Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
Moving on from the silliness, I might with maximum charity make up a similar position and use it to illustrate points about NKS and common misconceptions about it, where they come from etc.
Practical modelers are already convinced they need to use computer programs to model complicated phenomena. But typically have no awareness of theoretical computer science or how the methods they are using actually work, at bottom. Oh they known how to program and they know how to model and their subject matter, not the point. They don't know what happens when the code leaves their hands and the hardware takes over.
What happens is their own elaborate mental conceptions of things as articulated in their code, are munged beyond recognition to make it more tractable for the particular machine they run it on. Nobody has to make new hardware to implement their latest idea about hierarchy or synching or network connectedness or what have you. The same underlying fixed instruction set is quite sufficient, and compliers translate everything into the few simple rules their computer actually "groks". It does the operations it understands enough times in the right order, to get exactly the same behavior or answer your own abstractions would have.
Now, when a modeler says, to model aspect X of my particular complicated phenomenon, I need to put X into my abstractions, that is fine and in no way contrary to NKS. NKS does not pretend that all complex systems have been modeled, but merely that modeling them will be done with computer programs and if they are sufficiently complex will involve irreducible amounts of specific detail, because the real systems depend on their details, etc.
But when someone instead claims that no simple rule can do what their computer program does, then they just show their ignorance of theoretical computer science and how their program actually works here in the real world.
And this is incredibly common. Because reseachers fixate on the techniques they learn. They think those will slice bread and anything that doesn't use them will not. But it is obvious from the fact that fixed instructions suffice to implement them, that somewhere out in the enumeration of programs using only those fixed instructions, each and every one of their specialized programs exists. If you just ran through the possible memory states of your laptop in order, you would at some point hit a Windows installation with Mathematica 5.2 installed, etc. That space is just enourmous.
Too enourmous for blindly raking through possible programs to be of much use, if the systems being sought for are specific enough. But since even quite simple and therefore short ones already do arbitrarily complicated things, we have in fact two directions in which we might proceed, not one. We can look at some empirical system and mimic its components programmatically - and that is modeling and NKS - or we are run through classes of programs seeing what they do, looking for cases close to some phenomena we see empirically. And that is search and is also NKS.
As for the specific bugaboo about hierarchy, partly in comes from previous ideas in complexity theory, specifically the investigation of fractals. The same appears prominently in NKS - just look at rule 90 and you will see how easily simple rules create intricate hierarchial forms. Whenever the cause of something does not depend on a scale, it may operate at multiple scales, and similar patterns may therefore be seen on those multiple scales.
Generalizing, power laws are one of the simplest possible mathematical forms data can take, right after lines and exponentials etc. This was a fruitful idea, mostly due to Mandlebrot. But it is not the essence of complexity (specifically), because complexity arises without it, and it can give forms that are quite simple.
People reasonably try to get additional mileage out of techniques they learned to deal with such cases. That's fine, and it involves no erroneous claims about what programs can or cannot do.
It is also quite possible for systems to have different simple rules on different levels of analysis. In classic systems theory terms, we simply do not regard them as the same system. A system is a formal abstraction out of a mass of particulars. It attempts to keep the essential generators of some phenomenon, while dropping accidental details. (A fine classic Aristotlean distinction, incidentally).
When the essential features are retained, the system behavior remains as it was. We say that system (or aspect of the behavior) is separable. If a rate of change depends only on a previous quantity, you always get exponentials, e.g. Which sort of thing they occur in does not matter, the form depends only on that relation existing between prior quantity and rate. Obviously, that relation may have physical limits - then the behavior will be true within them but other factors will enter beyond them, etc.
There is nothing wrong with wanting to build nested computer models of some empirical system - or for some technological purpose. I advocate and use them - each level being a simple rule, the whole a program etc. But claims that X cannot be done or that no program exists with such behaviors except when started that way, are unsound, as a matter of known theorems. You might make a search claim about it. You can't make an existence claim.
Anything any program can do, some simple program can do. That is the basis of the "new" in a new kind of science. It is the reason to expect arbitrarily intricate behavior may arise from simple components - which we clearly see it does, incidentally, metaphysical longing for gaps notwithstanding. It is the reason to expect computer models to be the way to move science forward. It is the reason formal experiment can will and does aid irreducible empirical work. It is the reason it is a new science with plenty to do dealing with intricate real cases that depend on details, instead of being over already with everything already done.
Science cannot be dictated to, and sound philosophers do not try. It goes where the truth can be found, and doesn't care a straw whose ox is or is not gored in the process. Whether of prior method or fashion, or of philosophical conviction or desired conclusion. Even sound theologians fully understand this, do not comically pretend to know things beforehand that no one knows, and recognize truth as the highest criterion. "X can't be because I don't like the consequences" is a whim in fiction, not seeking the truth, and nobody can possibly take it seriously.
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