Gödel, Escher, Bach: An Eternal Golden Braid (120 page)

FIGURE 128.
Bongard problem 58. [From M. Bongard, Pattern Recognition
.]

FIGURE 129.
Bongard problem 61. [From M. Bongard, Pattern Recognition.]

extremely helpful to compare the starkest boxes from the two Classes. But how can you tell which boxes are stark until you have descriptions for them? Well, one way of detecting starkness is to look for a box with a minimum of the features provided by the preprocessor. This can be done very early, for it does not require a pre-existing template; in fact, this can be one useful way of discovering features to build into a template. BP 61 (Fig. 129) is an example where that technique might quickly lead to a solution.

Science and the World of Bongard Problems

One can think of the Bongard-problem world as a tiny place where "science" is done-that is, where the purpose is to discern patterns in the world. As patterns are sought, templates are made, unmade, and remade;

FIGURE 130.
Bongard problems 70-71. [From M. Bongard, Pattern
Recognition
.]

slots are shifted from one level of generality to another: filtering and focusing are done; and so on. There are discoveries on all levels of complexity. The Kuhnian theory that certain rare events called "paradigm shifts" mark the distinction between "normal" science and "conceptual revolutions" does not seem to work, for we can see paradigm shifts happening all throughout the system, all the time.

The fluidity of descriptions ensures that paradigm shifts will take place on all scales.

Of course, some discoveries are more "revolutionary" than others, because they have wider effects. For instance, one can make the discovery that problems 70 and 71 (Fig. 130) are "the same problem", when looked at on a sufficiently abstract level. The key observation is that both involve depth-2 versus depth-1

nesting. This is a new level of discovery that can he made about Bongard problems. There is an even higher level, concerning the collection as a whole. If someone has never seen the collection, it can be a good puzzle just to figure out what it is. To figure it out is a revolutionary insight, but it must be pointed out that the mechanisms of thought which allow such a discovery to be made are no different from those which operate in the solution of a single Bongard problem.

By the same token, real science does not divide up into "normal" periods versus

"conceptual. revolutions"; rather, paradigm shifts pervade-there are just bigger and smaller ones, paradigm shifts on different levels. The recursive plots of INT and Gplot (Figs. 32 and 34) provide a geometric model for this idea: they have the same structure full of discontinuous jumps on every level, not just the top level-only the lower the level, the smaller the jumps

Connections to Other Types of Thought

To set this entire program somewhat in context, let me suggest two ways in which it is related to other aspects of cognition. Not only does it depend on other aspects of cognition, but also they in turn depend on it. First let me comment on how it depends on other aspects of cognition. The intuition which is required for knowing when it makes sense to blur distinctions, to try redescriptions, to backtrack, to shift levels, and so forth, is something which probably comes only with much experience in thought in general.

Thus it would be very hard to define heuristics for these crucial aspects of the program.

Sometimes one's experience with real objects in the world has a subtle effect on how one describes or redescribes boxes. For instance, who can say how much one's familiarity with living trees helps one to solve BP 70% It is very doubtful that in humans, the subnetwork of concepts relevant to these puzzles can be easily separated out from the whole network. Rather, it is much more likely that one's intuitions gained from seeing and handling real objects-combs, trains, strings, blocks, letters, rubber bands, etc., etc.-

play an invisible but significant guiding role in the solution of these puzzles.

Conversely, it is certain that understanding real-world situations heavily depends on visual imagery and spatial intuition, so that having a powerful and flexible way of representing patterns such as these Bongard patterns can only contribute to the general efficiency of thought processes.

It seems to me that Bongard's problems were worked out with great care, and that they have a quality of universality to them, in the sense that each one has a unique correct answer. Of course one could argue with this and say that what we consider "correct"

depends in some deep way on our being human, and some creatures from some other star system might disagree entirely. Not having any concrete evidence either way, I still have a certain faith that Bongard problems depend on a sense of simplicity which is not just limited to earthbound human beings. My earlier comments about the probable importance of being acquainted with such surely earth-limited objects as combs, trains, rubber bands, and so on, are not in conflict with the idea that our notion of simplicity is universal, for what matters is not any of these individual objects, but the fact that taken together they span a wide space. And it seems likely that any other civilization would have as vast a repertoire of artifacts and natural objects and varieties of experience on which to draw as we do. So I believe that the skill of solving Bongard

problems lies very close to the core of "pure" intelligence, if there is such a thing.

Therefore it is a good place to begin if one wants to investigate the ability to discover

"intrinsic meaning" in patterns or messages. Unfortunately we have reproduced only a small selection of his stimulating collection. I hope that many readers will acquaint themselves with the entire collection, to be found in his book (see Bibliography).

