Marvin Minsky

Marvin Minsky Artificial Intelligence Laboratory Massachusetts Institute of Technology Cambridge, Massachusetts 02139 Why Do We Like Music? Why do we like music? Our culture immerses us in it for hours each day, and everyone knows how it touches our emotions, but few think of how music touches other kinds of thought. It is astonishing how little curiosity we have about so pervasive an "environ-mental" influence. What might we dis- cover if we were to study musical thinking? Have we the tools for such work? Years ago, when science still feared meaning, the new field of research called artificial intelligence (AI) started to supply new ideas about "representation of knowl- edge" that I'll use here. Are such ideas too alien for anything so subjective and irrational, aesthetic, and emotional as music? Not at all. l think the prob- lems are the same and those distinctions wrongly drawn: only the surface of reason is rational. I don't mean that understanding emotion is easy, only that understanding reason is probably harder. Our cul- ture has a universal myth in which we see emotion as more complex and obscure than intellect. In- deed, emotion might be "deeper" in some sense of prior evolution, but this need not make it harder to understand ; in fact, I think today we actually know much more about emotion than about reason. Certainly we know a bit about the obvious pro- cesses of reason—the ways we organize and repre- sent ideas we get. But whence come those ideas that so conveniently fill these envelopes of order? A poverty of language shows how little this concerns us: we "get" ideas; they "come" to us; we are "re- minded of" them. I think this shows that ideas come from processes obscured from us and with which our surface thoughts are almost uninvolved. Instead, we are entranced with our emotions, which are so easily observed in others and ourselves. Per- This is a revised and updated version of A.1. Memo No. 616. The earlier version will also appear in Music, Mind, and Brain: The Neuropsychology of Music edited by Manfred Clynes, and pub- lished by Plenum, New York. 0 1981 by Marvin Minsky Music, Mind, and Meaning haps the myth persists because emotions (by their nature) draw attention, while the processes of rea- son (much more intricate and delicate) must be pri- vate and work best alone. The old distinctions among emotion, reason, and aesthetics are like the earth, air, and fire of an an- cient alchemy. We will need much better concepts than these for a working psychic chemistry. Much of what we now know of the mind emerged in this century from other subjects once considered just as personal and inaccessible but which were explored, for example, by Freud in his work on adults' dreams and jokes, and by Piaget in his work on children's thought and play. Why did such work have to wait for modem times? Before that, chil- dren seemed too childish and humor much too hu- morous for science to take them seriously. Why do we like music? We all are reluctant, with regard to music and art, to examine our sources of pleasure or strength. In part we fear success itself— we fear that understanding might spoil enjoyment. Rightly so: art often loses power when its psycho- logical roots are exposed. No matter; when this happens we will go on, as always, to seek more robust illusions! I feel that music theory has gotten stuck by try- ing too long to find universals. Of course, we would like to study Mozart's music the way scientists analyze the spectrum of a distant star. Indeed, we find some almost universal practices in every musi- cal era. But we must view these with suspicion, for they might show no more than what composers then felt should be universal. If so, the search for truth in art becomes a travesty in which each era's practice only parodies its predecessor's prejudice. (Imagine formulating "laws" for television screen- plays, taking them for natural phenomenon unin- fluenced by custom or constraint of commerce.) The trouble with the search for universal laws of thought is that both memory and thinking inter- act and grow together. We do not just learn about things, we learn ways to think about things; then we learn to think about thinking itself. Before long, 28 Computer Music Journal EFTA00284089 our ways of thinking become so complicated that we cannot expect to understand their details in terms of their surface operation, but we might un- derstand the principles that guide their growth. In much of this article I will speculate about how lis- tening to music engages the previously acquired personal knowledge of the listener. It has become taboo for music theorists to ask why we like what we like: our seekers have forgot- ten what they are searching for. To be sure, we can't account for tastes, in general, because people have various preferences. But this means only that we have to find the causes of this diversity of tastes, and this in turn means we must see that music theory is not only about music, but about how people process it. To understand any art, we must look below its surface into the psychological details of its creation and absorption. If explaining minds seems harder than explaining songs, we should remember that sometimes enlarg- ing problems makes them simpler! The theory of the roots of equations seemed hard for centuries within its little world of real numbers, but it sud- denly seemed simple once Gauss exposed the larger world of (so-called) complex numbers. Similarly, music should make more sense once seen through listeners' minds. Sonata as Teaching Machine Music makes things in our minds, but afterward most of them fade away. What remains? In one old story about Mozart, the wonder child hears a lengthy contrapuntal mass and then writes down the entire score. (I do not believe such tales, for his- tory documents so few of them that they seem to be mere legend, though by that argument Mozart also would seem to be legend.) Most people do not even remember the themes of an evening's concert. Yet, when the tunes arc played again, they are rec- ognized. Something must remain in the mind to cause