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Conway’s Game of Life and Tegmark’s Mathematical Universe Hypothesis

New Era of Philosophy

The Game of Life, devised by British mathematician J. H. Conway, is familiar to many people. It represents some sort of universe governed by very simple rules. First of all, it is a grid with cells each of which could be either live or dead. And there are four rules to manage states of the cells:

  1. Under-population: if the live cell have fewer than two living neighbors, it becomes dead
  2. Stability: any live cell with 2 or 3 living neighbors, remains live.
  3. Overcrowding: live cell with more than 3 neighbors dies
  4. Reproduction: any dead cell which has exactly 3 living neighbors, become alive.

And that’s it. Amazingly, this decent set of trivial rules can lead to much more complicated patterns, like glider guns, which can be seen here, for example:

http://www.youtube.com/watch?v=pvUiA-Q-3hM

And even something more awesome:

http://www.youtube.com/watch?v=f2dETmyeiK0

Also, exploring this unusual universe, we can deduce some rules which are observed, but were not specified initially (we had only 4 rules, remember?).
Stephen Hawking and Leonard Mlodinow in their brilliant book “The Grand Design” mention the following rules — “blocks never moves”, “gliders move diagonally” and consequences of colliding of these objects. Neither objects themselves (blocks, gliders, etc) nor the concepts of their interaction (moving, colliding, whatever) are present in the initial design of the Game.

It actually tempts us to speculate about the possible nature of our own Universe — what if all the intricacies of the real world that we can observe with all that quantum weirdness and all other “wibbly-wobbly timey-whimey stuff”(c)BBC, are just twisted corollaries of the similar set of the trivial rules?

It could be so, why not? Contemplating such possibility nowadays leads us into the fields of sheer speculation and philosophy, and some people would call it a waste of time. But at least these speculations could partially satisfy our intrinsic human curiosity which obviously is a strong force. Throughout our history this kind of curiosity gave birth to religions, philosophical concepts, and, to my mind, it brings sort of a soul (in metaphorical sense) to science, making it inspire and fascinate people.

So, being okay with “useless” speculations, let’s imagine a huge Game of Life grid — billions of billions of trillions of squares. Or even more. Let’s imagine that some sort of biological evolution started in this grid and it led to self-aware objects who are speculating about nature of their own existence. Let one of them be called John. Let’s suppose that all this grid is stored and processed in some supercomputer in our Universe. And the engineers make a strict backup copy of the whole grid and restore it inside the other supercomputer and run it.

The 2 universes are identical, so, can we conclude that there are 2 separate Johns out there? The answer seems to be obvious — yes, there are. But let’s move on. If we switch both supercomputers off forever will it kill John and the other inhabitants of this simulated universe? Ok, let’s imagine we switch the power off. But all the states of the grid are anyway potentially computable. They all (including future ones) exists from the very beginning, as a mathematical structure, and computer simulation is just a way for us to see these states. And the question is — Does mere existence of this mathematical structure in the space of all possible mathematical structures make our John to be alive and self-aware? Or do we need to switch on the simulation to bring John to life? But, as I have already mentioned, this simulation is only for us to observe this Game of Life universe, so does it really matter for John whether we can observe him or not?

This leads us to something similar to the Mathematical Universe Hypothesis in which its author, Swedish-American cosmologist Max Tegmark, supposes that our own Universe is a consistent mathematical structure which is complex enough to contain self-aware entities evolved through time (which is, also a compound element of the structure itself). His main assumption is that all possible mathematical structures with self-aware inhabitants seem to be real from the inhabitants’ point of view, and our Universe is just one of them.

Actually, it implies 2 additional assumptions:

  1. Our consciousness is computable in principle.
  2. Mathematical regularities observed in our Universe do not cease at any level of our reality.

First assumption is disputable — for example, English mathematical physicist Sir Roger Penrose would disagree with that.

The second one is also tricky and thought-provoking. Actually, this is a debate about the nature of mathematics itself — is it something intrinsic of our reality or it is just a human adaptation, and for example species from remote star cluster would devise some fundamentally different sort of “mathematics” which could be more advanced than ours.

Also it brings some thoughts about complexity or our Universe — atoms and electrons are not simple balls of something just because other way our universe would be so simple that self-aware structures would not basically emerge. Complex structures require complex elements. But, as we have seen with analogy of Game of Life, these complex elements could just be the twisted combinations of very simple things like cells governed by four trivial rules.

These questions are interesting and not so obvious to have immediate and consistent answers, and this is brilliant side of them.

“Philosophy is dead” — the book “The Grand Design”, mentioned earlier, contains this provocative statement on the very first page. It is quite true for “usual” philosophy, which is all based on the knowledge that humanity had before exploring weirdness and possible consequences of quantum mechanics or understanding evolutionary roots of our own behaviour and way of thinking.

But innate desire to think about Big Questions is so strong with many of us, that obviously, new era of philosophy can emerge. I believe that things which were explored in this post is this kind of philosophy, in which the modern and relevant concepts are taken into account.

Useful links:

http://en.wikipedia.org/wiki/Conway's_Game_of_Life

http://www.amazon.com/Grand-Design-Stephen-Hawking/dp/055338466X — I mentioned this book in the post

http://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809 — here Max Tegmark explores his Mathematical Universe Hypothesis and tackles some interesting and awesome questions about our reality

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