I've been thinking about Daniel Dennett's Concept of Universal Design Space, which is closely akin to Borges' Library of Babel.

How can we make maps of human aesthetic creations?

An analogy: Musical Design Space

Take a very simple 12-tone melody, played on a small piano perfectly (collapsing, for now, the difference between musical text and musical performance). Let's use the first phrase of Mary Had a Little Lamb. The design space occupied by this piece of music has two axes: you only need two two dimensions to represent the music in Cartesian space. Along the X axis, time steps, of some standard size. Along the Y axis, running above the baseline, points or lines which indicate the pitch. A time step without a mark above it is a silence. Only one note at a time can be played.

In this two-dimensional musical design space, Mary Had a Little Lamb would look like the following (in this rendition, I've put gaps between the notes).

E | -       - - ----

D |   -   -

C |     -

  +----------------

This set of axes is the whole design space needed to explore all the mini-melodies in the universe. The "Mary" graph is one shape within that design space; its melody forms one possible constellation, and a fairly strong one, judging by its endurance in culture. Whoever invented this melody made some "good moves".

The universal set of all (extremely simple) mini-melodies in this particular design space is directly analogous to the set of all books in the Library of Babel. Here, however, the alphabet has only 13 characters (sticking to notes from one octave, plus silent "note"). So for melodies of 16 time-steps in length (like this one), there are 13^16 possible mini-melodies, or. . . 665 quadrillion. That is an enormous number. When I first imagined this example, I was hoping for a tractable corner of the Library of Babel, a little garden whose combinatorics could be managed by the human brain. But despite the fact that this particular corner of musical Babel is extremely boring -- with a time-step of 1/3 a second, only accomodates melodies of 4 seconds in length -- is is completely unexlporable, within this universe, with any machine, when treated strictly as a combinatorial problem.

From this (and other considerations) I conclude that people do not deal with problems of musical creation as combinatorial problems -- or, if they do, they must encounter design spaces of a significantly different _shape_ than the one I imagined above. We know empirically that the brain's capacity for sheer computation is quite limited. The brain could probably not actually perform anything like an exhaustive search, or even a random search, of our mini-design space.

That is, when writing the novel, people do not open the door to Borges' Library of Babel. Indeed, there must be paths through design space: "a largely invisible set of maze walls -- or channels or railroad tracks -- in the space of apparent possibility."

But I want to flesh out an account of how that might work, formally. What does the maze actually look like? What kind of maps or design space are actually possible, maybe tractable? Forms may seem "emergent" while someone engages in the work of fashioning -- of discovering -- a particular thing, and in retrospect, certain developments _seem_ inevitable.

(But is there any such thing as inevitability?

We cannot know. That is one of the fundamental insolubles -- a subset of the problem of free will, determinism, Lucretius' swerving atoms, and Schrodinger's dying cat. Therefore, I'd like to approach questions of creation from the perspective of the creator's timeframe. I'd like to avoid invoking the concept of inevitability, and stay clear of the tower of retrospection, from which everything seen seems fated. I'd even like to avoid the concept of emergence, fond of it though I am, until its content can be specified without reference to some sort of determinism.)

I want to explore the specificity of the pathfinding creative process. In human experience, it's not a railroad track -- it may be 'emergent' in some sense, there may be some sense in which it has reality as a 'trace'. But is the concept of the trace doing any real work here? I'm not sure about the utility of positing the existence of entities which only exist in retrospect -- can only be seen from the tower. The trace may be important as a logical placeholder, but it sounds so strongly unfalsifiable that I'd rather steer clear. I'd like to think a little bit about what people actually do, in time, faced with the pre-existed design envelopes in culture and in their heads.

What work does the creating mind -- endowed, perhaps, with a certain "energy" -- do within a design system? In general terms, they encounter the rules, constraints, and customary proportions of the system before them, and they create a form which has a lively relation to those rules and proportions. This brings pleasure for the artisan and for the audience (pleasure of more and less rarefied kinds, more and less sacred kinds, broader and narrower kinds). These pleasures are why aesthetic forms exist.

