Chapter 12: The Principle of Computational Equivalence

Section 10: Intelligence in the Universe

[Ideas of] meaning in programs

Many issues about meaning arise for computer languages in more defined versions of the ways they arise for ordinary languages. Input to a computer language will immediately fail to be meaningful if it does not conform to a certain definite syntax. Before the input can have a chance of specifying meaningful action there are often all sorts of issues about whether variables in it refer to entities that can be considered to exist. And even if this is resolved, one can still get something that is in effect nonsense and does not usefully run. In most traditional computer languages it is usually the case that most programs chosen at random will just crash if run, often as a result of trying to write to memory outside the arrays they have allocated. In Mathematica, there is almost no similar issue, and programs chosen at random tend instead just to return unchanged. (Compare page 101.)

For the kinds of systems like cellular automata that I have discussed in this book programs chosen at random do very often produce some sort of non-trivial behavior. But as discussed in the main text there is still an issue of when this behavior can reasonably be considered meaningful.

For some purposes a more direct analog of messages is not programs or rules for systems like cellular automata but instead initial conditions. And one might imagine that the very process of running such initial conditions in a system with appropriate underlying rules would somehow be what corresponds to their meaning. But if one was just given a collection of initial conditions without any underlying rules one would then need to find out what underlying rules one was supposed to use in order to determine their meaning. Yet the system will always do something, whatever rules one uses. So then one is back to defining criteria for what counts as meaningful behavior in order to determine—by a kind of generalization of cryptanalysis—what rules one is supposed to use.

From Stephen Wolfram: A New Kind of Science [citation]