Reason • Reality • Philosophy • Science • Psychology • Spirituality
Complexity from Simplicity
While the concept of a “supernatural Creator” has been shown to be completely unnecessary for the creation of the universe – since the universe itself is eternal – it is often thought that such a being may at least be necessary to explain certain things within the universe. Such explanations are often seen as particularly necessary regarding biological life. Many people feel that the existence and complexity of all sorts of forms of life, including but certainly not limited to human life, could not have come into being or evolved “randomly” or “by accident,” and therefore must have required some sort of “intelligent creator” for their existence.
Mathematicians and computer scientists have studied the emergence of complexity from simplicity, in very fundamental and detailed ways, and have made some very revealing discoveries. Two types of information processors, the “Universal Turing Machine,” and “cellular automata,” are particularly relevant and illuminating.
Introduced by Alan Turing in 1936-1937, the Universal Turing Machine (UTM) is essentially an extremely simple type of computer which can simulate the action of any other computer. While Alan Turing's version of a UTM was a purely theoretical construct, our computers of today are all essentially real-world UTMs, within the limits of their memory, processing speed, and other such considerations. While modern computers are much more complex in design and operation than Alan Turing's original UTM, this added complexity only serves to increase the speed and efficiency of their information processing capabilities, but does nothing to increase the amount or complexity of the information they can process. The UTM is an example of a very simple system which can model any other system or device, no matter how large or complex.
The concept of “cellular automata” was first studied by Stanislaw Ulam and John von Neumann in the 1940s. John Conway sparked popular interest in cellular automata in the 1970s, with his “Game of LIFE.” Stephan Wolfram began a systematic study of cellular automata in the 1980s, and published “A New Kind of Science” in 2002, describing in detail some of the implications of his work. At their simplest, cellular automata are abstract patterns consisting of “cells,” each of which is in some “state,” and each of which stands in some “relationship” to the other cells. These “cells” can be thought of as squares on a checkerboard, or nodes in a network. The “state” can be thought of as the color of a checkerboard square, or whatever piece occupies that square, or a combination of the two, or it may be thought of as the action of some node in a network. The “relationship” to the other cells can be thought of as the “place” of each square on a checkerboard in relation to all of the other squares, or as the “place” of each node in a network in relation to all of the other nodes. Cellular automata have “rules” which govern various aspects of the behavior of the cells of which they are comprised, such as how their states and their relationships to other cells should change under various conditions. It has shown, many times, that the combined activity of simple cellular automata very often gives rise to very complex, and sometimes completely unpredictable behaviors.
The behavior of UTMs has been replicated using very simple cellular automata. Conversely, very simple cellular automata have been replicated using UTMs (and computers). In other words, UTMs can simulate the activity of simple cellular automata, and cellular automata can simulate the activity of UTMs. Since UTMs can model arbitrarily complex things to any degree of precision, and since cellular automata can replicate the action of UTMs, it follows that cellular automata can model arbitrarily complex things, to any degree of precision.
Taken to its logical conclusion, cellular automata could actually model the world we live in, with complete precision and including consciousness, provided that the cells themselves (or their “states,” or “relationships,” as used above) were inherently and irreducibly conscious, or “contained,” or “consisted
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