. The first tool of measurement marked off in smaller units. The first ruler. The Babylonians had long ago used ropes to measure distances of twenty reeds. But the new Egyptian tool would be a rope that was marked off. Marked off in twelve cubits—marked off in twelve forearms. Marked off with twelve knots.  Read more at location 2231

HOW TO HYPNOTIZE A GREEK: MATH AS A TOURIST ATTRACTION 

How obsessively did the Egyptians pursue the arts that would lead to axioms? In roughly 1800 BCE, over thirteen hundred years before the writing of the Bible, the Egyptians issued one of their first books of practical mathematical problems and solutions. It was the Rhind Mathematical Papyrus, “written during…the 12th dynasty [the reign of] King Amenemhet III (ca. 1844–1797 BCE).”  Read more at location 2336

In roughly 552 BCE, over twelve hundred years after the Egyptians wrote their first compendium of arithmetic problems and solutions, Pythagoras also took a trip to Egypt to learn the secrets of the harpedonapts.  Read more at location 2367

After more than a third of a century of travel and of idea absorption, Pythagoras headed back north and returned to his island home of Samos.  Read more at location 2437

SEDUCE ’EM WITH NUMBERS: HOW TO DO A PYTHAGORAS 

Pythagoras traveled 713 miles west to Italy, and settled in the Greek colony of Magna Græcia in the city of Croton. In 530 BCE, Pythagoras began to recruit followers.188 Followers so anxious to be with him that they went through five painful years of initiation rites to be close to him.189 If you wanted to become an acolyte, you had to go through five years without talking. Not a word. And you had to demonstrate utter submission. Utter submission to Pythagoras.  Read more at location 2451

Said Aristotle, “the Pythagoreans maintained that Number was the beginning of things, the cause of their material existence. 

...The elements of Number are odd and even. The odd is finite, the even infinite. Unity, the one, partakes of both these, and is both odd and even. All Number is derived from the one.”  Read more at location 2464

according to Pythagoras you can extract an entire cosmos from just the number one. In his view, a primal unity—a one—differentiates. It buds. It splits into two. Into two opposites. And those two opposites spawn a system that goes all the way to the infinite. To Pythagoras numbers are the cosmos.  Read more at location 2467

Aristotle explains the Pythagorean beliefs like this: The heavens, as we said before, are composed of numbers…. The finite, the infinite, and the one, they [the Pythagoreans] maintained to be not separate existences, such as are fire, water, etc.; but the abstract infinite and the abstract one are respectively the substance of the things of which they are predicated, and hence, too, Number is the substance of all things.  Read more at location 2469

as Iamblichus put it, Pythagoras “was intently considering music, and reasoning with himself whether it would be possible to devise some instrumental assistance to the sense of hearing so as to systematize it, as sight is made precise by the compass, rule, and telescope, or touch is made reckonable by balance and measures.”195 Pythagoras was pondering a basic problem of translation. A problem of translation from one medium to another.  Read more at location 2510

The sound of the same two notes at different places on the musical scale, one high and one low, came from a ratio, a doubling, a relationship of one to two, 6:12 = 1:2. Pythagoras then hammered at the string from which his eight-pound weight hung and simultaneously whacked the string from which his twelve-pound weight dangled. He got the strange harmony known as a fifth. What does the ratio of twelve to eight boil down to? 8:12 = 2:3.  Read more at location 2529

*********  So ratio equals harmony. Ratio equals beauty. Ratio equals music. And what is ratio? The relationship between numbers. Conclusion? Numbers equal cords. Numbers equal beauty. Numbers equal whatever in the human spirit is roused by music. Music equals something deep in your emotional structure and mine. To put it in terms of A = A, math = emotion = numbers. So math and emotion operate on the basis of some sort of shared deep structures. Deep structures that we are literally tuned into.  Read more at location 2537

what are the pegs of a stringed instrument? Tension makers that ape the impact of Pythagoras's weights. Number = music = weight = tension. What an amazing chain of radically different A's that equal each other. But Pythagoras went even further. He showed that music = numbers = harmony = beauty = emotions = hammers = weights = strings.  Read more at location 2547

According to Iamblichus, he “extended the experiment to other instruments, namely, the striking of pans, to pipes and to monochords [and] triangles.” And what did Pythagoras discover? Implicit properties. Iteration. Translation. Repetition of the same thing in a new medium. Number. Ratio. “He found the same ratio of numbers to obtain.” As Iamblichus puts it, “He discovered the harmonic progression.”  Read more at location 2553

Iamblichus says that “having reduced it to a system, he delivered it to his disciples as being subservient to everything that is most beautiful.”197 And Iamblichus does mean everything. Having spotted a deep structure in music, a number structure, a chicken-fish-sheep-and-scratch-mark structure, Pythagoras hunted for that same structure in everything above and everything below. He looked for the rules of musical harmony in the hearts, souls, moods, and bodies of humans like you and me. He made number the base for a new system of nutrition, medicine, and psychotherapy. But that was just the beginning. To show just how high these deep structures of harmony went, Pythagoras took a giant leap of generalization. He climbed to the very heavens. He claimed to prove that the ratios of music and number made sense of the mysteries of the heavens.  Read more at location 2565

How did the invention of the sphere arise? And how did we manage to picture spheres in the heavens? Spheres in the skies? Step one was the perception of the sky as a circle. From the time of Homer in roughly 800 BCE to Thales in 600 BCE, the Greeks saw the world as what Jamie James in his book The Music of the Spheres: Music, Science, and the Natural Order of the Universe calls “a round island floating on the cosmic ocean.”  Read more at location 2596

for Anaximander, the earth was the round, flat top of a column “floating in air.”205 Actually, it was more like the top of an enormous hockey puck.  Read more at location 2610

As Plutarch tells it, “Anaximander says, that the Sun is a circle eight and twenty times bigger than the Earth.” OK, the sun is twenty-eight times the size of Earth. An astonishing leap. But more important, the sun is a circle. Plutarch gives more of Anaximander's views. The sun, he says, “has a circumference which very much resembles that of a chariot-wheel, which is hollow and full of fire; the fire of which appears to us through its mouth, as by a hole in a pipe.”  Read more at location 2617

Anaximander, says Plutarch, declared that the stars and planets “are moved by those circles and spheres on which they are placed.”210 Yes, that magic word, that magic image, that magic metaphor, the sphere. What's more, Diogenes Laertius credits Anaximander with making a model of his new system of the heavens. Building it, crafting it, or paying a metalworker to put it together for him. What was this strange device, this model of the heavens? A σφαίρα. A ball.211 The sort of ball that Greeks used in games.  Read more at location 2628

Here's the trick. Balls were not under the noses of the Babylonians and the Egyptians. The Babylonians do not appear to have had ball games.  Read more at location 2636

It takes a tremendous leap of insight, an inventive leap, to turn the everyday into a tool of thought. You can live with something like the sphere and not “see” it for thousands of years. The Greeks were the first to reinvent the game ball as a geometric object. They were the first to come up with the idea of the sphere. They were the first to add the sphere to the tool kit of the mind.  Read more at location 2650

Everything you and I see around us, Pythagoras felt, was a translation of basic number ratios into a new medium. Philolaus says that Pythagoras believed that even “the soul is introduced and associated with the body by number.” Number knit your soul into your body when you were born. Number holds your body and soul together. And, says Philolaus, to Pythagoras the number relationship that weaves your body and your soul together is musical. It is “a harmony simultaneously immortal and incorporeal.”  Read more at location 2693

One is “unity, Identity, Equality, the purpose of friendship, sympathy, and conservation of the Universe.”225 The force of the number one is literally what keeps the cosmos together. It is “persistence in Sameness.” How does one pull this off? “Unity in the details harmonizes all the parts of a whole.”  Read more at location 2699

Two is the great separator. The great competition creator. “The principle of dichotomy.”228 The principle of change. One holds things together and keeps their identities solid. Two tears things apart and makes them grow, morph, and fade.  Read more at location 2704

Three tosses time into the picture. It gives things an envelope of birth, maturity, and decay. Three is “a beginning, a middle, and an end.”  Read more at location 2706

Pythagoras summed all of this up in what became known as the tetractys.  Read more at location 2718

One is the start of all things. One is infinite. All begins in unity. Two kicks off the separation into entities and identities. Three puts time into play. And three gives birth to four, the beginning of the world of the perfect mathematical forms. Add them up, and they come to the perfect number, ten. Ten, the number of the “bodies revolving in the heavens”—five  Read more at location 2721

Using ratios, number, and music, Pythagoras “devised medicines calculated to repress and cure the diseases of both bodies and souls.”236 To Pythagoras, healthcare was a matter of bringing “the hot and the cold, the moist and the dry” into harmony.  Read more at location 2739

Or, as a young Pythagorean put it when Pythagoras was old and had been preaching his doctrine of numbers for nearly twenty years, health was “the harmonious mixture of the qualities.”240 Health was music! And health was numbers!  Read more at location 2744

The Greeks also applied Pythagorean notions of ratio, harmony, and beauty to their architecture—to buildings like the Parthenon. Ratio and harmony have remained in the artistic ideals of the beautiful body, the beautiful face, and the beautiful building ever since.  Read more at location 2803

****  the tetractys, the shape that says everything begins with opposites—with unity and division. Everything begins with togetherness and separation. Everything begins with differentiation and integration. The Pythagoreans believed that opposites are joined at the hip, and that the struggle of opposites is built into the bone and marrow of this world. The followers of Pythagoras clung to ten key opposites.  Read more at location 2816

****  (Note:   Interesting to meditate on these opposites and all of their metaphorical corollaries)  Aristotle calls these ten opposites the “ten first principles.” Here's how Aristotle lists them in his Metaphysics:   Limited Unlimited, Odd Even, One Many, Right Left, Male Female, Rest Motion, Straight Curved, Light Dark, Good Bad, Square Oblong  Read more at location 2820

****  To Aristotle, the idea that opposites coexist is irrational. But when Aristotle uses the term “rational,” he is using a Pythagorean term. In fact, when you and I use the word “rationality,” we are using a Pythagorean term, too. Rationality is a term that comes from the word to which the Pythagoreans gave meaning—“ratio.”256 λόγος. Rational thoughts are thoughts based on mathematical relationships. Relationships between numbers like 2:1 and 2:3. When we use the word “logic,” we are also leaning on a Pythagorean notion—the idea that logos, λόγος, underlies everything. And logos, again, is ratio. Pythagorean ratio.  Read more at location 2829

SQUARING YOUR WAY TO FAME: PYTHAGORAS'S HOT NEW THEOREM 

****  Pythagoras's discovery of the ratios behind musical beauty was one of humanity's most important attempts to use numbers to grab hold of the hidden properties of an invisible mystery.  Read more at location 2845

The Babylonians and the Egyptians had used math to solve the problems of bricks, slabs of stone, rubble, storage containers, and grain. But these were solid things. When Pythagoras used number to grab hold of music, he pinned down the hidden patterns of something ephemeral, something you can sense but that you can't hold in your hand or perceive with your eyes. And that translation was central to Pythagoras's achievement. But Pythagoras unfolded something else invisible: implicit patterns. And he gained twenty-five hundred years of fame for one last grand demonstration of how you can pull invisible implications from numbers.  Read more at location 2848

You square the two short sides. You add those two squares together. Then you find the square root of the total. That is the Pythagorean theorem. And that is how Pythagoras invented “squaring.” Multiplying numbers by themselves.  Read more at location 2890

The Egyptians and the Babylonians were missing the metaphor. They were missing a metaphor that would set multiplying a number by itself apart in the next twenty-three hundred years of math. They were missing the metaphor that would give a tool to Newton and Einstein. The metaphor that would give us E = mc2. They were missing the metaphor that would show up wherever the syllable “quad” appears in math. As in quadratic equations. And in quadrature. They were missing the metaphor added by Pythagoras. The metaphor of the square.  Read more at location 2896

CHAPTER 4: HOW ARISTOTLE INVENTED THE AXIOM

A TRIP TO PLATO'S CAVE 

I am only interested in the Platonic essence of a situation, so that I can weave it into a beautiful mathematical theory, so that I can lay bare its inner soul. —Gregory Chaitin1  Read more at location 2905

Plato's “idea of the good” is secular, but Plato makes it sound very much like a god. “The idea of the good” is the sun that illuminates the reality outside of the cave. “The idea of the good” is “the universal author of all things beautiful and right, parent of light and of the lord of light in this visible world, and the immediate source of reason and truth in the intellectual.”8 So a philosopher who has stared “the idea of good” in the face sees a real truth that makes the world of the senses look shabby by comparison.  Read more at location 2956

To put it differently, an exit from the cave is “the ascent of the soul to the realm of thought.” An ascent into the light of the sun. Again, the sun is the Good.9 And that sunlike Good is “the source of all things right and beautiful.” Including “truth and reason.” What additional differences are there between the world of the cave and the world in the sunshine? Why is the world of the cave “the world of becoming”? And why is the realm of the real things beyond the cave “the world of being?”10 Because the things within the cave will solidify, then decay. But the things outside the cave are “things divine?”11 They are eternal. They were here before the beginning began. And they will be here forever. They are “the eternal pattern” from which all passing things are copied.  Read more at location 2963

In the Timaeus, Plato uses the phrase “the eternal archetype.”13 But usually Plato simply calls his perfect templates “ideas.”14 One way or the other, whether in the Timaeus, the Republic, or both, Plato came very close to the notion that the cosmos is based on primal patterns.  Read more at location 2975

But, says Aristotle in all of this, Plato was merely “treading on the heels”15 of, guess who? Pythagoras. And how does Aristotle himself fit into all of this? He hit the jackpot. He invented the axiom. And he invented one of the most powerful recruitment strategies in history.  Read more at location 2979

What is a recruitment strategy? A process that keeps its shape second by second by second. A process that imposes its identity insistently even if the matter flowing through it is constantly changing. A pattern that makes matter and energy do a strictly patterned dance. A social dance. Heraclitus's river is a recruitment strategy. The whorl in a trout stream is a recruitment strategy. Theseus's ship is a recruitment strategy. Your body, which replaces over a billion cells a minute16 yet retains its identity, is a recruitment strategy. Your personality, a rapid-fire flood of changing communiqués between a hundred billion neurons, is a recruitment strategy. So is mine. A recruitment strategy is both a noun and a verb. It is a process that maintains a shape. It is an action that turns itself into a thing. And it is a thing that turns itself into an action. Above all, a recruitment strategy is social.  Read more at location 3047

It is so powerful that it survives despite obstacles and attacks. It is Plato's archetype. But Plato's archetypes are stable and unchanging things. A recruitment strategy is a rider, a glider, and a guider of change.  Read more at location 3056

Why call these things recruitment strategies. Why humanize them? Why give them will? Why give them intention? Because a recruitment strategy is purposeful. It is insistent. It persists. It is not matter. And it is nowhere—no where. It is in no permanent location. Yet a recruitment strategy imposes its shape on matter over and over and over again. It imposes its way of doing things. In location after location after location. If a recruitment strategy is no where and no thing, then what the hell is it? I'm not quite sure. Are you? But I can tell you this. A crystal of salt is a recruitment strategy. A snowflake is a recruitment strategy. A genome—a gene team—is a recruitment strategy. A column in a termite nest is a recruitment strategy. A religion is a recruitment strategy. A philosophy is a recruitment strategy. A game is a recruitment strategy. Puzzles, paradoxes, and questions are recruitment strategies. And Aristotle was one of the most potent recruitment strategy crafters in Western history.  Read more at location 3067

****  What recruitment strategy did Aristotle invent? Modern science. Or, as he called it, “demonstrative science.”19 More specifically, Aristotle invented the modern scientific vocabulary. The modern scientific mindset. He also invented some of the puzzles that modern science would pursue. And some of the key prejudices that modern science would be hobbled by. Aristotle forged one key prejudice in particular—the notion that metaphor is unscientific and that only “analogy” is acceptable. And the notion that the difference between metaphor and analogy is profound.  Read more at location 3077

ARISTOTLE FIGHTS FOR ATTENTION—OR ZEROING ZENO 

philosophy was crowded with greats, with monumental men, with men of towering reputations—Thales, Anaximander, Anaxagoras, Pythagoras, Xenophanes, Heraclitus, Parmenides, Zeno, Empedocles, Leucippus, Protagoras, Gorgias, Thrasymachus, and two megastars, Socrates and Plato. How was Aristotle going to carve out a niche in this overcrowded attention space?  Read more at location 3086

Attention is the oxygen of the human soul. If we get it, we thrive. If we don't get it, we shrivel and die. Without attention our immune system shuts down and brain cells in our hippocampus kill themselves off. So we all compete for a space in the eyes, minds, and hearts of others.  Read more at location 3092

The tendency to microdifferentiate—to split up and become different in order to penetrate new niches—exists among all creatures, big and small,  Read more at location 3111

What's more, Dolomedes triton water spiders in Alberta, Canada, have very different dances from those of Dolomedes triton water spiders in Lynchburg, Virginia, or in Ohio. Measurably different dances. Dances in which they concentrate on the footwork and don't wave their forelegs. Like the rebel competing with the good kid for attention, groups that settle a new pond subtly take off in a direction that's all their own. To probe their opportunities, new spider groups become new-pattern generators. This sort of differentiation is all over the place in the realm of living things. In the cells of your eye it shows up in what biologists call “lateral inhibition.” The light sensors on your retina compete to be the first to identify an incoming stream of photons—the first to figure out what the incoming bit of light is.  Read more at location 3131

The photosensor that “thinks” it's got the answer nudges its neighbors out of the game. It sends out a signal that tells its closest neighbors on the iris to shut up and let it take over. By inhibiting its neighbors, the light sensor sets up the equivalent of a trench around itself, a trench that makes it stand out, a trench of silence that radically differentiates it. Standing out—differentiating—by shutting up your neighbors is called “lateral inhibition.”  Read more at location 3143

What are the light and touch receptors of horseshoe crabs, rats, and humans competing for? Attention. The attention of the higher brain regions to which they send their guesses about what's going on in the world around us.  Read more at location 3152

Thales did something few sages before him had pulled off. He visited Egypt.36 More than that, he “practiced philosophy” in Egypt.37 Then Thales stripped down the Egyptian and Babylonian contribution. He reinvented it. How? By translating it into a radically new medium. Thales tossed away the role of priest, got rid of the Babylonian and Egyptian gods, and forgot about the elaborate bureaucratic structure in which priests were a part. Thales shredded the special relationship between Babylonian and Egyptian mathematical thinkers and the state and crafted something that an individual, an entrepreneur of the mind, could develop and promote on his own—the cult of personality. In Egypt and Babylon, the form of mass attention called fame had been primarily the monopoly of rulers. But Thales built a whole new kind of spectacle and mounted it on the stage of attention. He went after fame for himself and in the process made fame available to mere thinkers. He democratized star power. And in the process, he democratized and secularized the Babylonian and Egyptian knowledge base. Recruitment strategies are clever. By the time Aristotle came along, says Ohio State University's historian of classical rhetoric James Fredal, Athens had become a “competitive arena” for a nonstop “contest.”38 A nonstop contest for honor, prestige, recognition, reputation, esteem, influence, and renown. A nonstop contest for attention. Especially in philosophy.  Read more at location 3176

(Note: Interesting and profoundly ironic given Heraclitian impermanence)  Heraclitus put it, “The best men chose one thing rather than all else: everlasting fame.”  Read more at location 3187

Aristotle laid out a whole new vocabulary for the philosophy of the future. And a whole new program. He laid out the new recruitment strategy he called “science.” A word he used nearly eighty times in just one book, his Posterior Analytics.  Read more at location 3198

****  (Note:   this is a statement re: language and semantics, not necessarily nature)  What was this basic notion that Aristotle told you and me we all agree on? A equals A. What later philosophers would call “the principle of identity.” What later philosophers would also call “the principle of noncontradiction.”45 Or, as Aristotle put it, “Things which are the same as the same are the same as one another.”  Read more at location 3205

First came Heraclitus, the philosopher who said that you can never step into the same river twice. Heraclitus, said Aristotle, had attacked the notion of A = A by declaring “that all nature is in a perpetual flux, so that nothing is in the same state for two successive moments.”  Read more at location 3212

(Note: Aristotle's desire for certainty and clean categorization is at root of his claim)  Aristotle dismissed Heraclitus's heresy with a single curt but muddy sentence. “From this it would follow that neither of two contradictories could be predicated with truth of any subject.”  Read more at location 3216

Anaxagoras of Clazomenae, the first foreign philosopher to settle in Athens. The friend of Pericles, Athens's leader in the city's golden age.51 Anaxagoras was the man who said that the moon was a stone and that the sun was a glowing hot ball of iron. What was Anaxagoras's sin against A = A? Says Aristotle, he “held that the ultimate elements could never be entirely separated; that nothing in nature was pure or simple.”52 In other words, A had bits of B and C in it. What's worse, every A had elements of its opposite, “opposite elements,”53 within it.  Read more at location 3220

How did Aristotle defeat Anaxagoras? With another version of the same simple sentence he'd used to clobber Heraclitus. If Anaxagoras is right, “it follows, that neither of two contradictories can be predicated absolutely of any subject.”54 Did Aristotle explain this mind-stumbling pronouncement? Did he offer any further reasoning? Any evidence? No.  Read more at location 3225

what was Protagoras's crime against A = A? Says Aristotle, he “taught that man is the measure of reality.”57 OK, that sounds harmless enough. What's the beef? Says Zilioli, Protagoras sinned with an “ancient” and “robust” form of what we now call relativism. He said that each man perceives A differently. As Aristotle puts it, Protagoras proposed that “the same objects produce different sensations and opinions in different men.”  Read more at location 3233

why does this defy A = A? Because it means “that truth may be self-contradictory.”59 And, worse, said Aristotle with venom, it means that “opinion is the criteria of truth.”  Read more at location 3237

Plato, he said, took on Heraclitus's doctrine and defeated it. Heraclitus said that all things are in a perpetual state of change. Plato proclaimed the opposite. He claimed that some things are eternal and unchanging. Why? Says Aristotle, “To avoid the consequences of the doctrine of Heraclitus.”61 Says Aristotle, it was to escape the errors of Heraclitus that Plato put forth the concept of the unchanging and eternal patterns, the concept of the exalted archetypes, the concept of the essential forms, the concept of patterns that things of mere matter only imitate. “To avoid the consequences of Heraclitus,” says Aristotle, “Plato…maintained the existence of the Ideas.”  Read more at location 3241

He declared that A = A was far more than a mere idea. He declared that A=A was a universal truth. One so basic and so fundamentally woven into the fabric of reality that all men would recognize its obviousness. But this “truth” was, in fact, an opinion. It was a hypothesis. Aristotle dodged his own demand for “demonstration.” He made the shady claim that you could prove A = A, but that you didn't have to. What later philosophers would call the “principle of identity,”63 he said, was “a necessary truth and necessarily believed.”  Read more at location 3249

Aristotle's presentation of A = A as an absolute bordered on flimflam, fakery, and forgery. But twenty-three hundred years of Western thinkers have fallen for Aristotle's trick. Why was Aristotle so insistent on the law of identity? Why was he so ferociously focused on the notion that A equals A? Because it was the basis for a whole new system.  Read more at location 3254

Aristotle was the boldest of the bold. He proposed a new logic, a new vocabulary, and an utterly new system. First off, he proposed looking for what he called “elementary laws.”  Read more at location 3271

Aristotle ordered that you lay out your definitions up front.69 Then he demanded that you state your “axioms.” Next he told you to use something else he called “theorems.”70 Finally, he told you to present something he called your “proof.”71 But that wasn't all. Aristotle handed you the concept of a “hypothesis.”72 He defined a modular nubbin of a whole new kind, a unit—a “unit as an indivisible quantity.”73 And he commanded that you ground your conclusions on “demonstration.”74 Aristotle did more. He called for dividing things into “genus”75 and “species.”76 He enunciated what would become the first rule of algebra—“if equals be taken from equals, the remainders are equal.” And he called his new package “science.”77 Or, to be more specific, a host of “sciences.” Among those sciences were two that Pythagoras had mapped out—arithmetic and geometry. Then there was “zoology,” knowledge about animals, a field Aristotle seems to have invented.  Read more at location 3276

Aristotle still wasn't finished. He introduced the opposition between “quantity” and “quality,”84 the basis of the distinction between merely describing something with words and grasping it mathematically. He laid the base for the prejudice against the “qualitative” and in favor of the “quantitative” that has driven modern science to prize the mathematical and to despise the descriptive.  Read more at location 3294

Under Aristotle's application of A's, B's, and C's is a hidden assumption. That assumption? That there are deep structures, underlying patterns, that apply to everything from ears to puffs of air to octopi, not to mention to planets and stars. And, in fact, that's the assumption established by Plato with his story of the cave and reinforced by Aristotle. But remember, it's an assumption. And every assumption is a hypothesis in disguise. But with A's, B's, and C's, Aristotle's staggering contribution was still not at an end. Aristotle mapped out the key principles of something that you and I use every day: logic. But he didn't call it that. He called it “induction,” “deduction,” “demonstration,”86 and “reasoning.”  Read more at location 3305

