NOTES · 23 JUNE
On the Nature of Consciousness
An attempt to define, measure and compare consciousness —
through language, lattice graphs, and an energy–complexity correlation
Handwritten notebook · 35 pages · summarized & typeset
Roadmap
How the argument unfolds across the notebook
02
1 · Definition
Consciousness C as a fraction of an object's fathomed complexity, with variable V for what it is about.
2 · Language & Lattice
Objects Oₓ, qualities Qᵧ, statements (Oₓ, Qᵧ) as lattice points of a reference graph.
3 · Measurement
Compare the reference graph with the observer's graph → conscious / schizo-conscious / unconscious parts.
4 · Comparing Minds
Nine scenarios for comparing two observers' consciousness about the same object.
5 · Energy Hypothesis
Subjective experience costs energy; more information ⇒ more energy. A continuum from 0 to saturation.
6 · The Hard Problem
Kolmogorov complexity is uncomputable; IIT's Φ fails. Proposal: energy–complexity correlation as the gauge.
What is Consciousness? (C)
The formal definition proposed in the notes
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C = Fathomed complexity of the object / Total complexity of the object
▸ Consciousness about an object = the fraction of complexity (amount of content / information) fathomed about the object by an observer at a particular moment in time.
▸ Fathomed complexity = the magnitude of content / information correctly labelled after assessment of the object.
▸ The quantity comes with a companion component V that signifies which part of the object's description the consciousness is about.
▸ C and V are dependent on the subjective experience of the person and what that experience is about.
Building a Language & the Lattice Graph
Gauging an observer's subjective experience at a point in time
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▸ Start by creating a language — words that describe things which can possibly become part of a subjective experience.
▸ Assign names to objects: O₁, O₂, O₃, … Oₙ
▸ Assign names to qualities that objects can possess: Q₁, Q₂, Q₃, … Qₘ
▸ A fact / statement “object Oₓ possesses quality Qᵧ” is written as the pair (Oₓ, Qᵧ).
▸ Place the Oₓ's on the x-axis and the Qᵧ's on the y-axis → every statement is a lattice point.
▸ The lattice points represent all statements that can be made using this language.
▸ The graph now acts as a way to gauge the consciousness of an observer about an object or a group of objects.
Lattice points = statements (Oₓ, Qᵧ)
The Gauge: Reference vs. Observer Graph
Conscious, schizo-conscious and unconscious parts
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▸ Reference graph: every statement labelled TRUE or FALSE as it actually is.
▸ Observer graph: the state of subjective experience of the observer about the object (has dotted what it actually is).
✔ CONSCIOUS part
Statements labelled correctly by the observer — the genuine content of his subjective experience.
✖ SCHIZO-CONSCIOUS part
Statements labelled incorrectly — asserted in experience but false of the object.
○ UNCONSCIOUS part
Statements not labelled at all — there was no subjective experience for them.
The paper = the state of consciousness of an object, as had by an observer. It also lets us compare states of consciousness of two different observers.
The Paper Method
An operational way to measure consciousness
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▸ After creating the reference & observer graphs, define objects using the set of statements that are TRUE about the object — what counts as an object can be chosen as desired.
▸ To measure consciousness of an observer about an object: write the true statements about it on a sheet of paper, and ask the observer to plot his subjective experience about the object.
▸ Use GREEN to mark statements predicted correctly, and RED to mark the ones labelled incorrectly.
▸ The green circle = the part labelled correctly; the red circle = the incorrect one. The two circles do not intersect.
▸ The sheet of paper now represents the state of consciousness of the object regarding the concerned observer.
▸ Schizo-consciousness and unconsciousness can be defined on the same paper (red region & remaining area respectively).
Comparing Two Observers — 9 Scenarios
Possible configurations while comparing observers I and II
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1 · Nested (I ⊂ II)
II is conscious of all I is, and more. I has clearly less consciousness; readable directly off the paper.
2 · Intersecting
Green circles intersect → observers share some consciousness about different parts of the same object.
3–6 · Touching / disjoint
Partial overlaps of correct & incorrect regions; circles may touch or lie apart in various ways.
7 · Opposite labeling
What I labels correctly, II mislabels and vice versa — crossed conscious/schizo regions.
8 · Separate clusters
Both observers' regions fully disjoint — no shared content about the object.
9 · Split regions
Each observer's experience scattered across several disjoint parts of the lattice.
More scenarios can be imagined — these are just for explaining purposes.
Reading the Scenarios
What the comparison actually tells us
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Scenario 1 — strict ordering
Observer I has clearly less consciousness than II, since II is conscious of all that I is conscious of — and more.
Here one can tell that II has more consciousness than I just by looking at the paper about the object.
Scenario 2 — intersection
The two green circles intersect → the observers share some consciousness about different parts of the same object.
Note: “more consciousness” means little here — although one can compare the magnitude of consciousness and its direction (which parts of the object the observers are conscious about).
Scenarios 2 & 3 are examples of cases where one can compare the amount of content / information / complexity and see which observer has a higher or lower amount of it.
