Mark Ward

BEYOND CHAOS

The Underlying Theory Behind Life, the Universe, and Everything

Thomas Dunne Books 2001

pg 97

Keywords: Cellular Automata - Universality - at critical points and phase transitions the properties of the parts of the system stop mattering. Instead it is the interactions and organisation that matter -

John Horton Conway - Game of Life - one-dimensional cellular automata (1-D CA) - Stephan Wolfram - Chris Langton - Alife - creating synthetic organisms - cellular automata as toy universes into which they unleash a variety of software creatures to relive and retrace evolution - Fractal patterns - phase transition - critical point - Universality - "edge of chaos" - at the critical junctures complex structures emerge and persist. Persistence, staying alive, demands the ability to process information about your surroundings and use it - dynamics of information - order and structure - organisational principle of all living things

pg 97

Cellular Automata

Strong evidence for what kind of chemistry was present at the birth of life may be missing but the evidence that Universality was there is easy to find. Using simple models many scientists have found persuasive evidence which suggests that Universality is built into living organisms as their, and our, defining dynamic. One of the abiding lessons of Universality is that it can be studied using simple models. At critical points and phase transitions the properties of the parts of the system stop mattering. Instead it is the interactions and organisation that matter.

Since the 1970s scientists have been using simplified models of the world called cellular automata to tackle a huge variety of research problems.

The field of cellular automata was kicked off by John von Neumann, who in the late 1940s drew up specifications for a machine that could reproduce. The elements of the machine would be the square boxes of a grid. Each box could be in one of several states. With the right rules von Neumann believed that he could create an artificial organism that could reproduce.

Von Neumann's creature was fiendishly complex. It occupied around 200 000 squares of the virtual grid and each cell could be in one of twenty-nine states. Not surprisingly it was a while before anyone took up the idea. However, in 1971 Cambridge mathematician John Horton Conway revisited the idea, tinkered with the rules, simplified it and created a new version that he initially played with squared paper and seashells. He called it the Game of Life but it only really took off when it was turned into a software.

The Game of Life is played out on an infinite grid. The selves of the grid exist in two states: alive or dead. Time advances in steps in the toy universe and the fate of every cell at each step is decided by the living or dead cells surrounding it. If three of the eight cells abutting an empty cell are filled then in the next time step that dead cell comes to life. If you cell has two neighbours it stays alive at the next time step. If it has less than two or more than three neighbours it dies.

But the Game of Life is not the only game in town. Since Conway came up with the idea other researchers have come up with versions called one-dimensional cellular automata (1-D CA), that have simpler rules and proceed line by line rather than up and down a grid.

Stephan Wolfram has been one of the pioneering cosmologists of these one-dimensional universes. Wolfram chose these simpler CAs because they make it possible to grasp with a glance just what kind of pattern is emerging. They also have fewer rules (256 in fact), which makes the mathematics easier. He has found that the patterns of the simple CAs, and by implication all CAs, produce fall into one of four categories.

Class 1 patterns go nowhere: they either disappear quickly or settle into a fixed state.

Class 2 patterns grow to a fixed size and then repeat forever.

Class 3 patterns yield chaotic patterns that look similar but never repeat.

Class 4 patterns produce complex patterns that grow and contract regularly.

Wolfram's work has been taken on an extended by Chris Langton, the pioneer of the field of Alife. As its name suggests artificial life is all about creating synthetic organisms. Unlike artificial intelligence research that begins with the brain and works down, artificial life begins with the boots and pushes up. They use cellular automata as toy universes into which they unleash a variety of software creatures to relive and retrace evolution.

Langton found that there was a fine line between the patterns that never changed or dwindled into nothing and those that bloomed into unpredictable chaos. Between disorder and boredom was a "sweet spot" where the most complex patterns emerged. In this region patterns propagated, extended over long distances before being superseded. Patterns bloomed, died and popped up again. Fractal patterns, a phase transition, the critical point. Universality.

Rather grandly Langton christened this point the "edge of chaos". The cusp between death and disaster. He found a small region in which the dynamics of organisation and information dominated. His work suggests the possibility that information dynamics which gave rise to life came into existence when global or local conditions brought some medium - perhaps water, perhaps some other material - through a critical phase transition.

Langton speculates that this is the niche that all living organisms occupy. At the critical junctures complex structures emerge and persist. Persistence, staying alive, demands the ability to process information about your surroundings and use it. Langton believes that this makes the critical region are good candidate for the place that life got going.

Langton suggests that at this point, the edge of chaos for want of a better term, the ability of the system to use and process information improves dramatically. Information in this sense means the ability of the different cells to influence each other and how well this is passed on or correlated.

The ferromagnet at the critical point is permanently uncertain. The clouds of magnetism that form and flutter along it and within it are formed when the microscopic magnets are "persuaded" to reverse their polarity by neighbouring units or thermal noise. This choosing - the flipping polarities in the magnet and alive or dead cells in the cellular automata - is what Langton means by a dynamics of information coming to dominate.

In essence the units make a decision about what they want to do based on the past behaviour of the other elements in the system. Order is preserved, propagated and acted upon. At this point then exists a tense struggle between the storage of information and its transmission. The cells in the CA struggle to stay alive (storage) but could easily be killed off by changes anywhere in the CA universe (transmission).

At the critical point order and structure are all-important. Physical properties cease to matter. It is this Langton suspects that gave rise to living organisms and, once and running, flying or swimming, is the dynamics they used to keep going. He, and many others in the Alife movement, think that this is more than just an analogy.

They see it as the defining organisational principle of all living things. They believe that organisms are riddled with critical points and the cause of this information, genetic or structural, is the key measure of life. Changes rippling through the system, which represent information, helpe the organism keep itself going. They are the motor of evolution and reveal how it is adapting to its environment. What is important about life is what did does, the process, not what it is made of.

 

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