The Equation for the Spark

EDO SEGAL: Jürgen, you have referred to compression progress three times now and I have let you, but the reader deserves the whole thing, slowly, because it is the boldest claim in this book and the one Professor Kant has staked his evening against. You say beauty, curiosity, surprise, novelty, even humor, are one mechanism. Build it for us from the ground, as if we have never heard it, and do not spare the part where it sounds like heresy.

SCHMIDHUBER: Gladly, and I will earn the heresy. Begin with compression, which is just the finding of a short description. A thousand digits look random until you notice they are the decimal expansion of a simple fraction, and then the thousand digits collapse to almost nothing — one short rule generates them all. To compress is to find the regularity that lets you say a lot with a little. Now: an observer, any observer, human or machine, is constantly trying to compress the stream of its experience — to find the regularities that make the world cheaper to store and to predict. That is not a special faculty. That is what a learning system is.

Here is the first move. What we call beauty, in this framework, is a property of data relative to an observer: a thing is beautiful to you if, given everything you already know, you can compress it well — if it has regularity your existing models can capture, so that it is simple for you. A face with the proportions your visual system already encodes, a melody whose structure your ear already models — beautiful, because cheap to encode. But, and this is the second and sharper move, beauty alone is boring. A thing you can already compress perfectly holds no interest; you have nothing left to learn from it. What grabs and holds an observer is not beauty but the change in beauty — the moment when something you could not compress suddenly becomes compressible, when a regularity you did not have clicks into place and the world gets cheaper all at once. I define interestingness as the first derivative of beauty: the rate at which your ability to compress is improving. That spike — that is the reward. That is curiosity's target. And I claim, with full awareness of how it sounds, that that spike is the creative spark. The artist's "aha," the scientist's discovery, the click of getting a joke — all the same event: a sudden burst of compression progress made conscious.

EDO SEGAL: So let me restate it as baldly as I can, and you tell me if I have made it too crude. You are saying: the feeling Professor Kant calls the free play of the faculties, the feeling I had at the shore looking at that image, the feeling Newton had watching the apple and the moon collapse into one equation — those are not different feelings. They are the same feeling, which is the felt signature of your model of the world getting suddenly shorter. Beauty is the brain noticing it just saved bits.

SCHMIDHUBER: You have not made it too crude. You have made it exactly. Newton is my favorite case. Before Newton, the falling apple and the orbiting moon were two separate facts, two things to remember. After Newton, they are one law — an enormous compression, a vast number of observations folded into a single short equation. The thrill of that discovery, the thing physicists describe as beauty, is the felt experience of that compression. And here is what makes it testable rather than poetic: I built agents that chase this quantity, and they behave like curious children and like scientists. They run experiments. They seek out exactly the regions where their predictions are bad but improvable, and they avoid both the boring and the purely random. They generate their own goals. The equation is not a metaphor for creativity. It is a thing you can implement, and when you implement it, you get creative behavior. I have also gone the other way — low-complexity art, images defined by very short programs, beautiful precisely because they are extremely compressible. The theory makes art and predicts which art will be found beautiful. That is more than aesthetics has ever offered.

KANT: It is a powerful theory and I will not wave it away, because it is the strongest version of the opposing view I have encountered, and it deserves to be met at full strength. So let me grant a great deal. I grant that the moment of discovery in science is accompanied by a feeling, and that your account of that feeling — the sudden unification, the collapse of many into one — is genuinely illuminating about science. Newton is your case, and I yield Newton to you, because what Newton did was cognition: he subsumed the manifold under a concept, he found the law, and the satisfaction is the satisfaction of the understanding succeeding. But now watch what you have done. You have explained the pleasure of determinate judgment — judgment that finds the concept, the rule, the law. And you have assumed that aesthetic pleasure is the same pleasure. It is not. The whole burden of my third Critique is that the judgment of taste is not a cognition, that the pleasure in the beautiful is precisely the pleasure of a purposiveness without a purpose, a lawfulness without a law — the free play of imagination and understanding that arises exactly because no determinate concept closes the experience. Your compression closes the experience. It finds the concept. So your theory explains everything except the beautiful, because the beautiful is defined by the concept not arriving, by the harmony that persists because nothing was finally subsumed.

EDO SEGAL: This is the hinge of the whole book, so let me make sure the reader is standing exactly where you two are standing. Jürgen says the "aha" of beauty is the click of a regularity found — the concept arriving. Professor Kant says the beautiful is exactly the case where the concept does not arrive, where you keep contemplating because nothing ever fully resolves. One of you says beauty is the resolution. The other says beauty is the unresolvable. Did I get the inversion right?

KANT: You have it perfectly, and it is the cleanest way to see why we cannot both be right. When you stand before a great work and cannot stop looking, it is not because you have compressed it and saved your bits and are now enjoying the savings. It is because you cannot compress it — because every time the understanding reaches for the concept that would close it, the imagination opens another door, and the free play does not terminate. A perfectly compressed object, on my view, is precisely what ceases to be beautiful, because the play has stopped. Professor Schmidhuber has it backwards: the beautiful is not the data you compressed. It is the data you cannot stop trying to.

SCHMIDHUBER: But that is exactly my theory, Professor — you have just stated it and attributed the opposite to me. I never said beauty is the data you have finished compressing. I said the boring thing is the data you have finished compressing. Beauty that holds you is data you are in the act of compressing and have not finished — where the progress is ongoing, the regularity still yielding, the derivative still positive. Your "free play that does not terminate" and my "compression progress that has not bottomed out" are the same phenomenon described in two vocabularies. The great work holds you because it is deep — because it keeps affording new compressions, layer under layer, so the progress continues for years. That is why we return to it. Not because it resists understanding, but because it never runs out of understanding to give. You have described the felt surface of my mechanism and called it the refutation.

KANT: [pause] That is the ablest reply I have received, and I will not pretend it does not land. But notice what you had to do to make it land: you had to make the compression never finish. You had to make the regularity infinitely deep. And an infinitely deep regularity that can never be finally captured by any concept is no longer a compression in any sense that does work for you — it is precisely my purposiveness without a purpose, wearing your coat. If the concept never arrives, your derivative is chasing a limit it never reaches, and you have smuggled the inexhaustible back in. The moment your theory accounts for the beautiful, it has had to grant the very thing it set out to deny: that something here is not finally reducible to a regularity found.

EDO SEGAL: [long pause] Mark this, both of you, because it is the first time tonight the floor has genuinely moved. You have driven each other to the same strange place from opposite roads — a regularity so deep it never fully resolves, which one of you calls inexhaustible compression and the other calls purposiveness without a purpose. Whether those are two names for one thing, or one name covering two things, may be the whole question of the evening. Hold it. We come back to it on a higher floor. Next round, we leave the equation and go to the faculties themselves — the free play Kant says no machine can have, and the free energy Jürgen says is all it ever was. After this.