this, and perhaps what we learn is not the music itself but a way of hearing it. Compare a sonata to a teacher. The teacher gets the pupils' attention, either dramatically or by the quiet trick of speaking softly. Next, the teacher presents the elements carefully, not introducing too many new ideas or developing them too far, for un- til the basics are learned the pupils cannot build on them. So, at first, the teacher repeats a lot. Sonatas, too, explain first one idea, then another, and then recapitulate it all. (Music has many forms and there are many ways to teach. I do not say that compos- ers consciously intend to teach at all, yet they are masters at inventing forms for exposition, including those that swarm with more ideas and work our minds much harder.) Thus expositions show the basic stuff—the atoms of impending chemistries and how some simple compounds can be made from those atoms. Then, in developments, those now-familiar com- pounds, made from bits and threads of beat and tone, can clash or merge, contrast or join together. We find things that do not fit into familiar frame- works hard to understand —such things seem meaningless. I prefer to turn that around: a thing has meaning only after we have learned some ways to represent and process what it means, or to under- stand its parts and how they are put together. What is the difference between merely knowing (or remembering, or memorizing) and understand- ing? We all agree that to understand something we must know what it means, and that is about as far as we ever get. I think I know why that happens. A thing or idea seems meaningful only when we have several different ways to represent it—different per- spectives and different associations. Then we can turn it around in our minds, so to speak: however it seems at the moment, we can see it another way and we never come to a full stop. In other words, we can think about it. If there were only one way to represent this thing or idea, we would not call this representation thinking. So something has a "meaning" only when it has a few; if we understood something just one way, we would not understand it at all. That is why the seekers of the "real" meanings never find them. This holds true especially for words like under- stand. That is why sonatas start simply, as do the best of talks and texts. The basics are repeated sev- eral times before anything larger or more complex is presented. No one remembers word for word all that is said in a lecture or all notes that are played Minsky 29 EFTA00284090 Fig. 1. Introductory mea- sures of Ludwig van Beethoven's Symphony No. 5 in C Minor. Flutes Mote Clarinets in Bb Broca Fla= in Bib Trumpets in C Timpani in C.G Violin I Violin II Viola Cello Br Allegro omAtorloOhasel -401/4 2 4Ai le! ' vvit - 4 4 I sr. C) ir—trribt, 1 it% 4a, Il (44 Allegro eoerio‘i • soe) 1,111C),rrr I I fr. '171-L1111±j--1D -3— ---L J I kJ in C) Crn1 tttt r cr-r- -CT ? ter in a piece. Yet if we have understood the lecture or piece once, we now "own" new networks of knowl- edge about each theme and how it changes and re- lates to others. No one could remember all of Bee- thoven's Fifth Symphony from a single hearing, but neither could one ever again hear those first four notes as just four notes! Once a tiny scrap of sound, these four notes have become a known thing—a locus in the web of all the other things we know and whose meanings and significances depend on one another (Fig. I). Learning to recognize is not the same as memo- rizing. A mind might build an agent that can sense a certain stimulus, yet build no agent that can re- produce it. How could such a mind learn that the first half subject of Beethoven's Fifth—call it A—prefigures the second half—call it B? It is simple: an agent A that recognizes A sends a message to another agent B, built to recognize B. That message serves to "lower B's threshold" so that after A hears A, B will react to smaller hints of B than it would otherwise. As a result, that mind "expects" to hear B after A; that is, it will discern B, given fewer or more subtle cues, and might "complain" if it can- not. Yet that mind cannot reproduce either theme in any generative sense. The point is that interagent messages need not be in surface music languages, but can be in codes that influence certain other agents to behave in different ways. (Andor Kovach pointed out to me that composers do not dare use this simple, four-note motive any more. So memorable was Beethoven's treatment 30 Computer Music Journal EFTA00284091 14 "IA rffrk t'k IR peas& f Pp '"S tRir kr 1 * if a a I 04 4 / a I O .in LJ 1 ,I77 a prism. a I I if ll - I - I - I - lypedAillikl II - l-t-I - + - A —eller r—tai f---tLr r 1 1 j WS r Cr II f Ji Ji a sik Cur f J j 't jjeJ a J k 4 40L) • nJ I r 141 rrr kr' I rrr 'a k 4 a J71 ,11 IT III 4 pin a C) CA, C- &CO ' i-AMEN -rtetfi&v r r id (sr if ft_ tin mb, r ■ nOActi -475- -2 Jig! rte& -4 I 'Ifs .1 4- I Minsky 31 4 EFTA00284092 'digit fir MC? r I tf I a ✓ 1 I P ir yt- -41 & 304 ettrtnit nittritt ii OFF tarit 4444 fr irr4 cm 0*-- e e e 4 4-7---4,137t4j i MIL.74 JJ -3giJJJ fin CH .147 d • • d ; i 1 i ' 4 -.1.1l 1 i .1 1 e v -. ef 3 1 1 I 4 Al _1 I i t di _..,1 _.... 4 0 ? ✓ ✓ ✓ f Ac-TiCrf ark — IMP 1 1 t lints II II Is A €f 5trrkp 1 f ; 40L *-kJ-4J- PP 4 lig-I-I -1-1- 1 - I - I 4 i 32 Computer Music journal EFTA00284093 that now an accidental hint of it can wreck another piece by unintentionally distracting the listener.) If sonatas are lessons, what are the subjects of those lessons? The answer is in the question! One thing the Fifth Symphony taught us is how to hear those first four notes. The surface form is just de- scending major third, first tone repeated thrice. At first, that pattern can be heard two different ways: (1) fifth and third in minor mode or (2) third and first, in major. But once we have heard the sym- phony, the latter is unthinkable —a strange con- straint to plant in all our heads! Let us see how it is taught. The Fifth declares at once its subject, then its near-identical twin. First comes the theme. Pre- sented in a stark orchestral unison, its minor mode