****  (Note:   places dualism (noncontradiction) and reductionism at feet of aristotle)  At the heart of Aristotle's logic were his variations on A = A. “Of two contradictories,” Aristotle decreed, “one or the other must be true.”89 With those words, Aristotle established the doctrine of dualism. The logic of either/or. The assumption that either A is A or it is not, and there is no compromise. The concept that it's either one thing or the other but not both. Or, as Jonathan Swift would someday put it, the debate over which end of an egg is up.90 Aristotle called this “dialectical reasoning.”91 And Aristotle invented another fundamental of modern Western thought—reductionism, breaking things down to their smallest units. “For the attributes of what is compounded of the elementary may be deduced from these.”  Read more at location 3314

If a = b and b = c, then a = c. That's Aristotle's key method, the syllogism. If “all men are animals,” and if “Socrates is a man; Socrates is an animal.”94 That's a syllogism.  Read more at location 3338

****  Aristotle's program for “science”—his “definitions,” “axioms,” “theorems,” and “proof”—would erect the stage on which modern science would someday strut and fret. So would Aristotle's logic, dualism, A's, B's, C's, categorizing things in genus and species, reducing things to their elements (reductionism), the search for elementary laws, and the demand to look at the evidence of the senses. These would be tools of enormous power. But many would also be blinders shutting out some of the most important secrets of cosmic creativity.  Read more at location 3363

HOW EUCLID MAKES ARISTOTLE'S “SCIENCE” STICK 

Euclid had Aristotle's commandments: give your definitions, state your axioms, give your propositions, then lay out your step-by-step proof. Euclid also had Aristotle's new invention of using A's, B's, and C's, the system of using letters to make concepts abstract. Letters may be as gnarly as a tangle of old thread, but they have an advantage. They focus attention on the method and its underlying universals, not on a particular practical problem.  Read more at location 3382

Socrates had established the tradition of questioning your assumptions.103 And Aristotle was working out a whole new system of analysis. A system based on a brand-new way of thinking that would later be called “logic.” A system that Aristotle called “science.” Questioning assumptions and logically analyzing what you're up against can help you win battles—and win the world. And even if it fails utterly on the battlefield, it can be a powerful identity tool. A powerful attentional magnet. It can give you status! So Philip hired the greatest Greek mind of the age to tutor his son. That man was Aristotle. In the process Philip made sure that Aristotle would achieve his goal—towering in greatness. Taking center stage in attention space. Achieving lasting fame. You know who Philip's son was. You've read about him many a time. That mere fact is a testament to the social magnetism he achieved. His name was Alexander. Known later in life as “Alexander the Great.”  Read more at location 3401

Alexandria.107 In Egypt. A city that repeated Athens's patterns in a new location. A city that spread Aristotle's influence. A city that Ptolemy turned into one of the greatest centers of learning the West had ever seen. A city that under Ptolemy built the most famous library in history.108 A city that drew intellectuals the way that honeycomb, “the sweet food of the gods,”109 draws ants at an outdoor “symposium,” an outdoor drinking party.110 One of those Alexandria drew was a mysterious figure, Euclid.  Read more at location 3415

In Greece, geometry had been a subject with its own way of looking at the world since Pythagoras in 520 BCE. It had been around for over two hundred years by the time Euclid came around. Geometry had taken the gift of Babylonian and Egyptian math and had added three things that were radically new—the concept of the angle, the concept of the sphere, and the notion of “perfect” geometric figures. Figures you could see with your mind. Figures isolated from all earthly purposes.  Read more at location 3444

Euclid breathed life into the form that Aristotle had sketched out: state your definitions, give your axioms, then proceed to theorems and proof. A form of presentation that Aristotle had conceived, but did not have enough lifetime to achieve. And when Euclid repeated the geometry of Pythagoras, Theaetetus, and Eudoxus in Aristotle's format, he changed geometry utterly.  Read more at location 3472

Geminus was looking for the perfect recruitment template, the perfect tool for iterating a system in as many minds as possible, the perfect tool for translating geometry into the varied psyches of students with different personalities and with different perspectives, the perfect way to translate a basic pattern into the medium of new minds, the book that could do the most to help teachers garden the ideas of geometry in as many brains as possible. And that's what Euclid's Elements turned out to be. Euclid's Elements starts with things we all take for granted, with “common notions,”135 with axioms, and it shows “the deduction of the theory from accepted ideas,”136 the deduction of theory from axioms. And, most of all, it uses the plan laid out by a master whose name Geminus doesn't mention: Aristotle. Over the door of Plato's Academy were written the words “Let no one enter here who is ignorant of geometry.”137 But after Euclid, that phrase was changed to “Let no one come to our school who has not learned the Elements of Euclid.”  Read more at location 3509

GALILEO'S DAD AND THE DRUG OF GEOMETRY 

Writes Galileo's daughter, Polissena, Galileo “had not advanced [with his tutor] so far as the end of the first book of Euclid. He proceeded secretly, wishing to attain at least as far as the forty-seventh proposition, then considered a famous one.”145 Yes, famous. As in “fame.” A lure used by a recruitment strategy. And the fame of a geometric proposition means that geometry was in the air. Geometry and its enticements, including its puzzles, its unsolved mysteries. Like the challenge of proving the forty-seventh proposition, the one that laid out the Pythagorean theorem. The key theorem on right angles. The theorem whose number triples even the Babylonians and the Egyptians had known.  Read more at location 3546

KEPLER: HOW TO TICKLE THE SOUL OF THE EARTH 

the Babylonians saw the sky in terms of their hottest hi-tech device—the chart drawn on clay. They saw the sky as a grid like a tic-tac-toe board. So they saw the twelve key constellations within a system of straight lines, cross-hatched straight lines. Yes, they had reduced their sixteen key constellations to twelve.150 And they had associated those constellations with the twelve months of their year. But the Mesopotamian constellations were in a “Shupuk shame,”151 a pileup. A mess. A mess that had been straightened out by imposing a hierarchical grid. By putting the sun to rule over one column, the moon to rule over another, and Venus to rule over a third. Then the Greeks had radically reperceived the sky. They saw the sky in terms of their new tool of thought—the circle. And the Greeks used their circle to reorganize the twelve key constellations. They remade those constellations from a piled-up grid, a chart, to a circle. And they called their new twelve-slice-of-pizza circular sky a “circle of little animals,” a “zodiac.”152 So far so good. But here's where things get strange. In laying out his Euclidean definitions and axioms, Kepler goes back to an idea that the Babylonians and Aristotle took for granted, but that you and I do not. He goes back to the notion that the planets control the weather. The idea that you can predict storms and sunny skies by looking at the dots of light in the night sky. “The formation of an angle [between the planets] at the Earth is followed by an effect on the Earth,” Kepler asserts. What is that effect? Tickling the Earth into exhaling. Tweaking the Earth into breathing out “the material of rains.”153 And tickling the Earth into breathing out the materials “of other occurrences in the sky.”  Read more at location 3582

Yes, that's exactly what Kepler is saying. The angles between planets change the weather by working on something deep within the Earth. Something “in the Earth itself.”155 What in the world does Kepler mean? He answers that question very quickly. He lays out definition number two. And in definition number two of an “influential”156angle of the planets, Kepler says that the angle between “the rays of a pair of planets…stimulate sublunary Nature.”157 The angle between planets also stimulates “the inferior faculties of animate beings to be more active.”  Read more at location 3600

The planets don't influence the weather by stirring vapors. They churn and mix the weather by waking up the soul of the Earth, “the sublunary soul of Nature,” and by reminding her of herself.  Read more at location 3625

to Kepler the concept of the soul of the Earth is rock solid. Why? The idea of a “world soul” comes from the best of all possible sources, the most believable, the most unimpeachable, the man who left the shadows of the cave behind and stared the sun of truth in the face—Plato.  Read more at location 3627

during the Creation the world became a living creature truly endowed with soul and intelligence by the providence of God.164 Those are Plato's very words. Plato's words in his book The Timaeus. The “world” is a “living creature.”  Read more at location 3632

****  According to University of Pennsylvania ancient philosophy specialist Charles H. Kahn, Plato's Timaeus, the book in which Plato laid out the idea of the world soul, “is particularly rich in Pythagorean numbers and cosmic geometry.”165 So to Plato, the world soul is both a seat of passion and a center of musical harmonies. Remember, musical harmonies are number ratios. So music equals numbers. And music equals emotion equals soul. Which means that numbers equal emotion. Yes, numbers equal emotion. This has a strange implication for Plato's idea of a world soul. And for Kepler's. The world soul is generated by numbers.  Read more at location 3637

****  (Note:   fascinating)  What's more, “Nature perceives the quantity of an angle, which two rays form at the Earth.” Yes, “Nature perceives.” And nature's taste in angles, like your taste in music and mine, is finicky. Geometrically finicky. Nature, says Kepler, “can…perceive the fitness of that angle, along with the others, for congruence.”169 Nature hears the “consonances” of angles.170 What in the world are consonances? Brace yourself. “Consonances…are sounds.”171 They are harmonies. They are music. Real music. The sort of music you can get, says Kepler, “by the striking of strings.”  Read more at location 3652

Nature has an aesthetic sensibility. Nature has a sensuality. Nature has a sensuality that is visceral. (Remember, to Kepler, the Earth has “bowels.”) That's why “the sublunary soul of Nature” is moved by angles.  Read more at location 3659

****  music is one of the most powerful manifestations of geometry, says Kepler. And the cosmos is geometric.174 The cosmos is geometry incarnate.  Read more at location 3667

The Earth has a soul. A soul that exhales. A soul that's a connoisseur of musical harmonies. A soul that can be “reminded of itself.” A soul you can sometimes think of in sexual terms. But these ideas are the very opposite of strange to Kepler. Why? Because in all of this, Kepler is standing on the shoulders of Pythagoras and Plato.  Read more at location 3670

KEPLER'S BOXES AND BALLS: YES, KEPLER'S FREAKY MATH 

Kepler's “angle” was not our angle. Why? Because one key trick that we take for granted was not a part of Kepler's vocabulary. One key technology. We mark off the circle in 360 equal units. And we number the markings. In other words, we turn a circle into a dial. We turn a circle into a protractor.  Read more at location 3682

Kepler measures angles by fitting geometric figures into circles. Here  Read more at location 3693

Geometry and music are one and the same. Geometry is the cosmos. Harmony is astronomy. God thinks in terms of ratios. And God is perfect. Perfection is beauty. Music is the most beautiful thing around. And since beauty is perfection and perfection is God, God and beauty are one. God and music are one. Which means that reason, music, and beauty are joined at the hip.  Read more at location 3731

clue number one to the distances between the orbits of the planets around the Sun is music. Clue number two? God is geometry. God thinks, eats, and breathes geometry. And God is perfection. What's perfect in geometry? Two things. The circle and its alter ego, the sphere. And the Platonic solids. The tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron.  Read more at location 3735

Clue number three? There are five planets. And there are five Platonic solids. Surely this is no coincidence. Surely this is a clue to God's thinking.  Read more at location 3740

Under everything Kepler did was a method. A method he assumed was it, the one and only technique when it came to science. Lay out your definitions. Give your axioms. Show the world your propositions. Then go for it. Prove them. Galileo, Kepler's contemporary in Italy, was also in the grip of definition, axiom, proposition, and proof.  Read more at location 3793

***********  And René Descartes, who was just a tad younger than Kepler and Galileo, used definition, axiom, proposition, and proof for the best known of his achievements: Cogito ergo sum, “I think therefore I am.”  Read more at location 3797

Descartes was a French intellectual who had adventured all over Europe as a soldier in the Thirty Years’ War.179 He had joined the hostilities out of anthropological curiosity, “to study the customs of men.”180 But Descartes had another obsession—the axiom. Not just any old axiom. The axiom. He was obsessed with finding the single most basic axiom of them all. And A = A did not satisfy him.  Read more at location 3799

What was left at the end of Descartes's experiment on himself? The fact that he was thinking. That's how Descartes found Cogito ergo sum—“I think therefore I am.” What was “I think therefore I am”? The ultimate given. The ultimate undeniable fact. The ultimate truth so basic that all men share it. The ultimate axiom.  Read more at location 3807

Fifty-three years later, in 1683 at Cambridge University, Isaac Newton, too, was in the grip of the definition, axiom, proposition, and proof game.186 He kicked off his central book, the Principia, with “Definitions.” Then, a mere eleven pages into the book, he presented his “Axioms,” the insights that would change the nature of physics and science, his “Laws of Motion.”187 For Newton, it was all a matter of definition, axiom, proposition, and proof.  Read more at location 3814

Hobbes injected axioms and propositions into political reasoning. And he influenced a crew of later political ponderers—the Founding Fathers of the United States. Yes, even the Founding Fathers of the American republic used the definition, axiom, proposition, and proof method. Where? In the Declaration of Independence. Remember these words? “We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.” Starting a document with your “self-evident” truths is starting with your axioms.  Read more at location 3824

The grand movement to use axioms to get at deep structures. And the grand movement that would raise a question: are deep structures and axioms figments of the human imagination or reflections of reality?  Read more at location 3831

CHAPTER 5: EVERYBODY DO THE FLIP

GUILLOTINING AN AXIOM: SEVERING THE NECK OF PARALLEL LINES 

In 1820, mathematicians and philosophers would still be trying to boil everything down to definitions, axioms, propositions, and proofs. They would still be in the grip of Aristotle and Euclid's recruitment strategy. Then would come a vital twist in the tale of the axiom. Take an old thing, repeat it in a new context, and you have something new. Sometimes something radically new.  Read more at location 3837

But there had been a restless dissatisfaction with one of Euclid's most fundamental axioms for roughly seventeen hundred years. That troublesome axiom is called the parallel proposition.  Read more at location 3842

perspective is all about the paradoxes of parallel lines.  Read more at location 3869

The parallel postulate controversy lurched forward from century to century. By 1833, says John William Withers, “Perronet Thompson of Cambridge published a book in which he brilliantly demonstrates the insufficiency of twenty-one different attempts to dispose of the Parallel postulate.”  Read more at location 3893

Then, in the nineteenth century, a few brave souls decided to see what would happen if Euclid was wrong and Kepler was right. What would happen if you were to challenge a basic assumption and turn it on its head?  Read more at location 3904

And these pioneers of assumption flipping did something else. They showed a very different facet of axioms. One that had been implicit ever since the days of Aristotle. But one that had never been proven before. The assumption flippers proved that with new axioms you can unfold new universes and impossible new worlds.  Read more at location 3908

When a new corollary is ripe and ready to be unfolded, it rises from the mire in more minds than just one. Why? It is in the zeitgeist. It is in the collective unconscious. It is in the spirit of the times. Zeit means time. And Geist means spirit.  Read more at location 3936

And the zeitgeist of the 1800s called for challenging old assumptions. It called for challenging antique intellectual hand-me-downs. And one antique axiom stood out in geometry. The one that had bothered geometers since the days of Ptolemy in roughly 150 CE.20 It was the parallel postulate.  Read more at location 3939

Karl Friedrich Gauss was clearly a man through whom the cosmos unfolds corollaries and implicit properties aching to be born.  Read more at location 3978

But Gauss says that since 1792, when he was a mere fifteen years old, something else had been nagging him. Poking and prodding from the back of his mind. A problem. A twenty-two-hundred-year-old problem. The problem of the parallel postulate.  Read more at location 3982

Gauss was born one year after the beginning of the American Revolution. He was twelve when the French Revolution unfolded only 429 miles away from his home. He was sixteen when the French began to load France's elegant aristocrats into carts as if they were animals and to trundle those carts to a slicing machine in a public square, a square that had once been called the Place de Louis Quinze, the square of Louis the XV, and was now known as the Place de la Révolution.31 The carts transported these epitomes of elegance to the guillotine, a high-tech machine that thwacked necks clear through, severing heads from their bodies, and leaving those heads to tumble into baskets like melons. Heads still grimacing with the facial expressions fixed by the emotions of their last second of life. Which means that assumption flipping was in the air. In the zeitgeist.  Read more at location 3985

In 1832, thirty-three years after Gauss's letter heaping doubt on the parallel postulate, Gauss's Transylvanian friend Farkas Bólyai published a two-volume book, An Attempt to Introduce Youth to the Fundamentals of Pure Science, Elementary and Advanced, by a Clear and Proper Method. The book was in Latin—but math's relationship to universal languages like Latin is a subject for later. The real surprise came at the book's end. It was an “Appendix Showing the Absolutely True Science of Space.”41 The appendix was an attempt to work out a geometry that would hold true whether the parallel axiom were true or not. And the “Appendix Showing the Absolutely True Science of Space” included a geometry of the sort of universe you'd get if the parallel axiom were false and if parallel lines did, indeed, meet. It was a rather surprising new geometry. Hyperbolic geometry.42 But the real surprise was not just this alternative geometry. It was the appendix's author. Not Farkas Bólyai. But his son. Thirty-year-old János Bólyai.  Read more at location 4018

“ONE MAN DESERVES THE CREDIT, ONE MAN DESERVES THE BLAME, AND NICOLAI IVANOVICH LOBACHEVSKY IS HIS NAME” 

At the age of twenty-five, Lobachevsky became the University of Kazan's rector. Five years later, he married and had a remarkable eighteen children. Then he went blind, lost his ability to walk, and died in poverty at the relatively young age of fifty-four. But long before his blindness and poverty, Lobachevsky tossed away the parallel postulate. He deep-sixed one axiom and replaced it with another. Two lines, he assumed, could meet. And they could do the opposite. They could fly away from each other. They could diverge. When Lobachevsky used logic to work out the implications of this new geometry, what did he get? Saddleback geometry. The geometry of the hyperbolic paraboloid.  Read more at location 4109

To work out the logic of his new geometry, Lobachevsky had to reverse the process used by Euclid. Euclid took propositions then worked his way backward. He took what seemed to be facts in geometry, then worked back to the axioms and tried to prove step by step that his propositions, his notions, were consistent with the axioms. Euclid already knew his answers in advance. But if this is a cosmos that starts from nothing then unfolds something, and an elaborate something at that, Euclid's approach has got it backward.  Read more at location 4114

The beauty of flipping the parallel postulate, the beauty of changing the parallel axiom, was that you worked your way into the unknown. You imitated the universe. In Lobachevsky's case, you used the rules of logic to find the implicit properties of a mini-universe. And what did Lobachevsky find? His saddleback geometry.55 Formally known as hyperbolic geometry,56 a.k.a., negatively curved space.  Read more at location 4119

Nikolai Lobachevsky's Geometrical Investigations on the Theory of Parallel Lines60 came out in 1832, seven suspicious-looking years after Bólyai had tried to get his father to pay serious attention to his new geometry.  Read more at location 4137

Why did two works—János Bólyai's and Nikolai Lobachevsky's—so closely, well, ummm, parallel each other? Because of the same phenomenon that produces 1087 identical quarks simultaneously. Because of the phenomenon that produces a million billion stars all doing pretty much the same thing at pretty much the same time. Because of two things: manic mass production and supersynchrony. Because non-Euclidean geometry was not the product of a single genius lunging outside the box. It was in the air. It was a corollary ripe to pop. It was an implicit property bulging in a pregnant zeitgeist, an implication aching to emerge. It was a recruitment strategy on the prowl.  Read more at location 4143

Through Karl Friedrich Gauss, János Bólyai, and Nikolai Lobachevsky, a group mind, not just an individual mind, was unfolding corollaries from axioms. A multigenerational group mind. And what, in the big picture, in the really big picture, is a group mind? It's a tool that the cosmos uses to feel out her implicit possibilities.  Read more at location 4152

BARE-NAKED MATH: PEANO STRIPS IT DOWN 

Peano boiled all of basic math down to just nine axioms. Then he realized that he could boil five of those axioms down to just one—Aristotle's principle of identity. He realized he could scootch five of his nine axioms down to the idea that A equals A. That brought Peano's nine axioms down to a mere five.  Read more at location 4194

****  Here's one version of the famous five, Peano's axioms, Peano's postulates, this time without Peano's new language of logical notation. This time in simple English. Well, not so simple. Zero is a number. The successor of any number is another number. There are no two numbers with the same successor. Zero is not the successor of a number. Every property of zero, which belongs to the successor of every number with this property, belongs to all numbers.67  Read more at location 4196

Axiom number one—zero is a number—is an idea that would have startled Pythagoras and Plato. There was no such thing as a zero in the mainstream mathematics of the ancient Greeks.68 The concept was not invented until 400 CE, seven hundred years after Aristotle. It was invented by the Indians. What did it represent? “An empty column on a counting board.”  Read more at location 4200

Peano's axiom number two: one number comes after another. In fact, Peano's axioms two through four are all ways of saying that one number comes after another.  Read more at location 4219

axiom number five, for all of its impossible language, is simple: all numbers share a tiny kernel of common properties. You can write numbers down. All of them. You can manipulate numbers with arithmetic. All of them.  Read more at location 4221

They are a form of animal, mineral, and vegetable unto themselves. Seven and seven million may be very different from each other. But when you compare them to cups of chai latte, volcanoes, light bulbs, and lamas, it's obvious that seven million and seven belong to the same species. It's obvious that all numbers share common characteristics. That's it.  Read more at location 4222

That's where you got the idea that the universe might simply be doing her homework—advancing one Planck step of time after another—1043 steps per second.74 That's where you got the idea that the cosmos might be working from a handful of magic beans, from a handful of simple rules, from a handful of axioms. That's where you got the idea that the universe might be unfolding what American physicist David Bohm would later call “implicate”75 properties.  Read more at location 4233

that's where you got the idea that when the cosmos belches forth old patterns in a new medium, those old patterns sometimes become new things. Very new things. That's where you got the idea that translation can sometimes be more than it seems. Far more. That's where you got the idea that translation can sometimes be transformation in disguise.  Read more at location 4242

Algebra is essentially a language.” —Eli Maor

Translation turned Giuseppe Peano from a good kid to a rebel. Translation turned Peano into an outsider, an explorer, and a heretic. In 1903, fourteen years after he published his first version of his axioms, Peano turned his attention to something that seemed to have nothing to do with math. Nothing whatsoever. Peano became obsessed with translation and language.  Read more at location 4249

With his geometric calculus, Peano translated Euclid's geometry into a new medium. Into the language that Galileo and Kepler did not have. The language of equations. Peano translated the kind of complex manipulations of squares, tetrahedrons, icosahedrons, spheres, triangles, and circles that Kepler had loved into nice, neat, easy-to-deal with algebraic formulae.  Read more at location 4256

Giuseppe Peano's interest in translation was more than a passing fancy. It was an obsession. An obsession that grew as he got older. Once he'd completed his axioms and his geometric calculus, Peano turned his attention to something that seemed utterly unrelated: a universal language. He called it a “Latin without grammar.”  Read more at location 4265

Peano spent the last twenty-nine years of his life shifting from an exclusive focus on math to the promotion of Latin without grammar.  Read more at location 4282

at the International Congress of Philosophy of 1900 in Paris, Peano made that huge impression we talked about before on Bertrand Russell. A life-changing impression.85 The impression that led Russell to say that “the most important year of my intellectual life was 1900.”86 Here's how Russell describes it: The Congress was a turning point in my intellectual life, because I there met Peano. I already knew him by name and had seen some of his work, but had not taken the trouble to master his [logical] notation. In discussions at the Congress I observed that he was always more precise than anyone else, and that he invariably got the better of any argument upon which he embarked. As the days went by, I decided that this must be owing to his mathematical logic. I therefore got him to give me all his works, and as soon as the Congress was over I retired to Fernhurst [Russell's home] to study quietly every word written by him and his disciples. It became clear to me that his notation afforded an instrument of logical analysis such as I had been seeking for years, and that by studying him I was acquiring a new and powerful technique for the work that I had long wanted to do.  Read more at location 4285

****  The quest to show that math and logic are just two different ways of expressing the same thing.88 Two translations of something primal into a different medium. Two different languages with which to express what Russell called “primitive ideas”—underlying patterns, deep structures, Ur patterns.  Read more at location 4295

TED COONS, DANCING WONDER: A TALE OF TWO TRANSLATIONS 

*********  Iteration is translation. And translation of the old into a new medium, into a new language, can be transformation. Translation can be an act of creation. Now reverse that. Retro-engineer it. When you find something radically new, dissect it. If you do, you will often discover that the staggeringly new is something old in disguise. You will often find a simple rule at work, a rule repeating itself in unexpected ways. You will often find a simple basic pattern at work. You will often find a deep structure. You will often find an Ur pattern.  Read more at location 4308

Coons's life poses a crucial puzzle to the scientific expedition that you and I are on. That puzzle: what connects dance, music, and the arts to science?  Read more at location 4321

