Monday, April 25, 2005

Structure Makes Structure

Structure makes structure

That might quite a general principle. Or that's at least what robotic orangutans and penne pasta have led me to believe.

Earlier today I was reading Steve Grand's fantastic book about the nature of intelligence, Growing Up With Lucy. Trying to build something is a really good way to understand it, and Grand is building a robotic orangutan in order to try and understand things about how intelligence works. It really is a fantastic, insightful book, and I would recommend it to anyone -- after all, who isn't interested in the nature of our selves?

One of the book's key points is that the brain seems to be made up of all sorts of different maps of things (of visual information, of where muscles are located, and so on), and a lot of what the brain is doing is transforming information between these maps.

It turns out that genes only need to specify a small proportion of the details of these maps and pretty blind and simple processes can "figure out the rest". Grand gives a plausible account of various ways this could happen, though acknolwedging that it's still speculative and it hasn't been fully put to the test.

One of the ways is how the mappings between the different "formats" used by the maps could be created simply by having the maps generate random information that, because it's coming from this map with a particular structure, reflects the structure of that map.

He also gives an account of how the structure in the environment can be used in a fairly blind way to build up important structures in the brain (the 'orientation detectors' in the primary visual cortex).

Anyway, both these things are examples of structure + non-structure makes more (or greater) structure. But I didn't really think of in these terms till I was making some pasta for lunch.

I don't usually use penne pasta, but there was this recipe I wanted to try and it called for penne and who am I to disobey? One of the reasons I don't usually use it is that it tends to clump together as it cooks, which means you have to take more time out to stir it[1].

The reason that penne tends to clump together, and most other pasta does not, has to do with their shape. Being cylinders, pieces can stick together along their lengths, and end up all pointing in the same direction. (I suspect that them being hollow cylinders might have something to do with it also, as the water currents flowing through them might cause them to line up with each other). Other pasta tends to be irregular shapes (at least as they become soft while they're cooking, anyway) that don't provide regular surfaces that can cause clumping like this.

With the ideas from Steve Grand's book bubbling away under the surface of my mind, it occurred to me that these clumps were a form of higher-level structure that were made possible by the lower-level structure of the pasta shapes. That is, structure making more complex structure. It seems like any structure that's there provides a hook that can be used for building more structure. I haven't really thought it through, but I suspect that this is the only way you can build structure... that sounds right to me.

I don't think this would be any surprise to people who have looked at things like complex systems. From what I've read, this is the kind of way they talk about complex systems. The only thing I can say is that I don't recall having read the point being made that explicitly.

I know there would be other ways of putting the concept, but just as a test I did a google search for this phrase. At the moment it only returns a single result, and that's a mis-hit (where the first 'Structure' is at the end of one sentence and the following 'Makes structure' is the start of the next sentence).

update: I thought I should explain a bit more about what I meant. When I said that structure makes structure, and that 'I suspect that this is the only way you can build structure' and that this view 'sounds right to me', I did have something more specific in mind. "Structure makes structure" describes what's going on with evolutionary processes, for one thing.

Evolution is a process whereby new structure is created by a process of unstructured changes to existing structure (random mutations of genetic structures) that are "guided" by the structure of the environment (what increases "fitness"). If the environment was "undifferentiated" or "random" this wouldn't happen. It has to have the pre-existing structure for the evolution to make use of. What I'm saying is that evolution is a blind process by which two existing sources of structure are used to make more structure. Thats existing structure making more structure -- an instance of structure makes structure.

If structure makes structure, then what makes structure in the first place? There's two kinds of answer to this -- the "ultimate" answer, and the "in this universe" one. The "ultimate" answer really concerns the question "what, ultimately, is the universe", which we don't know the answer to. The "in this universe" answer concerns the question of "where in this universe does the structure come from". The answer to that is, it comes from the nature of the actual laws of physics (not our formulation of them, but whatever they actually are). These cause matter to interact with other matter in regular (that is, structured) ways, and, at least according to the view expressed in this post, all other structure emerges from this lowest level form of structure.

[1] If that sounds somehow petty to you, then it's probably because you're confusing the explicit listing of reasons "penne clumps, means more stirring, thus avoid buy", which were written in that way for the purposes of explaining something in this post, with some "logical" train of reasoning that you imagine I must go through. If you, on the other hand, you think that it's a bit petty to make the effort to avoid penne like I'm doing, then re-read the previous sentence. Going further afield in my digressions, I suspect that a vague sense of "pettiness" we can feel about such things comes from our persistent "moralising" about things in which, amongst other things, says its somehow bad to do anything that might give you slight conveiences. Don't think I'm saying morals aren't important; I'm just pointing out that we need to think about those we're using.

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