Occasionally, a craftsman so fully understands the constraints of the aesthetic system that sees constraints that had gone unnoticed by other. Perhaps (in the modernist tale) he wishes to exceed or change them. Other times, a craftsman does not have a full understanding of the constraints, and his limited understanding leads him to trammel the constraints in ways which turn out, retrospectively, to have been valuable for some audience. Sometimes people intend to imitate, but end up innovating by mistake. Fortuitous accidents happen.

In any case, it seems important that, in the process of exploring certain items within creative design space, most of the items conform to the design space most of the time. Sometimes an item is encountered which falls outside of known space, but it only violates the ordinary constraints in one or two ways. There are no jazz scales in Mozart.

It also seems important than in the exploration process -- whether ordered or chaotic -- there comes a moment of _recognition_. The artisan apprehends that some element may be aesthetically useful, and the definition of use-value in the arts is that something may be repeated. Repetition is at the heart of aesthetic meaning. An item springs from the void, by chance or experiment; the creating mind recognizes it; and then he intends it.

(It's a bit like eating. I as a body am made of the materials that I have eaten, materials that were once lying around in the world in complete inanition. Musical design space, by analogy, is made of elements that have been won from the void, elements that we now know that we can digest. The second time I eat a thing -- a berry, a harmony -- it is food.)

What might have been accidental the first time (a note played wrongly) becomes incorporated into the artist's whole array of the deliberate. He may seek out that sound again, later, that strange mistaken harmony, not even knowing that that is the object of his search. Consciousness is not as important as intent here; artists often describe their flights of creative intuition in terms of hunch, restlessness, and hunting. The second time the artist finds the weird harmony, there is meaning, and the design system is enlarged -- from the inside.

And even if this particular harmony, new to the artist, is old hat to others, his personal design system has been extended. This is how an artist takes possession of a design envelope: by intending aesthetic elements that fall within larger and larger tracts of the possible. Older artists will teach a younger one what they can impart (and what he can accept) of their design system, their set of acceptable harmonies, melodic shapes, what-have-you. But the most vital of his aesthetic extensions (those that lie closest to his "identity" as an artist, whatever we suppose that to mean), are those which take their root in his own capability to recognize. Accidents always happen, and are products of historical contingency. But recognition does not always -- in fact usually does not -- happen.

By recognizing, and then repeating, a certain perceptible notion as though it were an aesthetic notion (an unusual harmony; a song structure; alliteration), someone states their idea of what the aesthetic envelope might include -- and what it might exclude, dispose of. (Innovation is certainly not the constant dragging of more and more camels under the tent.) To say the same thing in food terms: by treating some world-thing as an item of food, to be taken into the mouth and swallowed (a live snail, say), someone makes possible a different definition of cuisine, an altered edible universe.

The artist (or their proxy, or their imitator, or their group) introduces the aesthetic notion into a public, where, if it succeeds in bringing pleasure, it can now be more broadly repeated. But perhaps we don't even need to talk of pleasure now -- if the notion incites the appetite for more repetition among some public, demand may arise to meet the supply.

There are often supply/demand imbalances between artists and a public: there is more supply than demand for jazz fusion. Artists wish to fashion aesthetic elements from within its design system, and share these, and most audiences do not comply. I think the same is true of American poetry.

Without a demand, the innovation runs into a dead end, and we (backward looking scholars, ranging over the high-water marks of an entire art or arts) may become their principal life-support system. Or we may never find out about them at all (as might have happened with, say, Christopher Smart's poetry).

How does design space grow?

Imagine that the two-dimensional musical design space graphed out above was a complete definition of (brief, single-tone) music: 665 quadrillion songs. Suppose Robinson Crusoe lives on a desert island with some well-tempered 12-tone conch shells. He sets the shells up in a row. Never having had much musical training in the first place, one of the only songs he knows is the melody of Mary Had a Little Lamb, which he plays by striking his conch shells with a stick. Suppose that one day a coconut falls out of a tree onto one conch, just as Robinson Crusoe strikes another conch with his stick. He is surprised, but he likes the sound. He finds another stick.