location in tonality is not yet made explicit, nor is its metric frame yet clear: the subject stands alone in time. Next comes its twin. The score itself leaves room to view this transposed counterpart as a complement or as a new beginning. Until now, fermatas have hidden the basic metric frame, a pair of twinned four-measure halves. So far we have only learned to hear those halves as separate wholes. The next four-measure metric half-frame shows three versions of the subject, one on each ascending pitch of the tonic triad. (Now we are sure the key is minor.) This shows us how the subject can be made to overlap itself, the three short notes packed per- fectly inside the long tone's time-space. The second half-frame does the same, with copies of the com- plement ascending the dominant seventh chord. This fits the halves together in that single, most familiar, frame of harmony. In rhythm, too, the halves are so precisely congruent that there is no room to wonder how to match them—and attach them—into one eight-measure unit. The next eight-measure frame explains some more melodic points: how to smooth the figure's firmness with passing tones and how to counter- poise the subject's own inversion inside the long note. (I think that this evokes a sort of sinusoidal motion-frame idea that is later used to represent the second subject.) It also illustrates compression of harmonic time; seen earlier, this would obscure the larger rhythmic unit, but now we know enough to place each metric frame precisely on the after- image of the one before. Cadence. Silence. Almost. Total. Now it is the second subject-twin's turn to stand alone in time. The conductor must select a symme- try: he or she can choose to answer prior cadence, to start anew, or to close the brackets opened at the very start. (Can the conductor do all at once and maintain the metric frame?) We hear a long, long unison F (subdominant?) for, underneath that silent surface sound, we hear our minds rehearsing what was heard. The next frame reveals the theme again, descend- ing now by thirds. (We see that it was the dominant ninth, not subdominant at all. The music fooled us that time, but never will again.) Then tour de force: the subject climbs, sounding on every scale degree. This new perspective shows us how to see the four- note theme as an appogiatura. Then, as it descends on each tonic chord-note, we are made to see it as a fragment of arpeggio. That last descent completes a set of all four possibilities, harmonic and direc- tional. (Is this deliberate didactic thoroughness, or merely the accidental outcome of the other sym- metries?) Finally, the theme's melodic range is squeezed to nothing, yet it survives and even gains strength as single tone. It has always seemed to me a mystery of art, the impact of those moments in quartets when texture turns to single line and forte- piano shames sforzando in perceived intensity. But such acts, which on the surface only cause the structure or intensity to disappear, must make the largest difference underneath. Shortly, I will pro- pose a scheme in which a sudden, searching change awakes a lot of mental difference -finders. This very change wakes yet more difference -finders, and this awakening wakes still more. That is how sudden silence makes the whole mind come alive. We are "told" all this in just one minute of the lesson and I have touched but one dimension of its rhetoric. Besides explaining, teachers beg and threaten, calm and scare; use gesture, timbre, quaver, and sometimes even silence. This is vital in music, too. Indeed, in the Fifth, it is the start of the subject! Such "lessons" must teach us as much Minsky 33 EFTA00284094 about triads and triplets as mathematicians have learned about angles and sides! Think how much we can learn about minor second intervals from Beethoven's Grosse Fuge in &fiat, Opus 133. What Use Is Music? Why on earth should anyone want to learn such things? Geometry is practical—for building pyra• mids, for instance—but of what use is musical knowledge? Here is one idea. Each child spends endless days in curious ways; we call this play. A child stacks and packs all kinds of blocks and boxes, lines them up, and knocks them down. What Syntactic Theories of Music is that all about? Clearly, the child is learning about space! But how on earth does one learn about time? Can one time fit inside another? Can two of them go side by side? In music, we find out! It is often said that mathematicians are unusually involved in music, but that musicians are not involved in mathematics. Perhaps both mathematicians and musicians like to make simple things more compli- cated, but mathematics may be too constrained to satisfy that want entirely, while music can be rig- orous or free. The way the mathematics game is played, most variations lie outside the rules, while music can insist on perfect canon or tolerate a ca- sual accompaniment. So mathematicians might need music, but musicians might not need mathe- matics. A simpler theory is that since music en- gages us at earlier ages, some mathematicians are those missing mathematical musicians. Most adults have some childlike fascination for making and arranging larger structures out of smaller ones. One kind of musical understanding involves building large mental structures out of smaller, musical parts. Perhaps the drive to build those mental music structures is the same one that makes us try to understand the world. (Or perhaps that drive is just an accidental mutant variant of it; evolution often copies needless extra stuff, and minds so new as ours must contain a lot of that.) Sometimes, though, we use music as a trick to misdirect our understanding of the world. When thoughts are painful we have no way to make them stop. We can attempt to turn our minds to other matters, but doing this (some claim) just submerges the bad thoughts. Perhaps the music that some call background music can tranquilize by turning un- der-thoughts from bad to neutral, leaving the sur- face thoughts free of affect by diverting the uncon- scious. The structures we assemble in that detached