“Non-algorithmic computing” is an up and coming thing these days, and has much to do with non-linear ways to describe life, the universe, and everything.

It makes sense for computer scientists to think about modeling biological processes (including emergent processes, such as evolution, and, probably, how the brain is designed and used) in an algorithmic context. After all, that is their professional specialty. However, there are no guarantees that nature “computes” anything like how IBM (for instance) would do it. In fact, I suggest that nature must work somewhat differently, for the following reason.

The modeling proposals—genetic algorithms, evolutionary computations, neural net emulations, and so on—of scientists like John Holland and Stephen Wolfram are beautiful and elegant. And, I believe, they can shed much light on how natural processes work. But they cannot be a complete answer. This is because they are written with the programmer as “God”. That is, they are rule-based, with the rules provided by the author of the program. Now, perhaps natural processes are, at the very bottom, rule-based as well (…and…just who, or what, made the rules?). But there are crucial differences. In evolution, for instance, the rules are not a given, but are a historical document of what has worked in the past. (This is probably true with human “cultural” learning as well, although there are undoubtedly “boot processes” that are included in the “firmware”, or as they say, “wetware”.)

So, in any algorithmic model (incidentally, when we use the term “algorithm:, most often, “heuristic” makes more sense: An algorithm implies that there is a fixed way to get the answers we wish, even if it is a hard and tedious process, while a heuristic suggests a somewhat quick and dirty way to get the deed done to a pretty close approximation of what we are seeking) or artificial life program, the constraints are a 1) pre-statable configuration space, and 2) a “theory of everything” provided by the designer. In natural contexts (more to the point, biological ones), however, the configuration space is not pre-statable—the space of all possibles is continually expanding (too fast for any conceivable computation) and evolving—hence the “theory of everything”, even if it truly exists in any meaningful physical way and can be discovered, will not tell us much about how nature plays itself out. In other words, for all practical purposes, biological creature-space is open-ended. In still other words, while a reductionist approach might be useful in a constrained, fully defined system, it quickly becomes intractable for systems where the rules themselves evolve.

(I believe, but I’m not sure that I could prove my contention rigorously, that this implies the following Uncertainty Principle analog: In the phase space of any unbounded dynamical system, it is not possible to know its state attractor at any one point in time. With some finite period of observation, it is possible to identify this attractor, but by that time, the knowledge of it is irrelevant. This is because the original phase space no longer exists. While there are always small eddies in the flow of the universe that living entities can pick up on, with some fuzzy amount of accuracy, to make a living, the big kahuna, the “God attractor”, is forever denied to all observers, including God.)

Are there really “laws of nature”? I side with those few cosmologists (and many biologists) who claim that physical “constants” are not really so constant after all, but have evolved along with everything else in the universe. Granted, they could be now evolving so slowly, relative to human perception, that they may as well be true constants. Yet, the point remains that the universe essentially makes it all up as it goes along: The space (both in the geographical sense and the mathematical one) we live in is unlike the fully constrained environment of computer-based models. (The “natural laws” of the latter may, in fact, evolves as well, but the confined determinism of computer-space is a much different kettle of fish than open-ended determinism [I wonder, is this one way of thinking about “free will”…?].) I am not sure, but I think this is another way of saying that the universe is not nearly so Newtonian as we used to think (and many physicists, engineers, and clockmakers still do…): You can’t, at least with most natural systems, argue both the facts from the laws and the laws from the facts. The tautology of the equation may have its limitations, both theoretical and practical.

How can we provide a simulation of open-ended “natural” algorithmic processes? I think the basic issue here is that, for biological creatures, “information” is stored almost completely in context, and, for humans, that context is largely cultural. By way of example, consider the following statement: “If Mom doesn’t call, pick her up at the airport at 4:00.” In this case, the “official” exchange of zero bits of information sets off a large complex of physical activity. The processors (brains, in particular—at least for most animals) keep, in local memory, relatively small amounts, which are essentially evolved sub-routines to guide the organism in its interactions with the Wide World “out there”. For computers, on the other hand, the context is all internal, or provided by “God”.

This need not be completely true, of course: Computers can be provided with “sense organs” and “motivation” to seek knowledge. We can, for instance, allow the computer access to large, open-ended databases, such as the Web. With the right search engine and information abstractor, the computer model can increase its knowledge of the world out there by a huge amount. Still, all the databases in the world are just a tiny fraction of the context available to biological creatures. And it’s still, at any one time, finite. What we want, I believe, if computer models are to provide truly useful emulations, is to allow their spaces of all possibles to evolve, as they do for biological entities.

But what kinds of “algorithms” and systems can we come up with to explore continuously fluctuating possibility-spaces? In a sense, we may be part way there already. The “God” mentioned above is only the (top-down) software deity. In the entire system’s pantheon is a second major god who constrains the software: the (bottom-up) rules necessitated by the computer’s physical design, promulgated by a (top-down) human designer. Then there is a meta-god: the gate-keeper who decides which software is allowed to run on the computer, and when. So, we have, in effect, coupled the bounded determinism of the software space to the bounded determinism of the hardware space to the unbounded “determinism” of designer space, programmer space and operator space. This potentially leads, I’m pretty sure, to a kind of super-chaos, or “intractable determinism”.

Still, this isn’t quite the same thing as an evolving space of all possibles in the fully human sense, so I think there is plenty of room to develop some meta algorithms based on giving, god-like (i.e., top-down), computer systems the (bottom-up) keys to at least part of the universe.