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NKS and the General Systems Idea
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Posted by: Jason Cawley
One issue that sometimes comes up is the relation between NKS and previous general formal modeling efforts. One of the better of these in my opinion was general systems theory, as explained by Bertalanffy (1968, book of that title). GST was a good idea but more structure than content (it also developed some windy hangers on, that didn't add very much). I think it is fair to say NKS fufills something of the promise of GST, in ways Bertalanffy did not forsee but would have applauded.
What GST already understood is that how systems are put together matters. That it is not enough to analyze things, to break them down into simple components, because the interaction of those components can and typically does contain non-trivial formal stuff. It understood the basic idea of an emergent property.
And GST understood that formal correspondance across systems with very different components was the basic factor that made a general approach possible. It did not have the PCE idea, with its idea of a threshold of maximal complexity. But it got this much: "a consequence of the existence of general system properties is the appearance of structural similarities or isomorphisms in different fields. There are correspondances in the principles that govern the behavior of entities that are, instrinically, widely different." Bertalanffy GST p. 33
Another thing GST got, early, was the idea that we can search through formal rules and find systems that match them. (This was apparently Ashby's idea rather than Bertalanffy's - ibid p. 94). Bertalanffy just didn't have enough formal rules to try, because he didn't have the simple program idea. He was using systems of equations, especially the simplest ODEs and a few low order PDEs.
What he actually did was go through the simplest imaginable ODEs and then note real world examples that follow each type of particular formal law. He didn't make them discrete and he left in parameters, in the form of coefficients e.g. He was willing to connect systems so described by flow charts and such, but empirically motivated, without thinking up ways of enumerating that side of things to explore it systematically. He did enumerate and explore the kinds of ODEs or PDEs involved.
Obviously there are tons of differences, things in NKS that are completely missing in GST. The programs idea, systematic search of those as a space, the emphasis on simplicity of each, discreteness, replacing continuous parameters with rule forms on the one hand and initial conditions on the other, moving away from the "first difference" focus (calculus thinking) to explicit evolution, extending the information contained in graphs from fundamentally 1-D functions to much more elaborate behavior. Etc. GST doesn't qualify as "N" KS. But NKS does qualify as an approach to GST.
Incidentally, from what I know of how it developed, I don't think there was any direct influence of GST on NKS. I don't think Wolfram knew Bertalanffy's work, not in any detail that is. He knew it existed and wondered what it was and how relevant it was. He researched some of that for his notes, and may have picked up an idea or two along the way. But he did not think of NKS as a way of fufilling the program Bertalanffy had called for in GST.
Bertalanffy was aware that other formal means might be applied to the GST idea. He mentions information theory, game theory, stochastic modeling, and operations research. But the formal systems he knows best are differential equations, so he tries to get as far as he can with those. He can naturally find a few things that way. But his basic formal means are so intractable *for systems with complex internal interaction* that he doesn't get all that far.
DEs were developed for and work best with additive, linear, field like behaviors. Meaning ones that can be more or less completely analyzed into point behaviors. Bertalanffy knew the systems phenomena of greatest interest weren't like that ("isolable units acting in one-way causality"), but still used DEs because they were what he knew. The new intuition about simple programs wasn't there yet.
I hope this is interesting.
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