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Kindle Notes & Highlights
by
Iwona Abrams
Read between
February 10 - February 15, 2022
Complex systems, in general, exhibit a property that mathematicians call attractors. Attractors represent the states to which the system eventually settles, depending on the properties of the system.
The cultural equivalent of attractors would be chiefs, tribes, states and what gives us identity, like religion, class and worldviews.
“chaotic” or “strange attractors”.
The strange attractors live in a mathematical construct known as phase space.
phase space represents the state of an object in a multi-dimensional plane.
What is strange about strange attractors? First: they look strange. A multi-dimensional imaginary object is bound to look strange. Second: the motion on the strange attractors has sensitive dependence on initial conditions. Third: strange attractors reconcile contradictory effects: (a) they are attractors, which means that nearby trajectories converge on them; and (b) they exhibit sensitive dependence on initial conditions, which means that trajectories initially close together on the attractors diverge rapidly. Fourth: and this is the tricky bit – while strange attractors exist in an infinite
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Lorenz is also associated with the idea of “the Butterfly effect”.
The equations of fluid flow are, in fact, mostly impossible to solve. They are nonlinear partial differential equations.
His work confirmed the idea that biological systems are governed by nonlinear mechanisms.
The machine is running down, and time can only run one way. You cannot make up for entropy – the universe faces heat death. Prigogine argued that time could only appear with randomness.
Irreversible processes are in fact the source of order
Order out of Chaos (1984).
"Order ab chaos!" Masonic motto
Prigogine: “Far-from-equilibrium studies led me to the conviction that irreversibility has a constructive role. It ma...
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Irreversible time is not an anomaly, but relates to reversible time. This is not an either/or situation. Reversibility applies in closed systems only. Irrevers...
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Prigogine defined self-organization as the phenomenon by which a system self-organizes its internal structure independent of external causes. Such self-organizing systems also exhibit other properties of chaos – non-linearity, feedback, fractal structures and sensitive dependence.
Self-organizing systems have three main features. 1. They are open and part of their environment, and yet they can attain a structure and maintain it in far-from-equilibrium conditions.
These systems also run contrary to the Second Law of thermodynamics which states that they should move towards molecular disorder, and not order.
2. The flow of energy in these systems allows them spontaneously to self-organize – creating and maintaining a structure in far-from-equilibrium conditions. Such systems also create novel structures and new modes of behaviour. Self-organized systems are thus said to be “creative”.
3. Self-organized systems are complex in two ways. First, their parts are so numerous that there is no way in which a causal relationship between them can be established. Second, their componen...
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Tien Yien Li and James Yorke, two mathematicians working at the University of Maryland, are credited with coining the term “chaos”. The term was first introduced in their much-quoted paper, published in 1975,
Any system that repeated itself in a period three oscillation would produce chaos. It cannot exist without it.
the overriding message of the theory is that simple processes in nature can produce edifices of complexity without real randomness.
The nonlinear dynamic systems studied by chaos theory are complex systems
These complex systems have the ability to balance order and chaos. This balance point – called the edge of chaos – where the system is in a kind of suspended animation between stability and total dissolution into turbulence, has many special properties.
The process of self-organization happens spontaneously – as though by magic! Think of a flock of birds taking off to fly to their place of migration.
Complex systems also highlight the inter-relatedness of things.
What is the difference between complexity and chaos theory? Complexity is concerned with how things happen, whereas chaos tends to observe and study unstable and aperiodic behaviour.
Chaos seeks to understand the underlying dynamics of a complex system. Complexity grapples with really big questions.
Science journalist Roger Lewin says that “as the theory of life at the edge of chaos, complexity includes the entire spectrum, from embryological development, evolution, the dynamics of ecosystems, complex societies, right up to Gaia – it’s a theory of everything.”
New variables occur over time and do not require an outside force in order to “be”. This is not a problem for physicists, but is more of a problem for biologists, because it appears to contradict Darwinian ideas.
And all living systems, and most physical systems, are complex systems.
“Together, chaos and complexity spell chaotics.”
stability in a three-body planetary system requires two essential conditions. The first involves resonance.
For three planets to be in stable orbits, it is necessary that their resonances are not in simple ratios like 1:2 or 2:3. In order to remain stable, the planets must be quasi-periodic – that is, the periods never exactly repeat themselves.
The second condition of stability involves gravitation.
Quantum physics is a theory of the microcosm which applies only to the atomic world.
For an imaginary body, known as a black body, the graph of radiation intensity versus frequency has a very well-known curve.
Spectral lines appear when the light from heated hydrogen is passed through a spectroscope.
This is where quantum theory now stands: probability waves in stationary humps.
Quantum theory works in the atomic world: particles are restricted to energy levels. The lowest level is the ground level in which the system usually exists. They leave these levels when a light is shone on them (or in particle terms, when they are hit by photons), jumping to higher energy levels or excited states.
atoms with electrons in states of extreme high energy and near to the transition between quantum and classical physics
Chaos and Economics
The world has been linked into a single global market ruled by instantaneous transfer of capital by electronic signals. Small changes can quickly multiply in the global electronic market and lead to serious perturbations.
Technological innovations proliferate rapidly, making nonsense of conventional ideas of a solid lead over competition.
chaos and complexity – or chaotics – provide us with a better understanding of what is happening than conventional economic theories. Indeed, chaos and complexity turn standard economics theories upside down – and also open up optimistic perspectives on wealth creation.
Negative feedback in economic terms is analogous to diminishing returns; positive feedback to increasing returns.
positive feedback makes the economy function as a nonlinear system. Positive feedback drives up sales once a threshold in economy has been reached and the market has been driven to a threshold of education and promotion. As more people adopt a specific technology, the more it improves and the more attractive it looks to the designers/adopters and to would-be manufacturers and sellers.
Sensitivity to initial conditions can also mean life and death for a product.
More companies are now working under increasing returns, and this situation has led to a de facto monopoly.
“driving using the rear-view mirror” – trying to judge the road ahead by what goes on behind.
