Prelude Ant Fugue

(for the Dalziell project)

from “Prelude … Ant Fugue” by Douglas Hofstadter, http://themindi.blogspot.com/2007/02/chapter-11-prelude-ant-fugue.html. There seem to be some typos. I’ve got the original book (somewhere).

Note that the ant colony is gendered female!

—

TORTOISE: Dr. Anteater. Could you tell us more about ant colonies, from a reductionistic point of view?

ANTEATER: Gladly. As Mr. Crab mentioned to you, my profession has me quite a long way into the understanding of ant colonies.

ACHILLES: I can imagine! The profession of Anteater would seem to be synonymous with being an expert on ant colonies!

ANTEATER: I beg your pardon. “Anteater” is not my profession; it is species. By profession, I am a colony surgeon. I specialize in correcting nervous disorders of the colony by the technique of surgical removal.

ACHILLES: Oh, I see. But what do you mean by “nervous disorders’ an ant colony?

ANTEATER: Most of-my clients suffer from some sort of speech impairment. You know, colonies which have to grope for words in every situations. It can be quite tragic. I attempt to remedy the situation

by, uhh-removing-the defective part of the colony. These operations are sometimes quite involved, and of course years of study are required before one can perform them.

ACHILLES: But-isn’t it true that, before one can suffer from speech impairment, one must have the faculty of speech?

ANTEATER: Right.

ACHILLES: Since ant colonies don’t have that faculty, I am a little confused.

CRAB: It’s too bad, Achilles, that you weren’t here last week, when Dr. Anteater and Aunt Hillary were my house guests. I should have thought of having you over then.

ACHILLES: Is Aunt Hillary your aunt, Mr. Crab? CRAB: Oh, no, she’s not really anybody’s aunt.

ANTEATER: But the poor dear insists that everybody should call her that, even strangers. It’s just one of her many endearing quirks.

CRAB: Yes, Aunt Hillary is quite eccentric, but such a merry old soul. It’s a shame I didn’t have you over to meet her last week.

ANTEATER: She’s certainly one of the best-educated ant colonies I have ever had the good fortune to know. The two of us have spent many a long evening in conversation on the widest range of topics.

ACHILLES: I thought anteaters were devourers of ants, not patrons of ant-intellectualism!

ANTEATER: Well, of course the two are not mutually inconsistent. I am on the best of terms with ant colonies. It’s just ants that I eat, not colonies-and that is good for both parties: me, and the colony.

ACHILLES: How is it possible that

TORTOISE: How is it possible that

ACHILLES: -having its ants eaten can do an ant colony any good?

CRAB: How is it possible that

TORTOISE: -having a forest fire can do a forest any good?

ANTEATER: How is it possible that

CRAB: -having its branches pruned can do a tree any good?

ANTEATER: -having a haircut can do Achilles any good?

TORTOISE: Probably the rest of you were too engrossed in the discussion to notice the lovely stretto which just occurred in this Bach fugue.

ACHILLES: What is a stretto?

TORTOISE: Oh, I’m sorry; I thought you knew the term. It is where one theme repeatedly enters in one voice after another, with very little delay between entries.

ACHILLES: If I listen to enough fugues, soon I’ll know all of these things and will be able to pick them out myself, without their having to be pointed out.

TORTOISE: Pardon me, my friends. I am sorry to have interrupted. Dr. Anteater was trying to explain how eating ants is perfectly consistent with being a friend of an ant colony.

ACHILLES: Well, I can vaguely see how it might be possible for a limited and regulated amount of ant consumption to improve the overall health of a colony-but what is far more perplexing is all this talk about having conversations with ant colonies. That’s impossible. An ant colony is simply a bunch of individual ants running around at random looking for food and making a nest.

ANTEATER: You could put it that way if you want to insist on seeing the trees but missing the forest, Achilles. In fact, ant colonies, seen as wholes, are quite well-defined units, with their own qualities, at times including the mastery of language.

ACHILLES: I find it hard to imagine myself shouting something out loud in the middle of the forest, and hearing an ant colony answer back.

ANTEATER: Silly fellow! That’s not the way it happens. Ant colonies don’t converse out loud, but in writing. You know how ants form trails leading them hither and thither?

ACHILLES: Oh, yes-usually straight through the kitchen sink and into my peach jam.

ANTEATER: Actually, some trails contain information in coded form. If you know the system, you can read what they’re saying just like a book.

ACHILLES: Remarkable. And can you communicate back to them?

