Complexity Theory

 
Complexity


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... living organisms are very complicated aggregations of elementary parts, and by any reasonable theory of probability or thermodynamics highly improbable. That they should occur in the world at all is a miracle of the first magnitude; the only thing which removes, or mitigates, this miracle is that they reproduce themselves. Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable.
                            John von Neumann, Theory of Self-Reproducing Automata
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John Horton Conway, a British mathematician at Gonville and Caius College, University of Cambridge, was playing around in the late 1960's with a few ideas for a simple cellular automaton. The first ideas for cellular automata were thought of by Ulam. John von Neumann used this idea to create complex cellular automata, which was able to produce non-trivial self-reproducing patterns. John von Neumann's machine has 29 states, however, so Conway was looking for something simple, yet interesting. More specifically, he defined the following criteria:

There should be no initial pattern for which there is a simple proof that the population can grow without limit.There should be initial patterns that apparently do grow without limit.There should be simple initial patterns that grow and change for a considerable period of time before coming to an end in three possible ways: fading away completely (from overcrowding or from becoming too sparse), settling into a stable configuration that remains unchanged thereafter, or entering an oscillating phase in which they repeat an endless cycle of two or more periods.

Conway and his graduate students played around with various rules, finally settling on the familiar "birth on 3 / survival on 2 or 3" rule. In those days (pre-1970), computers were very primitive, so most of the team's explorations were done with physical checker pieces. One of their greatest discoveries was the glider, which they found while trying to determine whether the R-pentomino was an infinite growth pattern.

The game was first published in the Scientific American in October 1970, in Martin Gardner's "Mathematical Games" column. A few other columns and articles appeared later, but there were more results than Scientific American could reasonably be expected to publish, so the LifeLine quarterly newsletter was invented, and it ran for 11 consecutive issues.

Not much more happened in the Life universe between 1974 and 1988. Then the appearance of more powerful computers, the availability of e-mail over the
Internet, and ideas about search engines created something of a Cambrian explosion in the Life universe, which continues to this day.


"What's the difference between the process of evolution in a computer and the process of evolution outside the computer? The entities that are being evolved are made of different stuff, but the process is identical.... These abstract computer processes make it possible to pose and answer questions about evolution that are not answerable if all one has to work with is the fossil record and fruit flies.
-Christopher G. Langton

"artificial life is "basically a fact-free science."
- John Maynard Smith of the University of Sussex

"At some point, artificial life drifts off into someplace where I cannot tell where the boundary is between talking about the world-I mean, everything out there-and really neat computer games and art forms and toys."
- Stuart Kauffman