Music had an astonishing power to stir emotions. But where did those emotions come from? And, in Coons's words, “how was form and its mathematics involved?” That question became more important to Coons than music.  Read more at location 4336

forty years later, Coons would still be stirring up the music scene. He would involve himself intensely in the American Festival of Microtonal Music's project to complete and perform legendary modernist composer Charles Ives's magnum opus, “The Universe Symphony.” Why did Coons throw himself into the completion of Ives's musical take on the entire cosmos? “Out of conviction with Ives and the early Greeks,” he says, “that music is in some way the image of the universe.”97 Kepler would have been pleased. So would Pythagoras.  Read more at location 4354

There was more than A = A to Aristotle. There was the basic Aristotelian syllogism, the one that's a cornerstone of logic: if a = b and b = c, then a = c. If all men are mortal and if Socrates is a man, then Socrates is mortal. In Ted Coons's case, the syllogism went something like this. If math = music, if music = emotion, and if math = the cosmos, then emotion = the cosmos.  Read more at location 4369

***********   emotion = music = math = the cosmos.  Read more at location 4373

Does the square you draw with pencil and paper equal the square you draw with your keyboard and your mouse? Does the signal your mouse sends to your microprocessor equal the square you drew on paper? And does the square you send to your Wi-Fi router equal the square you see on your monitor? What in the world does “equal” really mean?  Read more at location 4408

how does Ted Coons's mystery of emotion = music = math = the cosmos relate to a square on paper = a square drawn by the muscle movements of fingers = the programming commands to draw a square in your computer = the square picked out by the LEDs of your monitor = the square that goes through the air to your router? When one A is seemingly so different from another A, how does A still equal A? And why?  Read more at location 4417

Translation from one medium to another plays a role in the God Problem. So does the role of translation as transformation.  Read more at location 4426

PRESTO, CHANGE-O: TRANSLATION'S LITTLE SECRET 

The brain translates chemicals, electrons, and the brainwide webbing of axons and dendrites into Aristotle's streams of logical argument.  Read more at location 4432

Giuseppe Peano's obsession with translation was an obsession with boiling things down. What sorts of things? Numbers, calculus, algebra, formulae, geometry, logic, and language. Symbol systems. Boiling them all down to a central core of underlying patterns. Translating a vast mass of things into a handful of “primitive”101 statements. Translating a vast mass of things. Translating them into a handful of magic beans. In a sense, Peano's quest was a repetition of a basic idea from Plato. It was another manifestation of Plato's conviction that behind the jungle of concepts we deal with, behind the wild variety of the things that we see and believe, there are a handful of universals, a handful of basics, a handful of ideas, a handful of archetypes, a handful of deep structures, a handful of Ur patterns.  Read more at location 4450

THE DAY YOU UPLOADED YOUR SELF: TRANSLATION SAVES YOUR LIFE 

I believe that nature uses the same small set of ideas over and over. —Joseph Polchinski, Kavli Institute for Theoretical Physics,  Read more at location 4462

I would not give a fig for the simplicity this side of complexity, but I would give my life for the simplicity on the other side of complexity. —Oliver Wendell Holmes  Read more at location 4464

You were certain that in some underlying way, art, poetry, religion, and science were the same. It was one of those things you knew in your bones. But you couldn't figure out how and why. Did science really equal art? And if so, why?  Read more at location 4491

Group Selection Squad—the cyberorganization you founded in 1995—was dedicated to overthrowing the scientific tyranny of individual selection—the idea that evolution is a battleground between selfish genes and selfish individuals. There was another view, group selection. Group selection said that individuals both compete and cooperate. They cooperate in groups. And the success or failure of those groups has an impact on genes. For example, the leading champion of group selection, an evolutionary biologist named David Sloan Wilson, argued that if you are a member of a tribe in South America or Africa that has chosen a weak form of social organization and you go up against a tribe whose organizational structure is strong, you will lose.104 And if you lose, you will lose your property and your women. Even if you don't lose your life, you will lose the right to reproduce.  Read more at location 4493

Or, to put it differently, the best cooperators make the strongest competitors.  Read more at location 4502

What had pulled ben-Jacob, a condensed matter physicist, into microbiology? He'd noticed that bacterial colonies in petri dishes spread out in fractal patterns. Patterns like the patterns you see in rocks in museum shops, rocks cut in half and polished to show their gorgeous internal structures, circles, sunbursts, and concentric rings.  Read more at location 4541

Eshel was on the hunt for underlying patterns, deep structures. And for their translation into a new medium—the medium of life. Then there was Eshel's friend Joel Isaacson, Professor Emeritus of Computer Science at Washington University.  Read more at location 4546

Isaacson had devised a mathematical gamelike system, a cellular automata, that accounted for the evolution of the elementary particles called “the baryon octet.”110 He'd done it using nothing but a tiny number of simple starting rules. Rules you might call deep structures. Fundamental patterns. Founding axioms. Ur patterns. What was Isaacson's most intriguing primary rule? A something exists as a something in part because of the space that separates it from something else. An empty space helps give things their identity.  Read more at location 4548

CHAPTER 6: IS METAPHOR A CRIME?

THE HUNGER OF THE STUTTERING FORMS: ISOMORPHIC SYMBOL SETS 

Reed Konsler injected three words into the discussions of the International Paleopsychology Project. Three words that would offer a clue to the mystery of translation. Three words that would help explain why metaphor works. Three words that would hint at the inner tricks of cosmic creativity. Konsler inserted the phrase “isomorphic symbol sets.” Konsler swears he got “isomorphic symbol sets” from Douglas Hofstadter, the mathematical and scientific deep thinker and author of the Pulitzer Prize–winning 1979 book Gödel, Escher, Bach.  Read more at location 4557

What are isomorphic symbol sets? Symbol sets that look very different, but that match up in some strange way. Symbol sets that explore the world in different terms but that correspond to each other.1 Symbol sets that can be translated into each other.  Read more at location 4564

The isomorphic symbol sets that produced the biggest payoff thrived. Some payoffs were purely social. Some symbol sets made you feel good. Some symbol sets helped you hold a tribe, a city, or an empire together. In which case accuracy didn't count. Astrology is a good example. Religion is another. But many symbol sets and their quirks hung on and grew because they had prediction power. The power to isomorph the real world. How many of these languages are synonymous—the language of math, the language of logic, the language of politics, the language of science, the language of visual art, and the language of fiction and poetry?  Read more at location 4581

****  Aristotle not only dictated a method for science. He dictated one of our scientific prejudices. The prejudice against metaphor. “Metaphorical reasoning is unscientific,”2 he said in his Posterior Analytics, the book in which he laid out his procedure for science.  Read more at location 4590

LEONARDO'S STONES: WHY METAPHOR WORKS 

Light, says current physics, is simultaneously a wave and a particle. And guess what? Though Aristotle says that “metaphorical reasoning is unscientific,” a wave is a metaphor. So is a particle. How did the highest of the modern sciences—physics—get the notion that light is both a wave and a particle? From metaphors. The tale begins nearly six hundred years ago on the western shores of Italy near the city of Piombino with Leonardo da Vinci and the detailed observations he writes down in his notebooks,  Read more at location 4597

(Note: Davinci uses wave metaphor for light)  Says Leonardo, “The water, though remaining in its position, can easily take this tremor from neighboring parts and pass it on to other adjacent parts.”26 To put it in different terms, Leonardo discovers that a form can travel without substance. A pattern can keep itself alive via a strange process. First it can recruit one sploosh of water, then another. All the while it can retain its process, its appearance, its uniqueness, its identity. Just as you retained your identity when you translated yourself into cyberspace. Or, to put it in God Problem terms, the wave is not a thing. It is a recruitment strategy. One that sustains itself with extraordinary stubbornness. What's more, Leonardo invents an experiment, one that will become a recruitment strategy in itself. An experiment that will echo down through history. An experiment that will transmit its “impression” like a wave.  Read more at location 4701

How does Leonardo account for this existence of a common pattern seemingly underlying the behavior of ripples, water, sound, the thrumming knife, and, of all things, light? He puts it down to a fundamental handful of rules underpinning all of nature, underlying all of “Necessity.” What is that handful of rules? Leonardo says it's called “reason.” It's the logic spoken of by Aristotle, Euclid, Peano, and Bertrand Russell. And, says Leonardo, reason controls the pattern of cause and effect.  Read more at location 4732

Back to Leonardo and his amazements: Who would believe that so small a space could contain the images of all the universe? O mighty process! What talent can avail to penetrate a nature such as thine? What tongue will it be that can unfold so great a wonder? Verily, none! This it is that guides the human discourse to the considering of divine things.32  Read more at location 4743

****  (Note:   hermetic, as above so below)  Leonardo says that even the smallest of things “contain images of all the universe.” He implies that the patterns of the heavens repeat themselves on earth. And he implies that the patterns on earth repeat themselves in the wonders of the skies. Leonardo's wonder is over the repetition of simple patterns—a “mighty process”—in new contexts and his awe at the way insubstantial patterns retain their identity—including their impression of what started them. What's more, Leonardo hits on something else crucial to the God Problem: translation. Translation from one medium to another.  Read more at location 4748

Yes, it was Leonardo who said “the eye is the window of the soul.”  Read more at location 4756

(Note: Newton uses particle metaphor for light)  As Leonardo had seen, light stubbornly retains its identity. And Newton, too, noted that light retained its identity whether it was traveling through air, water, or glass. But as far as Newton was concerned, the case was closed. Light was not Leonardo's wave. Light was a small body. Light was what you and I call a particle.  Read more at location 4773

With Leonardo and Newton, the battle of the metaphors for light began. No matter how unscientific Aristotle claims metaphorical thinking is.  Read more at location 4780

metaphor is the key to human understanding. And metaphor is central to something that Aristotle invented: science.  Read more at location 4783

PLAID IN THE POOL: THE EYE DOCTOR WHO GAVE YOU WAVES 

In 1799, when Thomas Young was twenty-six years old, Egyptian hieroglyphics were considered an incomprehensible mystery. There were only the faintest clues to what they meant. Even the scholars with the highest brows and the biggest brains were baffled. But the new stele—the Rosetta Stone—promised to provide a perceptual key.  Read more at location 4805

The Rosetta Stone had three texts in three different writing systems, three different symbol sets—Egyptian hieroglyphs plus yet another unknown Egyptian symbol system, the shorthand script known as demotic (the alphabet of the demes, the writing system of the common people). Below the hieroglyphic and demotic texts was a text in a very well-known language, Greek. A text celebrating the accession of Ptolemy V,47 who had come to the throne at the tender age of five. The Rosetta Stone declared that Ptolemy V is the ever living god, the beloved of Ptah, and the lord who makes benefactions materialize out of nowhere.  Read more at location 4809

No one knew how to decipher the two Egyptian writing systems. At the age of forty-five, Thomas Young threw himself into the problem…one  Read more at location 4817

Using the ripple tank, Young showed precisely what happens when you repeat Da Vinci's experiment and throw two stones into a pond. Yes, as Leonardo noted, the ripples do retain their identity. In the face of considerable opposition. They hold on to their shape despite slamming into each other, a crash that should lead to disintegration. A crash that should lead to entropy. And, yes, they do retain the “impression,” to use Leonardo's word, of the force that gave them birth. But the two rings of ripples colliding do something else. Something mathematical.  Read more at location 4855

Young introduced a term he gets full credit for. He called his highly patterned ripple grid and the phenomenon of multiplication and addition that generated it “interference.”  Read more at location 4863

What does a basin of water have to do with the brightness that literally lights up our life? Good question. In 1801,53 Young answered it by inventing yet another experiment, an experiment that would join the axiom as a basic recruitment strategy. An experiment that would ripple its way into modern quantum physics. Young's “demonstration” (to use Aristotle's,54 Euclid's,55 and Galileo's56 word) is called “the two-slit experiment.”  Read more at location 4869

Said Young, the stripes of light on your wall are due to interference. Where two peaks of light meet, they add to each other. They make lines of brightness. Where two troughs meet, they deepen57 each other. They make lines of darkness. Hence light is not a particle. It is a wave. A wave like the waves in water.  Read more at location 4893

In a rational world, light and water are violently different things. There is no reason whatsoever that water and light should be the same. And in truth, every laboratory demonstration, every chemical reaction in a test tube, every act of genetic analysis in a sequencing machine, every experiment on pigeons, rats, or pygmy chimps, every test of drugs on dogs or rabbits, and every social science study based on sampling makes no sense. Every one of these assumes that you can capture a pattern in one small patch of territory, in one manifestation of nature, and blow it up big. What's worse, every one of these assumes that you can grab hold of a pattern in one kind of thing and generalize it to radically different things. Every one of these assumes that you can take a basic pattern and translate it the way Young translated the Rosetta Stone. That you can translate it to something that is grotesquely different. And every one of these carries another hidden assumption. That the real translator, the real duplicator of a basic pattern in radically different mediums, is not you. The hidden assumption is that the real translator is nature.  Read more at location 4906

every act of science makes a vast and peculiar unspoken assumption, a giant leap of faith. It contains a deeply buried axiom. It assumes that scratch marks on clay, wax, or paper can capture the habits of planets and stars.  Read more at location 4914

Science assumes that the cell-and-protein mush of a brain thinking about lines and triangles can feel out the shape of the universe. Yes, science assumes that a scrawl of equations, words, and neurons can imitate, express, grab hold of, and translate a hidden shape of the cosmos.  Read more at location 4921

Not all metaphors are valid—remember poor Johannes Kepler's ball-and-box solar system mistake. The Kepler cockup. But some metaphors are on target. And when they are, they pay off big time. Metaphorical thinking works. But why? The answer is in Reed Konsler's isomorphic symbol sets. The answer is in iteration. The answer is in translation. The answer is in Giuseppe Peano and Bertrand Russell's “primitives.” The answer is in Ur patterns.  Read more at location 4925

HOW FORM GOES MANIC—WHAT'S AN UR PATTERN? 

“Beauty is truth, truth beauty,”—that is all Ye know on Earth, and all ye need to know. —John Keats  Read more at location 4930

Ur patterns are implicit in the hidden assumptions of science and of everyday life. Ur patterns are what we stab to reach when we do lab experiments. They are what we stab to reach with religion. And they are what we summon to the surface when we do art. They are underlying patterns that we are sure hide behind the realities that assail us. The underlying patterns behind the weather. The underlying patterns behind the seasons. The underlying patterns behind the movements of the sun, the moon, and the stars.  Read more at location 4931

(Note: Akin to archetype)  Why call them Ur patterns? Ur in German means the first, the primeval, the essential pattern on which all copies are built. When philologists, language experts, dig down to find a protolanguage, a language from which an entire family of modern languages is derived, they call that primitive font of words and syntaxes an Ur language.  Read more at location 4939

***********  Ur patterns are the most basic patterns we can find. Patterns that appear over and over again in vastly different mediums, in vastly different frames of reference, in vastly different raw materials, and at vastly different levels in the evolution of the cosmos. There is a good chance that Ur patterns were among the earliest patterns to spin off from the starting rules of the universe. There is a good chance that Ur patterns appeared in the first burst of cosmic creativity—the big bang. And there is a good chance that Ur patterns have been repeating ever since. Repeating in forms that are ever more gaudy and ornate. Reappearing in surprising disguise. When a metaphor works, it's because it taps that basic pattern in a new medium. The way that the interference patterns of water also appear in light. Two different mediums—liquid and brightness. But the same pattern. The same Ur pattern.  Read more at location 4949

Thomas Young found a single pattern at work in both water and in light, two vastly separated things. And this is flabbergastingly unlikely.  Read more at location 4970

water is a collection of matter that behaves in very peculiar ways. It sloshes, it puddles, it dissolves sugar and salt, it wets leaves, it soaks your clothes. Water is substantial. Yet water is not hard as a rock. You can dip your finger into it, lift your finger, and watch a drop form on your fingertip. Water is an amazement. Water is a mystery. Light is an amazement, too. Yet it is water's opposite. It has no substance that you can feel at all. You can do cartwheels in the sunshine and the soup of photons will not stop you. What's more, light and water evolved at vastly different times in the cosmos. Photons—the wave/particles of light—appeared in the first instant of the big bang. Water came billions of years later.  Read more at location 4974

In other words, water and light are two very different mediums. Vastly and absurdly different. Logically, there should be no relationship between them. But there is. Thomas Young proved it. Thomas Young proved that a primal pattern, an Ur pattern, repeats in two bizarrely separate mediums. And that, ladies and gentlemen, is the essence of metaphor. Finding a pattern in one medium and applying it to another.  Read more at location 4989

it works because there are deep structures. It works because of Ur patterns. Is metaphor “unscientific”? Far from it. It is the very core of science.  Read more at location 4994

Many of these pattern hunters called Ur patterns “natural laws.” Why not simply continue with that simple phrase? Why Ur patterns? The idea of natural law is based on a metaphor that you and I have discussed before. It's the metaphor of a kinglike God commanding a cosmos into being. It's the metaphor of an edict from a dictatorial deity, a divine architect. But we are not hunting down the mind of a creator God. We are hunting down the secret of a cosmos that creates itself. We are not hunting for the creative secrets of a top-down universe. We are hunting for the creative secrets of a universe that built itself up from the bottom.  Read more at location 5011

Law was not the only metaphor that men like Kepler, Galileo, and Newton relied on to describe the underlying patterns of the cosmos. Their second metaphor was “reason.”  Read more at location 5016

Is the cosmos really like a diligent math pupil unfolding corollaries from a handful of axioms? Does the universe really yank an implicit order from its hiding place and pull it into the light of everyday reality? Then there's metaphoric candidate number two. The cosmos behaves like a termite accidentally building an edifice. A termite following a simple rule: clean up the mess. A termite unintentionally collaborating with two million others to build an architectural masterpiece. Without an architect. Both the metaphor of the student and the metaphor of the termite get at the very same thing. The question of whether the material world innovates by extracting the implications from a set of simple starting rules. From a handful of axioms. Which leads to a question: Are ornate complexities really hidden in simple rules waiting to be discovered? And if so, how in the world did they get there?  Read more at location 5032

When you build a pyramid, to what extent are you inventing and to what extent are you discovering the simple rules that make triangular forms stable? To what extent are you inventing the pyramid and to what extent is a pyramid using you to invent itself?  Read more at location 5056

the Olmecs of Mexico knew nothing about the Egyptians. But they built their first pyramids in roughly 1500 BCE.70 Despite a separation of 7,700 miles from the Egyptians. And like the masterminds of Catalhöyük, the Mesoamerican Zapotecs invented the city. Without knowing a thing about Catalhöyük. So to what extent did the city use the Zapotecs and the geniuses of Catalhöyük to invent itself? To what extent were the pyramid and the city recruitment strategies? Forms and functions with a life of their own? Here's a hint: insects invented cities, too.  Read more at location 5057

Plato claimed that the abstract forms, the underlying patterns, the patterns of the sort that geometry revealed, were more real than your touchable, squeezable, everyday things. He made a case for what Noam Chomsky would one day call “deep structures,” deep structures of the cosmos.  Read more at location 5064

Aristotle derived yet another form of deep structure. Another distillation of simple rules. He boiled everything down to “logic” and “reason,” reason based on something he called “axioms.” In fact, Aristotle went even further. He turned the human pattern hunt into a new kind of recruitment strategy: science. Then Euclid transformed Aristotle's program of definition, axiom, proposition, and proof into an even more powerful recruitment strategy.  Read more at location 5066

*  modern science followed Aristotle's commands and claimed to despise metaphor. But in reality, it used metaphor over and over again. The metaphor of geometry. The metaphor of the particle. And the metaphor of the wave. But there was more. Modern science in its early centuries also used Aristotle and Euclid's technique—definition, axiom, proposition, and proof. And the early modern scientists, the “natural philosophers”—Leonardo,71 Galileo, Kepler, and Newton—swore that Nature herself had used the same method. God and His obedient servant, Nature, they were convinced, had been geometers. And God and Nature had used reason to create. Yes, “reason,” a word based on Pythagoras's number ratios. And guess what? The supposition that the cosmos was based on metaphor and the simple rules of reason worked. It helped generate systems that successfully predicted the movements of the planets and the heavens. Chalk up another victory for the notion that simple rules underlie the cosmos. Score another point for the notion that deep structures, Ur patterns, are for real.  Read more at location 5076

János Bolyai and Nikolai Lobachevsky flipped just one of Euclid's axioms and left the rest intact. They flipped the parallel axiom. And what did they find? If you change just one axiom, you get new implicit properties. In fact, you get a different universe. A universe that you did not invent. A universe that took you by surprise. A universe that you found. So the complex really was hidden in the simple. A whole new geometric universe really was hidden in axioms. Then Giuseppe Peano showed the opposite: that the simple was hidden in the complex. Peano demonstrated that you could boil the entire natural number system down to five axioms. In other words, Peano showed that if you dig hard enough, you can find what Plato and Aristotle called “ideas.”  Read more at location 5086

Wave-and-particle metaphors—primary metaphors of science from the sixteenth to the twentieth centuries—miss something big.  Read more at location 5107

REAL ESTATE IN THE EMBRYO: LOCATION, LOCATION, LOCATION—KARL ERNST VON BAER AND HANS ADOLF EDUARD DRIESCH 

The origin of life, the evolution of increasing biological complexity, and the development of the embryo from a single egg cell, all seem miraculous at first sight, and all remain largely unexplained. —physicist Paul Davies72  Read more at location 5114

Many others will win a prize. But the palm will be won by the fortunate man for whom it is reserved to trace the formative forces of the animal body back to the general forces that direct the life of the universe. —Karl Ernst von Baer73  Read more at location 5117

one of the most important candidates for Ur pattern status—is differentiation. And the tale of differentiation takes us to an ironic destination. Why? Because the metaphor that put differentiation on the map is one missing from most of today's science. It is a metaphor that may have to be reinserted if science is to make sense.  Read more at location 5120

It is the metaphor of the embryo. That metaphor was at its peak in the nineteenth and early twentieth centuries when two men, Karl Ernst von Baer and Hans Adolf Eduard Driesch, were doing seminal work on embryonic development.  Read more at location 5124

von Baer was the first to use his scalpel and his microscope to discover that mammals like dogs and women have embryos.  Read more at location 5137

Von Baer watched through his microscope as an embryo unfolded what von Baer calls one “type of organization”79 after another. In the beginning, the embryo of a chick is a tiny ball of tissue. It can just as easily become a snail, a sea anemone, or a starfish. Then it differentiates. It takes on the “type of organization” of an all-purpose land vertebrate—a landwalker with a backbone. Next the embryo becomes even more specialized. It avoids the pattern of a mammal and takes on the “type of organization” of a bird. But that is not the end of its branching off on a path of its own. Once again it specializes further. The chick embryo differentiates away from the “type of organization” of ducks and seagulls, from the type of sea birds. It shows the very special pattern, the “type of organization,” of a land bird. Finally it parts company with other land birds and takes on the special “type of organization” that will someday make a chicken.  Read more at location 5140

****  von Baer watched as embryos went through the process of producing finer and finer distinctions, finer and finer specializations. And more and more unique large-scale structures, more and more unique “types of organization.” Von Baer seldom used the word “differentiation.”81 The year 1821 was eighteen years before the rise of cell theory.  Read more at location 5148

**********  with or without cells, von Baer came up with Baer's principle: “Development proceeds inexorably from the general to the special.”83 Von Baer's principle would become the core principle of differentiation.  Read more at location 5154

Hans Adolf Eduard turned embryology into a philosophy, a philosophy that dared to challenge Newton's idea of the cosmos as a machine. And a philosophy that dared propose that the embryo provides a far more useful metaphor with which to understand the evolution of the cosmos than the gears (a word, you may remember, that Newton never used—he called them “wheels”)84 in the belly of Newton's windmill.  Read more at location 5159

****  (Note:   fractal information)  The phenomenon that amazed him the most was how developing cells seemed to know the goal they were heading toward. It looked as if sheets and mobs of cells had a sense of their final product, whether that product was an octopus, a tree, or a human being. The cells seemed to have a final big picture as their guide. If you removed a single cell from a developing organism at the right time, it could start all over again from scratch, divide, and make yet another complete organism. “Take the ovary of our sea urchin for instance,” Driesch wrote, “and there you have a morphogenetic system every element of which,” every cell of which, “is equally capable of performing the same complex morphogenetic course—the production of the whole individual.”  Read more at location 5168

Cut any part of a branch or a bulge from the sea squirt and that tiny fragment can remake itself into a new, complete, multibranched sea squirt. “The branchial apparatus,” Driesch says, “is able to give rise to a complete little organism.” And the scrap of sea squirt doesn't even have to bother to make new cells. It can reengineer the cells it's already got. It can repurpose, reassign, and rearrange them as if it had a built-in blueprint, a built in bauplan.88 A blueprint for a sea squirt adult.  Read more at location 5175

Driesch looked for the force, for the power that made the possible emerge from nearly nothing. Whatever that mystery might be, Driesch came up with a name for it, “entelechy.”92 And he challenged Newton. The mystery Driesch sought, he said, was “not a machine.”93 It was not a mechanism like the cogs and wheels in the bowels of Newton's windmill. No machine, Driesch said, could repair itself.  Read more at location 5183