kind of listening might be wholly solipsistic webs of meaninglike cross-references that nowhere touch "reality" In such a self-constructed world, we would need no truth or falsehood, good or evil, pain or joy. Music, in this unpleasant view, would serve as a fine escape from tiresome thoughts. Contrast two answers to the question, Why do we like certain tunes? Because they have certain structural features. Because they resemble other tunes we like. The first answer has to do with the laws and rules that make tunes pleasant. In language, we know some laws for sentences ; that is, we know the forms sentences must have to be syntactically acceptable, if not the things they must have to make them sensible or even pleasant to the ear. As to melody, it seems, we only know some features that can help—we know of no absolutely essen- tial features. I do not expect much more to come of a search for a compact set of rules for musi- cal phrases. (The point is not so much what we mean by rule, as how large a body of knowledge is involved.) The second answer has to do with significance outside the tune itself, in the same way that asking, Which sentences are meaningful? takes us outside shared linguistic practice and forces us to look upon each person's private tangled webs of thought. Those private webs feed upon themselves, as in all spheres involving preference: we tend to like things that remind us of the other things we like. For ex- ample, some of us like music that resembles the songs, carols, rhymes, and hymns we liked in child- hood. All this begs this question: If we like new tunes that are similar to those we already like, where does our liking for music start? I will come back to this later. 34 Computer Music Journal EFTA00284095 The term resemble begs a question also: What are the rules of musical resemblance? I am sure that this depends a lot on how melodies are "repre- sented" in each individual mind. In each single mind, some different "mind parts" do this different ways: the same tune seems tat different times) to change its rhythm, mode, or harmony. Beyond that, individuals differ even more. Some listeners squirm to symmetries and shapes that others scarcely hear at all and some fine fugue subjects seem banal to those who sense only a single line. My guess is that our contrapuntal sensors harmonize each fading memory with others that might yet be played; per- haps Bach's mind could do this several ways at once. Even one such process might suffice to help an improviser plan what to try to play next. (To try is sufficient since improvisers, like stage magicians, know enough "vamps" or "ways out" to keep the music going when bold experiments fail.) How is it possible to improvise or comprehend a complex contrapuntal piece? Simple statistical ex- planations cannot begin to describe such processes. Much better are the generative and transforma- tional (e.g., neo-Schenkerian) methods of syntactic analysis, but only for the simplest analytic uses. At best, the very aim of syntax-oriented music theo- ries is misdirected because they aspire to describe the sentences that minds produce without attempt- ing to describe how the sentences are produced. Meaning is much more than sentence structure. We cannot expect to be able to describe the anatomy of the mind unless we understand its embryology. And so (as with most any other very complicated matter), science must start with surface systems of description. But this surface taxonomy, however elegant and comprehensive in itself, must yield in the end to a deeper, causal explanation. To un- derstand how memory and process merge in "lis- tening," we will have to learn to use much more "procedural" descriptions, such as programs that describe how processes proceed. In science, we always first explain things in terms of what can be observed (earth, water, fire, air). Yet things that come from complicated pro- cesses do not necessarily show their natures on the surface. (The steady pressure of a gas conceals those countless, abrupt microimpacts.) To speak of what such things might mean or represent, we have to speak of how they are made. We cannot describe how the mind is made with- out having good ways to describe complicated pro- cesses. Before computers, no languages were good for that. Piaget tried algebra and Freud tried dia- grams; other psychologists used Markov chains and matrices, but none came to much. Behaviorists, quite properly, had ceased to speak at all. Linguists flocked to formal syntax, and made progress for a time but reached a limit: transformational grammar shows the contents of the registers (so to speak), but has no way to describe what controls them. This makes it hard to say how surface speech re lates to underlying designation and intent—a baby- and-bath-water situation. The reason I like ideas from AI research is that there we tend to seek pro- cedural description first, which seems more appro- priate for mental matters. I do not see why so many theorists find this ap- proach disturbing. It is true that the new power de- rived from this approach has a price: we can say more, with computational description, but prove less. Yet less is lost than many think, for mathe- matics never could prove much about such com- plicated things. Theorems often tell us complex truths about the simple things, but only rarely tell us simple truths about the complex ones. To be- lieve otherwise is wishful thinking or "mathemat- ics envy" Many musical problems that resist for- mal solutions may turn out to be tractable anyway, in future simulations that grow artificial musical semantic networks, perhaps by "raising" simulated infants in traditional musical cultures. It will be ex- citing when one of these infants first shows a hint of real "talent." Space and Tune When we enter a room, we seem to see it all at once; we are not permitted this illusion when lis- tening to a symphony. "Of course," one might de- clare, for hearing has to thread a serial path through time, while sight embraces a space all at once. Ac- tually, it takes time to see new scenes, though we are not usually aware