ANTEATER: Without any trouble at all. That’s how Aunt Hillary and I have conversations for hours. I take a stick and draw trails in the moist ground, and watch the ants follow my trails. Presently, a new trail starts getting formed somewhere. I greatly enjoy watching trails develop. As they are, forming, I anticipate how they will continue (and more often I am wrong than right). When the trail is -completed, I know what Aunt Hillary is thinking, and I in turn make my reply.

ACHILLES: There must be some amazingly smart ants in that colony, I’ll say that.

ANTEATER: I think you are still having some difficulty realizing the difference in levels here. Just as you would never confuse an individual tree with a forest, so here you must not take an ant for the colony. You see, all the ants in Aunt Hillary are as dumb as can be. They couldn’t converse to save their little thoraxes!

ACHILLES: Well then, where does the ability to converse come from? It must reside somewhere inside the colony! I don’t understand how the ants can all be unintelligent, if Aunt Hillary can entertain you for hours with witty banter.

TORTOISE: It seems to me that the situation is not unlike the composition of a human brain out of neurons. Certainly no one would insist that individual brain cells have to be intelligent beings on their own, in order to explain the fact that a person can have an intelligent conversation.

ACHILLES: Oh, no, clearly not. With brain cells, I see your point completely. Only … ants are a horse of another color. I mean, ants just roam about at will, completely randomly, chancing now and then upon a morsel of food…. They are free to do what they want to do, and with that freedom, I don’t see at all how their behavior, seen as a whole, can amount to anything coherent-especially something so coherent as the brain behavior necessary for conversing.

CRAB: It seems to me that the ants are free only within certain constraints. For example, they are free to wander, to brush against each other, to pick up small items, to work on trails, and so on. But they never step out of that small world, that ant-system, which they are in. It would never occur to them, for they don’t have the mentality to imagine anything of the kind. Thus the ants are very reliable components, in the sense that you can depend on them to perform certain kinds of tasks in certain ways.

ACHILLES: But even so, within those limits they are still free, and they just act at random, running about incoherently without any regard for the thought mechanisms of a higher-level being which Dr. Anteater asserts they are merely components of.

ANTEATER: Ah, but you fail to recognize one thing, Achilles-the regularity of statistics.

ACHILLES: How is that?

ANTEATER: For example, even though ants as individuals wander about in what seems a random way, there are nevertheless overall trends, involving large numbers of ants, which can emerge from that chaos.

ACHILLES: Oh, I know what you mean. In fact, ant trails are a perfect example of such a phenomenon. There, you have really quite unpredictable motion on the part of any single ant-and yet, the trail itself seems to remain well defined and stable. Certainly that must mean that the individual ants are not just running about totally at random.

ANTEATER: Exactly, Achilles. There is some degree of communication among the ants, just enough to keep them from wandering off completely at random. By this minimal communication they can remind each other that they are not alone but are cooperating with teammates. It takes a large number of ants, all reinforcing each other this way, to sustain any activity-such as trail building-for any length of time. Now my very hazy understanding of the operation of brains leads me to believe that something similar pertains to the firing of neurons. Isn’t it true, Mr. Crab, that it takes a group of neurons firing in order to make another neuron fire?

CRAB: Definitely. Take the neurons in Achilles’ brain, for example. Each neuron receives signals from neurons attached to its input lines, and if the sum total of inputs at any moment exceeds a critical threshold, then that neuron will fire and send its own output pulse rushing off to other neurons, which may in turn fire-and on down the line it goes. The neural flash swoops relentlessly in its Achillean path, in shapes stranger then the dash of a gnat-hungry swallow; every twist, every turn foreordained by the neural structure in Achilles’ brain, until sensory input messages interfere.

ACHILLES: Normally, I think that I’m in control of what I think-but the way you put it turns it all inside out, so that it sounds as though “I” am just what comes out of all this neural structure, and natural law. It makes what I consider my self sound at best like a by-product of an organism governed by natural law and, at worst, an artificial notion produced by my distorted perspective. In other words, you make me feel like I don’t know who-or what-I am, if anything.

TORTOISE: You’ll come to understand much better as we go along. But Dr. Anteater-what do you make of this similarity?

ANTEATER: I knew there was something parallel going on in the two very different systems. Now I understand it much better. It seems that group phenomena which have coherence-trail building, for example-will take place only when a certain threshold number of ants get

involved. If an effort is initiated, perhaps at random, by a few ants in some locale, one of two things can happen: either it will fizzle out after a brief sputtering start

ACHILLES: When there aren’t enough ants to keep the thing rolling?

