TORTOISE: That is why it would be reasonable to think of mapping your brain, Achilles, onto an ant colony, but not onto the brain of a mere ant.
ACHILLES: I appreciate the compliment. But how would such a mapping be carried out? For instance, what in my brain corresponds to the low-level teams which you call signals?
ANTEATER: Oh, I but dabble in brains, and therefore couldn’t set up the map in its glorious detail. But—and correct me if I’m wrong, Mr. Crab—I would surmise that the brain counterpart to an ant colony’s signal is the firing of a neuron; or perhaps it is a larger-scale event, such as a pattern of neural firings.
CRAB: I would tend to agree. But don’t you think that, for the purposes of our discussion, delineating the exact counterpart is not in itself crucial, desirable though it might be? It seems to me that the main idea is that such a correspondence does exist, even if we don’t know exactly how to define it right now. I would only question one point, Dr. Anteater, which you raised, and that concerns the level at which one can have faith that the correspondence begins. You seemed to think that a signal might have a direct counterpart in a brain; whereas I feel that it is only at the level of your active symbols and above that it is likely that a correspondence must exist.
ANTEATER: Your interpretation may very well be more accurate than mine, Mr. Crab. Thank you for bringing out that subtle point.
ACHILLES: What does a symbol do that a signal couldn’t do?
ANTEATER: It is something like the difference between words and letters. Words, which are meaning-carrying entities, are composed of letters, which in themselves carry no meaning. This gives a good idea of the difference between symbols and signals. In fact it is a useful analogy, as long as you keep in mind the fact that words and letters are passive, symbols and signals are active.
ACHILLES: I’ll do so, but I’m not sure I understand why it is so vital to stress the difference between active and passive entities.
ANTEATER: The reason is that the meaning which you attribute to any passive symbol, such as a word on a page, actually derives from the meaning which is carried by corresponding active symbols in your brain. So that the meaning of passive symbols can only be properly understood when it is related to the meaning of active symbols.
ACHILLES: All right. But what is it that endows a symbol—an active one, to be sure—with meaning, when you say that a signal, which is a perfectly good entity in its own right, has none?
ANTEATER: It all has to do with the way that symbols can cause other symbols to be triggered. When one symbol becomes active, it does not do so in isolation. It is floating about, indeed, in a medium, which is characterized by its caste distribution.
CRAB: Of course, in a brain there is no such thing as a caste distribution, but the counterpart is the “brain state.” There, you describe the states of all the neurons, and all the interconnections, and the threshold for firing of each neuron.
ANTEATER: Very well; let’s lump “caste distribution” and “brain state” under a common heading, and call them just the “state.” Now the state can be described on a low level or on a high level. A low-level description of the state of an ant colony would involve painfully specifying the location of each ant, its age and caste, and other similar items. A very detailed description, yielding practically no global insight as to why it is in that state. On the other hand, a description on a high level would involve specifying which symbols could be triggered by which combinations of other symbols, under what conditions, and so forth.
ACHILLES: What about a description on the level of signals, or teams.
ANTEATER: A description on that level would fall somewhere in between the low-level and symbol-level descriptions. It would contain a great deal of information about what is actually going on in specific locations throughout the colony, although certainly less than an ant-by-ant description, since teams consist of clumps of ants. A team-by-team description is like a summary of an ant-by-ant description. However, you have to add extra things which were not present in the ant-by-ant description—such as the relationships between teams, and the supply of various castes here and there. This extra complication is the price you pay for the right to summarize.
ACHILLES: It is interesting to me to compare the merits of the descriptions at various levels. The highest-level description seems to carry the most explanatory power, in that it gives you the most intuitive picture of the ant colony, although strangely enough, it leaves out seemingly the most important feature—the ants.
ANTEATER: But you see, despite appearances, the ants are not the most important feature. Admittedly, were it not for them, the colony wouldn’t exist; but something equivalent—a brain—can exist, ant-free. So, at least from a high-level point of view, the ants are dispensable.
ACHILLES: I’m sure no ant would embrace your theory with eagerness.
ANTEATER: Well, I never met an ant with a high-level point of view.
CRAB: What a counterintuitive picture you paint, Dr. Anteater. It seems that, if what you say is true, in order to grasp the whole structure, you have to describe it omitting any mention of its fundamental building blocks.
ANTEATER: Perhaps I can make it a little clearer by an analogy. Imagine you have before you a Charles Dickens novel.
ACHILLES: The Pickwick Papers—will that do?
ANTEATER: Excellently! And now imagine trying the following game: You must find a way of mapping letters onto ideas, so that the entire Pickwick Papers makes sense when you read it letter by letter.
ACHILLES: Hmm.... You mean that every time I hit a word such as “the,” I have to think of three definite concepts, one after another, with no room for variation?
ANTEATER: Exactly. They are the “t”-concept, the “h”-concept, and the “e”-concept—and every time, those concepts are as they were the preceding time.
ACHILLES: Well, it sounds like that would turn the experience of “reading” The Pickwick Papers into an indescribably boring nightmare. It would be an exercise in meaninglessness, no matter what concept I associated with each letter.
ANTEATER: Exactly. There is no natural mapping from the individual letters into the real world. The natural mapping occurs on a higher level-between words, and parts of the real world. If you wanted to describe the book, therefore, you would make no mention of the letter level.
ACHILLES: Of course not! I’d describe the plot and the characters, and so forth.
ANTEATER: So there you are. You would omit all mention of the building blocks, even though the book exists thanks to them. They are the medium, but not the message.
ACHILLES: All right—but what about ant colonies?
ANTEATER: Here, there are active signals instead of passive letters, and active symbols instead of passive words—but the idea carries over.
ACHILLES: Do you mean I couldn’t establish a mapping between signals and things in the real world?