of this. That totally compel- Minsky 35 EFTA00284096 ling sense that we are conscious of seeing every- thing in the room instantly and immediately is certainly the strangest of our "optical" illusions. Music, too, immerses us in seemingly stable worlds! How can this be, when there is so little of it present at each moment? I will try to explain this by (1) arguing that hearing music is like viewing scenery and (2) by asserting that when we hear good music our minds react in very much the same way they do when we see things.' And make no mis- take: I meant to say "good" music! This little the- ory is not meant to work for any senseless bag of musical tricks, but only for those certain kinds of music that, in their cultural times and places, com- mand attention and approval. To see the problem in a slightly different way, consider cinema. Contrast a novice's clumsy patched and pasted reels of film with those that transport us to other worlds so artfully composed that our own worlds seem shoddy and malformed. What "hides the seams" to make great films so much less than the sum of their parts—so that we do not see them as mere sequences of scenes? What makes us feel that we are there and part of it when we are in fact immobile in our chairs, helpless to deflect an atom of the projected pattern's predetermined destiny? I will follow this idea a little further, then try to ex- plain why good music is both more and less than sequences of notes. Our eyes are always flashing sudden flicks of dif- ferent pictures to our brains, yet none of that sac- cadic action leads to any sense of change or motion in the world; each thing reposes calmly in its "place"! What makes those objects stay so still while images jump and jerk so? What makes us such innate Copernicans? I will first propose how this illusion works in vision, then in music. We will find the answer deep within the way the I. Edward Fredkin suggested to me the theory that listening to music might exercise some innate map-making mechanism in the brain. When I mentioned the puzzle of music's repetitious- ness, he compared it to the way rodents explore new places: first they go one way a little, then back to home. They do it again a few times, then go a little farther. They try small digressions, but frequently return to base. Both people and mice explore new territories that way, making mental maps lest they get lost. Mu- sk might portray this building process, or even exercise those very parts of the mind. mind regards itself. When speaking of illusion, we assume that someone is being fooled. "I know those lines are straight," I say, "but they look bent to me." Who are the different l's and me's? We are all convinced that somewhere in each person struts a single, central self; atomic, indivisible. (And se- cretly we hope that it is also indestructible.) I believe, instead, that inside each mind work many different agents. (The idea of societies of agents (Minsky 1977; 1980a; 19806) originated in my work with Seymour Papert.) All we really need to know about agents is this: each agent knows what happens to some others, but little of what happens to the rest. It means little to say, "Eloise was unaware of X" unless we say more about which of her mind-agents were uninvolved with X. Think- ing consists of making mind-agents work together; the very core of fruitful thought is breaking prob- lems into different kinds of parts and then assign- ing the parts to the agents that handle them best. (Among our most important agents are those that manage these assignments, for they are the agents that embody what each person knows about what he or she knows. Without these agents we would be helpless, for we would not know what our knowing is for.) In that division of labor we call seeing, I will sup- pose that a certain mind-agent called feature-finder sends messages (about features it finds on the ret- inal to another agent, scene-analyzer. Scene- analyzer draws conclusions from the messages it gets and sends its own, in turn, to other mind- parts. For instance, feature-finder finds and tells about some scraps of edge and texture; then scene- analyzer finds and tells that these might fit some bit of shape. Perhaps those features come from glimpses of a certain real table leg. But knowing such a thing is not for agents at this level; scene-analyzer does not know of any such specific things. All it can do is broadcast something about shape to hosts of other agents who specialize in recognizing special things. (Since special things—like tables, words, or dogs— must be involved with memory and learning, there is at least one such agent for every kind of thing this mind has learned to recognize.( Thus, we can hope, this message reaches table-maker, an agent 38 Computer Music Journal EFTA00284097 specialized to recognize evidence that a table is in the field of view. After many such stages, descen- dants of such messages finally reach space-builder, an agent that tries to tell of real things in real space. Now we can see one reason why perception seems so effortless: while messages from scene- analyzer to table-maker are based on evidence that feature-finder supplied, the messages themselves need not say what feature-finder itself did, or how it did it. Partly this is because it would take scene- analyzer too long to explain all that. In any case, the recipients could make no use of all that infor- mation since they are not engineers or psychol- ogists, but just little specialized nerve nets. Only in the past few centuries have painters learned enough technique and trickery to simulate reality. (Once so informed, they often now choose different goals.) Thus space-builder, like an ordi- nary person, knows nothing of how vision works, perspective, foveae, or blind spots. We only learn such things in school: millennia of introspection never led to their suspicion, nor did meditation, transcendental or mundane. The mind holds tightly to its secrets not from stinginess or shame, but simply because it does not know them. Messages, in this scheme, go various ways. Each motion of the eye or head or body makes