Some of the problems of visual pattern recognition which we human beings seem to have completely "flattened" into our unconscious are quite amazing. They include: recognition of faces (invariance of faces under age change, expression change, lighting change, distance change, angle change, etc.)

recognition of hiking trails in forests and mountains-somehow this has always impressed me as one of our most subtle acts of pattern recognition-and yet animals can do it, too

reading text without hesitation in hundreds if not thousands of different typefaces
Message-Passing Languages, Frames, and Symbols

One way that has been suggested for handling the complexities of pattern recognition and other challenges to Al programs is the so-called "actor" formalism of Carl Hewitt (similar to the language "Smailtalk", developed by Alan Kay and others), in which a program is written as a collection of interacting actors, which can pass elaborate messages back and forth among themselves. In a way, this resembles a heterarchical collection of procedures which can call each other. The major difference is that where procedures usually only pass a rather small number of arguments back and forth, the messages exchanged by actors can be arbitrarily long and complex.

Actors with the ability to exchange messages become somewhat autonomous agents-in fact, even like autonomous computers, with messages being somewhat like programs. Each actor can have its own idiosyncratic way of interpreting any given message; thus a message's meaning will depend on the actor it is intercepted by. This comes about by the actor having within it a piece of program which interprets messages; so there may be as many interpreters as there are actors. Of course, there may be many actors with identical interpreters; in fact, this could be a great advantage, just as it is extremely important in the cell to have a multitude of identical ribosomes floating throughout the cytoplasm, all of which will interpret a message-in this case, messenger RNA-in one and the same way.

It is interesting to think how one might merge the frame-notion with the actor-notion. Let us call a frame with the capability of generating and interpreting complex messages a
symbol
:

frame + actor = symbol

We now have reached the point where we are talking about ways or implementing those elusive active symbols of Chapters XI and XII; henceforth in this Chapter, "symbol" will have that meaning. By the way, don't feel dumb if you don't immediately see just how this synthesis is to be made. It is not clear, though it is certainly one of the most fascinating directions to go in AI. Furthermore, it is quite certain that even the best synthesis of these notions will turn out to have much less power than the actual symbols of human minds. In that sense, calling these frame-actor syntheses "symbols" is premature, but it is an optimistic way of looking at things.

Let us return to some issues connected with message passing. Should each message be directed specifically at a target symbol, or should it be thrown out into the grand void, much as mRNA is thrown out into the cytoplasm, to seek its ribosome? If messages have destinations, then each symbol must have an address, and messages for it should always be sent to that address. On the other hand, there could be one central receiving dock for messages, where a message would simply sit until it got picked up by some symbol that wanted it. This is a counterpart to General Delivery. Probably the best solution is to allow both types of message to exist; also to have provisions for different classes of urgency-special delivery, first class, second class, and so on. The whole postal system provides a rich source of ideas for message-passing languages, including such curios as selfaddressed stamped envelopes (messages whose senders want answers quickly), parcel post (extremely long messages which can be sent some very slow way), and more. The telephone system will give you more inspiration when you run out of postal-system ideas.

Enzymes and AI

Another rich source of ideas for message passing-indeed, for information processing in general-is, of course, the cell. Some objects in the cell are quite comparable to actors-in particular, enzymes. Each enzyme's active site acts as a filter which only recognizes certain kinds of substrates (messages). Thus an enzyme has an "address", in effect. The enzyme is "programmed" (by virtue of its tertiary structure) to carry out certain operations upon that "message", and then to release it to the world again. Now in this way, when a message is passed from enzyme to enzyme along a chemical pathway, a lot can be accomplished. We have already described the elaborate kinds of feedback mechanisms which can take place in cells (either by inhibition or repression). These kinds of mechanisms show that complicated control of processes can arise through the kind of message passing that exists in the cell.

One of the most striking things about enzymes is how they sit around idly, waiting to be triggered by an incoming substrate. Then, when the substrate arrives, suddenly the enzyme springs into action, like a Venus's flytrap. This kind of "hair-trigger" program has been used in Al, and goes by the name of demon. The important thing here is the idea of having many different "species" of triggerable subroutines just lying around waiting to

be triggered. In cells, all the complex molecules and organelles are built up, simple step by simple step. Some of these new structures are often enzymes themselves, and they participate in the building of new enzymes, which in turn participate in the building of yet other types of enzyme, etc. Such recursive cascades of enzymes can have drastic effects on what a cell is doing. One would like to see the same kind of simple step-by-step assembly process imported into
AI
, in the construction of useful subprograms. For instance, repetition has a way of burning new circuits into our mental hardware, so that oft-repeated pieces of behavior become encoded below the conscious level. It would be extremely useful if there were an analogous way of synthesizing efficient pieces of code which can carry out the same sequence of operations as something which has been learned on a higher level of "consciousness". Enzyme cascades may suggest a model for how this could be done. (The program called "
HACKER
", written by Gerald Sussman, synthesizes and debugs small subroutines in a way not too much unlike that of enzyme cascades.)