Yet embryonic cells and even some adult cells could build a copy of the organism from which they were wrenched. The entire organism! These cells seemed to contain a sense of the big picture they were laboring to construct. Driesch felt that this big-picture fixation, this goal-directedness, was not limited to cells. “The universe is an organism or rather is the one organism,”  Read more at location 5189

to Driesch even the universe, in some strange way, seemed to know where it was going. It seemed to sense the form toward which it was aiming. So did human history. History, said Driesch, is like phylogeny—like the evolutionary process that produces new species—like the process of biological evolution. And history unfolds in a seemingly purposeful way. History, says Driesch, seems driven by “unifying causality,”  Read more at location 5194

(Note: Polanyi Self-Transcendence)  What's more, Driesch observed that as a system unfolds, its rules change, its laws morph. It seems to reach toward making even higher and previously impossible-to-imagine new orders.  Read more at location 5199

quarks spring together to form impossible new structures: protons and neutrons. Three hundred eighty thousand years later protons and neutrons whump together with electrons to make another inconceivable shock: atoms. Atoms crowd together and nearly a billion years later unfold two more unimaginable forms, galaxies and stars.  Read more at location 5204

********  In the cosmos of six monkeys at six typewriters, in the cosmos of randomness, more things should mean more crazed lunacy, more chaos. But when you get mobs and masses, you don't get entropy. You don't get a confused soup. You get new big pictures. New sanities. New gestalts. To use Driesch's word, you get new “unities.”  Read more at location 5209

(Note: Again, Polanyi Self-Transcendence)  “More Is Different.” The piece's point? That mobs, masses, and plethora produce emergent properties. Even if those piles, plurals, and plethoras are of absolutely identical things. What's more, Driesch was right. Each layer of emergent properties produces new laws. More than just new laws. Whole new hierarchies of being.  Read more at location 5214

As an embryo climbs the stairway of implicit order, it unfolds radically new laws. Or, as Driesch put it, “In biological embryology we know that the law of mere cleavage for instance holds good for say ten cell divisions.”102 Then everything changes. Bigger gangs beget bigger structures, higher degrees of the ornate, higher degrees of form and interaction. Higher orders of sociality. Higher orders of choreography. More intricate big pictures. The form that's assumed by a mere ten cell divisions, a mere 1,024 cells, is just a ball. But that “is then followed by the law of organ formation.” At 1,024 cells, a whole new law kicks in. A whole new recruitment strategy shows its face. Form itself seems hungry to emerge from possibility space. The form of the head, the heart, the liver, and the arms and legs. All seem eager to gain their opportunities to escape mere implication. Eager to grab the privilege that you and I take for granted every minute of the day. Existence. Form seems eager to be.  Read more at location 5219

****  the pattern of the eye will do almost anything to be. It will take so many routes to becoming that some experts claim it has evolved separately, yes, on its own, dozens of times in radically different forms and in radically different kinds of life. The eye “wants” to be in as many creatures as possible. And it succeeds. Ninety-five percent of the species on this planet have eyes.  Read more at location 5226

To Driesch, it seemed as if the cosmos and history are not just pushed along by causality. It seemed as if the cosmos and history are not just flicked ahead by their past. It seemed as if they are pulled ahead by their future. As if they are rushing toward a place in a bigger picture. It seemed as if implicit order has a magnetism, as if the implicit has its own form of attraction, its own form of gravity. Formally, the idea that the future pulls us toward itself is called “teleology.” And it's one of Aristotle's ideas. Aristotle called it “final cause.”  Read more at location 5232

But 128 years after Newton's death, the idea of the future as a cause, the idea of teleology, was banished from science.108 It was banished with the publication in 1855 of a book by a German physiologist and physician, Ludwig Büchner: Force and Matter or Principles of the Natural Order of the Universe.  Read more at location 5241

Büchner's Force and Matter also became the Bible of a new movement, “Free Thinking,” otherwise known as atheism.110 Büchner did not mince words about the role of the future in shaping the present, about final cause and teleology. Teleology, he said, was “short-sighted,” “empty,” and “superficial.”111 Not to mention “anthropomorphic.”  Read more at location 5251

MASTER OF THE UNIVERSE: HERBERT SPENCER, GRAND UNIFIER AND FLIRT 

Herbert Spencer is one of the most underrated thinkers of the late-nineteenth century. He was nominated for a Nobel Prize in Literature in 1902. And with good reason. Among other things, he coined the phrases “survival of the fittest” and “theory of evolution”  Read more at location 5262

He dedicated his life to a grand unified vision, a big picture that would sew all of the sciences together with the threads of a small number of unifying principles. He called that grand vision a “synthetic philosophy.”116 Spencer married omnivorous curiosity to diligent work.  Read more at location 5268

****  (Note: Aye! Existence itself!)  The cosmos hides her creativity by preying on the way we oh-so-quickly become blasé. She covers up her bombshells and her breakthroughs by tricking us into seeing the extraordinary as mundane.  Read more at location 5450

THE SCANDAL OF THE CENTURY: GEORGE ELIOT AND HER APE 

the Westminster Review's skeptical, heretical, and sometimes atheistic take on religion. Which means something important about its coverage of science, coverage handled largely by T. H. Huxley. The Westminster is challenging creationism and intelligent design—the creationism and intelligent design that Kepler, Galileo, and Newton had believed in—and is pushing a brand-new secular approach: “theories of organic…evolution.”216 And the Westminster is doing this eight years before Charles Darwin publishes his first book, The Origin of Species  Read more at location 5625

George Henry Lewes was about to enter a realm with enough intellectual luminaries to burst the walls of a railroad carriage. He was about to enter a social group in which the arts, the sciences, and philosophy—three of the great fiefdoms of metaphor—propelled each other to greater heights. He was also about to meet Herbert Spencer and Mary Ann Evans. And above all he was about to provide a tool with which to confront the problem of how a cosmos without a god creates.  Read more at location 5668

Lewes was not an airhead. He was in deadly earnest about two things: philosophy—the field he'd lectured on—and the rapidly developing field of physiology. But the philosophy of the day was really psychology. Philosophy was an attempt to see what makes minds tick. Especially Scottish philosophy. The two major Scottish philosophers—David Hume and the founder of economics, Adam Smith—had probed the human psyche. Now it seemed as if physiology would provide a missing link, helping to understand that psyche with hard science. That was the project Lewes wanted to undertake: the unification of Scottish philosophy—psychology—with physiology.  Read more at location 5687

Goethe was a philosopher who had dabbled in science. A poet who had dabbled in something very specific: the mystery of form. Goethe had written an entire book on the way that form changes, the way it progresses. His Metamorphosis of Plants had revealed that though plants look very different, they are all variations on the same theme and they all share the same organs. How very much like the embryo observations of Karl Ernst von Baer!  Read more at location 5694

in 1837 Lewes took off for Berlin. He was probably pursuing what he called “the spirit of Faust.” The spirit of Goethe's Faust. Here's how Lewes expressed that spirit: Some of us, he said, refuse to think about the future and work only for today's pleasures. We work for ourselves, not for others. And that damns us. Only those who set aside immediate gratification and work on behalf of our fellow humans are blessed. Wrote Lewes many years later, “The solution of the Faust problem is embodied in his dying speech: the toiling soul, after trying in various directions of individual effort and individual gratification, and finding therein no peace, is finally conducted to the recognition of the vital truth that man lives for man, and that only in as far as he is working for humanity, can his efforts bring permanent happiness.”  Read more at location 5706

None of Lewes's books would stand the test of time. But one of Lewes's words would. That word? Emergence.  Read more at location 5718

BULGING FORTH FROM NOTHING: THE EMERGENCE OF “EMERGENCE” 

Comte had put forth “the fundamental law of human evolution.” Yes, that magic word, “evolution.” And Comte's “law of evolution…is of the same importance to the science of history, as the law of universal attraction was to the science of astronomy.”253 What's more, Comte's “law of evolution” came a full fifteen years before Charles Darwin's Origin of the Species. What was Comte's “Law of Evolution”?254 Comte had invented something he called “sociology.” It had been traditional to regard human societies as perpetually decaying. Crumbling. Falling apart. Ever since man had littered the perfect garden, Eden, with original sin. Comte pointed to Rousseau as one of the primary purveyors of this gloomy doctrine.255 But Comte had invented a vision of history as a series of steps in the opposite direction from decay, in the opposite direction from entropy. Comte had reperceived history as a series of self-generated steps up. Self-generated steps of “transformation” built, he said, by “invariable natural laws.”256 Self-assembled on a “gradual series of former transformations.”  Read more at location 5741

What's more, said Comte, societies are “social organisms…analogous to…the animal organism with the one difference that in sociology they are more complex.”258 Societies advance in “three stages of progress,”259 Comte said. Those stages are the “Theological,” the “Metaphysical,” and the “Positive.”260 Roughly speaking, that's the religious, the philosophical, and the scientific. Societies “evolve” through these stages like “organisms.”261 Or, as Lewes saw it, like embryos. “As in Embryology,” Lewes would write about Comte's view of societies, “we record…stages of evolution…the passage from the simple to the complex—the Inorganic to the Organic.”262 That “passage from the simple to the complex” exists in all living things. And it exists in human societies.  Read more at location 5752

George Henry Lewes had met John Stuart Mill in 1835, thirteen years before Herbert Spencer got his job at the Economist. So how does Herbert Spencer enter Lewes's life? Good question. As you'll recall, Herbert Spencer has date after date with Mary Ann Evans. He takes every opportunity he can get to be with her. But he is not interested in romance. And she is. Meanwhile, George Henry Lewes has shown up at a dinner party, a soiree, at book publisher John Chapman's establishment at 142 on the Strand in 1850.  Read more at location 5763

Patterns like the quark, the atom, the nebula, the star, the cell, and the human being. Not to mention the empire, the nation-state, the democracy, and the railroad train. Instead, Lewes and John Stuart Mill have noticed something peculiar in chemistry. What is it?  Read more at location 5778

Hydrogen is an element that keeps showing up in this book. That's in part because it is the most abundant element in the cosmos. It's in part because it is one of the three oldest atoms in the cosmos. And it's in part because you and I are descended from hydrogen atoms. You and I have hydrogen in our family tree. We have hydrogen in every cell and nearly every molecule of our body. But hydrogen is a hot new item in 1835 when Lewes starts brainstorming with John Stuart Mill.  Read more at location 5781

In 1766, Henry Cavendish discovers that this gas has unique properties. Among other things, it catches fire easily. So Cavendish names the new gas “phlogiston,” Greek for easily set on fire.268 And in 1781, Cavendish also discovers that if you burn phlogiston—hydrogen—you get something totally unlikely. You don't get just a gas. You get a liquid. You get water. Ordinary water. A gas and a bit of fire produce a liquid?  Read more at location 5787

In Newton's world, things follow the laws of math. The laws of logic. The laws of Aristotle. The laws of one plus one equals two. But in 1835, when John Stuart Mill and George Henry Lewes first meet, it is known that two gases—hydrogen and oxygen—refuse to follow Newton's laws. And they refuse to follow the rules of Aristotle's logic. Input does not equal output. Two gases in do not equal two gases out. In fact, the two gases equal something radically new. They equal a semisolid. A semisolid with strange qualities. Flabbergasting properties. Unlike its two parent gases, this new something is visible. Unlike its two parent gases, this new stuff does not allow light to pass through it unimpeded. It wiggles, wobbles, and refracts light.  Read more at location 5830

How likely is it that something formed at 380,000 ABB (after the big bang) from a plasma—hydrogen—and something formed at two billion ABB—oxygen—something formed from the agonies of star death, could ever get together? How likely is it that the two could pull off a joint project? If this is a cosmos of six monkeys at six typewriters, how likely is it that the joint product of these two substances would be something this cosmos had never seen before—a liquid?  Read more at location 5859

****  Let me repeat this for emphasis: If they make anything at all, hydrogen, oxygen, and flame should make, at most, two hot gases. Gases heated by the flame. But hydrogen gas, oxygen gas, and the merest spark make a huge explosion.279 And they make water. They make a liquid.  Read more at location 5863

George Henry Lewes also called the water that comes from putting hydrogen gas with oxygen gas an “emergent liquid.”282 He wrote, “I propose to call the effect an emergent. It arises out of the combined agencies, but in a form which does not display the agents in action.” “The emergent,” Lewes explained, “is unlike its components…and it cannot be reduced either to their sum or their difference.”283 And the term “emergent” took off.  Read more at location 5877

Lewes said that emergence is a challenge to the science that relies on mathematics. It is a challenge to the science of geometry and equations. It is a challenge to the math that men like Bertrand Russell twenty-six years later would feel is logic in disguise. It is a challenge to logic itself.  Read more at location 5884

**********  Says Lewes, “Were all effects simple resultants, in the sense here specified, our deductive power would be almost absolute; a mathematical expression would include all phenomena. It is precisely because effects are mostly emergents that Deduction is insecure.”  Read more at location 5886

****  a tremendous number of the phenomenon in the world around us are emergent properties. In fact, since Lewes's day, the number of emergent properties we've discovered is staggering. The big bang is an emergent property. Pressure waves in the plasma at the start of the universe are emergent properties. Quarks, atoms, galaxies, and stars are emergent properties. Leonardo da Vinci and Thomas Young's interference patterns are emergent properties. So are Leonardo and Thomas Young. And so are Isaac Newton's machines. Puzzles, questions, answers, and perceptions are emergent properties. Your atheism at the age of thirteen is an emergent property. The gods inside of us, the gods that you have been hunting since you were thirteen, are emergent properties. And nearly all of the phenomena we can see from our café table at the beginning of the universe, nearly all of the cosmos's supersized surprises, are emergent properties. Says Lewes, “Strictly speaking, the real effect is always an emergent.”286  Read more at location 5892

CHARLIE DARWIN SHOWS UP LATE 

The word “evolution” does not appear anywhere in Charlie Darwin's Voyage of the Beagle. Yet it will appear forty-one times in George Henry Lewes's 1853 book summarizing Auguste Comte, Comte's Philosophy of the Sciences: Being an Exposition of the Principles of the Cours de Philosophie Positive of Auguste Comte.295 And when Lewes's book on Comte emerges, it will be another six years before Darwin will publish his Origin of Species. It will be another six years before Darwin will benefit from the abilities of Lewes's friend Thomas Henry Huxley to promote a theory of evolution. But as far back as 1844, Lewes has written with longing that “the urgent want of the age is…a general doctrine. The general laws of the evolution of society have to be discovered and organized.”  Read more at location 5930

When Darwin finally publishes The Origin of Species in 1859, he will at last offer what the evolutionists have starved and lusted for for over twenty years. He will give a clue to emergents in action.  Read more at location 5941

Natural selection, nature's pickiness, nature's way of playing favorites, her way of putting her creatures through a game that gives procreational privileges to the winners, that will be Charles Darwin's contribution to a theory that has been around since the days of his grandfather sixty-four years earlier. And the concept of nature's pickiness will give people like George Henry Lewes, George Eliot, and Herbert Spencer what they are aching for—a secular creation myth.302 A new story of Genesis. A new big picture. A new secular alternative to religion.  Read more at location 5952

But there will be a big problem with Charles Darwin's theories. And Darwin will know it better than anyone. Nature's pickiness will explain only a part of evolution. It will not explain nature's creativity. It will not explain nature's ability to fashion amazements. It will not explain emergent properties.  Read more at location 5962

in 1852 Herbert Spencer introduces Miss Evans to George Henry Lewes.310 John Chapman, the publisher on the other side of the street from the offices of the Economist, the publisher at 142 on the Strand, also does his best to throw Lewes and Miss Evans together. In fact, putting them together is easy. They are both regular guests at John Chapman's soirees. And the relationship takes. Lewes is ugly as sin. Thomas Carlyle's wife calls him “the ape.”311 But he is a liberated man. An unconventional man. A man who is married, but who has an “open” relationship with his wife.312 In fact, his wife has had children by other men during the course of the marriage.  Read more at location 5978

Mary Ann Evans will take Herbert Spencer's advice. She will try writing fiction. And she will churn out seven novels, novels riddled with philosophy and shot through with a brand-new thing called psychology, a field Herbert Spencer will name and pioneer.  Read more at location 5989

Mary Ann will write under an assumed name. Her nom de plume? George Eliot. 

THE ZYGOTE SNABS HERBERT SPENCER

Yes, differentiation and the metaphor of the embryo will enter Herbert Spencer's thinking three years after he comes to the Economist and one year after he begins to frequent John Chapman's soirees. Says Spencer, “In 1851, I became acquainted with von Baer's statement that the development of every organism is a change from homogeneity to heterogeneity.”  Read more at location 6002

Says Spencer, in early societies, everyone did everything—hunting, fishing, and tool and weapon making. But as societies evolved, some men specialized in hunting and fishing and others became full-time tool or weapons makers—full-time spear and fishing hook experts. Way, way down the line, really advanced societies invented machines like railroad engines with hundreds of parts.  Read more at location 6018

The result? Says Spencer, societies are like organisms. And their advance toward higher levels of complexity is like “the development of an embryo or the unfolding of a flower.”  Read more at location 6025

Just as Driesch could break off a branch of a sea squirt322 and see it become an entire, independent sea squirt, Spencer says that you can divide a primitive tribe, an indigenous tribe, and both halves will become complete tribes able to operate on their own. Why? Because each of these contains every element which the whole did—is just as self-sufficing, and quickly assumes the simple organization constituting an independent tribe.  Read more at location 6029

this interdependence of specialized parts is not mere theory, says Spencer. It is a blunt fact. Stub a toe and the whole body limps.  Read more at location 6045

a multivolume book called The Science of Logic. In it, Hegel had said that “contradiction is the root of all movement and life.” That's a pretty big claim. But Hegel had gone even further. He'd said that “it is only in so far as something has a contradiction within it that it moves, is possessed of instinct and activity.”  Read more at location 6055

****  boiled down Hegel's life-giving contradictions to a magic phrase: “thesis, antithesis, and synthesis.”330 What does that mean? When opposites struggle against each other, the appearance of battle is deceptive. Without knowing it, the opposites are working together to give birth to something new. Something larger, something occasionally novel, something occasionally surprising, something that occasionally makes one plus one far greater than two.  Read more at location 6059

Spencer got wind of Hegel's drift, he refused “to read further any work in which it is displayed.”333 He refused to read any more Hegel. But opposites joined at the hip show up all over Spencer's work. The opposites in this case are differentiation and integration.  Read more at location 6080

the iteration of simple rules would mean nothing without the emergence of big pictures. Big pictures within which the smaller units fit. The brick would be nothing without the vision of the wall. The wall would be nothing without the vision of the apartment complex  Read more at location 6092

And just as differentiation can be lethal without integration, integration can be dangerous without increasing levels of differentiation. Integration can be poisonous without increasing levels of individuation. Too much togetherness among cells does not produce fingers or toes. It produces a stump.  Read more at location 6099

*********  opposites are joined at the hip. Individuation only works when it's integrated into a big picture. And integration grows amazing things when individuation gives it new powers.  Read more at location 6104

Few people bother to remember Herbert Spencer. But when they do, they often slam him for his insistence on something totally antientropic—his sense of progress. Progress in the evolution of inanimate matter.337 Progress in the evolution of simple life forms. And progress in the evolution of man. Spencer, like Driesch, felt the pull of the future beckoning. In the development of human societies and in the development of all of life, Spencer said, “progress…is not an accident, it is a necessity.”  Read more at location 6108

****  (Note:   philosophical naivity in science as reductionism. Presumes a metaphysical paradigm of physicalism)  emergence has been derided as voodoo science. It's been called a word that doesn't belong in the scientific vocabulary. A word “without the conceptual clarity that would have helped real scientific research.”344 In other words, a word that makes no testable predictions and that generates no testable experiments. In science, emergence has often been set aside like the metaphorical systems of art and music. As late as 2011, high-profile string physicist Brian Greene would say with pride, “I believe that a physical system is completely determined by the arrangement of its particles. Tell me how the particles making up the Earth, the Sun, the galaxy, and everything else are arranged, and you've fully articulated reality.” And Greene would delight in pointing out that he is not alone. “This reductionist view,” he would say, “is common among physicists.”  Read more at location 6126

THE EMBRYO GOES COSMIC 

in the late-twentieth century, as we've seen before, Newton's obsession with devices, gadgets, and machines, his fixation on “mechanisms,” came back so strongly that when theories were proposed, it was required that they have a “mechanism.” Required absolutely.  Read more at location 6137

But the embryo and one of its most important deep structures, differentiation, was hidden at the very heart of the scientific worldview. Where? In the least likely place—the hardest of the hard sciences,346 theoretical physics and cosmology.  Read more at location 6141

(Note: Cosmic egg is same metaphor as many religious origin stories)  Georges Lemaître, the highly influential Belgian physicist/priest, first conceived the idea of the big bang in 1932, he called the initial pinprick from which all arose the “Cosmic Egg.”347 And when George Gamow used the lessons from atom-bomb making—from nuclear physics—to take Lemaitre's big bang theory mainstream, he identified what happened after that “cosmic egg”  Read more at location 6143

The word that came from an unlikely metaphor. The metaphor of the embryo. George Gamow said that in the beginning, there was “differentiation.”  Read more at location 6147

s differentiation shows up from the bottom of this cosmos to its top, from the most primitive level to the most complex. Differentiation shows up in the basic patterns that keep one atom separate from another and that keep all the matter in the cosmos from clumping together in one giant undifferentiated ball. Differentiation shows up in the repulsive forces of cosmic inflation, electromagnetism, and even dark energy. Differentiation shows up in patterns of evolution, physics, biology, psychology, and history. Differentiation even shows up in Frank Sulloway's birth-order studies, his battle between brothers and sisters for attention space.  Read more at location 6159

What is the form maker? What generates giant leaps like the jump from two gases to a liquid, from two gases to water? Driesch's and Lewes's challenges call on us to come up with a science that can do the impossible, a science that can predict the next great future shock, the next great leap up the ladder of complexity, the next great act of implication unpacking, the next great cosmic invention, the next inconceivable surprise, the next grand cosmic breakthrough, the next big leap beyond mere life, consciousness, music, science, megacities, and megasocieties.  Read more at location 6168

CHAPTER 7: EINSTEIN TURNS AN AXIOM INSIDE OUT

THE MAN WHO GAVE STAR TREK ITS SPACE: BERNHARD RIEMANN 

In their 2010 book The Grand Design, Stephen Hawking and Leonard Mlodinow distinguish between two kinds of causality. And two kinds of explanation. Bottom up and top down.  Read more at location 6177

Constructing systems from axioms is a bottom-up approach.  Read more at location 6179

Metaphor and big pictures, on the other hand, are top down.  Read more at location 6180

Recruitment strategies are also top down. So are emergent properties. At the other extreme sit Peano's axioms and the city-building termites. They are bottom up.  Read more at location 6181

Do systems based on axioms, on simple rules, have any relationship to the real world? Or is axiom-twiddling merely the self-indulgent play of a bunch of hyperintellectuals doing the things that only nerds would understand? The answer would lie in the amazing fate of non-Euclidean geometry. And the man who would pave the way for that amazement was a man named Bernhard Riemann. Bernhard Riemann lived a short but brilliant life.  Read more at location 6196

Riemann started off in one prime territory of the God Problem, one isomorphic symbol set with which we humans grasp the mysteries of a slippery reality: theology. But Riemann soon switched to the secular side of deep structures. He moved into math and physics.  Read more at location 6214

The dissertation Riemann wrote for Gauss touched on an issue vital to the God Problem: the translation of patterns from one medium to another. It included work on “conformal mapping.” What's conformal mapping? Mathematically translating a shape from one medium to another. Specifically from one kind of space to another—for example, translating the patterns on the globe in your den to a two-dimensional sheet of paper  Read more at location 6219

Riemann wanted to probe the base of invisible assumptions on which geometry was built. The assumptions that no one else had ever seen. The result was a paper that would give us Star Trek and a massive hunk of modern science fiction. A paper that would give us relativity and string theory. And a paper whose key points would enter even your vocabulary and mine. In his first sentence, Riemann announced that he intended to dig down to something preposterous. “Geometry assumes, as things given [as axioms],” wrote Riemann, “…the notion of space.”  Read more at location 6231

****  Riemann said that space is not geometry's only hidden assumption. Geometry also assumes, declared Riemann, that you can “construct” things in space—circles, triangles, squares, temples, and pyramids. These, said Riemann, are not unquestionable facts. They are “axioms” and “assumptions.”  Read more at location 6238

Said Riemann, we haven't taken a good, hard look at the notions that there is space and that we can construct shapes within it, we haven't tested and probed to see how and if these two things—space and our constructions—are true. Riemann was truly looking at things right under his nose as if he'd never seen them before.  Read more at location 6242