If the conch-chord becomes part of Crusoe's regular repertoire, this breaks our simple design space -- there's no way to represent two sounds happening at once within that system. So if we wish to create a map of the outer perimeters of Crusoe's musical potential, our analysis of his music must change. We must have a larger and more complex mathematical system to account for his possible aesthetic products. 665 quadrillion is far too small. Crusoe has begun exploring a design universe larger than the one he was in before.

Say that Crusoe plays the melody notes of Mary Had a Little Lamb with his left hand, and begins to pair each note with a right-handed harmony conch. The only way we can accomodate this in our two-dimensional Cartesian design space is to state that Crusoe is playing two different songs. But since he clearly isn't, we want an analysis that says that Crusoe is, indeed, playing only one song, and that that song is possible within one design space. The difficulty with this, however, is that the song incorporates simultaneous events, and our two-dimensional graph has no notion of co-occurence.

How can we add this notion? One way of doing this would be to adopt the MIDI style of musical notation. MIDI is a way of writing down musical events as a list. "At time step 1, note F is played. At time step 3, note D is played. At time step 6, note F is stopped. At time step 7, E is played. At time step 8, note D is stopped. At time 11, E is stopped." This list of MIDI events is notationally equivalent to writing out a graph like the following:

F | -----

E |        ----

D |   -----

  +----------------

One can easily see that, for more complex music, the graph will soon
resemble the sheets that are fed into a player piano. It also resembles, not accidentally, those illuminated hymnals which monks used to sing over during the early development of polyphony. But the graph is no longer a simple Cartesian function, pairing one set of axes with one function -- it is two functions laid on one set of axes. It still doesn't allow a single Cartesian function to describe our music.

Another way to represent Crusoe's altered musical design space would be as as a three-dimensional graph, with one axis pointing out of the page. From each mark on our Mary Had a Little Lamb graph, imagine a bar sticking out of the page a certain distance (bigger interval, longer bar).

Say that, for every note in the melody of Mary Had A Little Lamb, Crusoe adds a perfect fifth note with his right hand. The graph we envision now looks like a roller coaster track, or a ribbon, exactly five steps wide.

What if the intervals are not all perfect fifths? What if they change? Then the width of the roller coaster changes. What if one of the melody notes doesn't have a harmony note to go with it? Then the roller coaster gets very thin, only as wide as a line.

Does this kind of ribbon-graph make any perceptual sense? It surely does, since human perception is chorded. We experience many things -- sounds, colors, smells -- by unconsciously adding their elements together. This faculty is so powerful we're often unable to analyze the compound into its component parts. (Most nonmusicians can never know which guitar strings are sounding which notes when someone strums the instrument.) Training or special talent can only partially undo the fact that our experience consists of co-occuring events that are blended into one perception-color. It seems unquestionable that there are many kinds of co-occuring events which humans are, in fact, neurally primed to understand in groupings. This isn't even a matter of brain science: it's in the structure of our eyes. It's in lower animals. We multitask and filter.

This chording is particularly true of our aesthetic experience, and for a very good reason: artists have historically taken special advantage of those perceptual groupings which humans are least able to untangle.

I'll come back to this later. For now, we have re-established a complete, if trivial, music, and a complete system for analyzing it. We know the outer bounds of its design space. No phenomena are missing from the graph that are present in the music.

But still we know that it's not a reasonable design space. It makes some reasonable abstractions, but soon Crusoe will be discovering musical dynamics (if only because of the contingency that his left arm is bigger and more powerful than his right), tempo shifts (if only because he can't keep good time), and so forth.

The model, to even begin to be formally rigorous, has got to start growing more, just to accomodate the real conditions under which music is played. How will loudness and softness levels fit into our graph? We'll have to add a fourth dimension (hard to visualize -- it could be done by coloring the bar). What if the two conches are struck with different firmness? A fifth dimension.

If, for aesthetic reasons of his own, Crusoe fires his musket at the climax of one of his songs, instead of hitting a conch, then he has discovered "found sound". He consciously invents a dimension along which variations can occur in his pieces of music -- invents an axis for the music-graph to occupy.

Axes can be invented (adding more dimensions to the space); axes can have their bounds extended (adding more notes to the scale -- more conches); axes can also be neglected.

To be continued.