Example: The Red Apple
Comparing amount of content fathomed (a crude illustration)
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Person A
Has consciousness about a “red apple” only.
Person B
Has consciousness about a green one, an orange, a strawberry & many other fruits.
It makes sense to say that the amount of content / magnitude of consciousness / information or complexity fathomed is HIGHER for the second person (who knows the rest but not the red apple) than the first (who knows only the red apple) — increasing just the outward appearance of the fruits as the description of them.
The Energy–Complexity Hypothesis
A crucial assumption behind the metric
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▸ Imagine an observer has a moment of subjective experience; some time later he has the same exact moment again — but some of it wasn't there the second time (someone sees a scenery; later a part of it isn't there).
▸ One thing inferred: the production of subjective experience must have required expenditure of usable energy, stored in the observer's neural networks (in humans: ATP, NADPH, GTP, etc.).
▸ When a subjective experience of a lower amount of information was induced, the energy expenditure related to it must have been lower also.
▸ It seems intuitively right to say that when the same neural network produces a subjective experience by ADDING something (instead of removing) to the prior experience, the energy expenditure must have increased.
▸ The information here: adding or removing parts to / from the same subjective experience produced by the same neural network → the neural network does not undergo any change in its defining parameters over this period.
▸ Any change in its defining parameters over this time period of adding & removing parts of subjective experience (or called the next moments of subjective experience) increases & decreases the energy expenditure — with increase & decrease in information in the subjective experience.
The Continuum of Subjective Experience
Mapping experience complexity to energy levels
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Ascending order of subjective experience (in terms of complexity) ⟶ increasing order of energy levels
▸ Method: take a specific subjective experience, induce it in a neural network (biological, not artificial), measure the corresponding energy expenditure; add cuts to it and add things to get less & more complex subjective experiences than it.
▸ Doing this gives an assessment of a continuum that will have subjective experiences of differing complexities, arranged in ascending order from 0 to higher numbers.
▸ 0 = the state where the whole of the subjective experience was subtracted (no subjective experience).
▸ The mapping holds for the neural network whose parameters remained the same throughout the process.
▸ While making up the subjective experiences, make sure you add or subtract only to the subjective experience we started with.
Terminology
Definitions used in the framework
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1 · Events
Any part of a description of any moment on the timeline.
2 · Event of Subjective Experience
Happens on the moment of arousal of subjective experience.
3 · Processing
The series of events that lead to the moment of subjective experience arousal after “stimulus”.
4 · Stimulus
The events that lead to the electrical activity on neuronal networks — which are a result of events other than neuronal electrical activity — and are the start of processing.
What Counts as a Single Neural Network?
A neural network = sensory ends + processing area + motor area
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▸ The neural networks in organisms (that have subjective experience) & artificial ones have this key difference: the results of processing are present as neural activity itself in biological systems — but in AI we use man-made symbols at the ends of the processing units to show outputs.
▸ If the same subjective experience was seen upon a particular neural activity at a certain point in time, but the neural activity was different later — yet parameters didn't change — then either the sensory inputs differed, or the networks are different (their sensory-to-experience processing units are connected differently).
▸ Enumerating the statements made about the neural networks here — the properties on the next slide.
Properties of a Neural Network (1–4)
Enumerated statements from the notes
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1 · Sensory end
A single neural network has a sensory end where neurons pick up stimuli. (We are only talking about subjective experience produced by stimuli from the environment — no self-stimulation like imaginations & dreams, although they have elements explainable in this framework.)
2 · Unique correspondence
Every subjective experience has only one corresponding pattern of activity of neurons.
3 · Parameters define the network
Change of parameters defining the neural network changes the network — one set of parameters corresponds to one neural network.
4 · One activity, two experiences
If one finds two different subjective experiences resulting from the same electrical activity, the electrical activity is not thoroughly assessed.
Properties of a Neural Network (5–8)
Enumerated statements from the notes
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5 · Efficiency
One might find two different neural activities resulting in the same subjective experience among different neural networks. It just means one is more efficient for that experience — it requires less energy.
6 · Convolution
If seen within the same neural network, the network is seen as a convolution of two different neural networks.
7 · Networks guide activity
Neural activity results in subjective experience; neural networks only guide the activity. If the activity is produced to be the same after eliminating them, the subjective experience should be there. (Activity is produced by electric potential spread over the networks.)
8 · Energy–time–complexity
ΔE · Δt ≥ ℏ/2 and the uncomputability of Kolmogorov complexity. As the energy–time uncertainty principle says: if a system exists longer, the certainty of its energy value increases. Since subjective experience is a result of spread of electric potential energy over neural networks, the certainty of what experience a person is having also increases with the time of existence of that excited state.
Some Principles
Working assumptions of the model
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▸ The neurons defined by how they guide the neural electrical activity aren't necessary for production of subjective experience — they only guide the electrical activity; subjective experience is a result of electrical activity.