Riemann said that it was time to go beyond mere two- and three-dimensional spaces, two- or three-dimensional “magnitudes” or “manifolds.”13 Said Riemann, he intended to explore “the general notion of multiply extended magnitudes,”14 a field that in his opinion “remained entirely unworked.”  Read more at location 6250

He looked at continuous spaces, at smooth, unbroken surfaces, versus surfaces divided up into atomlike bits, bits to which he gave a new name, “quanta,”18 a name that would one day be embedded in the name of a new form of physics, “quantum” physics. And Riemann asked another peculiar question. Is the geometry and math of things that approach the infinitely big the same as the geometry and math of things that approach the infinitely small?  Read more at location 6260

Bernhard Riemann had come up with the idea of a geometry that could do more than merely change the axioms of Euclid. He had come up with the idea that you could map out the geometry of universes with a vast change at their base—the number of dimensions into which they extended. You could use geometry and equations to map out what he called “the manifoldness of n-dimensions.”  Read more at location 6275

Without mind tools, we cannot think. With n-dimensions, with multiple dimensions, Riemann added a whole new landscape of possibility. In fact, an infinite stack of new landscapes. Riemann also gave science the mathematical tools with which to feel out these unexplored wildernesses. New formulas in differential calculus,23 modern analytic geometry, differential geometry,24 and complex function theory.  Read more at location 6284

Riemann also drew a strange line between two types of apparent infinities. He drew a distinction between things that are endless and things that are infinite.  Read more at location 6290

(Note: Like a circle)  Riemann showed how you can have a universe that's endless but not infinite.26 Endless but limited in size.  Read more at location 6296

ALBERT EINSTEIN'S PAJAMAS

Albert Einstein. A high school dropout. A university graduate so marginal that, as you know, he couldn't get a job in science or math and had to settle for work in a patent office.  Read more at location 6316

A man who worked on the most perplexing problems of physics in his spare time. Worked on them with all his might. Worked on them until, at the age of twenty-six, he had twenty-six papers ready for publication in Europe's leading physics journal.  Read more at location 6320

Albert Einstein was the ultimate outsider. And the ultimate abstract thinker. The ultimate unpacker of implicit properties from axioms. He didn't work in a lab. He didn't use a telescope. He didn't do research. He didn't design experiments. He didn't even have a job as a real scientist. And in a high school essay on what he wanted to do with the rest of his life, he said he wanted to dive into math and physics because of what he called “my disposition for abstract and mathematical thought, and,” here comes the kicker, “my lack of imagination and practical ability.”28 The result? Albert Einstein was a full-time thinker.  Read more at location 6323

Albert Einstein put everything he had into one big problem—figuring out the mind of God.29 Hunting down the “reason,” “beauty,” and “structure” of what he called a “God, who reveals himself in the lawful harmony of the world.”30 Hunting for God's own geometry. That's why Albert walked out of the house in his pajamas. Every synapse and neuron of his brain was dedicated to really big questions. There was no brainpower left for pants and shoes.  Read more at location 6331

Einstein was a brilliant integrator of the ideas and the findings of others. What's more, Einstein picked and chose the ideas that utterly baffled others. Einstein adopted ugly ducklings. At the end of the nineteenth century, ugly ducklings, counterintuitive findings, were piling up.  Read more at location 6368

As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. We call such a system of thought a theory. The theory finds the justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the “truth” of the theory lies. —Albert Einstein31  Read more at location 6374

Ugly Duckling Number One: 

The thinker who proposed that light might have a speed was Isaac Beeckman, and he designed an experiment to measure the time it takes for a cannon's flash to travel to a mirror on a hill a mile away and to come back again. Alas, Beeckman never tried the experiment. But the idea that light sets out on a journey and takes time to arrive did not die.  Read more at location 6384

the very idea that light traveled, that it had a speed, was surprising. And it would prove vital to Albert Einstein.  Read more at location 6392

Ugly Duckling Number Two: 

Ernst Mach came up with the peculiar idea of “relativity.”32  Read more at location 6394

Mach upended two axioms—the Newtonian idea of time and the Newtonian idea of space. There was no rigid framework of time and no rigid framework of space, no universal grid containing all of the cosmos, Mach said. Time and space came from the relationship between things, between things like clocks, railroad trains, billiard balls, and stars. Time and space are relative. Mach laid all this out in his 1883 book The Science of Mechanics.  Read more at location 6398

Ugly Duckling Number Three: 

Carl Friedrich Gauss, János Bólyai, Nikolai Lobachevsky, and Bernhard Riemann laid out their non-Euclidean geometry, the geometry of curved space. The geometry of saddlebacks and hyperbolic surfaces. And in 1854, twenty-five years before Einstein's birth, Riemann gave mathematicians an infinite number of dimensions to play with. What's more, Riemann and Gauss turned their strange geometries into equations. But what in the world did this have to do with the real world? Even Lobachevsky and Bólyai could not find a connection.  Read more at location 6403

Ugly Duckling Number Four: 

In 1861, British physicist James Clerk Maxwell came up with equations for light. As Maxwell saw it, a wave of light is two waves for the price of one. Two forces—electricity and magnetism—do a zigzag dance.  Read more at location 6409

An electromagnetic wave. The electrical field flips up and down. The magnetic field flips from side to side. And both move forward in a straight line.  Read more at location 6414

Ugly Duckling Number Five: 

In 1887, Albert Abraham Michelson and Edward Williams Morley in the inelegant American city of Cleveland, Ohio, set up an experiment with one of the most puzzling results of all.  Read more at location 6423

A big problem: no interference pattern. No matter what direction Michelson and Morley turned their table,44 the two rays of light were still apparently moving at the same speed. Exactly the same speed. Which meant, god forbid, no ether. And nothing for light to wave in. The result was so unbelievable that Michelson and Morley ran the experiment again and again. Still no interference patterns. The Western world's physicists were baffled.  Read more at location 6480

Ugly Duckling Number Six: 

Classical physics did just fine at handling many of the electromagnetic waves that came from the hole. But there was a problem with ultraviolet light. When you used classical equations to predict how much ultraviolet light the heated “black body” would give off, your equations broke down. Totally. Your classical equations predicted an outpouring of infinite ultraviolet energy. Infinite!  Read more at location 6492

Planck's new math implied that matter punches out energy in modular packets—in the energy equivalent of bricks.  Read more at location 6500

to Plank, who didn't even believe in atoms at the time,53 quanta were nonsense. They were an absurdity. And even the math was hideous. Einstein would show how quanta fit perfectly into a new view of the universe.  Read more at location 6507

Ugly Duckling Number Seven: 

In 1904,54 when Einstein was twenty-five, Dutch theoretical physicist Hendrik Lorentz threw in what Einstein called his “epoch-making theoretical investigations.”  Read more at location 6510

The speed of light is constant, no matter how fast you're moving. No matter how fast the light's source is moving toward you. Or away from you. Just as the Michelson-Morley experiment had shown.  Read more at location 6529

Hendrik Lorentz tortured time and matter to keep light speed the same no matter what. Things in motion contract, said Lorentz. Hard and fast things squoomph and squash. In fact, even time is rubbery. The faster you go, the slower time becomes for you.59 The faster you go, the slower your clock will run.  Read more at location 6536

Then Come the Ugly Duckling Stragglers: 

There's Maxwell's idea that all forces travel at the speed of light. There's Thomas Young's coining of the word “energy”62—a word Sir Isaac Newton only used once in his Principia.63 There's Christian Doppler's idea of the Doppler effect,64 the idea that waves seem to have a higher frequency when they come from a body rushing toward you and that they seem to have a lower frequency when they come from a body that's rushing away. And there's Hippolyte Fizeau's discovery that light in moving water isn't sped up by moving with the current or slowed down by going against the flow. An observation that seemed to knock the particle concept of light out of the box for good.  Read more at location 6552

EINSTEIN GIVES SEVEN UGLY DUCKLINGS A HOME: THE YEAR OF MIRACLES 

Einstein published four articles in the Annalen der Physik, four articles that would change the shape of physics. But in theory, Einstein had no right to be in such a journal. None at all. Why? Albert Einstein was only twenty-six years old, and he was still a graduate student at the Zurich Polytechnic.  Read more at location 6562

Like George Henry Lewes and Herbert Spencer, learning was Einstein's sport, his pleasure, and his play. Which is strange. Because Einstein's sister recalls that he was so late in learning to talk that the family was afraid that he was retarded.79 However, Einstein was fascinated by electrical and magnetic phenomena.  Read more at location 6597

when Einstein was five, his dad had showed him a compass. Said Einstein, “This experience made a deep and lasting impression on me. Something deeply hidden had to be behind things.”81 The rest of Albert Einstein's life would be a hunt for that “deeply hidden…something…behind things.” A hunt for deep structures. But what tools would Einstein use to find the mysterious “something”? The answer arrived when Einstein was ten years old.82 Despite the fact that Einstein was still just a little kid, his Uncle Jacob did something ridiculous. He explained the Pythagorean theorem to this child with the curly hair. And Einstein reciprocated by doing something very strange for a ten-year-old. Something that would have pleased Euclid. He devised a proof.83 A proof for the theorem.  Read more at location 6602

When he was twelve, Albert Einstein wanted to skip ahead in math in school. How? By teaching himself during the summer vacation. After all, he had compiled a magnificent track record in self-teaching with Euclid's Elements. So his parents bought him textbooks in geometry and algebra. The prepubescent Einstein not only solved the problems in the books, but, once again, tried to prove the theorems behind them. Recalls his sister Maja, “Play and playmates were forgotten. Days on end he sat alone, immersed in the search for a solution, not giving up before he had found it.”89 What Maja didn't understand was that for young Einstein, math was play. So from the age of twelve to the age of sixteen, Einstein also taught himself two forms of math that were beyond Max Talmud: analytic geometry and calculus.  Read more at location 6624

When kid Einstein was thirteen, Talmud took an intellectual gamble. He introduced Einstein to Kant's Critique of Pure Reason. And Einstein awed him. Says Talmud, “At that time he was still a child, only thirteen years old, yet Kant's works, incomprehensible to ordinary mortals, seemed to be clear to him.”92 By twelve, Einstein's reading of science and math had thrown him into what he called “a positively fanatic orgy of freethinking,”93 an orgy of agnosticism. One book had hit him particularly hard: Ludwig Büchner's Force and Matter,94 the book that got Büchner fired from his position as a professor of medicine at Tübingen University in the 1850s, the “Bible of Materialism.” More specifically, the Bible of “freethinking.”  Read more at location 6632

The year was 1895, and Albert Einstein was a mere sixteen years old. But during that summer, he penned his first scientific paper, on the “state of ether in [a] magnetic field.”  Read more at location 6653

(Note: Science and religion)  Einstein performed his first gedanken experiment, his first thought experiment. Possibly one of the first ecstatic flights that later led him to describe a scientific insight as “a sudden illumination, almost a rapture.”  Read more at location 6655

At Aarau, Albert and his teachers got along much better. But he still learned geometry, calculus, and theoretical physics on his own. And later in life, he'd continue learning without the benefit of a school.  Read more at location 6667

It appears that the teenage Albert Einstein ate, lived, and breathed the controversies and questions raised in the pages of the Annalen.  Read more at location 6672

Einstein hinted that quanta are the units of light, light's equivalent to atoms. Or, in Einstein's words, “energy [comes in] quanta that are localized in points in space, move without dividing, and can be absorbed or generated only as a whole.”116 And Einstein treated those quanta as both particles and waves.117 As particles that oscillate like waves. Einstein gave these oscillating bricks the properties of energy and matter simultaneously. In fact, Einstein's oscillating bricks would later be called photons.118 And Max Planck's loose end would become a thread in Einstein's weave.  Read more at location 6702

Einstein was still a graduate student. So what was the impact of his proposal about the nature of light? It should have been zilch. But in the words of the Lambeth Palace Library's Hugh Cahill, it “revolutionized the theory of light.”  Read more at location 6707

A second puzzle nagging the minds of early-twentieth-century scientists was this: Is matter, too, made up of particles? If we call those particles atoms, do these atoms exist? Many an august figure said that atoms were sheer fantasy.  Read more at location 6710

Inanimate things like grains of finely ground charcoal, glass, rocks, and metal jittered in water, too. And no one knew why. Einstein tied this nervous botanical quiver of pollen grains in a liquid to something from a radically different field—thermodynamics. Specifically something the atomists had come up with. The idea that heat might be a result of movement. The movement of atoms.  Read more at location 6721

Einstein said they jiggled and whumped because they were being bumped. Bumped by what? By the moving atoms that the kinetic heat theorists said should be there. Bumped by the very jostle that these theorists said made heat. The jostle of atoms.  Read more at location 6728

And in the process he helped validate two theories—the highly controversial atomic theory and the widely accepted thermodynamic theory of heat. Brilliant!  Read more at location 6732

In 1909 the French physicist Jean Perrin proved that Einstein's math was, indeed, on target. In the process, Perrin helped Einstein drive home the notion that atoms were for real.  Read more at location 6736

So in his first paper, Einstein redefined light. And in his second paper he helped redefine matter. Not bad for a grad student still working on his thesis.  Read more at location 6738

Paper number three challenged our notions of time, space, and the solidity of everyday things. Einstein's thought experiment when he was sixteen had involved running after a beam of light. That fantasy had tapped the power of muscular metaphor, the power of visceral comprehension. Einstein had tried to imagine what things must look and feel like to someone catching up with the beam and running next to it. And he came to a simple conclusion. Everything would look perfectly normal.  Read more at location 6744

What if the speed of light is an absolute limit? A barrier you can't pass? How in the world could the universe enforce this top speed? Einstein's answer was so far outside the box it was ridiculous. It was Lorentz's answer. The answer of the Lorentz contractions. The cosmos could impose a top speed by treating space and time as if they were something introduced to Europe from South America in 1736128—rubber.  Read more at location 6754

(Note: Religious metaphor is fascinating: God is light, can never quite reach God in a sense... as material beings, always infinitely out of reach of Light speed, no matter how close to 'speed' of Light we go)  In this universe, no matter how fast you're traveling, everything seems normal. But the closer you get to the speed of light, the more time expands and the more space stretches around you. The more time and space play their rubber tricks to keep you from going faster than the speed of light.  Read more at location 6768

the cosmos is playing rubber tricks to keep me from exceeding the speed of light. Einstein called this “the relativity of lengths and times.”129 And it explained why the Michelson-Morley apparatus measured the speed of light as precisely the same whether its beams of lantern light were getting a speed boost by moving in the direction of the Earth's movement or were shunning that speed boost by moving at right angles to the Earth's zoosh through space. The distance in the direction of Earth's movement stretches like rubber to keep the speed of light the same.  Read more at location 6772

What did Einstein's fourth paper say? That matter and energy are one. Or, as Einstein put it, “The mass of a body is a measure of its energy content.”132 To take it out of Einstein's language and to put it in the terms we've been using in this book, energy and matter are translations. They are isomorphic. They map onto each other. Because they are each other. Matter is energy in disguise.  Read more at location 6786

Einstein presented the idea at the heart of the most famous equation of the twentieth century, E = mc2.  Read more at location 6790

four published papers in five months wasn't enough for Albert Einstein. In the midst of it all, Einstein handed in his thesis at Zurich Polytech. Called “A New Determination of Molecular Dimensions,”134 it presented a way to calculate the number of molecules in a unit of substance. In other words, like his paper on Brownian motion, Einstein's thesis helped support the newly emerging atomic view of matter.  Read more at location 6792

Ten years later,136 Einstein would decide on a name for that first installment: “the special theory of relativity.” Special because it only applied in special cases. It only applied in cases where you didn't take gravity into account. And, as Einstein said, gravity was one thing you could not escape.137 Ten years later, in 1915, Einstein would publish the second installment, his general theory of relativity. A theory that put gravity into the picture.  Read more at location 6798

In the 1905 special theory of relativity, Einstein had turned a speed—the speed of light—into the only rigid measuring rod in the cosmos and had turned time and space to rubber. Now, in the general theory of relativity, Einstein showed how gravity dimples, ripples, curves, rumples, and dents space's rubbery sheet. The general theory of relativity said that the sheet of space and time is “a manifold.” And who did Einstein take that manifold and much of its math from? Bernhard Riemann.  Read more at location 6802

**********  Princeton physicist John Wheeler says that in Einstein's theory of relativity, matter tells space how to bend and space tells matter how to move.138 The tool that matter uses to bend space is gravity. The tool that space uses to give matter its traveling instructions is also gravity. In other words, gravity is a language.  Read more at location 6813

From 1905 to 1915, Albert Einstein made no bones about the fact that he was knitting together the ideas of others. In fact, he gloried in it. Gauss's and Riemann's names pop up thirty times in an anthology of Albert Einstein's work pieced together by über physicist Stephen Hawking.141 Hendrik Lorentz's name comes up sixty-three times. James Clerk Maxwell's name appears sixty times. Ernst Mach's name pops up twelve times. And Max Planck is credited fifteen times. Einstein was piecing together implicit properties no one else had the vision, the off-kilter imagination, to see. And he was knitting them together in something crucial—a new big picture. A new tapestry.  Read more at location 6823

EINSTEIN'S SECRET WEAPON: ARISTOTLE'S INVENTION 

understanding Einstein's axiom flip is the key to understanding the theory of relativity.  Read more at location 6830

****  Einstein was like Riemann. He was on a prowl for assumptions. On a prowl for axioms. For axioms that mislead. For axioms that blind us.  Read more at location 6833

Then came the movement at the end of the nineteenth century, when Einstein was a kid, to reduce all math and logic to axioms, the movement of which Giuseppe Peano was a part. Einstein was disturbed by the way that some of the axiomatizers tried to make math a pure thought process with no relationship to reality. There is no such thing, Einstein says, as math without the real world. “Mathematics generally,” he writes, “and particularly geometry, owes its existence to the need which was felt of learning something about the relations of real things to one another. The very word geometry, which, of course, means Earth-measuring, proves this.”146 Those are Einstein's words. Even non-Euclidean geometry, he says, is not just a thought exercise, an exercise in logical deduction. It's a hypothesis about the real world.  Read more at location 6841

The universe is non-Euclidean. Gauss, Bólyai, Lobachevsky, and Riemann were onto something basic in the cosmos. Not something absurdly abstract. Something absurdly real. Again, do axioms have anything to do with Einstein's work? At heart, Einstein says, his work is all about overturning an axiom. Yes, just one axiom. His work, he says, overturns what he calls “the axiom of the absolute character of time.”  Read more at location 6850

“Concepts which have proved useful for ordinary things,” he writes, “easily assume so great an authority over us, that we forget their terrestrial origin and accept them as unalterable facts.” Our assumptions become invisible to us. We think that they are unchangeable realities. And in science, says Einstein, our assumptions “then become labelled as ‘conceptual necessities,’ a priori situations, etc.” They become labeled as basics we should not contest.  Read more at location 6859

digging out assumptions, bringing them to the light, and questioning them is crucial to science. And it is crucial to your life and mine. Hauling assumptions out of the darkness by any means necessary. “It is therefore not just an idle game,” Einstein writes, “to exercise our ability to analyse familiar concepts, and to demonstrate the conditions on which their justification and usefulness depend.” Take a good, hard look at your axioms, says Einstein. Especially the ones it's hardest to see. When you drag an assumption from its hiding place into the spotlight, you may kick start a vital scientific process. “In this way,” says Einstein, your assumptions “are deprived of their excessive authority.”  Read more at location 6865

****  The speed of light, Einstein said, is a measuring rod. A measuring rod like the Nippur Ell in Babylon. In fact, the speed of light is the only unchanging measuring rod in the universe.  Read more at location 6876

From that axiom flip comes the notion that everything else in this cosmos is flexible, bendable, and rubbery. From that axiom flip comes the idea that the rubbery stuff includes time, space, and matter.  Read more at location 6880

THE ADVENTURES OF EINSTEIN'S PREDICTIONS 

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? —Albert Einstein, “Geometry and Experience,”  Read more at location 6905

The theory of relativity didn't present a formula to explain the constancy of the speed of light. It used the unchangeability of the speed of light as an axiom. And that axiom “solved” the Michelson-Morley problem.  Read more at location 6913

Einsteinian prediction number two centered around a tiny twist that Isaac Newton's math could not account for. A tiny rotation in an ellipse. A rotation in the ellipse of Mercury's orbit.  Read more at location 6915

The equations in Einstein's tool kit were derived from non-Euclidean geometry,170 the non-Euclidean geometry that described space's rubbery potholes. They were equations based on the work of Bólyai, Lobachevsky, Gauss, and Riemann. And they predicted a difference of 43 seconds of arc per century.171 As Einstein put it triumphantly, 42.98 seconds of arc, the real figure, “does not differ sensibly from” relativity's figure of “43 seconds of arc per century.”  Read more at location 6951

the math of Einstein's theory of relativity, the abstract math of the nineteenth century's non-Euclidean geometers, the math based on unpacking the meaning of an axiom flip, wasn't just ivory tower fluff. You could start with simple rules—with a handful of axioms—and you could use logical deduction to build (or find) a system implicit in those rules. You could use an axiom shift to build a picture of the universe.173 And that picture could match reality.  Read more at location 6955

The explanation of the Michelson-Morley experiment was validation number one. The explanation of the precession, the peculiarity of Mercury's orbit, was validation number two. But what was validation number three? In 1907, in what he calls “a memoir,”174 Albert Einstein predicted “that rays of light, passing close to the sun, are deflected by its gravitational field.”175 Einstein predicted that the gravity of the sun would bend a ray of light.  Read more at location 6960

Einstein said that acceleration is more than just a form of entertainment. It is an equivalent of gravity. Both acceleration and gravity plaster you against something.  Read more at location 7058

The idea that gravity and acceleration are in some way the same is what Einstein calls “the equivalence principle.”204 Here's how Einstein's reasoning goes: “It is impossible to discover by experiment whether a given system of coordinates is accelerated, or whether…the observed effects are due to a gravitational field.”  Read more at location 7061

The “equivalence principle” is translation from one medium to another run amuck. It's the peculiar process of A = A, the peculiar process of “equation” gone hog wild.  Read more at location 7068

Remember, in 1905,206 Einstein figured out that speed should slow clocks. The closer you get to the speed of light, the more your clock slows down. The closer you get to light speed, the longer an hour stretches out. It's all a part of nature's plot to keep you from passing the speed-of-light speed limit. And, brace yourself for a stretch, since gravity is the equivalent of speed, gravity, too, should slow clocks.  Read more at location 7070

One of the most basic ways of keeping time is feeling your pulse. Your pulse pounds away at roughly one beat per second.  Read more at location 7076

The chambers of the heart bunch like a fist, then relax again. And they do it rhythmically. Squeeze, relax, squeeze, relax. In other words, your heart is an oscillator. Like the crystal oscillators we use in quartz crystal clocks,208 cesium clocks, and atomic clocks. What else is an oscillator with a dependable pulse, an oscillator with a dependable frequency? Hang on to your socks. Light.  Read more at location 7079

It may be strange to think of it this way, but green light pulses at 590 trillion beats per second.209 Yellow light is slower. It pulses at 540 trillion beats per second. And red light is even slower. It slogs along at a mere 440 trillion beats per second. Now here's the trick. If gravity slows down clocks and oscillators, it has to slow down light. Specifically, if Einstein is right, gravity has to slow light's clock. Light's clock is its beat, its pulse, its oscillation. What happens if you slow light's pulse down? It changes color. It gets redder.  Read more at location 7083

Triumph number one had been the explanation of the Michelson-Morley experiment. Triumph two had been the explanation of the peculiar wobble in the orbit of Mercury. Triumph three had been the prediction that the gravity of the sun bends starlight. And triumph four had been the prediction that gravity slows light's pulse—the prediction of the gravitational red shift. Then came prediction number five. This prediction didn't come from Einstein himself.  Read more at location 7108

In his 1920 book Space, Time, and Gravitation: An Outline of the General Relativity Theory,217 Eddington extracted yet another prediction, prediction number five, from Albert Einstein's math. It was called “gravitational lensing.”218 A lens magnifies the words on the page in front of your nose by bending rays of light coming from the page. But only at a precise distance.  Read more at location 7126

So, said Eddington, according to Einstein's principles, a sun should act like a whompingly big lens. When light from a very distant star passes around the edges of another star on its way to your eye, the near star's gravitational curve should bend the light of the star behind it and serve up a distorted image of that star. In fact, said Eddington, when one star is directly behind another star, the light coming around one side of the blocking star should produce one image, and the light passing around the obstructive star's other side should produce yet another image. Yes, the light of a star completely hidden behind another star should reach your eye despite the obstacle. But it should reach your eye as multiple images.  Read more at location 7131

1979, when a multinational team of astronomers—two Brits and an American—using the 2.1-meter telescope at the Kitt Peak Observatory in Arizona, discovered two images of the high redshift quasar Q0957+561 separated by 6.1 arc seconds. Two images of a quasar eight billion light-years away.  Read more at location 7141

