mustache, black-rimmed round glasses, a fake nose, and an unlit cigar. He then encounters an identically dressed real Groucho, who decides that he is seeing himself in a mirror. (Both Groucho and the alleged reflection are wearing long white nightgowns, nightcaps, and socks.) Chico plays along by trying to mirror Groucho’s every posture and move. The two make faces, wiggle their behinds, go on all fours, and do a couple of silly walks that may have inspired the much later opus by Monty Python. The spell is broken when Harpo, also made-up and dressed as Groucho, joins them, with predictable consequences.
The two Grouchos’ aping of one another is funny because it is sustained for several minutes, because it is occasionally imperfect, but most of all because while it lasts it appears improbably well coordinated. They begin each silly walk while separated by a wall; they then amble, skip, and sashay in near-perfect unison across an open space where they are in plain view of each other; then another wall comes between them and the increasingly suspicious real Groucho starts plotting his next move, designed to expose his “reflection” as a fake. The fake Groucho’s success in mirroring the real one’s moves makes us laugh because intuitively we know just how unlikely it is that two people could execute a dance in lockstep without orchestrated timing and a thorough rehearsal. 11
Rehearsal on the part of the system that aims at representing the world helps it shape its dynamics by giving experience an opportunity to make its imprint. How this happens is best understood using the no. 4 conceptual tool of representation space, from Chapter 3. Under conditions that favor learning, experiencing a series of stimuli—activating in quick succession a series of points in a representation space—causes them to become associated with one another, in the order of their activation. Repeatedly traversing such a learned trajectory consolidates it into a memory trace that is both a record of past experience and a basis for prediction. If a later event has just caused the first and then the second element in a sequence of representations to be activated, chances are that whatever it is that causes the third element to become excited will come along soon; the system now has some idea what to expect next.
Computationally, the knowledge of ordered sequential dependencies among representations has the form of conditional probabilities. This means that its acquisition and use obey the Bayes Theorem—the Promethean gift of probability theory to cognition. Once learned (through accumulation of experience, subjected to statistical inference), a pattern of sequential dependencies can be used to predict where a sequence is likely to go, given where it comes from in the space of possibilities. Like a quad on a college campus or a pedestrian square in a city after a heavy snowfall, this initially pristine representation space becomes covered with a skein of forking paths, some deeper and wider than others, which grow in response to experience.
Our encounters with the world come in fits and starts, one event at a time, with not much happening in between. Not all possible situations that could in principle be represented given the brain’s resources get to be experienced, and those that do are not experienced all at once. This is what imparts to a possibility space the characteristic structure of a crisscrossing network of paths that run through an otherwise untrodden territory. The paths are punctuated with occasional stops that correspond to distinctive, hence memorable, events. At each of these stops, there is a cache of information. Because different tasks require different kinds of possibility spaces, the contents of those representational caches, as well as the pattern of paths, vary from one task to another.
The least abstract possibility spaces are those that represent aspects of actual physical space and time. To learn how to aim, or aim
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