In Part 1 of the look at Chapter 2 of A New Kind of Science, we’ll summarize the chapter, and bring forth a few possible points of discussion. In Part 2 we’ll take a look at some code you can use to conduct your own investigations relative to the ideas in Chapter 2.
The basic idea presented is finding a theory of simple programs by studying their behavior. This is in contrast to some traditional scientific methods, which suggest we conduct specific experiments on specific systems in order to get specific behavior with predictable elements.
In other words, it’s an investigation of processes rather than modeling to achieve particular outcomes.
Another field that fundamentally studies processes is cybernetics, but the systems studied are restricted to those systems which have goals and participate in circular, causal chains. Processes in NKS, while deterministic, do not have to be circular.
Wolfram describes his impetus for investigating simple programs which yield complex results, and talks about the general history of scientific inquiry into those same simple programs. For instance, while CAs had been used in the early 1950s to represent some idealized models in biology, it was always assumed more complex models would have to have more complex rules.
In fact, Wolfram makes the observation that, when traditionally encountering complex behavior resulting from simple rules, the traditional scientific intuition is to try (sometimes in vain) to find patterns or regularities in the behaviors. Examples: computing a prime is simple, but the distribution of primes is for all intents and purposes random; computing the digits of Π is simple, but the digit sequence is apparently random.
Stay tuned for Part 2 of our look at Chapter 2, where we”ll introduce some Mathematica code which can help you in your own research.