▸ If one produces electrical activity in a region that is akin to the case when neurons are there but produces the activity without them, it will still result in the same subjective experience.
▸ A rise & change of electrical potential at any point results in arousal & change in subjective experience — though we are not saying this is the only way in which it can exist & happen; there is still a possibility that subjective experience is not a direct result of electrical potential but is just a way of attenuation that results in subjective experience, & its evolution is thus guided by it.
▸ The nervous system can be said to be a referer (referrer) of possible subjective experiences that can be generated by it — that means, if one maps out the defining parameters (those that guide the electrical activity) of a neural network, one can find all the possible states of subjective experience it can produce, each of which has a correspondence (one, or possibly more) in the states of electrical activity produced by the neural network as a result of the stimuli & how it affected the neuronal signals.
▸ The corresponding electrical activities produced by the neural networks might be one or more (possibly) — the principle is that the energy expended by the neural network to produce a specific subjective experience might have a single value or possibly more, but here we are taking as principle that there will be a lower bound on those energy levels even in that case, for the specific subjective experience's production.
Artificial vs. Natural Neural Networks
The key difference
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Artificial Neural Network
A network in which the processing of the inputs results in the output present at the end of the neural network. Such a network can give outputs only in those discrete outputs; if one wants a part of an output that is already there as a possible output, they need to add the output as a possibility to the end of processing in the neural network.
That is, produce a new output by changing the neural network — just by changing the stimuli & not tweaking the defining parameters of the neural network.
Natural Neural Network
Gives the output in the form of subjective experience:
“If a natural neural network can produce a subjective experience, the ‘portions’ of it can also be produced by it in the same way.”
Portions: parts of a well-defined subjective experience — can include a part of the description, the whole description, or none of it, of the subjective experience.
The outputs (portions that are possible) of natural neural networks might be discrete or not — that seems to need experimentation / contemplation (not necessarily true).
The Measurement Problem of Complexity
Why consciousness is so hard to measure
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▸ Consciousness & the measurement problem of complexity (amount of information): on the reason behind why giving a metric for consciousness so as to have a meaningful measure of it is hard, or has failures?!
▸ One thing that can be said is that a measure of consciousness is dependent on the “complexity of subjective experience” — but complexity itself is subject to fundamental facts such as the incomputability of Kolmogorov complexity.
▸ While we do have efficient methods of representing subjective experience (shared languages such as binary or English), they might not act as efficient ways of gauging complexity.
▸ When one tries to measure complexity as how much resource was used from these languages for representing it, the question seems to lack an objective & concrete answer.
In this model we are treating complexity as a thing to be measured, not something dependent on some modifiable axioms — the languages used to represent it are the gauge used for what the subjective experience is, and that is done by linearity or English pretty well; but what about giving a measure of complexity of subjective experience?
A Look at Integrated Information Theory
For intuition — and where Φ falls short
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▸ IIT talks about Φ — the number of possibilities a state of a neural network could have originated from, and the number of possibilities it can result into in the future.
▸ The quantity Φ that represents consciousness is dependent — but the problem in this is that a person who wants to find Φ will note that changing the mechanism (that is, changing the system) such that the possibilities that a state can originate from / the possibilities it can result into end up changing, will result in a change in the value of Φ for the same subjective experience.
▸ And also, it should be possible to know the amount of consciousness just by knowing the subjective experience that is aroused, or the state of the neural network (this seems like a testable principle, because in the end consciousness is a result of the subjective experience).
The principle we are following here is that if one knows or can derive the state of what an observer's subjective experience is, he or she should also be able to find the measure of amount of consciousness. The method to calculate it should need only the description of the subjective experience — such that having it should be enough, in any case in which one knows it is there.
The Proposed Way Forward
The energy–complexity correlation
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“The principle is that energy & complexity are correlated such that energy expended by the neural network in producing a subjective experience & complexity of subjective experience increase with each other.”
▸ The languages like binary, English or programming languages can act as efficient ways of representing subjective experience — and as the gauge of its description.
▸ What we are going to do here is to base the method of complexity calculation on a principle that seems to attribute the measure quite meaningfully.
▸ But before that — let's have a look at a scenario to build some intuition… (the notebook ends here).
SUMMARY IN ONE SLIDE
Consciousness, as sketched in these notes
▸ C = fathomed complexity / total complexity of the object, with V telling what it is about.
▸ A language of objects & qualities gives a lattice graph; comparing it with an observer's graph splits experience into conscious / schizo-conscious / unconscious.
▸ Nine scenarios allow comparison of two observers — magnitude and direction of consciousness.
▸ Subjective experience costs energy; complexity of experience tracks energy expended — a continuum from 0 (no experience) to saturation, for a fixed neural network.
▸ Networks guide but don't constitute experience; parameters define a network; energy–time uncertainty links duration of a state to certainty of the experience.
▸ Against Kolmogorov incomputability and IIT's Φ, the notes propose measuring complexity directly, anchored in the energy–complexity correlation.
Source: “On the Nature of Consciousness” — handwritten notes, 23 June (35 pp.)