https://sites.google.com/site/matteorichiardi/teaching/complexity-economics

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Matteo Richiardi

Complexity Economics

University of Turin

February-April 2024

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Lecture 2:�What is Complexity�Features

Matteo Richiardi

Complexity Economics

University of Turin

February-April 2024

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Sources:

• Bookstaber, ch. 4
• Mitchell, ch. 7
• Miller & Page, ch. 4

Common properties of complex systems

• Simple components (w.r.t. the whole system)
• Nonlinear interactions among components
• No central control
• Networks
• Emergent behaviour (hierarchies)
• Signalling and information processing
• Adaptation / evolution
• Heuristics
• Non-ergodicity
• Radical uncertainty / Reflexivity

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Emergence

• The properties of the system cannot be easily understood from an understanding of the individual components.
• Collective outcomes, which need to be understood at the system level (e.g. ‘wetness’ from water).
• Hierarchical organisations: How do these hierarchies emerge in the first place? How do different levels interact?
• Information processing: The system as a whole gain information from the environment, and processes it.
• Evolution and adaptation learning

Hierarchical laws

• Each hierarchical level is typically governed by its own set of laws.
• The laws of a higher level (emergent properties) must not violate the laws of lower levels, and must be consistent with interactions specified at the lower levels.
• Often these laws refer to scaling (self-similarity).
• Self-similarity means that a smaller part of an object or a pattern resembles the whole thing (e.g. branches, snowflakes, broccoli)

Core disciplines

• Dynamical systems: the study of continually changing structure and behavior of systems.
• Information theory: the study of representation, symbols, and communication.
• Computation: the study of how systems process information and act on the results.
• Evolution: the study of how systems adapt to environments that change over time.

🡪 independent research areas, brought together in the science of complexity.

Major goal 1: Cross-disciplinary insights

• Development of mathematical and computational tools that lead to cross-disciplinary insights.
• For example, by studying the behavior of ant colonies as an instance of information processing, we can ask how similar or different that information processing is to that done in a city.
• Or, to what extent is the flow of information in a brain network similar to that in an economic network.
• These cross-disciplinary insights are, to date, the greatest success of complex systems science.

Major goal 2: General theorising

• Development of a general theory of complexity, that unites the previously disparate disciplines that make up complex systems research.
• Controversial: many people don't think it's realistic, or even possible; but it remains a holy grail for some.

Methods

Analysis of complex systems almost always turns on finding patterns in th e system’s ever changing configurations:

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• Experiments / empirical work
• Theoretical work
• (increasingly) what's coming to be known as the third scientific methodology: Computer simulation.

Definitions of Complexity

• “Complexity" (like life and consciousness) is hard to define.
• Seth Lloyd's paper: 42 different definitions or ways of measuring complexity

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• Different types and levels of complexity

Source: Beinhocker (2013)

Complexity as…

• Entropy (surprise)
• Algorithmic Information Content (shortest computer program)
• Logical Depth
• Thermodynamic Depth
• Computational Capacity
• Statistical complexity
• Fractal Dimension
• Degree of Hierarchy

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Weaver (1948)

• Problems of Simplicity: only a few variables 🡪 19^th and early 20^th century physics, chemistry, biology, etc.
• pressure and temperature in thermodynamics
• Relationship between current, resistance, and voltage in electricity
• Population growth
• Problems of Disorganized Complexity: many variables, but with little interaction 🡪 Statistical physics (averages)
• temperature and pressure as arising from trillions of disorganized air molecules in a room or in the atmosphere.
• Problems of Organized Complexity: moderate to large number of interacting variables.

Weaver’s prescience

• “These problems... are just too complicated to yield to the old 19th century techniques, which were so dramatically successful on two-, three-, or four-variable problems of simplicity. These new problems, moreover, cannot be handled with the statistical techniques so effective in describing average behavior in problems of disorganized complexity.”
• “These new problems – and the future of the world depends on many of them – require science to make a third great advance, an advance that must be even greater than the 19th-century conquest of problems of simplicity or the 20th-century victory over problems of disorganized complexity. Science must, over the next 50 years, learn to deal with these problems of organized complexity.”

Complexity: a working definition

• A complex system is a system in which large networks of components with no central control and simple rules of operation give rise to nontrivial emergent and self-organizing (collective) behavior, sophisticated information processing, and adaptation via learning or evolution.

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How can complexity be measured?

🡪 Many different measures of complexity have been proposed; however, none has been universally accepted by scientists.

Non-linear dynamics

• Dynamics is the general study of how systems change over time.
• Planetary dynamics studies the movement of planets under the force of gravity and characterizes their orbits, deviations from their orbits, eclipses and so on.
• Fluid dynamics studies flow of fluids and includes things like study of ocean flows, hurricanes, gas clouds in space and turbulent air flow.
• Electrical dynamics studies the flow of electricity in circuits.
• Climate dynamics looks at how climate changes over time in terms of temperature, pressure and so on.
• Crowd dynamics look at how crowds of people act and move, either in an ordered way or in a disordered way (e.g. stampede).
• Population dynamics looks at how populations vary over time.
• Financial dynamics looks at phenomena related to stock prices or other financial activity.
• Group dynamics looks at how groups of animals or humans form and how they work together to accomplish tasks.
• Social dynamics study the dynamics of conflicts and cooperation.

includes many sub-branches including calculus, differential equations, iterated maps