ANTEATER: Exactly. The other thing that can happen is that a critical mass of ants is present, and the thing will snowball, bringing more and more ants into the picture. In the latter case, a whole “team” is brought into being which works on a single project. That project might be trail making, or food gathering, or it might involve nest keeping. Despite the extreme simplicity of this scheme on a small scale, it can give rise to very complex consequences on a larger scale.

ACHILLES: I can grasp The general idea of order emerging from chaos, as you sketch it, but that still is a long way from the ability to converse. After all, order also emerges from chaos when molecules of a gas bounce against each other randomly-yet all that results there is an amorphous mass with but three parameters to characterize it: volume, pressure, and temperature. Now that’s a far cry from the ability to understand the world, or to talk about it!

ANTEATER: That highlights a very interesting difference between the explanation of the behavior of an ant colony and the explanation of the behavior of gas inside a container. One can explain the behavior of the gas simply by calculating the statistical properties of the motions of its molecules. There is no need to discuss any higher elements of structure than molecules, except the full gas itself. On the other hand, in an ant colony, you can’t even begin to understand the activities of the colony unless you go through several layers of structure.

ACHILLES: I see what you mean. In a gas, one jump takes you from the lowest level-molecules-to the highest level-the full gas. There are no intermediate levels of organization. Now how do intermediate levels of organized activity arise in an ant colony?

ANTEATER: It has to do with the existence of several different varieties of ants inside any colony.

ACHILLES: Oh, yes. I think I have heard about that. They are called “castes,” aren’t they?

ANTEATER: That’s correct. Aside from the queen, there are males, who do practically nothing toward the upkeep of the nest, and then —

ACHILLES: And of course there are soldiers-glorious fighters against communism!

CRAB: Hmm . . . I hardly think that could be right, Achilles. An ant colony is quite communistic internally, so why would its soldiers fight against communism? Or am I right, Dr. Anteater?

ANTEATER: Yes, about colonies you are right, Mr. Crab; they are indeed based on somewhat communistic principles. But about soldiers Achilles is somewhat naive. In fact, the so-called “soldiers” are hardly adept at fighting at all. They are slow, ungainly ants with giant heads, who can snap with their strong jaws, but are hardly to be glorified. As in a true communistic state, it is rather the workers who are to be glorified. It is they who do most of the chores, such as food gathering, hunting, and nursing of the young. It is even they who do most of the fighting.

ACHILLES: Bah. That is an absurd state of affairs. Soldiers who won’t fight!

ANTEATER: Well, as I just said, they really aren’t soldiers at all. It’s the workers who are soldiers; the soldiers are just lazy fatheads.

ACHILLES: Oh, how disgraceful! Why, if I were an ant, I’d put some discipline in their ranks! I’d knock some sense into those fatheads!

TORTOISE: If you were an ant? How could a myrmidon like you be an ant? There is no way to map your brain onto an ant brain, so it seems to me to be a pretty fruitless question to worry over. More reasonable would be the proposition of mapping your brain onto an ant colony. … But let us not get sidetracked. Let Dr. Anteater continue with his most illuminating description of castes and their role in the higher levels of organization.

ANTEATER: Very well. There are all sorts of tasks which must be accomplished in a colony, and individual ants develop specializations. Usually an ant’s specialization changes as the ant ages. And of course it is also dependent on the ant’s caste. At any one moment, in any small area of a colony, there are ants of all types present. Of course, one caste may be be very sparse in some places and very dense in others.

CRAB: Is the density of a given caste, or specialization, just a random thing? Or is there a reason why ants of one type might be more heavily concentrated in certain areas, and less heavily in others?

ANTEATER: I’m glad you brought that up, since it is of crucial importance in understanding how a colony thinks. In fact, there evolves, over a long period of time, a very delicate distribution of castes inside a colony. And it is this distribution that allows the colony to have the complexity that underlies the ability to converse with me.

ACHILLES: It would seem to me that the constant motion of ants to and fro would completely prevent the possibility of a very delicate distribution. Any delicate distribution would be quickly destroyed by all the random motions of ants, just as any delicate pattern among molecules in a gas would not survive for an instant, due to the random bombardment from all sides.

ANTEATER: In an ant colony, the situation is quite the contrary. In fact, it is just exactly the constant to-ing and fro-ing of ants inside the colony which adapts the caste distribution to varying situations, and thereby preserves the delicate caste distribution. You see, the caste distribution cannot remain as one single rigid pattern; rather, it must constantly be changing so as to reflect, in some manner, the realworld situation with which the colony is dealing, and it is precisely the motion inside the colony which updates the caste distribution, so as to keep it in line with the present circumstances facing the colony.

TORTOISE: Could you give an example?

