Summary of Hofstadter's Prelude... Ant Fugue

This is a summary of the full dialogue, which you should certainly read first, available at Mind's I, Ch 11

[A dialogue between Achilles, the Tortoise, Crab, and Anteater]


The characters have a playful discussion of Fermat's Last Theorem. They've found a practical application: it enables them to reconstruct the sound of Bach playing his Well-Tempered Clavier from the small perturbation the performance left on molecules in today's atmosphere. They present this recording to Crab. Allegedly, Tortoise has found both a solution to Fermat's equation and a proof of Fermat's conjecture that no solutions exist. Of course that is inconsistent. This is why the discussion is "playful."

The characters listen to the recording, while Crab brings out an illustrated book containing the score. They discuss the musical relations between the matched preludes and fugues. Some of these relations turn out to also be exemplified by the rhetorical structure of the dialogue.

Crab compares listening to the music when he was young and it was all fresh, and listening to it now when it's already very familiar---though he keeps noticing new subtleties. They discuss how his "thrill" of hearing the music for the first time is encoded as memories in his brain, and can be revived by seeing Achilles' excitement at hearing the music new.

The characters mention Escher's lithograph Cube with Magic Ribbons. Achilles likens that print to his experience of being able to listen to the individual voices in a fugue, or to the total effect, but never to both at the same time. Other characters agree this is also their experience. You can't grasp the "whole essence" of the fugue at once.

Anteater: Fugues are interesting because each voice is a separate piece of music in itself (altough they are coordinated with each other); and also the whole combination is another piece of music.

The characters keep discussing the dichotomy of perceiving something as a whole vs as a collection of parts. They come upon the illustration:

Each of them reports seeing this picture a different way. Here is what the first three of them say (not in the same order they say it).

Anteater: It says "reductionism," meaning that a whole is just the sum of its parts.

Crab: It says "holism," meaning there is more to a whole than comes from the parts. I reject reductionism, because a reductionist account of the brain can never explain consciousness.

Achilles: It says mu, which is a Zen idea that in this context means we should reject the assumption that we have to choose between holism and reductionism.

Anteater: I reject holism, because a holistic description of an ant colony won't tell us anything that's not already implied by the description of the individual ants and their relationships to each other.

Tortoise then pipes up and also says the answer is "mu." Achilles says that's what he said. Tortoise suggests he might be looking at a different level than Achilles. (At the smallest level, the picture is built out of tiny little "mu"s.)

Anteater starts giving a reductionist description of an ant colony. His profession is fixing "nervous disorders" in the whole colony by surgically removing individual ants. Ant colonies like Aunt Hillary are in fact able to converse by "writing" with the trails their ants make. Anteater has very different attitudes towards the larger colony and its individual ants. It's curious then why he has chosen as the spokesperson for reductionism. Hofstadter seems to be covertly suggesting that there's no conflict between the reductionist idea that a whole can be explained in terms of its parts, and admitting that wholes can be well-defined units having properties that their parts don't themselves have.

Achilles: There must be some amazingly smart ants in that colony.

Anteater: No, the individual ants are dumb and can't converse. It's the colony Aunt Hillary who is intelligent and entertaining.

Tortoise compares this all to the human brain and the neurons that make it up. Achilles accepts that what they're saying is true of brains and neurons, but has a hard time believing it about ant colonies and ants. The ants just roam around randomly.

Crab: Ants are only free within certain constraints. They don't step out of their ant system.

Anteater: Even if the individual ants are bumping about randomly, the statistics of their whole population follows certain regular trends. (Consider the slogan, order emerging from chaos.) That's how their behavior can add up to the coherent organization of Aunt Hillary's mind. Neurons work similarly.

Anteater: Part of the organization of the colony is how different "castes" of ants are distributed throughout the colony: this isn't a single rigid pattern, but rather something constantly moving and evolving.

Anteater: Individual ants are afraid of me, but their panicked running around when I arrive creates a pattern that becomes Aunt Hillary's delighted greeting. You should think of little clusters of ants as "signals," like the electrical signals that cascade in waves through our brains.

The characters discuss how you can look at the movement of a signal in micro-level terms that don't invoke any concepts like "purpose", or you can look at the same event in terms of what the ant colony needs at a given moment, and what purpose the signal plays in meeting that need.

Crab (who had championed holism): Colonies survive because of their caste distribution, and this is a holistic property, that's invisible if you look too micro-level.

Anteater: If you look at how a single colony fits into the larger evolutionary picture, its patterns and mechanisms no longer seem to have "meaning" or "purpose." These ideas are just a matter of our perspective, not something inherent in the ant colony itself.

Achilles: Didn't you talk with Aunt Hillary? Didn't she mean things when she talked to you?

Anteater: Sure, that is, I find it natural to adopt the perspective which attributes "meanings" to her behavior.

Anteater: A signal isn't always made up of the same ants between its creation and dissolution. The ants break off and get replaced. Signals cluster together into teams, they cluster into larger teams, and so on. We can call sufficiently complex teams "symbols"---but these are more like the dynamic patterns in a running computer program than like passive shapes of ink on a piece of paper. All these layers of structure are what enable an organism like Aunt Hillary to store the kinds of information that enable her to be "intelligent." At a certain level of abstraction, Aunt Hillary's organization is just like the organization of our brains.

Anteater emphasizes the difference between passive symbols on a piece of paper, that observers' brains have to read meaning into, and the dynamic symbols in our brains and in Aunt Hillary's complex activity, that can cause other symbols to be triggered and so can legitimately have meanings in themself.

Anteater: You can't understand a Dickens novel if you try to map each individual letter onto a different concept. You have to understand it by clumping letters together into words, and words together into plot and characters. So too we won't understand our brains or Aunt Hillary if we only look at the most micro-level.

Anteater: I hope you can all now see how Aunt Hillary's thoughts emerge from the movements of symbols composed out of teams composed out of signals composed out of the lowest level ants. Yay for reductionism!

Achilles: Who is manipulating the symbols?

Anteater: The whole system, Aunt Hillary.

Anteater: I "read" the top level of the ant colony as easily as Achilles read the "mu" in our picture. Achilles, you "read" your own brain in the same way.

Achilles: That's weird; it's like reading Dickens without seeing the individual letters or even words.

Crab: But that's what you did when you read "mu" without perceiving the lower level "holism" or "reductionism."

They notice that what they had seen as the smallest letters were really made up of tiny "mu"s (as Tortoise had seen from the beginning).

Anteater tells a story about Aunt Hillary where some of the ants made up a symbol that was making her tell him to eat those very ants.

Achilles expresses amazement that the ants were part of a higher-level pattern without being conscious of it. (Ironically, at this point in the dialogue he is an illustration of the same phenomenon.)

Anteater discusses how individual ants are communistic, but Aunt Hillary herself is a rich libertarian. (The example of the latter view you're most likely to be familiar with is the "Tea Party.")

The characters look at some other illustrations, and discuss the previous owner of Aunt Hillary's home. That was another ant colony who died during a sudden rainstorm. None of the individual ants that made it up died: they just got so disorganized that the patterns that made up the colony's memories, personality, and so on were lost. In fact when the ants got reorganized, the new colony they made up, with a new personality, was Aunt Hillary.