feature- finder start anew, and such motions are responses (by muscle-moving agents) to messages that scene- analyzer sends when it needs more details to re- solve ambiguities. Scene-analyzer itself responds to messages from "higher up." For instance, space- builder may have asked, "Is that a table?" of table- maker, which replies (to itself), "Perhaps, but it should have another leg—there," so it asks scene- analyzer to verify this, and scene-analyzer gets the job done by making eye-mover look down and to the left. Nor is scene-understander autonomous: its questions to scene-analyzer are responses to re- quests from others. There need be no first cause in such a network. When we look up, we are never afraid that the ground has disappeared, though it certainly has "dis-appeared." This is because space-builder re- members all the answers to its questions and never changes any of those answers without reason; mov-ing our eyes or raising our heads provide no cause to exorcise that floor inside our current spatial model of the room. My paper on frame-systems (Minsky 1974) says more about these concepts. Here we only need these few details. Now, back to our illusions. While feature-finder is not instantaneous, it is very, very fast and a highly parallel pattern matcher. Whatever scene- analyzer asks, feature-finder answers in an eye flick, a mere tenth of a second (or less if we have image buffers). More speed comes from the way in which space-builder can often tell itself, via its own high-speed model memory, about what has been seen before. I argue that all this speed is another root of our illusion: if answers seem to come as soon as questions are asked, they will seem to have been there all along. The illusion is enhanced in yet another way by "expectation" or "default." Those agents know good ways to lie and bluff! Aroused by only partial evi- dence that a table is in view, table-maker supplies space-builder with fictitious details about some "typical table" while its servants find out more about the real one! Once so informed, space-builder can quickly move and plan ahead, taking some risks but ready to make corrections later. This only works, of course, when prototypes arc good and are rightly activated—that is what intelligence is all about. As for "awareness" of how all such things are done, there simply is not room for that. Space- builder is too remote and different to understand how feature-finder does its work of eye fixation. Each part of the mind is unaware of almost all that happens in the others. (That is why we need psy- chologists; we think we know what happens in our minds because those agents are so facile with "de- faults," but we arc almost always wrong.) True, each agent needs to know which of its servants can do what, but as to how, that information has no place or use inside those tiny minds inside our minds. How do both music and vision build things in our minds? Eye motions show us real objects; phrases show us musical objects. We "learn" a room with bodily motions; large musical sections show us musical "places." Walks and climbs move Minsky 37 EFTA00284098 us from room to room; so do transitions between musical sections. Looking back in vision is like re- capitulation in music; both give us time, at certain points, to reconfirm or change our conceptions of the whole. Hearing a theme is like seeing a thing in a room, a section or movement is like a room, and a whole sonata is like an entire building. I do not mean to say that music builds the sorts of things that space- builder does. (That is too naive a comparison of sound and place.) I do mean to say that composers stimulate coherency by engaging the same sorts of interagent coordinations that vision uses to produce its illusion of a stable world using, of course, dif- ferent agents. I think the same is true of talk or writing, the way these very paragraphs make sense— or sense of sense—if any. Composing and Conducting In seeing, we can move our eyes; lookers can choose where they shall look, and when. In music we must listen here; that is, to the part being played now. It is simply no use asking music-finder to look there because it is not then, now. If composer and conductor choose what part we hear, does not this ruin our analogy? When music- analyzer asks its questions, how can music-finder answer them unless, miraculously, the music hap- pens to be playing what music-finder wants at just that very instant? If so, then how can music paint its scenes unless composers know exactly what the listeners will ask at every moment? How to en- sure—when music-analyzer wants it now—that precisely that "something" will be playing now? That is the secret of music; of writing it, playing, and conducting! Music need not, of course, confirm each listener's every expectation ; each plot de- mands some novelty. Whatever the intent, control is required or novelty will turn to nonsense. If al- lowed to think too much themselves, the listeners will find unanswered questions in any score; about accidents of form and figure, voice and line, tem- perament and difference -tone. Composers can have different goals: to calm and soothe, surprise and shock, tell tales, stage scenes, teach new things, or tear down prior arts. For some such purposes composers must use the known forms and frames or else expect misunderstanding. Of course, when expectations are confirmed too often the style may seem dull; this is our concern in the next section. Yet, just as in language, one often best explains a new idea by using older ones, avoiding jargon or too much lexical innovation. If readers cannot understand the words themselves, the sentences may "be Greek to them." This is not a matter of a simple hierarchy, in which each meaning stands on lower-level ones, for example, word, phrase, sentence, paragraph, and chapter. Things never really work that way, and jab- berwocky shows how sense comes through though many words are new. In every era some contempo- rary music changes basic elements yet exploits es- tablished larger forms, but innovations that violate too drastically the expectations