ANTEATER: But all that we know of it is Sebastiant’s description of it, which he wrote in the margin of his copy of Buxtehude’s Preludes and Fugues for Organ. The last words which he wrote before his tragic demise were:
I have composed a truly marvelous fugue. In it, I have added together the power of 24 keys, and the power of 24 themes; I came up with fugue with the power of 24 voices. Unfortunately, this margin is too narrow to contain it.
And the unrealized masterpiece simply goes by the name “Fermant’s Last Fugue.”
ACHILLES: Oh, that is unbearably tragic.
TORTOISE: Speaking of fugues, this fugue that we have been listening to is nearly over. Toward the end, there occurs a strange new twist on its theme. (Flips the page in the Well-Tempered Clavier.) Well, what have we here? A new illustration-how appealing! (Shows it to the Crab.)
CRAB: Well, what have we here? Oh, I see: it’s “HOLISMIONISM,” written in large letters that first shrink and then grow back to their original size. But that doesn’t make any sense, because it’s not a word. Oh me, oh my! (Passes it to the Anteater.)
ANTEATER: Well, what have we here? Oh, I see: it’s “REDUCTHOLISM,” written in small letters that first grow and then shrink back to their original size. But that doesn’t make any sense, because it’s not a word. Oh my, oh me! (Passes it to Achilles.)
ACHILLES: I know the rest of you won’t believe this, but in fact this picture consists of the word “HOLISM” written twice, with the letters continually shrinking as they proceed from left to right. (Returns it to the Tortoise.)
ILLUSTRATION BY THE AUTHOR.
TORTOISE: I know the rest of you won’t believe this, but in fact this picture consists of the word “REDUCTIONISM” written once, with the letters continually growing as they proceed from left to right.
ACHILLES: At last—I heard the new twist on the theme this time! I am so glad that you pointed it out to me, Mr. Tortoise. Finally, I think I am beginning to grasp the art of listening to fugues..
Reflections
Is a soul greater than the hum of its parts? The participants in the preceding dialogue seem to have divergent views on this question. What is certain and agreed upon, however, is that the collective behavior of a system of individuals can have many surprising properties.
Many people, on reading this dialogue, are reminded of the seemingly purposive, selfish, survival-oriented behavior of countries that emerges somehow from the habits and institutions of their citizens: their educational system, legal structure, religions, resources, style of consumption and level of expectations, and so on. When a tight organization forms from distinct individuals—particularly when contributions to the organization are not traceable to specific individuals in the lower level we tend to see it as a higher-level individual and often speak of it in anthropomorphic terms. A newspaper article about a terrorist group described it as “playing its cards extremely close to its chest.” It is often said of Russia that it “desires” world recognition of its might because it “suffers” from a “long-standing inferiority complex” with respect to Western Europe. While admittedly metaphors, these examples serve to demonstrate how strong the urge is to personify organizations.
The component individuals of organizations—secretaries, workers, bus drivers, executives, and so on—have their own goals in life, which, one might expect, would come into conflict with any higher-level entity of which they formed a part, but there is an effect (which many students of political science would regard as insidious and sinister) whereby the organization co-opts and exploits these very goals, taking advantage of the individuals’ pride, need for self-esteem, and so on, and turning them, back to its own profits. There emerges from all the many low-level goals a kind of higher-level momentum that subsumes all of them, that sweeps them along and thereby perpetuates itself.
Therefore it is perhaps not so silly for the Tortoise to object to Achilles’ comparison of himself to an ant and to prefer an attempt by Achilles to “map himself,” at a suitable level, onto an ant colony. Similarly, we may sometimes wonder to ourselves “What is it like to be China? How different from that would it feel to be the United States?” Do such questions makes any kind of sense at all? We shall postpone detailed discussion of them until after Nagel’s piece on bats (selection 24). Nonetheless, let us think a bit right now about whether it makes sense to think of “being” a country. Does a country have thoughts or beliefs? It all comes down to whether a country has a symbol level, in the sense that Aunt Hillary does. Instead of saying that a system “has a symbol level,” we might instead say, “It is a representational system.”
This concept of “representational system” is a crucial one in this book, and needs a somewhat precise definition. By “representational system” we will mean an active, self-updating collection of structures organized to “mirror” the world as it evolves. A painting, no matter how representational, would thus be excluded, since it is static. Curiously, we mean also to exclude mirrors themselves, although the argument could be made that the set of images in a mirror keeps quite up to date with the world! The lack in this case is twofold. First, the mirror itself does not make any distinction between images of different objects—it mirrors the universe, but sees no categories. In fact, a mirror makes only one image it is in the eye of the beholder that the mirror’s single image breaks up into “separate” images of many distinct objects. A mirror cannot be said to perceive—only to reflect. Second, the image in a mirror is not an autonomous structure with its own “life”; it depends directly on the external world. If the lights are turned off, it goes away. A representational system should be able to keep on going even if cut off from contact with the reality it is “reflecting”—although you now see that “reflection” is not quite a rich enough metaphor. The isolated representational structures should now continue to evolve in a way that reflects, if not the true way the world will evolve, at least a probable way. Actually, a good representational system will sprout parallel branches for various possibilities that can be reasonably anticipated. Its internal models will, in the metaphorical sense defined in the Reflections on “Rediscovering the Mind,” go into superpositions of states, each with an associated subjective estimate of likelihood.
In brief, then, a representational system is built on categories; it sifts incoming data into those categories, when necessary refining or enlarging its network of internal categories; its representations or “symbols” interact among themselves according to their own internal logic; this logic, although it runs without ever consulting the external world, nevertheless creates a faithful enough model of the way the world works that it manages to keep the symbols pretty much “in phase” with the world they are supposed to be mirroring. A television is thus not a representational system, as it indiscriminately throws dots onto its screen without regard to what kinds of things they represent, and the patterns on the screen do not have autonomy—they are just passive copies of things “out there.” By contrast, a computer program that can “look” at a scene and tell you what is in that scene comes closer to being a representational system. The most advanced artificial intelligence work on computer vision hasn’t yet cracked that nut. A program that could look at a scene and tell you not only what kinds of things are in the scene, but also what probably caused that scene and what will probably ensue in it—that is what we mean by a representational system. In this sense, is a country a representational system? Does a country have a symbol level? We’ll leave this one for you to ponder on.