ANTEATER: Gladly. When I, an anteater, arrive to pay a visit to Aunt Hillary, all the foolish ants, upon sniffing my odor, go into a panic-which means, of course, that they begin running around completely differently from the way they were before ’I arrived.

ACHILLES: But that’s understandable, since you’re a dreaded enemy of the colony.

ANTEATER: Oh, no. I must reiterate that, far from being an enemy of the colony, I am Aunt Hillary’s favorite companion. And Aunt Hillary is, my favorite aunt. I grant you, I’m quite feared by all the individual ants in the colony-but that’s another matter entirely. In any case, you see that the ants’ action in response to my arrival completely changes the internal distribution of ants.

ACHILLES: That’s clear.

ANTEATER: And that sort of thing is the updating which I spoke of. The new distribution reflects my presence. One can describe the change from old state to new as having added a “piece of knowledge” to the colony.

ACHILLES: How can you refer to the distribution of different types of ants inside a colony as a “piece of knowledge”?

ANTEATER: Now there’s a vital point. It requires some elaboration. You see, what it comes down to is how you choose to describe the caste distribution. If you continue to think in terms of the lower levels —

individual ants-then you miss the forest for the trees. That’s just toy microscopic a level, and when you think microscopically, you’re bound to miss some large-scale features. You’ve got to find the proper high-level framework in which to describe the caste distribution-only then will it make sense how the caste distribution cal encode many pieces of knowledge.

ACHILLES: Well, how do you find the proper-sized units in which t~ describe the present state of the colony, then?

ANTEATER: All right. Let’s begin at the bottom. When ants need to get something done, they form little “teams,” which stick together t~ perform a chore. As I mentioned earlier, small groups of ants are constantly forming and unforming. Those which actually exist for while are the teams, and the reason they don’t fall apart is that there really is something for them to do.

ACHILLES: Earlier you said that a group will stick together if its size exceeds a certain threshold. Now you’re saying that a group will stick together if there is something for it to do.

ANTEATER: They are equivalent statements. For instance, in food gathering, if there is an inconsequential amount of food somewhere which gets discovered by some wandering ant who then attempts to communicate its enthusiasm to other ants, the number of ants who respond will be proportional to the size of the food sample-and a inconsequential amount will not attract enough ants to surpass the threshold. Which is exactly what I meant by saying there is nothing to do-too little food ought to be ignored.

ACHILLES: I see. I assume that these “teams” are one of the levels c structure falling somewhere in between the single-ant level and the colony level.

ANTEATER: Precisely. There exists a special kind of team, which I call “signal”-and all the higher levels of structure are based on signal In fact, all the higher entities are collections of signals acting is concert. There are teams on higher levels whose members are no ants, but teams on lower levels. Eventually you reach the lowest-level teams-which is to say, signals-and below them, ants.

ACHILLES: Why do signals deserve their suggestive name?

ANTEATER: It comes from their function. The effect of signals is to traps port ants of various specializations to appropriate parts of the colony. So the typical story of a signal is thus: It comes into existence by exceeding the threshold needed for survival, then it migrates for

some distance through the colony, and at some point it more or less disintegrates into its individual members, leaving them on their own.

ACHILLES: It sounds like a wave, carrying sand dollars and seaweed from afar, and leaving them strewn, high and dry, on the shore.

ANTEATER: In a way that’s analogous, since the team does indeed deposit something which it has carried from a distance, but whereas the water in the wave rolls back to the sea, there is no analogous carrier substance in the case of a signal, since the ants themselves compose it.

TORTOISE: And I suppose that a signal loses its coherency just at some spot in the colony where ants of that type were needed in the first place.

ANTEATER: Naturally.

ACHILLES: Naturally? It’s not so obvious to me that a signal should always go just where it is needed. And even if it goes in the right direction, how does it figure out where to decompose? How does it know it has arrived?

ANTEATER: Those are extremely important matters, since they involve explaining the existence of purposeful behavior-or what seems to be purposeful behavior-on the part of signals. From the description, one would be inclined to characterize the signals’ behavior as being oriented toward filling a need, and to call it “purposeful.” But you can look at it otherwise.

ACHILLES: Oh, wait. Either the behavior is purposeful, or it is not. I don’t see how you can have it both ways.

ANTEATER: Let me explain my way of seeing things, and then see if you agree. Once a signal is formed, there is no awareness on its part that it should head off in any particular direction. But here the delicate caste distribution plays a crucial role. It is what determines the motion of signals through the colony, and also how long a signal will remain stable, and where it will “dissolve.”

