Le Confident

Ideas tête-à-tête

Game of Life – Universal Computer

This is something I want to briefly talk about, because it comes along with endless speculative possibilities and is unknown to laymen (and women – the google doodle informed me!)

The game of life is a mathematical model, designed in 1970 by British mathematician John Conway. It’s basically a plane with white and black spots on it. Depending on the relative location of these spots, black spots can turn white and vice versa until some final state of equilibrium is reached.
It is governed by 4 simple rules: a black spot with two or three black neighbours stays, a black spot with more than three vanishes, and one with less then two also. Lastly, a white cell with three black neighbours becomes black.
Conway himself used the metaphor of life for this, black cells being alive, the reasons for their change in existence being over- or underpopulation and reproduction.

The model has been studied intensively, because it behaves like complex (and maybe chaotic) systems do. Now this alone is a very interesting fact, as it shows the possiblity to model in quite a clear way very complicated dynamics, like natural geometry, human society, economics and so on. But in 2000, Paul Rendell designed a distribution of black points that could only adhering to the mentioned four rules, actually calculate simple things like smaller prime numbers. In 2010 he finished off his design as what is called a universal computer or universal turing machine, that is a computer that could run any problem you might give him, under the condition of sufficient memory. How is this possible?

Let me give you the links to an youtube video showing the esthetical side of this, as well as one of Conway talking about his model. I’ll also add a site which explains the basic concepts and recommend also Melanie Mitchell’s online course about complex systems, which I talked about earlier.

But let’s think together for a second. This is something to go crazy about, like Max Cohen did in Pi – and it has nothing to do with numbers! You want a system, that can decide logical expressions. For this you need operators and names. It shows that you need only the basic operators to do this, and some authors have reduced the number of essential operators to two: or – not. Okay, so language provides those, and evidently our brain does. But once you have this processing mechanism, you can do your thinking with any kind of descriptions. So we can use words, or numbers, or colored stones, or – whole networks of things?
Of course we could use relations between phenomena around us as new metaphors for the logical operations we want to carry out. But that would be unnecessarily complicated. This is not what happens here.
What Paul Rendell did, was to invent both the processing unit, the brain, and the essential set of logical operators. In this case, the brain is a configuration of black dots, that is stable according to the four rules of the Game of Life and the logical operators are controlled variations of this stable state. So you would code a primenumber, say, as an initial distribution of black and white dots, that would result in a string of black dots being sent left, let’s say, where there is a structure that will result in a final state, that you the programmer will understand as “prime”. Now this is a switch. You need to add a certain number of those in order to make a processor, that can actually calculate more useful things. But I have always found it fascinating, that you do not need physical objects for this. It can be some model from the scientific world like the Game of Life, or a real game like Minecraft. But this in turn means, that information processors or intelligences, really can exist on any level of virtuality – a computer, within a computer, within a computer… Now we have to go the final measure: the Game of Life is an accurate model of complex systems: it behaves like them, it develops like them, it looks like them. This would mean, that intelligence can actually exist as a quality of this system.
I used to get very excited about this. And since I’ve been studying physics online it even struck me as something utterly unreal, because it has as a consequence something that is known as Maxwell’s demon, that is an intelligence that could violate the laws of physics, by not doing any physical work. I didn’t know until very recently, that this problem has been solved before the dawn of the digital age and really with it: Leo Szillard proposed in 1929, that the work an intelligence does should be equated with chemical work and this is something on which nowadays everything is founded: information is counted in bits, elementary decisions, and these necessitate work and cost energy like everything else in the physical system. But then again… a chemical system or physical system can lose heat by radiation. Do complex system like human societies radiate informational energy? Food for thought.

Here the material:

Introduction Game of Life at Cornell



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