Tuesday, November 10, 2009

Backgrounds, Media, Envronments

Bees and Cellular Automata - quintessentially fluid:
Bees can fly freely about, but not too far from the hive
Must interact with other bees for survival
Structures in CAs can move and deform in myriad ways, but always with direct predictable relationships to the previous state

Both exhibit swarm properties, the sort of emergent behavior Terranova concentrates on in chapter 4. The properties of the system are not obvious from the properties of the individual:
You can cut up a bee (even one of each role) and not find any indication of hive ecology, swarming behavior, etc.
You can look at a dot in a grid (or more reasonably, the rules to Conway's Game of Life) and find no hint at the existence of the Glider or any of the other objects, complex and dull, documented here: http://www.pentadecathlon.com/objects/objects.php.
In both cases, those properties only arise when there are lots of the unit near each other: lots of bees in a hive, or lots of dots-obeying-the-rules forming a Glider. But though that's as far as Terranova takes it, that's not quite it. Both need a medium:
I can put as many and as many varieties of bees as I want into space, or into my aquarium full of water, and no swarm behavior will emerge. I can even put them in space in which they will survive without guaranteeing it: say I create in the lab an environment where bees can breathe and have easy access to food, but it's too dark for them to see other bees and too slippery to build anything on and there are no flowers. It is only in a very complex ecosystem of air, sunlight, trees, flowers, etc., all in the right proportions, that bees exhibit complex emergent behavior.
The game of life is traditionally played on a cartesian grid. I'm sure someone has extended it into 3d. (yep, and it's beautiful: http://www.ibiblio.org/e-notes/Life/Game.htm) But a space is necessary, and it must have certain properties. Let's say i just draw some squares at random on a piece of paper and put dots in some of them and then apply the rules of Life: at most a few of them will be adjacent, the rules will almost never be relevant, and everything will 'die'. Similarly, life on a one-dimensional line of cells isn't very interesting either. There must be a certain density of connections for the cells to exhibit swarm behavior.

The importance of the space in which 'biological computation' occurs is generally overlooked in discussion of the field, despite being very great indeed. Terranova does hint at this when she mentions von Neumann's 'model physics' which "had to have a geometry and a set of locally defined laws that held at every point in the geometry", and when she says that CA systems "differ in terms of the number of dimensions considered" (where she does not even mention 3d CAs, much less the infinitude of fractional and fractal dimensions of connection that could be explored), but in general she ignores this issue.


In random other notes, she way overstates the unpredictability of CAs: of course you can predict their behavior! Just create a computational model with the same rules, space, and starting configuration, run it for a while, and voila! More seriously, this actually raises a very interesting point about the nature of prediction/determination/provability. The result of a CA computation is clearly deterministic if no random process is a part of the rule set, and thus it's behavior should in a certain sense always be 'predictable'. Certainly be definition we can know that the same computation will always have the same result. But for a computation whose result we do not yet know, can we say that its result is 'predictable' if the only method of prediction is to carry out the computation itself? Can we ever infer the result of a computation by looking at known results of previous computations? The answer is definitely sometimes yes, (a glider + a dot a thousand cells away is the same as a glider after generation 1) but maybe not always, and that is what's troubling. How is one to prove general theorems about the behavior of systems in which an infinite number of individual cases may have to be evaluated for the totality of their potential behavior to be understood? Or is property merely an illusion created by their great complexity?

Also the writing is incredibly sloppy and the copyediting terrible. I do not think there are three consecutive pages in which I could not find at least one flaw of each type. Blargh.

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