ACHILLES: So everything depends on the caste distribution, eh?

ANTEATER: Right. Let’s say a signal is moving along. As it goes, the ants which compose it interact, either by direct contact or by exchange of scents, with ants of the local neighborhoods which it passes through. The contacts and scents provide information about local matters of urgency, such as nest building, or nursing, or whatever. The signal will remain glued together as long as the local needs are different

from what it can supply; but if it can contribute, it disintegrates, spilling a fresh team of usable ants onto the scene. Do you see now how the caste distribution acts as an overall guide of the teams inside the colony?

ACHILLES: I do see that.

ANTEATER: And do you see how this way of looking at things requires attributing no sense of purpose to the signal? ACHILLES: I think so. Actually, I’m beginning to see things from two different vantage points. From an ant’s-eye point of view, a signal has no purpose. The typical ant in a signal is just meandering around the colony, in search of nothing in particular, until it finds that it feels like stopping. Its teammates usually agree, and at that moment the team unloads itself by crumbling apart, leaving just its members but none of its coherency. No planning is required, no looking ahead; nor is any search required to determine the proper direction. But from the colony’s point of view, the team has just responded to a message which was written in the language of the caste distribution. Now from this perspective, it looks very much like purposeful activity.

CRAB: What would happen if the caste distribution were entirely random? Would signals still band and disband?

ANTEATER: Certainly. But the colony would not last long, due to the meaninglessness of the caste distribution.

CRAB: Precisely the point I wanted to make. Colonies survive because their caste distribution has meaning, and that meaning is a holistic aspect, invisible on lower levels. You lose explanatory power unless you take that higher level into account.

ANTEATER: I see your side; but I believe you see things too narrowly. CRAB: How so?

ANTEATER: Ant colonies have been subjected to the rigors of evolution for billions of years. A few mechanisms were selected for, and most were selected against. The end result was a set of mechanisms which make ant colonies work as we have been describing. If you could watch the whole process in a movie-running a billion or so times faster than life, of course-the emergence of various mechanisms would be seen as natural responses to external pressures, just as bubbles in boiling water are natural responses to an external heat source. I don’t suppose you see “meaning” and “purpose” in the bubbles in boiling water-or do you?

CRAB: No, but —

ANTEATER: Now that’s my point. No matter how big a bubble is, it owes its existence to processes on the molecular level, and you can forget about any “higher-level laws.” The same goes for ant colonies and their teams. By looking at things from the vast perspective of evolution, you can drain the whole colony of meaning and purpose. They become superfluous notions.

ACHILLES: Why, then, Dr. Anteater, did you tell me that you talked with Aunt Hillary? It now seems that you would deny that she can talk or think at all.

ANTEATER: I am not being inconsistent, Achilles. You see, I have as much difficulty as anyone else in seeing things on such a grandiose time scale, so I find it much easier to change points of view. When I do so, forgetting about evolution and seeing things in the here and now, the vocabulary of teleology comes back: the meaning of the caste distribution and the purposefulness of signals. This not only happens when I think of ant colonies, but also when I think about my own brain and other brains. However, with some effort I can always remember the other point of view if necessary, and drain all these systems of meaning, too.

CRAB: Evolution certainly works some miracles. You never know the next trick it will pull out of its sleeve. For instance, it wouldn’t surprise me one bit if it were theoretically possible for two or more “signals” to pass through each other, each one unaware that the other one is also a signal; each one treating the other as if it were jus part of the background population.

ANTEATER: It is better than theoretically possible; in fact it happens routinely!

ACHILLES: Hmm…. What a strange image that conjures up in my mind. I can just imagine ants moving in four different directions, some black, some white, criss-crossing, together forming an orderly pattern, almost like-like

TORTOISE: A fugue, perhaps?

ACHILLES: Yes-that’s it! An ant fugue!

CRAB: An interesting image, Achilles. By the way, all that talk of boiling water made me think of tea. Who would like some more?

ACHILLES: I could do with another cup, Mr. C.

CRAB: Very good.

An “ant fugue” drawn by M. C. Escher (woodcut, 1953.)

ACHILLES: Do you suppose one could separate out the different visual “voices” of such an “ant fugue”? I know how hard it is for me-

TORTOISE: Not for me, thank you.

ACHILLES: -to track a single voice

ANTEATER: I’d like some too, Mr. Crab

ACHILLES: -in a musical fugue

ANTEATER:-if it isn’t too much trouble.

ACHILLES: -when all of them

CRAB: Not at all. Four cups of tea —

TORTOISE: Three!

ACHILLES: -are going at once.

CRAB: -coming right up!