Prediction number six came from Karl Schwarzschild, the former physics prodigy, who continued laboring mightily to extract new implications from Einstein's math.  Read more at location 7147

A truly humongous gravity ball would swallow the light trying to shoot from it. It would make it impossible for light to escape. It would make it impossible for light to go beyond the spherical boundary that came to be called a “Schwarzschild radius.” Gravitational bodies of this sort, gravitational bodies so extreme that they would imprison light, would come to be called black holes. But Schwarzschild was convinced that his “theoretical solution is physically meaningless.”225 In other words, a black hole cannot exist. It is a sheer figment of mathematics.  Read more at location 7165

The black hole was Einstein's victory number six.  Read more at location 7174

Prediction number seven from Einstein's theory helped end World War II. It came from E = mc2. What does E = mc2 mean? That energy and matter are different versions of the same thing. Different translations.  Read more at location 7177

But the equality is very unequal. From a tiny amount of matter, you can get a huge amount of energy. And from a huge amount of energy, you can get only a tiny amount of matter.  Read more at location 7180

Only in a Euclidean universe, a flat universe, will things stay the same. But Einstein's math didn't allow for a flat universe. It implied that the universe was either spherical or saddlebacked. There was no middle ground. The cosmos was doomed to either fly apart or collapse.  Read more at location 7241

How could Einstein get his math to describe a flat universe, a nice, calm, stable universe? Tiamut had inserted a brace. He'd “fixed the crossbar.”244 Einstein inserted his own crossbar. A brace to hold the universe in place. A brace to make the geometry of the space-time manifold stay flat. That brace was a mystery force. A repulsive force that kept the universe from caving in on itself. From crunching into a dense apocalypse, undone by its own gravity. Albert the Frizzy, Einstein the Great, called this artificial force, this cross brace, the “cosmological constant.”  Read more at location 7247

What does Einstein's story reveal about the God Problem, the problem of how the cosmos creates? It's all about axioms, iteration, and simple rules. Ur patterns. Not to mention recruitment strategies. And it's all about something else, big pictures. What in the world do big pictures have to do with simple rules? They reweave old threads in new ways. In fact, they turn old patterns, old disconnected iterations, into threads of a new tapestry. They make a new sense of old things.  Read more at location 7275

CHAPTER 8: THE AMAZING REPETITION MACHINE

FORGET INFORMATION: OR HOW CLAUDE SHANNON GOT IT WRONG 

Theories permit consciousness to jump over its own shadow, to leave behind the given, to represent the transcendent, yet, as is self-evident, only in symbols. —Hermann Weyl, mathematician, logician,  Read more at location 7302

Einstein's theory of relativity is about, guess what? Relationships. In Einstein's words, it is about “the relationships of real things to one another.” In its own strange way, relativity is a theory about how things beckon each other.  Read more at location 7306

One of those who helped bring us the computer made a big mistake. A mistake that influences the way that you and I think—or misthink—today. That mistake? He failed to see the essence of relationships, the essence of sociality. He misled us about relationships’ central carrier—communication. Not to mention translation from one medium to another. How? He misled us about the nature of information. Or, to put it differently: Forget information. It's all about meaning.  Read more at location 7314

Back in the late-nineteenth century, just a few decades before Claude Shannon was born, people like Bertrand Russell had suspected that logic was math in disguise and that math was just logic wearing a different costume. As you and I already know, the late-nineteenth century was an era of stripping things of their costumes in the hope of finding that they were all the same naked body underneath. It was an era of boiling things down. It was the age in which Giuseppe Peano boiled the natural number system down to five axioms. And it was the era in which an Englishman named George Boole managed to boil down all of logic to a tiny number of symbol strings16 that looked like equations. The language of those simple equations was called Boolean algebra.  Read more at location 7360

Boole boiled this down to what was called “symbolic logic.”  Read more at location 7373

symbolic logic would bust loose in ways that even Bertrand Russell never imagined. Symbolic logic would penetrate every nook and cranny of your life and mine. And this explosion would take place because of Claude Shannon.  Read more at location 7379

The ons and offs in Shannon's thesis did more than just work out George Boole's symbolic logic. They handled yet another symbol set. The symbol set of math. If you wanted to flip from logic to arithmetic, when a switch was on, it represented a one. And when it was off, it represented a zero. With ones and zeroes you could represent any mathematical function you wanted. As long as you used a binary number system—a system with only two numbers, one and zero. (A system pioneered by Gottfried Leibniz 247 years earlier.18) Talk about translation from one medium to another! This was isomorphic symbol sets gone berserk.  Read more at location 7397

****  Legendary physicist David Bohm points out a crucial trap in science. He warns that you make a huge mistake when you get the math right and the metaphor wrong. And when it came to Shannon's biggest theoretical contribution, he got something very wrong indeed.  Read more at location 7407

H = –∑p(i)log2p(i)  Read more at location 7416

Richard W. Dillman, former chair of the communications department at a small, exclusive school in Maryland, McDaniel College, put it better than the Ivy Leaguers: “Claude Shannon's famous formula provides a way to compare one code against the other to find out which can send the most messages with the smallest number of symbols.”  Read more at location 7417

Shannon had to name the factor his equation described. He had to figure out what to call the big H at the formula's beginning. The big H that the whole formula hinged on. Claude Shannon had to name what he'd identified. That name would determine the metaphorical interpretation, the common interpretation, of his theory for as long as that theory lasted. And theories whose math is right, but whose metaphor is wrong, can be dangerous.  Read more at location 7422

John von Neumann recommended that Shannon label the big H with the word for something that we've fingered in this book as a toxic concept—entropy.  Read more at location 7426

Probability rules, say the entropists. More specifically, all power goes to the equations of probability theory. Which is why you and I do not exist. The odds are against us. At least in theory. In reality, universes with complex form seem to be far more probable than universes of soup. But that is something that the entropists deny.  Read more at location 7438

Whatever its flaws, it turns out that the math behind this sort of probabilistic reasoning—the math behind the equations of entropy—is very helpful in understanding the electrical impulses that carry telephone calls down wires. It's useful in compressing the greatest number of messages into the smallest amount of cable space.  Read more at location 7441

Hence Shannon's formula is almost precisely the same as the formula for entropy. That's why John Von Neumann thought that entropy seemed like a logical name.  Read more at location 7449

****  He called his math “information theory.” But beware. Do not get your math right and your metaphor wrong. What was the problem? What was the big mistake? Claude Shannon saw communication as a form of juggling. “The fundamental problem of communication,” he wrote, “is reproducing at one point either exactly or approximately the message selected at another point.”  Read more at location 7457

to put it in Bell Labs terms, the challenge is to transmit them accurately. Hence, from an information theory point of view, the messages are the same. They are identical. That's the Bell Telephone point of view. What you say into your phone receiver is up to you. Our job is to get whatever it is to whoever you are talking to. Content is not our business. We are in the transport trade. And Shannon's formula dealt with transport only.  Read more at location 7468

As Shannon's information theory conceived things, handling communication and its central ingredient, information, was a bit like juggling fortune cookies. In the case of JFUEJSHUHESEFJ and CONSTANTINOPLE, that would be fourteen fortune cookies. And from an information theory point of view, your job as a juggler is to get all fourteen fortune cookies from your right hand to your left hand in one piece. In the right order. But here's the key. Your job, from an information point of view, is not to read the messages.  Read more at location 7473

According to the ultimate source on the English language, the twenty-volume Oxford English Dictionary, the word “information” means, and I quote, the “communication of instructive knowledge.” Information, says the OED, is the “communication of the knowledge or ‘news’ of some fact or occurrence.” In other words, information is not the mere act of tossing a fortune cookie from one hand to the other. Information is not information until you open the fortune cookie and read it. To repeat, information is the act of getting across a message.  Read more at location 7479

In Shannon and Warren Weaver's A Mathematical Theory of Communication, the missing ingredient was what Shannon and Weaver called “meaning.” In information theory, the word information has nothing to do with the message you are trying to get across, says Weaver.33 Weaver tells us point blank in the book he coauthored with Shannon that “the word information, in this theory, is used in a special sense,” a special engineering sense. Continues Weaver, it “must not be confused with its ordinary usage.”34 And Weaver warns the world that “in particular, information must not be confused with meaning.” But is information without meaning really information? Is the mere transport of information really communication?  Read more at location 7491

Reports James Gleick, “Margaret Mead and others, felt uncomfortable with the notion of information without meaning.”35 The Viennese physicist Heinz von Foerster was more than uncomfortable. He said, “I wanted to call the whole of what they called information theory signal theory.” Why? “Because information was not yet there. There were ‘beep beeps’ but that was all.”36 Von Foerster was on to something.  Read more at location 7504

Shannon's mistake would count. If his math was right but his metaphor was wrong, his error would have enormous consequences. Why? Shannon's information theory would turn the use of the word “information” into a scientific fad.  Read more at location 7511

Information theory claimed to explain everything from brains to black holes. Information theory claimed to explain everything from the pile of neurons with which Pythagoras did his pondering to Einstein and Schwarzschild's heavenly bodies from which light could not escape.  Read more at location 7518

THE CASE OF THE CONVERSATIONAL COSMOS 

**********  What does Claude Shannon's mistake have to do with the hypothesis that simple axioms, basic algorithms, and corollary generation were the source of the bricks of the cosmos? Not to mention the universe's mortar, its rules for bricklaying, and perhaps even the universe's architecture? A great deal more than you might think. Why? Because the information theorists are right about one thing: at bottom this is an informational universe. It is a conversational cosmos. This is a cosmos of constant communication.  Read more at location 7539

********  restricting communication and meaning to humans is a big mistake. Meaning has been here since the first flick of the cosmos.  Read more at location 7547

Skinner. B. F. Skinner did not understand the human psyche. And he made no bones about it. Very strange for a psychologist. But Skinner had a greater impact on mid-twentieth-century psychology than any thinker since Sigmund Freud. Why? The mind, B. F. Skinner said, was an “explanatory fiction.”46 His critics said that Skinner saw the mind as a “black box.”  Read more at location 7566

You could only see one thing, said Skinner. You could see what stimulus and response amounted to. You could only see behavior. So the form of psychology that Skinner put on the map was called “behaviorism.” And it was so successful in policing and intimidating mainstream psychologists that the word “psyche” was banished in the 1950s and 1960s. From psychology.  Read more at location 7580

To repeat, all psychology, according to the pope of mid-twentieth-century psychology B. F. Skinner, comes down to what's visible.  Read more at location 7588

Though many spiritually oriented folks and even a few scientists believe that the universe began with consciousness, I think that is extremely unlikely. Consciousness is an animal and a human thing. It is not a thing of protons and stones. But it's very different for stimulus and response. Stimulus and response are not just human. Not at all. Stimulus and response are at the very core of the cosmos.  Read more at location 7591

How do we know? Stimulus and response. No quark is an island. No quark can live on its own. A quark must gang up with other quarks. Instantly. And each quark comes with that inner rule book of attraction and repulsion I keep jabbering about. Each quark comes with an etiquette book built into it that tells it who to rush toward and embrace. Not to mention which other quarks to dodge, to escape, and to flee. So how do quarks gang up in groups of three? By reading each other's meaning.  Read more at location 7597

if current theory about quarks is right, quarks are all about behavior. Behavior, in turn, is all about stimulus and response. And the response a quark makes depends on its interpretation of information.  Read more at location 7605

********  we still haven't explained how they work. We still don't know how “attraction at a distance” does its thing. Yet we do know one thing. Objects in this cosmos somehow communicate with each other. They do it using the strong force, the weak force, the electromagnetic force, and gravity. They do it by curving space. They read each other's signals. And they move according to the social rules built into them. They  Read more at location 7616

The signal, whatever it may be, is a stimulus. And the movement toward or away from each other is a response. The instant skitter toward or away from each other is translation of a signal into another language—the language of travel, the language of getting a move on.  Read more at location 7621

University of Calgary evolutionary biologist Valerius Geist, author of the landmark book Life Strategies, Human Evolution, Environmental Design, will eventually conclude that every act of communication between bacteria, plants, animals, or humans boils down to attraction cues and repulsion cues. That's right: attraction and repulsion.58 Every act of communication, no matter how primitive or complex. Attraction and repulsion will show up on level after level of emergence. Every time it appears, it will be something very old becoming something very new.  Read more at location 7629

****  This is a communicative cosmos. Electrons communicate with protons via the electromagnetic force. Gas wisps communicate with each other via gravity. So do stars, planets, and galaxies. And the macromolecules in the center of your cells and mine use millions of electromagnetic pluses and minuses, millions of nodes of attraction and repulsion, to carry out the complex communication between molecules that created life nearly four billion years ago. And that sustains life from second to second within you and me today.  Read more at location 7644

The very shape of the universe is semiotic and linguistic. Space tells matter how to move and matter tells space how to bend. Note the word “tells.”  Read more at location 7649

****  The conversational nature of the cosmos may be why archphysicist John Archibald Wheeler, a man who collaborated with Einstein at Princeton and who taught physics legend Richard Feynman, says that this is a “participatory universe.”60 It may even be why Wheeler sees that at its heart this is a cosmos of signal exchange. A cosmos of communication. Says Wheeler, “The universe…is built upon query…and reply.”61 The result? “All things physical are information-theoretic in origin.”62 Or, to repeat the way loop quantum gravity master Lee Smolin puts it, all things physical are “relational.”  Read more at location 7653

HOW GOSSIP GROWS THE UNIVERSE 

Eshel ben-Jacob had done breakthrough work on the group behavior and the emergent properties of two very similar self-assembling complexities: bacterial colonies and neurons, the communities of cells that colonize your gut and the communities of cells that make up your brain.  Read more at location 7668

************  Information is not information until it has been interpreted, until it has been understood.  Read more at location 7683

If meaning is anything that a receiver can understand, if meaning is anything that an entity can interpret, if meaning is in the eye of the beholder, then how do you know when a thing or a person “understands” something? Follow the B. F. Skinner rule. Watch his or her behavior. Watch for the signs of stimulus and response. Watch to see if the receiver does something in response to the stimulus.  Read more at location 7688

****  There are several strange corollaries to the proposition that information is in the eye of the beholder, the idea that information is anything a receiver or a translator can decode. Corollary one is this—information is anything you can turn into a fortune cookie. Anything in which you can read a message. Even if no one or no thing “sent” that message.  Read more at location 7697

A fossil ceases to be a deaf and dumb piece of stone in 180664 when you develop paleontology and can “read” its “message.” It ceases to be just a lump when you “find” its “meaning.” Yet no one has sent a message.  Read more at location 7700

So information is not necessarily two-way communication. Information can go one way. What turns it into information? Translation. Interpretation. In other words, the key to making something neutral into information is Shannon's missing ingredient: meaning.  Read more at location 7703

***********  information is any signal that can be turned into a response.  Read more at location 7709

If meaning is anything that a translator can understand, anything that a translator can interpret, anything that a translator can decode, then the amount of meaning in this cosmos is constantly increasing. Meaning defies the law of entropy, the second law of thermodynamics. Meaning does not ebb away. It is not erased by disorder. It is on the rise. It is constantly piling up.  Read more at location 7711

Claude Shannon's style of information may or may not have been on the increase. But meaning was rocketing.  Read more at location 7764

Today there are over 1.5 million cuneiform tablets in museums around the world.77 Needless to say, not all of them concern astronomy. But all are translations of experience into isomorphic symbol sets. How very much like cyanobacteria translating sunlight into a language of biochemicals. How very much like leaves translating sunlight into panels, sheets, threads, and stems of cells.  Read more at location 7772

Had the amount of starlight making it to the surface of Earth gone up? Not a single iota. But had the amount of information shot up? Had the number of meanings and the number of creatures paying attention to those meanings skyrocketed? Had responses to the tiny bits of light from the stars been fruitful and multiplied? Even in Claude Shannon's crippled terminology, the amount of meaning had soared.  Read more at location 7779

We've used lenses and mirrors to magnify starlight. We've used drawings on paper and images on glass photographic plates and on cellulose film to capture the images of stars and to record their positions. We've turned that data into electron flows, into Claude Shannon's pluses and minuses, ons and offs, ones and zeros, into binary numbers and into Shannon's brilliant language of electronic circuits—the language of computers. We've stored these translations of starlight on magnetic film and hard drives. And we've used starlight, the streams of photons from the stars, to theorize about the origins of the universe and about the universe's future.  Read more at location 7793

Has the amount of starlight falling on this planet at night increased? Not a sliver. Not a scratch. So what has gone up? The quantity of interpretation. The quantity of translation. The quantity of response to a stimulus. The quantity of action. The quantity of repetition in a new context. The quantity of raw glass, iron, steel, and money dedicated to starlight. And most important, the quantity of meaning.  Read more at location 7800

has the amount of “information” gone up? Or is this merely an explosion of “meaning”? It's a semantic quibble. A quibble you can decide better than I can. But something has been on the increase. Something has shot up dramatically. Something complex. Something extremely social. Something profoundly conversational. Something that utterly defies the pessimistic predictions of entropy. And something that seriously challenges an information theory without meaning.  Read more at location 7806

THE MAGIC ONION OF MEANING 

(Note: Similar idea to Tonini IIT)  Your meaning—the meaning that you have whether you are a quark, a quadruped, or a quantum physicist—comes from the number of big pictures into which you can fit. Your meaning comes from the number of schema, the number of frameworks, the number of emergent properties to which you can prove useful.  Read more at location 7813

(Note: Same idea as Polanyi)  a “nested hierarchy”80 of meanings.  Read more at location 7831

Every level of emergent property is a kidnapper, seducer, and recruiter. And every level of emergent property is seduced, kidnapped, and recruited. It's a two-way process.  Read more at location 7845

****  At every stage a new emergent property makes a big difference in your destiny. It makes a big difference in how, where, and when you will be transported. And it makes a big difference in why. Every level of emergent property is responsible for what we might call your fate. Every layer of emergent property is a stimulus and it produces a response. It influences your meaning.  Read more at location 7852

Emergent properties crop up in part because this cosmos is profoundly social. Emergent properties crop up as forms of group behavior. Like the group behavior of those hundred billion neurons in your brain. Like the group behavior that turns you and me into members of families, subcultures, political parties, and civilizations, not to mention participants in the 2.5-million-year-old group project of technology and ideas, the 2.5-million-year-old group project of human culture.  Read more at location 7858

DOING THE GLYCERIN TWIST: DAVID BOHM 

ornately strange outcomes can nest invisibly in a handful of axioms. Bohm called his concept “implicate” order.  Read more at location 7878

words are not really naked. They are uttered in a context. They are uttered in a nest of meanings. A nested hierarchy. An onion of meanings.  Read more at location 7893

Google was stumped trying to find the right nest of meanings when you and I use the word “dog.” Do we mean a pooch or a skinny sausage in a long roll? Says Levy, “The problem was fixed by a breakthrough late in 2002 that utilized Ludwig Wittgenstein's theories on how words are defined by context.  Read more at location 7895

To get a grip on what Bohm saw on his TV screen, imagine this little kitchen experiment. Take a pitcher. Put a tall drinking glass inside of it. Right in the center. That leaves a gap, a space, a canyon, a ravine, an empty circular cleft between the outside walls of your drinking glass and the inner walls of your pitcher. Now pack Vaseline®, petroleum jelly from the drugstore, into that circular space between the outer wall of the drinking glass and the inner wall of the pitcher. Then take an eyedropper and drip a drop of ink onto the surface of the Vaseline.  Read more at location 7953

Later, Bohm apparently tried the experiment himself. He discovered that if you put five drops of ink on the glycerin instead of just one, the five drops will disappear as you turn the central cylinder. Then the five drops will reappear again when you twist the central cylinder back to its starting position. And if you lay out the drops on the glycerin in a pattern—say a stick figure of a human—you can twist the central cylinder and make the stick figure disappear. Then you can turn the cylinder back to its starting point and watch the stick figure seemingly self-assemble from the nothingness.  Read more at location 7978

Bohm became enthusiastic about yet another approach. This one is hard to describe, so bear with me. Hold the handle of the outer pitcher tight so the pitcher doesn't move. Put an ink drop on the glycerin, turn the inner cylinder a few degrees, then, move your dropper a tad to the right, lay down another drop, turn the inner cylinder again, move the dropper a tad farther to the right, drop another drop, then turn the inner cylinder, move your hand, and drop again and again. You've just laid down a line of dots. Now stop squeezing out drops of ink. If you turn the center cylinder far enough, all of your ink drops disappear. You now have a nothingness in your glycerin. Now do the turning in reverse. Slowly rotate the center cylinder back to its starting position. Your ink drops will reappear one at a time.  Read more at location 7982

Bohm took his leap a step further. He guessed that “perhaps the movement of enfoldment and unfoldment is universal.”102 Perhaps there is continual oscillation between enfoldment and unfoldment in the entire universe. How did Bohm fit the big bang and the history of the cosmos into this? Bohm saw the big bang as just “a little ripple…in the immense ocean of cosmic energy.”103 Just another drop emerging from the nothingness of the glycerin. A drop that was hidden but implicit all along. A drop that lay invisibly in the emptiness the way that a drop of ink lies invisibly in your seemingly empty Vaseline.  Read more at location 7992

That's the metaphor that made it from a BBC-TV studio into Bohm's mind in the 1960s and became the basis for his “implicate order”—an order hidden in the nothingness. An order aching to reveal itself. An order aching to translate itself into a hard and fast reality.  Read more at location 8000

****  To Bohm, it seemed that a vast menagerie of somethings lay implicit in the chaos at the moment of the big bang the way that the ink drop lay invisibly in your Vaseline.104 But to Bohm, there was no chaos.  Read more at location 8004

Bohm wrote in his 1980 Book Wholeness and the Implicate Order that “what we call empty space contains an immense background of energy, and that matter as we know it is a small, ‘quantized’ wavelike excitation on top of this background, rather like a tiny ripple on a vast sea.”105 Space, he said, is “full not empty.”106 Full of what? Implicate order.  Read more at location 8006

With encouragement from Albert Einstein, he created a reformulation of the mathematics of quantum physics.107 And his new mathematical approach seemed to be as effective at making predictions as the standard math of mainstream quantum physics.  Read more at location 8010

There was, in fact, a severe limit to Bohm's metaphor. A mistake. Bohm's error was the equivalent of running a video of a breaking wine glass backward, then claiming you'd just shown a video of how the glass was made.  Read more at location 8023

the hidden presence of the past is the Achilles heel, the fly in the glycerin, the giant weakness in Bohm's central metaphor for implicate order. It is also the flaw in a metaphor that Immanuel Kant and many others have used to describe the way a universe springs from nothing. Kant used the metaphor of the seed.  Read more at location 8035

The metaphor of the glycerin and the metaphor of the seed translate a past into a hidden code, then reassemble it. They sidestep the God Problem. But  Read more at location 8071

BENOÎT MANDELBROT ZIGS AND ZAGS 

****  this is a social cosmos. It is a communicating cosmos. It is a conversational cosmos. It is an informational cosmos. It is a cosmos of meaning. And it is a cosmos of form production and emergent properties.  Read more at location 8077

Over a hundred years of experiment proved that the abstract, ivory-tower math of axiom flippers and of implication extractors can uncover the secrets of something very real, the cosmos. The eight validations of Einstein's predictions hinted that the math of axioms and logic can actually uncover what Einstein called “deeply hidden” secrets. Secrets that may be basic patterns, deep structures, patterns that repeat at level after level of the cosmos. Ur patterns. The basic patterns that allow math and metaphor to work.  Read more at location 8081

Math was obsessed with smooth curves and smooth sheets. Albert Einstein, for example, had come out with a theory that explained the cosmos in terms of rubbery sheets of space and time. Rubbery sheets as smooth as smooth as smooth can be. But in 1918 in France, Gaston Julia122 had discovered an odd set of patterns that were the very opposite of smooth. These patterns were jagged and bumpy—so jagged that their contours couldn't be measured. They were even more jagged than the zigzag patterns of the Babylonians. They looked something like the coast of England. A coastline with big indentations, small indentations, and microscopic indentations. Measure those indentations with a big measuring rod and you get one number. Measure them with a smaller measuring rod and you are able to fit that measuring device into more of the indentations of the crevasses, crags, and outcrops. So the measure you get of the coastline shoots up. Try using a microscopic measuring rod to measure the boundaries of these zigzag patterns, and you run into a size problem. The zigzags of the coast's indentations continue right down to the microscopic level. With your super-tiny measuring rod, you're able to measure the microjags and indentations of even more ragged outcrops and inlets. You're able to measure even the microscopic indentations of sand and stone. So the length you get from your measurement soars even higher. In theory, if you were to use an infinitesimally small ruler, the length you'd get would be…infinite.  Read more at location 8099

In math, infinities bollox things up. Divide a simple number like one by infinity and you no longer get numbers. You get nonsense. So mathematicians labeled these jagged objects “monstrosities” and said they did not belong in mathematics. Yes, mathematicians banished a reality.  Read more at location 8109

