If you have not read Wolfram's book, it can be found here. It is a result of Wolfram's 20 years of work in the field of complexity and cellular automatons. In it, he shows how complexity can follow from simple rules applied to simple initial conditions. He then continues to state that most of modern science is about atacking complexity with complex explanations. Wolfram is a strange guy. If you get to talk to him, he really is one of those people who consumed a lot of scientific fields, almost to a point that he acts as a "live" convergence point for many of the principles and concepts of various sciences. Unfortunately, it seems like many people have not accepted his view of the world as a computer (at least not as a system of cellular automaton rules). People like Ray Kurzweil point out interesting things that Wolfram does not address (see the comment here. Kurzweil (like many others) thinks that it is fine that a cellular automaton rule like 110 is a universal computer, however, the secret to explaining the world is not in the computer, it is in the software. Kurzweil also (in my opinion validly) wonders about the order of complexity in the behavior of automata. Basically, the complexity never increases. The question is why not?

Wolfram Inc. (or whatever its full name is) seems like an interesting place to work at. It is headquartered in Urbana-Champaign (Illinois) but apparently his immediate surrounding NKS crowd lives and works in various places like Vienna, Paris, Italy, Boston etc. Seems to work for them.

I have a couple of pet-peeves with NKS. Firstly, for many complex problems in the "real" world, the sea of possible rules that could be applied to "fit" the data is almost infinite. One usually does not even know where to start. Wolfram states that in classical science we come up with a law or a formula only because the system we are observing is simple enough to be "shortcut". In real complexity we do not have the luxury of a shortcut but instead need to run the system to find out where it goes. However, if we look at our own reasoning processes as inherently complex (or at least we think so now), deciding on a subset of rules to apply based on some constraint or on what we know about the system is essentially shortcutting the process. So, does this imply that our reasoning is simple? If so, why have we not found a shortcut for it yet? Or have we?

Another point of contention, in my mind, is the fact that there is no real methodology to approaching the chosing of a certain rule to apply to a real problem. Apparently, NKS was invented to address Wolfram's dissatisfaction with the state of current science. But, it is not easier to solve an applied problem in NKS than in the traditional world (the problem of the enormous amount of rules that are possible to apply).

Currently majority of the NKS research is focused on the "pure" side of the science. People will come up with a rule and then expore its behavior (almost always graphical/visual analysis). Some more serious people will do mathematical and statistical analysis of the results. It is clearly easier to do this kind of "pure" research than to chase rules to fit real world data. However, every science needs basic research.

This post was initially about the NKS conference and the summer school held in 2006 at Brown University in Providence, RI. The conference was in Washington DC, June 16-18. I must say I left the conference disappointed - most of the presentations were on pure NKS research and they looked unfinished (or barely started). The authors saw some potentially interesting behavior, however, it seems like the tools and the methodology for the analysis of this behavior is in the eye of the beholder. One could definately benefit from some kind of a manual on the topic. Anyways, most of the presentations ended up with "I am confident that automata will yield such and such revelation when I continue my research". Suffice it to say, many people would yell "Show me the bacon!".

The summer school is somewhat more scientific. The people around Wolfram give lectures daily and it is not uncommon to see a line go by on the screen that says "All complexity in nature can be explained by simple rules". What such lines are missing is a big, red, flashing "HYPOTHESIS" word in front. Gentleman, we need to prove such grand statements. There are also people who are very serious and systematic in their study of classical science. These people tend to have more serious lectures. Wolfram's talks are somewhat confused. He is obviously a very knowledgeable man and it seems to make his discussions move from point to point in a Brownian fashion. His live experiments are similar but also full of speculation that is somewhat unfounded (at least to people like me). For example, one of the problems was to generate a certain imaginary crystalline structure from certain elements (constraints). Presumably, this could be synthesized in a lab as a novel material. This is fine and this kind of science is fascinating. However, Wolfram went on to speculate what this crystal would be used for, in his opinion, one of the uses would be filtration. His next statement was that it was essentially like a kidney glomerule. When he googled up an image of a glomerule, it was clear the two are completely unrelated. One has to wonder how many such wild speculations the man makes in front of people who are unable to google-challenge him or are unwilling to. My take on this is: stick to your specialty: physics, mathematics, automatons, whatever it is.

Finally, I will finish with the big question: WHY? If you manage to model DNA, stock market, social networks or whatever with an automaton rule - what does it say about the DNA or the stock market. OK, we fit the data but the question is WHY?