of the culture can- not meet certain kinds of goals. Of course this will not apply to works whose goals include confusion and revolt, or when composers try to create things that hide or expurgate their own intentionality, but in these instances it may be hard to hold the audience. Each musical artist must forecast and predirect the listener's fixations to draw attention here and distract it from there—to force the hearer (again, like a magician) to ask only the questions that the composition is about to answer. Only by establish- ing such preestablished harmony can music make it seem that something is there. Rhythm and Redundancy A popular song has 100 measures, 1000 beats. What must the martians imagine we mean by those mea- sures and beats, measures and beats! The words themselves reveal an awesome repetitiousness. Why isn't music boring? Is hearing so like seeing that we need a hundred glances to build each musical image? Some repeti- tive musical textures might serve to remind us of things that persist through time like wind and stream. But many sounds occur only once: we must hear a pin drop now or seek and search for it; that is 38 Computer Music Journal EFTA00284099 why we have no "ear-lids." Poetry drops pins, or says each thing once or not at all. So does some music. Then why do we tolerate music's relentless rhythmic pulse or other repetitive architectural fea- tures? There is no one answer, for we hear in dif- ferent ways, on different scales. Some of those ways portray the spans of time directly, but others speak of musical things, in worlds where time folds over on itself. And there, I think, is where we use those beats and measures. Music's metric frames are tran- sient templates used for momentary matching. Its rhythms are "synchronization pulses" used to match new phrases against old, the better to con- trast them with differences and change. As dif- ferences and change are sensed, the rhythmic frames fade from our awareness. Their work is done and the messages of higher-level agents never speak of them; that is why metric music is not boring! Good music germinates from tiny seeds. How cautiously we handle novelty, sandwiching the new between repeated sections of familiar stuff! The clearest kind of change is near-identity, in thought just as in vision. Slight shifts in view may best re- veal an object's form or even show us whether it is there at all. When we discussed sonatas, we saw how match- ing different metric frames helps us to sense the musical ingredients. Once frames are matched, we can see how altering a single note at one point will change a major third melodic skip at another point to smooth passing tones; or will make what was there a seventh chord into a dominant ninth. Matching lets our minds see different things, from different times, together. This fusion of those matching lines of tone from different measures (like television's separate lines and frames) lets us make those magic musical pictures in our minds. How do our musical agents do this kind of work for us? We must have organized them into struc- tures that are good at finding differences between frames. Here is a simplified four-level scheme that might work. Many such ideas are current in re- search on vision (Winston 1975). Feature-finders listen for simple time-events, like notes, or peaks, or pulses. Measure-takers notice certain patterns of time- events like 3/4, 4/4, 6/8. Difference -finders observe that the figure here is same as that one there, except a per- fect fifth above. Structure -builders perceive that three phrases form an almost regular "sequence." The idea of interconnecting feature-finders, dif- ference-finders, and structure-builders is well exemplified in Winston's work (1975). Measure- takers would be kinds of frames, as described in "A Framework for Representing Knowledge" (Minsky 1974). First, the feature-finders search the sound stream for the simplest sorts of musical signifi- cance: entrances and envelopes, the tones them- selves, the other little, local things. Then measure- takers look for metric patterns in those small events and put them into groups, thus finding beats and postulating rhythmic regularities. Then the dif- ference-finders can begin to sense events of musical importance; imitations and inversions, syncopa- tions and suspensions. Once these are found, the structure-builders can start work on a larger scale. The entire four-level agency is just one layer of a larger system in which analogous structures are re- peated on larger scales. At each scale, another level of order (with its own sorts of things and differ- ences) makes larger-scale descriptions, and thus consumes another order of structural form. As a result, notes become figures, figures turn into phrases, and phrases turn into sequences ; and notes become chords, and chords make up progressions, and so on and on. Relations at each level turn to things at the next level above and are thus more easily remembered and compared. This "time- warps" things together, changing tone into tonality, note into composition. The more regular the rhythm, the easier the matching goes, and the fewer difference agents are excited further on. Thus once it is used for "lining up," the metric structure fades from our attention because it is represented as fixed and constant (like the floor of the room you are in) until some metric alteration makes the measure-takers change their minds. Sic semper all Alberti basses, um-pah-pahs, Minsky 39 EFTA00284100 and ostinati; they all become imperceptible except when changing. Rhythm has many other functions, to be sure, and agents for those other functions see things different ways. Agents used for dancing do attend to rhythm, while other forms of music de- mand less steady pulses. We all experience a phenomenon we might call persistence of rhythm, in which our minds main- tain the beat through episodes of ambiguity. I pre- sume that this emerges from a basic feature of how agents are usually assembled ; at every level, many agents of each kind compete (Minsky 1980b). Thus agents for 3/4, 4/4, and 6/8 compete to