Mandelbrot, however, had a mathematical curse. Or was it a blessing? He “often preferred to draw pictures of data rather than write equations.”  Read more at location 8147

In 1976, Benoît Mandelbrot gave these mathematical elephant men a name—fractals.  Read more at location 8160

CHAPTER 9: ITS FROM BITS: THE TWO-BIT TARANTELLA

HOW MATH LOST ITS PICTURES…AND HOW IT GOT THEM BACK AGAIN  

The computer would allow Benoît Mandelbrot to develop fractals.  Read more at location 8164

It all came down to counting simple, modular things. Over and over and over again. Repeating was the heart of math.  Read more at location 8173

But the computer is the ultimate repeater. The ultimate iterator. It can do in one second more calculations, more iterations, more tiny steps, than all of the mathematicians in history.1 It can do in a second more than the calculations that men like Gauss were able to carry out in a lifetime.  Read more at location 8179

The computer can unfold the implicit properties of axioms. And it can unfold them without having the answer built in. It can unfold a vision of a future without having that future tucked into it in advance.  Read more at location 8185

But starting in the 1960s with Benoît Mandelbrot, the computer would be able to yank pictures and calculations together in radical new ways. The computer would give metaphor's core—visions, things you can picture—predictive powers. The computer would give pictures and metaphors predictive powers that wouldn't need equations.  Read more at location 8196

a computer has a hard time understanding an equal sign. It has a hard time with Aristotle's identities. It has a hard time with equations. And that handicap is the computer's advantage. Why? Because the computer “thinks” with a different kind of logic than your standard equation-juggling mathematician. Instead of working with “this equals that,” it works with “and” and “or.” It works with “if-then” statements.  Read more at location 8218

Reality often ignores equals and goes with if-then. It often works with “if x and y happen, then z will occur.” Even if z is radically different from just x and y.  Read more at location 8223

If-then statements fit a world that has sequences in time. Sequences of causality.  Read more at location 8231

a computer can also do what Thomas Young and Giuseppe Peano were obsessed with, translation. A computer can speak many languages. It can translate to many isomorphic symbol sets. Like the Rosetta Stone, the computer is a translator. It can translate numbers, words, and letters on a screen into the language of the binary number system, the language of electrical impulses, and the language of an increasing number of computer programs. And it can translate that language of offs and ons, the language of electron flows, into the language of printed text and even into the language of speech. Despite its difficulties, the computer can even translate into or out of equations. But most important, the computer can translate equations and programs into a visual language.  Read more at location 8234

Why are pictures such a big deal? Pictures reveal the meaning of relationships instantly. They reveal why the parts relate to the whole,  Read more at location 8241

During most of its six thousand years of development, math was done with pictures. In 300 BCE, Euclid did math by drawing with a compass made of string5 and with a straight edge. He used pictures. In 1619, Johannes Kepler did math by drawing as many as forty trianglelike lines within a circle.  Read more at location 8243

But in the late-nineteenth and early-twentieth centuries, mathematicians like G. H. Hardy and the Bourbaki group abandoned pictures. They hid their math by using the magic of isomorphic symbol sets. They banished pictures and used a language that held the same meanings but was nearly impossible for normal mortals like you and me to understand.  Read more at location 8250

FUSE AND FIZZ, THOU SHALT BUD: FRACTALS AND THE BOUNCE FROM BOOM TO BUST

Science is possible because the world seems very complex but is actually governed by a small set of laws. —Gregory Chaitin9  Read more at location 8263

Fractals produce pictures that explode. Pictures that erupt with bulging, budding circles forming swirls, curls, spindles, spires, straight lines, rosettes, florets, blossoms, and blazes of tracery. Pictures that appear to bloom with something stunning and stunningly God Problem-ish: creativity.  Read more at location 8272

A Mandelbrot set is based on an equation like Z = Z2 + C.  Read more at location 8282

In English, Z = Z2 + C means gather together around a common core. Make a circle. Then bud out. Rebel. Separate. The rule of the Mandelbrot set is very much like Frank Sulloway's rule for rebellion, the rule that often dictates how the second baby in a family will carve out a niche in attention space.  Read more at location 8285

Then what? You congregate around a common core again. A new common core, a rebel common core. A core of outriders. You integrate. And then? What's the next step? The same step you began with. Bud. Separate.  Read more at location 8293

integrate then differentiate. Then integrate and once again differentiate. Old rules. Very old rules. The rules of attraction and repulsion.  Read more at location 8295

fractals do make one thing very clear. They overcome the Bohm Cheat. They don't resurrect a hidden past. They burst with genuine surprise.  Read more at location 8317

the Mandelbrot set is one of the first metaphors, one of the first mathematical systems, that does something genuinely God Problemish.  Read more at location 8324

****  (Note:   If the same equation produces the same form every time, then its future IS built in. It is not indeterminate)  It starts from a simple rule, a simple equation. An equation with no future built in.  Read more at location 8327

Fractal patterns are real as real can be. Fractals show up in coastlines, their point of origin. But fractals also appear in clusters of galaxies, in chromosomes, in DNA, in broccoli, in cabbages, and in trees. Fractals even show up in human sexual behavior.  Read more at location 8334

Then there are even higher-level fractal relations to reality. The fractal variation on attraction and repulsion is similar to something that primatologists in the 1970s called the “fission-fusion search strategy.”  Read more at location 8338

The fission-fusion strategy is a search strategy. A way of finding new things. Humans unknowingly follow the fission-fusion strategy, too. We have recessions roughly every 4.75 years.  Read more at location 8347

underneath your frenzies and your fears are the rules of the Mandelbrot fractal: huddle together in fear, then rebel, bust out, explore. Then huddle tight in a state of insecurity again. When the Mandelbrot rules are translated into the social medium of living things—from bacteria to human beings—they are transformed into the template for a search strategy. Which means that you are right when you speculate. But you are also right when you are terrified that you've thrown your money away.  Read more at location 8364

A recruitment strategy based on oscillation, the wobble back and forth between opposites. Based on the fact that opposites are joined at the hip. A recruitment strategy that is aped, mirrored, simulated, and metaphored by the Mandelbrot set.  Read more at location 8426

*********  Fission and fusion are attraction and repulsion in disguise. They are among the oldest patterns of the cosmos. They are good candidates for the cosmos's starting rules. And they are rules of sociality. They are rules of communication. They are rules of information. They are rules of meaning.  Read more at location 8431

THE SORCERY OF SIMPLE RULES

Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity.27 —Lewis Fry Richardson,  Read more at location 8434

In math and in computer programming, it all comes down to “iteration.” And here's the secret. The secret to why one A does not equal another. The repetition of an old pattern changes the nature of the cosmos. Stuttering forth the same old thing in a new time and place changes the very nature of the medium in which the next iteration—the next repetition—takes place.  Read more at location 8442

(Note: Unexpected is different than indeterminate. Are Mandelbrot sets indeterminate?)  Mandelbrot-like iterations working simultaneously can produce unexpected surprises even in the simplest of natural things.  Read more at location 8459

This is a universe of more than just occasional simultaneity. It is a universe of supersimultaneity. A universe of supersynchrony.  Read more at location 8460

THE JAPANESE SWORD MAKER AND THE ALCHEMY OF ITERATION 

****  There is a secret at the center of Leonardo's, Gaston Julia's,28 and Benoît Mandelbrot's work. It's iteration. Repetition. Repetition of an old rule in a new context. Repetition in a relational context. Repetition in a social context. Repetition in the social context that the rule itself has made. Manic repetition in a social context has the ability to make one plus one equal something very different from two.  Read more at location 8466

GAMING YOUR WAY TO FAME: JOHN CONWAY ENTERS THE SCENE 

Win a game and you get more than just two minutes of praise, envy, and attention. If you win, your biology rewards you. It perks you up and tunes your immune system to high.54 It gives you a dopamine rush,55 a testosterone boost,56 and an endorphin57 lift. Lose too often and your biology goes into a slump. Your mind gets dazed and foggy and your immune system dials down a notch or two. You are slowed by stress hormones, glucocorticoids. And that's not all. Win and you become more attractive to others. Lose and you lose your popularity. So winning or losing is a bigger deal than most game critics think. Why did evolution build our zest for games into our biology?  Read more at location 8637

could it be because games are something crucial to human survival: prediction practice?  Read more at location 8648

AXIOMS IN SILICON: CONWAY'S GAME OF LIFE 

The really hard part to understand is how and why a glider arises on the game board and retains its identity. The answer is that the glider is an implicit property. It's the real deal of what Bohm called an “implicate property.” It's implicit in the rules of the Game of Life. Those three extremely simple rules of sociality, cozy companionship, overcrowding, and survival. Rules of relationship. The glider is also implicit in something else—the medium in which it exists, the chessboard. The computerized chessboard. It's implicit in the way the rules interact with a pattern of lit squares that you lay out on the game board before you hit the start button. And it's implicit in the starting pattern you lay out before you let your computer churn out its iterations. The glider is implicit in a tiny number of axioms. In a tiny number of magic beans. Does the Game of Life apply to anything real? Or is it just a computer hobbyist's whimsy? Says Wikipedia—today's summary of our collective knowledge—the Game of Life has been used by “computer scientists, physicists, biologists, economists, mathematicians, philosophers, generative scientists…to convey the somewhat counter-intuitive notion that ‘design’ and ‘organization’ can spontaneously emerge in the absence of a designer.”  Read more at location 8719

GOOD-BYE TO EQUATIONS: STEPHEN WOLFRAM'S NEW KIND OF SCIENCE 

Says one of Stephen Wolfram's bios, “At 14, he wrote his first book on particle physics. At 17, the scientific journal Nuclear Physics published a paper he'd written. At 18, he wrote a widely acclaimed paper on heavy quark production.”70 Wolfram also became the youngest person71 to win a MacArthur Genius Award.  Read more at location 8763

Why not use equations? After all, Wolfram was masterful at handling the complex mathematics of his era. In fact, when he was twenty, Wolfram had created what his website calls “the first modern computer algebra system, called SMP.” But, says Wolfram, “there is some kind of secret ingredient that nature is adding to make stuff complex,” some kind of secret ingredient “that we don't know from a scientific point of view.”  Read more at location 8784

In fact, in Wolfram's opinion, science was blind to many of the most important mysteries of the real world. For example, science seemed good at handling physics, but Wolfram pointed out that it wasn't able to achieve a major goal it had been lusting after for nearly three hundred years, “an ultimate theory of the universe.”78 Worse, Wolfram pointed out that science was a flop in turning “the biological and social sciences” into principles “we can calculate.”79 Why? There was a culprit.  Read more at location 8787

The equation. There's an old saying attributed to psychologist Abraham Maslow: “When all you have is a hammer, everything looks like a nail.”80 The nails of science for three hundred years had been equations.81 And, said Wolfram, in a statement that most scientists would have found outrageous, a statement that threatened to overturn the scientific applecart entirely, “It's our reliance on mathematical equations and traditional mathematics that have made us miss what's going on.”  Read more at location 8793

Explained Wolfram, “It's often imagined that mathematics somehow covers all arbitrary abstract systems. But that's simply not true.”  Read more at location 8798

****  In the end, it all comes down to axioms. Says Wolfram, “When one starts investigating the whole computational universe” it turns out there are tons of “possible axiom systems that might be used to define mathematics.”  Read more at location 8801

like the shift of just one axiom in non-Euclidean math, each “axiom system” produces what Wolfram calls another “possible mathematics,” another “alternative mathematics,”85 a whole new mathematical universe. Says Wolfram, if you explore all the possible axioms, you'll find “lots and lots of axiom systems that seem just as rich as anything in our standard mathematics. But they're different.”  Read more at location 8803

Explains Wolfram, “It's just a particular formal system that arose historically from the arithmetic and geometry of ancient Babylon. And that happens to have grown into one of the great cultural artifacts of our civilization.”  Read more at location 8808

****  We tend only to ask questions that we know we can answer with the mathematical tools we have at hand. And that cripples us. Says Wolfram, “The questions that get asked in a sense always tend to keep to the region of computational reducibility.”88 We only ask the questions we can answer with equations. “Natural science,” Wolfram adds, “has been limited too—in effect to just those kinds of phenomena that can successfully be captured by traditional mathematics!”  Read more at location 8814

The math of equations has become the kind of unquestioned axiom that Einstein warned can blind us. It's the kind of unspoken assumption that Einstein warned us to hold up to the light so we can see it clearly. And so we can question it.  Read more at location 8820

Said Wolfram in 1998, “If, instead of using mathematical questions, one thinks about things in terms of simple computer programs, then one can quite quickly see what's going on.” By what's going on, Wolfram means the “secret ingredient” of complexity. And Wolfram has a very specific plan in mind for exploring these “simple computer programs” that uncover the world's secret ingredients. What is it? Model as many simple programs in the computer as your time, your patience, and your access to computers will allow. Model every simple system conceivable.  Read more at location 8828

Here's how Wolfram methodically pawed through “the computational universe” to “see what's there.”100 He simplified John Conway's checkerboard.  Read more at location 8844

in Wolfram's cellular automata, rules were repeated upon themselves. They were repeated on the environment they themselves had made. As row after row unfolded, the simple rule changed the nature of the context in which it was repeated. In the process, it generated massive new patterns. New patterns like John Conway's sliders and gliders. New big pictures. Astonishing recruitment patterns.  Read more at location 8858

What did Wolfram find? Tons of simple rules that produced nothing of interest. And some simple rules that produced amazements. Some rules that produced order. Order peppered with astonishing complexity. Peppered with ornate forms. And peppered with something even more important than ornate complexity. Peppered with patterns that sometimes switched from brilliant structure to astonishing chaos.  Read more at location 8876

****  Simple rules can produce wonders of order. And they are so good at producing complexity that they can even generate what looks like the ultimate form of disorder, a storm of nonsense—chaos. Which means that behind every nonsense, there may be a sense that's astonishingly simple. Behind every chaos, there may be simple rules.  Read more at location 8892

****  After running hundreds of millions of these miniverses for roughly a billion billion generations, what other conclusions did Stephen Wolfram come to? Once again, that equations were too narrow a tool. That equation-based math was what Wolfram called “one of the biggest shortcomings of present-day science and technology.”  Read more at location 8896

He also concluded that cellular automata based on simple rules, cellular automata unfolded from simple axioms, could ape the behavior of everything from the actions of elementary particles and the flow of liquids in Heraclitus's eddies and whirlpools to the behavior of human beings. He concluded that cellular automata could take you beyond equations and could allow you to use your computer “to find by simulation what a system will do.”112 Just about any system.  Read more at location 8899

Wolfram explains, “When I searched, for example, for Boolean algebra (logic), I did indeed find a tiny axiom system for it.”121 But finding that axiom system wasn't easy. Remembers Wolfram, “It turned out to be about the 50,000th axiom system in the enumeration I used.”122 Then came a problem: “Proving that it was correct.” And “proving that it was correct,” Wolfram says, “took all sorts of fancy automated-theorem-proving technology.”123 Technology that used tens of thousands of central processing units, the equivalent of tens of thousands of personal computers. But by 2007, Wolfram was hunting bigger game.  Read more at location 8949

Does Wolfram have what he calls “candidate universes” yet? Says he, “The answer is yes.”126 And what, pray tell, may the candidate cosmoses be like? What may their starting rules be? The leading candidates, says Wolfram, are “small networks.”127 Networks that work according to what Wolfram calls “causal invariant rules.”128 And what are “causal invariant rules”?129 Explains Wolfram, they are “rules which have the property that whatever order they're applied in, they always give the same causal network.”130 And what makes Wolfram feel that these may be the rules of the really big enchilada, the tossed salad to beat all tossed salads, the universe? For one thing, causal invariant rules seem to cough out time and space. But not just any time and space. They “imply the particular relation of space and time that is special relativity.”  Read more at location 8959

****  Wolfram seems to have pulled both rabbits—relativity and quantum physics—from the same hat. Which means he's found a way to unify relativity with quantum physics. He's done it with his “small networks” using “causal invariant rules.” Says Wolfram with glee, “In a network” of this sort “one doesn't just have something like local 3D space, it looks as if one automatically starts to get a lot of the core phenomena of quantum mechanics.”132 Yes, says Wolfram, you get the probabilistic unpredictability of quantum mechanics “even from what's in effect a deterministic underlying model.”133 You get relativity and quantum mechanics from the same set of simple rules.  Read more at location 8970

Wolfram is confident that “our whole universe and its complete history could be generated just by starting with some particular small network, then applying definite rules.”134 But one universe is not enough to satisfy Wolfram. He feels he is on the track of simple rules that can spill forth every universe that could ever be.  Read more at location 8976

Says Wolfram, “Over and over again I've found these systems doing things that I was sure wouldn't be possible—because I couldn't imagine how they'd do them.”139 And that is the mark of a crucial achievement. It is a mark of a system that cuts free from the Bohm Cheat. Wolfram's surprise was an indication of the fact that at last he and John Conway had devised a simulation that starts with axioms, that starts with simple rules, then spills forth things that no human can predict.  Read more at location 8988

With his cellular automata, Wolfram has developed a new metaphor with which to confront the God Problem, the problem of how the cosmos creates.  Read more at location 8993

CHAPTER 10: WHAT ARE THE RULES OF THE UNIVERSE?

THE CASE OF THE OBSESSIVE-COMPULSIVE COSMOS  

(Note: Persistence suggests a teleological meaning... a sense of purpose)  There's good reason for calling this a driven, motivated cosmos. A persistent cosmos. This is a cosmos that keeps pushing forward, no matter what. This is a cosmos that's kept up that push for 13.73 billion years. It's a cosmos that's kept up that push for 4.3298928 × 1017 seconds. A number way up there in the hundreds of quadrillions. This is a cosmos that has shown a primitive precursor of will. A primitive precursor of stubbornness.  Read more at location 9017

There is something arrogant about the conviction that all anthropomorphism is a criminal offense against sanity and reason. For example, we humans believe that we invented free will. But renowned Princeton Institute for Advanced Study physicist Freeman Dyson disagrees.4 So do the Santa Fe Institute's arch complexity theorist Stuart Kauffman and the Game of Life's father, master mathematician John Conway. Dyson says, “There is a certain kind of freedom that atoms have to jump around, and they seem to choose entirely on their own without any input from the outside, so in a certain sense atoms have free will.”  Read more at location 9030

Where did Kauffman get the quote labeling “the free decisions of particles and humans…free will”? From the Game of Life's John Conway and from Conway's fellow Princeton mathematician Simon Kochen. In 2006, Conway and Kochen set out what they boldly called “the free will theorem.” In its opening lines they asked an old question: “Do we really have free will, or, as a few determined folk maintain, is it all an illusion?” And they gave an outrageous answer, “We don't know, but will prove in this paper that if indeed there exist any experimenters with a modicum of free will, then elementary particles must have their own share of this valuable commodity.”  Read more at location 9041

when metaphors work, it is often because they capture Ur patterns, patterns repeated on many levels of emergence. It is often because they capture deep structures of the cosmos. Structures as deeply embedded as axioms. Why deeply embedded? Because they are often structures that have been here from the beginning. Structures on which everything around us has been built. Structures the cosmos has repeated in new mediums, iterating them the way the swordmaker flattens and folds his iron. Repeating old rules in a way that makes something very old into something very new. The Ur pattern Blümel refers to here is the photon's “selection” of a choice. “Selection of a choice”? Isn't that unacceptable anthropomorphism?  Read more at location 9051

****  Dropping from several states to just one is called quantum decoherence. And quantum decoherence is the very phenomenon that Dyson, Kauffman, Kochen, and Conway all zero in on when they tell you that your oldest ancestors and mine, particles and atoms, have free will. The implication of Kauffman, Dyson, Kochen, and Conway's argument is devastating. Devastating to the notion that anthropomorphism is a scientific sin. If elementary particles have free will, then will, volition, and decision making began in the first tiny nanosliver of a second that gave birth to particles. Free will began in the first flick of the big bang.  Read more at location 9067

Yagi, Hatsuda, and Miake spell out chains of reasoning based on quantum mechanics and information theory to prove that the entire cosmos had to make a choice. It had to decohere. That primal “decision” gave us “a classical universe”—the  Read more at location 9077

But will is not the only primitive pattern that we inherited from the particles and atoms that came before us and from the particles and atoms that we are made of. We also think we invented competition. We did not. Competition is not a product of patriarchal societies bent on evil. And it is not a product of agriculture, industrialism, or capitalism. It is in the deep structure of the cosmos. Like free will, competition appears to be a primal recruitment strategy, a primal building strategy, and a primal way of knitting together new networks of relationships. New onionskins of meaning.  Read more at location 9092

It was the era of the Great Gravity Crusades. Atoms clustered and competed. Competed for what? To kidnap, seduce, and recruit yet more atoms. Those atom clumps that grew the fastest grabbed and swallowed atom masses that grew more slowly. The big ate the small in what, as you probably remember, astrophysicists and astronomers call cannibalism. The biggest winners became galaxies. The smaller winners became stars. The winners in the number three slot became planets. And the runners up became moons. Those Great Gravity Crusades continue today.  Read more at location 9097

We also think we invented war. We did not. Like protons and photons, colonies of bacteria are among our ancestors. And they began making war nearly four billion years ago. Their armies were eleven million times the size of Napoleon's mass conscription forces. And their weapons were weapons of mass destruction. Chemical weapons. Weapons of utter extermination.  Read more at location 9104

We also think that we invented dominance hierarchies, pecking orders. We did not. Dominance, too, appeared on the scene shortly after the big bang. In the first seconds of this explosively expanding cosmos, when the forces of compression jammed two protons together, the meeting was not so cordial. In fact, the struggle for dominance began. One proton—the winner—retained its identity. The other proton lost. It submitted and decayed. It lost its identity and dissolved into a neutron and a positron.18 A neutron that hung around as a subordinate to the proton it had been jammed into. The result was a deuteron, the one-proton-plus-one-neutron nucleus of a deuterium atom.  Read more at location 9107

The top crayfish, lobster, lizard, chicken, dog, or chimpanzee gets certain privileges. He or she (yes, there are dominant females) gets influence and power. And the top dog, lobster, lizard, or chimp commands attention. Lots of it. Does anything like that happen when two protons pair during a post-big-bang mashup? You bet. The proton that retains its identity hangs on to its ability to seduce and recruit electrons. It holds on to its electrical charge, to its force of attraction. Meanwhile, the submissive neutron gives up that privilege. It becomes “electrically neutral.”19 It has no ability to attract an electron. It has no influence.  Read more at location 9114

It all begins with a primitive precursor of love. Up until now, electrons and protons were like bump-em cars in a superhot plasma, a soup in which particles slammed into each other at unbelievable speeds, then bounced away, only to ricochet off yet another particle. Up until now the slam, smash, crash, and ricochet were nonstop. But, as you know, at 380,000 ABB (after the big bang), the plasma cooled down. Which means that particles slowed down. And once the particles of the early plasma slowed, you remember what happened. Electrons discovered something strange. They were attracted to very unlikely mates. They were attracted to particles 1,837 times their size.20 And those humongous particles found that they, too, were attracted. To what? To the tiny particles that swooned over them, to electrons. This match was so unlikely it was absurd. But it turned out that the “needs” of the proton fit the “desires” of the electron perfectly. With absolute precision. Could this match have been the primitive pattern upon which human love would someday be built? Then came the pecking order. Once a proton and an electron joined, hierarchy took over. The proton was dominant. The electron was subordinate.  Read more at location 9120

****  The proton handles the form of movements produced by bulk. The proton handles the job of traveling. And the electron takes care of social chores. Does this sound familiar? A bit like male-female partnerships among human beings? And if it does, to what extent do our male-female duos repeat the patterns native to the atoms of which we are made?  Read more at location 9136

***************  there is more than an even chance that we humans have free will, competition, dominance hierarchies, love, and war because we inherited them from the cosmos that gave us birth. There is more than an even chance that we have free will, competition, dominance hierarchies, love, and war because these things were basic patterns that shaped the behavior of the earliest particles, atoms, and colonies of cells. There is also more than an even chance that we have these nasty—and sometimes brilliantly creative—characteristics because they are deep structures, Ur patterns.  Read more at location 9152

There is also a good chance that we have free will, competition, dominance hierarchies, love, and war because they are among the earliest outgrowths of attraction and repulsion, among the first manifestations of differentiation and integration. There is a good chance that we have free will, competition, dominance hierarchies, love, and war because they are outgrowths of the starting rules of the universe.  Read more at location 9162

TIME, THE GREAT TRANSLATOR: AN INFORMATION THEORY OF TIME 

Mainstream physicists like Caltech's Sean Carroll, author of one of the most definitive popular books on time in the early twenty-first century, From Eternity to Here: The Quest for the Ultimate Theory of Time, are absolutely certain that time must be defined in terms of entropy.  Read more at location 9172

Vladislav Čápek of Charles University in Prague and Daniel Peter Sheehan of the University of San Diego dare to disagree with Eddington. Yes, they use Eddington's quote too. But in their book Challenges to the Second Law of Thermodynamics: Theory and Experiment they point out that “there is no general theoretic proof” for the second law.25 No general theoretical proof that all things tend to disorder, to entropy.  Read more at location 9191