find best fits. Once in power, however, each agent "cross-in- hibits" its competitors. Once 3/4 takes charge of things, 6/8 will find it hard to "get a hearing" even if the evidence on its side becomes slightly better. When none of the agents has any solid evidence long enough, agents change at random or take turns. Thus anything gets interesting, in a way, if it is monotonous enough! We all know how, when a word or phrase is repeated often enough it, or we, begin to change as restless searchers start to am- plify minutiae and interpret noise as structure. This happens at all levels because when things are regular at one level, the difference agents at the next will fail, to be replaced by other, fresh ones that then re-present the sameness different ways. (Thus meditation, undirected from the higher men- tal realms, fares well with the most banal of re- petitious inputs from below.) Regularities are hidden while expressive nuances are sensed and emphasized and passed along. Rubato or crescendo, ornament or passing tone, the alterations at each level become the objects for the next. The mystery is solved; the brain is so good at sensing differences that it forgets the things them- selves; that is, whenever they are the same. As for liking music, that depends on what remains. Sentic Significance Why do we like any tunes in the first place? Do we simply associate some tunes with pleasant experi- ences? Should we look back to the tones and pat- terns of mother's voice or heartbeat? Or could it be that some themes are innately likable? All these theories could hold truth, and others too, for nothing need have a single cause inside the mind. Theories about children need not apply to adults because (I suspect) human minds do so much self- revising that things can get detached from their ori- gins. We might end up liking both Art of Fugue and Musical Offering, mainly because each work's sub- ject illuminates the other, which gives each work a richer network of "significance." Dependent cir- cularity need be no paradox here, for in thinking ,(unlike logic) two things can support each other in midair. To be sure, such autonomy is precarious; once detached from origins, might one not drift strangely awry? Indeed so, and many people seem quite mad to one another. In his book Sentics (1978), Manfred Clynes, a physiologist and pianist, describes certain specific temporal sensory patterns and claims that each is associated with a certain common emotional state. For example, in his experiments, two particular pat- terns (that gently rise and fall) are said to suggest states of love and reverence; two others (more abrupt) signify anger and hate. He claims that these and other patterns—he calls them sentic—arouse the same effects through different senses—that is, embodied as acoustical intensity, or pitch, or tactile pressure, or even visual motion—and that this is cross-cultural. The time lengths of these sentic shapes, on the order of 1 sec, could correspond to parts of musical phrases. Clynes studied the "muscular" details of instru- mental performances with this in view, and con- cluded that music can engage emotions through these sentic signals. Of course, more experiments are needed to verify that such signals really have the reported effects. Nevertheless, I would expect to find something of the sort for quite a different rea- son: namely, to serve in the early social develop- ment of children. Sentic signals (if they exist) would be quite useful in helping infants to learn about themselves and others. All learning theories require brains to somehow impose "values" implicit or explicit in the choice of what to learn to do. Most such theories say that certain special signals, called rein forcers, are in- volved in this. For certain goals it should suffice to use some simple, "primary" physiological stimuli like eating, drinking, relief of physical discomfort. 40 Computer Music Journal EFTA00284101 Human infants must learn social signals, too. The early learning theorists in this century assumed that certain social sounds (for instance, of approval) could become reinforcers by association with in- nate reinforcers, but evidence for this was never found. If parents could exploit some innate sentic cues, that mystery might be explained. This might also touch another, deeper problem: that of how an infant forms an image of its own mind. Self-images are important for at least two reasons. First, external reinforcement can only be a part of human learning; the growing infant must eventually learn to learn from within to free itself from its parents. With Freud, I think that children must replace and augment the outside teacher with a self-constructed, inner, parent image. Second, we need a self-model simply to make realistic plans for solving ordinary problems. For example, we must know enough about our own dispositions to be able to assess which plans are feasible. Pure self- commitment does not work; we simply cannot carry out a plan that we will find too boring to complete or too vulnerable to other, competing in- terests. We need models of our own behavior. How could a baby be smart enough to build such a model? Innate sentic detectors could help by teaching children about their own affective states. For if dis- tinct signals arouse specific states, the child can as- sociate those signals with those states. Just know- ing that such states exist, that is, having symbols for them, is half the battle. If those signals are uni- form enough, then from social discourse one can learn some rules about the behavior caused by those states. Thus a child might learn that concilia- tory signals can change anger to affection. Given that sort of information, a simple learning machine should be able to construct a "finite-state person- model." This model would be crude at first, but to get started would be half of the job. Once the baby had a crude model of some other, it could be copied and adapted in work on the baby's self-model. (This is more normative and constructional than it is descriptive, as Freud hinted, for the self-model dictates more than portr