But they explain that “for more than a century” the concepts of entropy and the second law have been “beyond the pale of legitimate scientific inquiry” in large part because of “peer pressure against such inquiry.” Nonetheless Čápek and Sheehan admit that the second law is an antique, a “remnant of nineteenth century physics, whose foundations were admittedly suspect.” And an end may be in sight. As Čápek and Sheehan report, “There grew around the second law a nearly unpenetrable mystique,” but that mystique “now is being pierced.”  Read more at location 9196

Pavel has a very strange theory of time. He calls it the hidden time theory. Here's how it goes: Imagine time as a stairway. Every stair is separated from the one below it by a riser, the vertical separator between one step and the step above it.  Read more at location 9214

Time exists only on the steps. Time exists only on the flat plane of the stair above and the equally horizontal plane of the stair below. So what's in the riser? No time. Timelessness.  Read more at location 9217

****  You propose to Pavel that the cosmos is social. And that the cosmos is conversational, gossipy, and communicative. What's more, you propose that the next stairstep in line looks back at the stairstep before it, allows the elements on that stairstep—the usual suspects: quarks, atoms, stars, galaxies, molecules, cells, plants, animals, neurons, and human beings—to compete for attention, then makes a decision about how to interpret those elements and their interaction. When it makes up its mind, the stairstep moves everything forward one turn and produces the present. Then the pattern of the present is locked in place and becomes the past. Meanwhile, the next stairstep in line has to look over the present and ponder it in the timelessness, in the non-time between the stairsteps. Then it has to come up with alternative translations, alternative interpretations, and make up its mind.  Read more at location 9223

So you look for a system of mass behavior to suggest how a cosmos of mobs and crowds may make up its mind. And you come up with your favorite mass behavers, bees. Bees have a problem.28 A life-and-death problem. And it's a problem with time. More specifically, a problem with a time limit. And a problem with decisions. There are roughly twenty thousand bees in each hive. And they have to act as a group brain, a collective intelligence. Why? The hive has only six weeks in which to gather enough pollen and nectar to make forty pounds of honey, the honey it will need to get it through the winter.  Read more at location 9233

In the words of bee researchers, how do they arrive at the “optimal decisions”?29 With a fine-tuned balance between fission and fusion, between differentiation and integration, between explorers and consolidators, between searchers and workers.  Read more at location 9242

Ninety-five percent of the bees are hard workers. The young ones, the adolescents and young adults, stay indoors and do housework. They take care of the queen, feed the babies, the pupae, store incoming foodstuff, repair the honeycombs, and keep the place clean and neat, literally. As they grow older, they graduate. They become outside workers, gatherers. They fly out time after time, day after day, to mine patches of linden flowers, sumac, goldenrod, red clover, hyacinths, crocuses, sunflowers, and raspberry bushes. They bring back the pollen, the nectar, and the water of which honey, the hive's daily bread, is made. Remember, they are up against a killer deadline. But something doesn't make sense. Roughly 5 percent of the bees seem to be infuriating time wasters. This irresponsible minority is a bunch of good-for-nothing Bohemian wanderers who go out on pointless, solitary rambles,  Read more at location 9246

Meaning is the sense that when you return home from a pollen flight, the unloaders will give you the kind of attention that you used to get when you landed with full pollen hairs at the loading dock just inside the hive. Or, to put it in human terms, meaning is a sense that you are contributing to something higher than yourself. Which is exactly what every bee does every day. Especially when she delivers the goods—pollen, nectar, and water. As for excitement, that seems a strange word to apply to bees. It's not. When a bee is excited, her temperature goes up. When she is depressed, her temperature goes down. It's as simple as that. Stimulus and response. And as you'll see in a second, emotions are an information engine. They are vital to the next big decision of the hive. Back to you, the unemployed bee, the bee who no longer gets attention, the bee who has to beg (yes, bees beg, they humble themselves and crouch close to the ground) for food.  Read more at location 9271

Roughly five of those damned bohemian bees have found flower patches that they think are hot. Flower patches that excite them. And they've come back home, have used the unloading dock just inside the hive as a stage, and are dancing their discoveries. They are dancing a figure eight that gives instructions on how to get to the patch that they are advertising. And a figure eight that also gets across how excited—or tepid—they are. How do these explorer bees flash their excitement? With the power and the length of their dance. Mildly excited explorer bees may dance for less than a minute. Wildly excited explorer bees may dance for as long as half an hour.31 You and your fellow unemployed sisters literally have nothing better to do. So you crowd around the dancers. Why? Because they excite you. Or, to put it in human terms, they entertain you. They lift your spirits. Those who dance for half an hour fire your enthusiasm more than those lukewarm bees who dance only a minute or two.  Read more at location 9279

The hive is up against a crucial choice. It may invest ten thousand bee miles of travel into the next flower patch to which it sends its conformists. If it picks the wrong flower patch, it won't outpace the cold of mother nature when winter comes. It will lose the bee-and-honey race. How does the hive handle its prediction problem? Out of many possibilities, how does it pick just one? The dancing bee, the bohemian bee, the explorer bee who excites the greatest number of backup dancers wins.  Read more at location 9290

Unemployment, depression, and a midwinter death are the sticks. Then there is the carrot. The same carrot that motivated Aristotle. Attention. Not to mention sex and procreation. If your hive pulls in a surplus of honey it will be in a position to reproduce. It will be in a position to feed a lot of kids, raise them to maturity, then hive off, to split in two, and to send out a daughter colony.  Read more at location 9297

************  Pavel Kurakin's hidden time model treats time as a form of communication. It treats time as a form of information extraction. It treats time as a form of translation. In fact, time is the ultimate extractor of implicate properties.  Read more at location 9321

(Note: Matches Varela, cog sci experiments of perception and cognition, anyway)  First off, Pavel Kurakin is not alone in regarding time as something like a flight of stairs. In the eyes of most modern physicists, time is not continuous.  Read more at location 9324

The stairsteps, floors, or rungs of time are in all probability spaced precisely one Planck unit apart from each other. What's one Planck unit? It's the time it takes a beam of light to traverse one Planck unit of distance. A Planck unit is 10-43 of a second. Which means that there are 1043 Planck units of time in every second of your life and mine.  Read more at location 9330

time is like a line in Stephen Wolfram's cellular automata “deciding” its configuration based on “reading” the line before. Making a decision based on reading the previous line's stimulus and producing a response. A response based on simple rules. Yes, it bears repeating. Time is a process of communication, information, translation, and of what Claude Shannon calls “meaning.”  Read more at location 9338

****  Quantum physics says that until a particle is measured, it is in several states simultaneously. But, you said, no particle is an island. There is no such thing as an unmeasured particle. Particles are not solitary, they are not loners. Particles do not wander around on their own. They travel in packs, in mobs, in armies, and in gangs. So does virtually everything in this universe. To understand the cosmos, you have to understand group behavior. Mass behavior. And the mass behavior of bees is just a suggestive start. More to the point, every particle in the cosmos influences others and is influenced by them. Nonstop. It's stimulus and response. No particle goes unmeasured. At least one fundamental assumption of quantum physics is wrong.  Read more at location 9351

The name of the book? Constructive Physics.36 So you downloaded Yuri Ozhigov's book from arXiv.org to your Kindle and read it. In it, Dr. Ozhigov suggested going beyond equations. Including the most revered equation of all, Schrödinger's equation. In fact, Dr. Ozhigov suggested abandoning traditional math altogether and doing a Wolfram, going entirely into computer models, diving into visual simulations. And beneath the new models of quantum physics, said Ozhigov, would be an escape from the fiction that particles flit about on their own, the fiction that particles manage to go without observers. In place of solitary particles, Ozhigov proposed focusing on “collective behavior.” In place of individual behavior, Ozhigov proposed using mass behavior. The behavior of crowds, mobs, and cliques. Cited in Ozhigov's book was your article with Pavel and George Malinetskii.  Read more at location 9360

****  Quantum physics is a game of mass behavior, and the groups that promote new ideas are often like the explorer bees who lose the competition and whose glad tidings are attended to briefly, then forgotten. Most new ideas ebb and disappear. The bottom line? Quantum physics is based on the idea that you can be alone. It is based on particles in isolation that only make up their minds when they finally make a connection. And the second law of thermodynamics is even worse. It says that patterns of relationship ebb and disappear, leaving particles in a random soup. But this is a conversational cosmos. It is a cosmos of crowds and communication. It is a cosmos that grows big pictures and onion layers of social structure. Even time is communicative. Time interprets, translates, and extracts implications.  Read more at location 9373

WRAP YOURSELF IN STRING: ITERATION AND EMERGENT PROPERTIES 

If I'd told you that there was a magic way to wrap string around you, a way that would hold the shape of your torso and your arms when you took the string off, you would have said I was gibbering nonsense. After all, string is string is string. Wrap string around you and you simply turn yourself into a giant spool. Unwrap the string to take it off and you have an appalling tangle on the floor. But invent a simple new rule, a stitch, and repeat that rule over and over upon itself fifteen hundred times, repeat it with maniacal persistence, and you get an amazing new process of transformation. An amazing new form of translation from one medium to another. You get knitting. Go a step further. Invent the sweater.  Read more at location 9393

*****  Looping, hammering, weaving, and stringing old things together using new simple rules produces the unexpected, the shocking, or the strange. Repeat the brick and you can get enough apartments to house sixty thousand people. Repeat the scratch mark in clay and you can get Mesopotamian mythology, astronomy, and astrology. Repeat the twenty-six letters of the Western alphabet and you can get Shakespeare. The trick is a big picture.  Read more at location 9400

(Note:  Summary of history of axioms)  Uncovering the power of axioms began with the Mesopotamians who invented math six thousand years ago. The Mesopotamians who invented the simple rule of solving problems tiny step by tiny step. And the Mesopotamians who based their mathematical system on simple modular units—the brick and the barleycorn. The hunt for the power of axioms gathered momentum in Greece when Aristotle invented and promoted a procedure that laid out definitions, axioms, propositions, and proofs and when Aristotle named that technique “science.” The hunt for the power of axioms crystalized as a recruitment strategy, a template with social magnetism, in Alexandria when Euclid showed how to use the axiom in his Elements. The hunt for the power of axioms plowed ahead in Europe in the works of Galileo, Kepler, and Newton. The hunt for the power of axioms spread into political philosophy in England and North America with Hobbes and the Founding Fathers. The hunt for the power of axioms showed the possibility of scoping out entire universes in Germany, Hungary, and Russia with the non-Euclideans of the nineteenth century, Gauss, Bólyai, Lobachevsky, and Riemann. The hunt for the power of axioms came to a point in Italy when Giuseppe Peano reduced the entire natural number system to five axioms. And the hunt for the power of axioms exploded in Switzerland in the theories of Einstein, theories based on what Einstein claimed was the change of just one axiom, the axiom of time. The axiom underlay the logic with which Kepler, Galileo, and Newton were certain that God had thought out the world. God, they felt, had used reason. And reason was based on axioms. But could a cosmos really be based on unfolding implications from axioms?  Read more at location 9405

Is axiomatic reasoning merely an indulgence, a playground for geeks? Is there any way to know? Yes, there is. And Einstein found it. Generate predictions, then see if they match the real world. Einstein generated eight of those predictions. Eight predictions based on building from axioms. And every one of those predictions turned out to be on the money. Every one of those eight predictions was spot on. But there's a problem. Twenty-two hundred years before Einstein, Euclid had cheated. He hadn't really extracted implications from his axioms.  Read more at location 9424

Peano had worked backward from the complex to the simple in order to derive his five postulates, his five axioms.  Read more at location 9432

At MIT in 1940, Claude Shannon translated logic and math into the ons and offs of electrical switches. Then came the child of Shannon's translation, the computer. And by the 1960s, Benoît Mandelbrot at an IBM office in Yorktown Heights, New York, showed that you could, indeed, unfold astonishments from just one simple rule. Astonishments that didn't cheat. Astonishments whose outlines were not packed into the starting rules in advance by their creator. Astonishments that stunned even the man who had let the simple rules loose, Benoît Mandelbrot. Next came John Conway in Cambridge in 1971 with his Game of Life. He showed how a system of simple rules could generate sliders and gliders, recruitment patterns, patterns that, like the waves of the sea, had a stubborn identity, an identity that hung in there even though the slider or glider was no thing, even though the slider or the glider yanked together one cluster of squares as its constituents, then abandoned them and yanked the next into its form.  Read more at location 9438

Mandelbrot, Conway, and Wolfram showed that you could, indeed, produce intricate astonishments by letting axioms and simple rules do their thing. Mandelbrot, Conway, and Wolfram showed that simple rules could generate new big pictures, big pictures that changed the meanings of everything within them.  Read more at location 9450

Corollary generator theory helps explain two peculiar aspects of this cosmos we live in—supersimultaneity and the Xerox Effect.  Read more at location 9464

If this were a cosmos of six monkeys at six typewriters, those “things,” those particles, would have come in a zillion different shapes and sizes. Not to mention a zillion colors and textures. And a zillion smells and tastes. But they did not. No way. Particles popped forth in only fifty-seven species.39 Separate species. With roughly 1086 copies of each. Identical copies. That's the Xerox Effect—a gaggle of identical things whooping into being. Then there's supersynchrony and supersimultaneity. The zillion copies of these fifty-seven species of particles spooshed from the sheet of space, time, and speed at precisely the same instant. They didn't copy each other. They had the same form because of something else.  Read more at location 9470

Could the high-precision sameness exist because the particles were all corollaries of the same basic assumptions? And could it be that you get a zillion copies of identical things when the cosmos has only gotten up to a primitive step in her axiom unpacking, in her Planck-step-by-Planck-step process of implication extracting?  Read more at location 9478

the number of stars is in the sextillions.41 Of all different sizes and shapes. But that isn't entirely true. The stars in the universe only vary in size by a factor of five hundred. No star is so big that it hogs up half the universe. And no star is so small that it can fit in your pocket. Then there's that shape, the sphere. It's cookie-cuttered into stars from the universe's guzzle to the universe's zatch. That's the Xerox Effect. The same thing happening all over the place.  Read more at location 9501

What could account for the Xerox Effect? Simple rules. Axioms unfolding their implicate properties.  Read more at location 9506

Take one corollary that the cosmos coughed out at roughly the ten-billion-year mark: life. All the life forms we know show the marks of the Xerox Effect. All use cells. And all use DNA. Even viruses. Viruses are so simple that they don't have cells. But they are cell-and-DNA dependent. They are a recruitment strategy that's evolved the ploy of the pirate, the ploy of hijacking the DNA and cells of others. Then using those captured cells and DNA to produce copies of themselves. So the number of forms of life on this planet is far more limited than we like to think. All are drawn from the implicate properties of what cells and DNA can achieve. And among those implicate forms and processes are you and me.  Read more at location 9520

****  why such sameness underlying what looks like rich and rollicking diversity? The simple rules. The axioms. We are all children of the big bang. We are all children of the same starting algorithms, the same deep structures, the same Ur patterns, the same handful of cosmic commandments. We are all children of attraction and repulsion and their spinoffs, differentiation and integration—children of opposites joined at the hip.  Read more at location 9525

****  We are all children of simple rules generating new big pictures and we are all children of new big pictures coaxing new implications from the simple rules that gave them birth. We are all emergent properties run amuck. But run amuck within a narrow range of possibilities. We are all children of the magic beans. We are all children of the axioms at the start of the cosmos.  Read more at location 9529

BAKING THE BIG BAGEL: HOW TO START AND END A UNIVERSE 

Uncle Albert says that to be a genius, it is not enough to come up with a theory only seven men in the world can understand. To be a genius, you have to be able to write that theory so simply and clearly that anyone with a reasonable degree of intelligence and a high school education can understand it. In other words, Einstein tells you that to be a scientific thinker, you have to have more than your knowledge of science. You have to become a writer.  Read more at location 9553

Dirac was dissatisfied with the existing equations for the peculiar movements of the electron. So he combined Einstein's relativity and a new piece of math—the math that described an electron's quantum leaps inside the atom. The math that described how an electron skips from one quantum shell to another without traveling through the space between.45 When Dirac put the two forms of math together he got a wild hybrid.  Read more at location 9596

Dirac's equation had a bizarre implicit property. It predicted an impossible symmetry. It predicted opposites joined at the hip. Specifically, it predicted a particle that would be a symmetrical counterpart to the electron. It predicted a “positron.” The electron has a negative charge. Dirac's fanciful positron, on the other hand, would be the spitting image of the electron, but it would have a positive charge. But that's not the freaky part. The positron would not be normal matter. It would be something few had ever imagined before: antimatter.  Read more at location 9600

But in 1932, four years after Dirac derived his equation, a twenty-seven-year-old American physicist, Caltech's Carl Anderson, saw a peculiar particle streaking through his cloud chamber.46 That particle fit the predictions made by Dirac's formulae. Dirac's mathematical glitch, the positron, turned out to be real.  Read more at location 9605

there should be an equal amount of matter and antimatter in this universe. But there isn't. There is, in fact, a lot of matter. And there is very little antimatter. So where has all the antimatter gone?  Read more at location 9617

You imagine that the cosmos is a torus.  Read more at location 9622

Gravity is a language, the language that the matter universe on top of the bagel shares with the antimatter universe on the bottom. Gravity is a form of communication, a form of stimulus and response with which the two universes call to each other. Gravity is a common whisper with which they beckon and seduce. And once the two universes run out of the energy that has shot them away from each other, they “sense” each other's call. They slowly begin to fall into each other's arms. They slowly begin to succumb to the pull of each other's gravity.  Read more at location 9644

So how does the universe end? Matter and antimatter meet on the bagel's outer rim. And they annihilate.  Read more at location 9649

Just as the electromagnetic force has two opposite and equal faces—attraction and repulsion—you feel that gravity has to have a repulsive side. And you tell Eshel, for Lord knows what reason, that we are about to discover it. The negative side of gravity. The repulsive side of gravity. A few months later, an announcement comes from the astronomical community. By tracking the redshift of “standard candles,” Type 1a supernovas,52 astronomers have arrived at a strange conclusion. Galaxies are accelerating.  Read more at location 9667

big bagel theory has an explanation for dark energy. What is it? Gravity. The gravitational pull that summons the matter universe on top of the bagel to rush toward the embrace of the antimatter universe on the bagel's bottom. The bagel's hump is crucial in all of this. Once they go over the bagel's hump, says big bagel theory, galaxies on the top of the bagel seem to flee from each other.  Read more at location 9683

And what is dark energy again? It's the gravity of the antimatter universe. The gravity of the matter universe and the antimatter universe rushing toward each other. Rushing toward annihilation in each other's embrace. Annihilation and rebirth.  Read more at location 9693

The bottom line? There are a lot of cyclic universe theories doing the rounds. But the big bagel appears to be alone in something crucial: explaining dark energy.  Read more at location 9738

WILL SILICON AXIOMS FLY? 

Axioms began twenty-three hundred years ago with Aristotle. They started as truths that Aristotle said we could all take for granted. Assumptions Aristotle thought were so basic that none of us could quibble about them. With Euclid, axioms began a journey. A journey that would turn them into the foundation stones on which you could build entire mathematical systems.  Read more at location 9757

Then the non-Euclideans—Karl Friedrich Gauss, János Bólyai, and Nikolai Lobachevsky—made something else clear: if you flip just one axiom, if you change just one of your foundation stones, the structure you extract will be very different.  Read more at location 9765

the non-Euclideans had only flipped one axiom and had kept all the rest. But Mandelbrot and John Conway had invented a new way to extract implications from axioms.  Read more at location 9784

working their way forward from nothing was exactly what Benoît Mandelbrot's fractals, John Conway's Game of Life, and Stephen Wolfram's cellular automata had done.  Read more at location 9802

Mandelbrot, Conway, and Wolfram had come up with far more convincing metaphors for cosmic creativity. They had come up with far more convincing clues to the God Problem—the problem of how a godless cosmos creates.  Read more at location 9807

There's one more test that cellular automata need to pass to prove that they, indeed, isomorph the real world. That they indeed reflect a deep structure of reality. That they capture Ur patterns. Cellular automata need to show that they can predict.68 So, like the work of Einstein in 1905, Stephen Wolfram's work awaits validation.  Read more at location 9812

*************  the history of the axiom demonstrates one simple thing—that the creativity of the cosmos may come from unfolding the implicate properties of simple rules.  Read more at location 9816

****  Aristotle said metaphor was unscientific. Yet at the heart of every scientific breakthrough there is a central metaphor.  Read more at location 9821

Why does metaphor work? Because it captures a primal pattern, an Ur pattern, a pattern showing its swirl, its twitch, its dance, its shape, its strategy.  Read more at location 9822

The swirl we see when we flush the toilet shows up in the swirls of electrons that slow down the flow of electricity in a superconductor.69 The same swirl pops up in the pinwheel spread of a Paenibacillus vortex bacteria colony in a petri dish, in the whorls of your fingertip, in the spiral twist of a nautilus shell, in the spiral of seeds on the face of a sunflower, in the spiral of clouds in a hurricane seen from a satellite, in the permanent twister two Earths in size that makes the Red Spot on Jupiter, in the vortices that make the dark spots on the surface of Neptune,70 and in the spiral arms of galaxies. Understand the spiral in the toilet and you have a key to understanding every other spiral that you see. From the submicroscopic to the unbelievably huge. What's more, you may well have a glimpse deep down into the structures that kicked off this universe. You may well have a specimen of an Ur pattern doing its thing.  Read more at location 9826

CONCLUSION: THE BIG BANG TANGO—QUARKING IN THE SOCIAL COSMOS 

Yes, corollary generator theory leaves you with a truckload of mysteries. If this is a universe that starts with a simple set of rules, a handful of magic beans, a tiny number of axioms, a universe that creates by doing 1043 homework assignments per second, how do corollaries and implications come to be?  Read more at location 9854

(Note: Notice dualistic assumption)  Are simple rules, deep structures, and Ur patterns mere fantasies that we use to simplify things for ourselves? Are they mere artifacts of our minds? Or are they things in the cosmos itself?  Read more at location 9866

Something vital is missing from the 2,350-year-long collective project of science. That missing something is an explanation for the mysteries that George Henry Lewes called emergence. An explanation for the mysteries that Herbert Spencer called progress. An explanation for the mysteries that the Santa Fe Institute folks called complexity.  Read more at location 9881

You've proposed a reversal of Aristotle's primary axiom. You've proposed that A does not equal A. And you've suggested that opposites are joined at the hip. Which means that sometimes A does equal A. Sometimes a frog is just a frog. But only sometimes.  Read more at location 9888

You've proposed a reversal of the basic rule of arithmetic. You've proposed that one plus one does not equal two. You've suggested that one plus one often equals something far, far off the number line. Sometimes one plus one summons an emergent property.  Read more at location 9890

You've proposed a reversal of the second law of thermodynamics, a reversal of the concept of entropy. You've proposed something that seems obvious: the universe is not running down, the universe is running up.  Read more at location 9892

You've proposed that randomness is not as random as it seems. You've proposed that randomness is rigidly constrained. Which, frankly, is just what you'd expect if the cosmos were unfolding from a handful of simple starting rules.  Read more at location 9893

And you've proposed that information theory is wrong. You've argued that the meat of the matter is something that Claude Shannon deliberately left out: meaning. Meaning comes from your place in a big picture. From your place in many big pictures at once. And most important, meaning comes from your place in a web of cosmic gossip. Meaning comes from your place in a cosmos that is profoundly “relational,” profoundly social…and profoundly conversational.  Read more at location 9895

****  Will, compulsion, drive, and unrelenting determination—these are virtues that we say belong only to conscious entities. In the process we've missed one of the most astounding things around us: the hunger of the stuttering forms. And we've made another mistake. We've been certain that we can understand the cosmos based solely on material things. But we've missed the astonishing capacity of immaterial things. We've missed the secular magic of a wave. A thing that is a no thing. An entity that is form and process all at once.  Read more at location 9901

Hegel said that all history is spirit becoming matter. And in a sense he was right. Your identity is a pattern holding sway over a hundred trillion cells that change constantly. Yet your “you” has a coherence, a shape, and a way of going about things that is all its own. Your self is a dance that uses matter to whisk from the invisible and the impossible into the gasses, dusts, and jellies of reality. Your “you” is spirit without the religious connotations. It is the secular equivalent to soul.  Read more at location 9915

We are patterns with ambition. We are big pictures on the prowl. We are spirit-in-action bursting forth in a cosmos devoid of gods, of afterlives, and of immortality. But we are not the first forms that immaterial pattern, spirit-in-action has donned. Immaterial identities also work their sorcery on quarks, quanta, atoms, stars, and galaxies. Recruitment strategies are alive in the search patterns of bacteria and bees.  Read more at location 9920

****  And never forget. Sometimes new questions are more important than new answers.  Read more at location 9930