Information theory is a mathematical field concerned with the processing of information—its quantity and quality, retrieval, compression, storage, and transmission. It finds applications across an enormous range of disciplines: communications, computing, engineering, physics, and even deep learning.

The central idea of information theory is that the more uncertainty there is, the more information there is. Take rock-paper-scissors. Always throwing scissors carries less information, in the information-theoretic sense, than throwing rock, paper, and scissors with equal probability. The latter is simply harder to predict. To put it more formally, we’d say it has “higher information entropy”—and there’s a way to actually compute how much.

But what on earth does any of this have to do with art?

From the standpoint of information theory, a work of art is also a kind of information. An artist creates the work, and an audience interprets it. So the information has its own entropy, too. If an artist deliberately introduces ambiguous elements, or packs in several implied meanings, a kind of information loss occurs. Uncertainty grows, and entropy increases. (This entropy is a different concept from entropy in physics.)

From here on, this is just my personal opinion. The way I see it, you can project a work of art onto the axis of entropy. And along this axis, the further you move in the negative direction, the more popular appeal it has; the further you move in the positive direction, the less. To put it more simply: the entropy of a work of art is negatively correlated with its popular appeal.

What kind of nonsense is this?

Let me first explain why lower entropy goes hand in hand with broader appeal. If the ending of a movie leaves it ambiguous whether the protagonist lived or died, the filmmaker had better brace for a chorus of bad reviews. Most ordinary viewers prefer the clear-cut over the open-to-interpretation. As a work becomes more ambiguous, its entropy rises and its information becomes harder to interpret.

But it’s different for people who are well-versed in art—critics, for instance. They’ve been trained to interpret works, so they’re skilled at extracting the underlying meaning, the information, even from within ambiguity. In other words, they can digest a high-entropy work without any trouble.

To be clear, I’m not trying to argue that one of these is better than the other. If anything, both extremes are dangerous. If a work’s entropy is so low that the artist’s intent comes across transparently to absolutely everyone, it can’t escape being called juvenile—like “Transparent Dragon,” once a favorite target of internet mockery.

On the other hand, if the entropy is so high that the work becomes nearly impossible to interpret, it ends up treated as no different from meaningless noise—like the film Resurrection of the Little Match Girl—and gets shunned by most people.

A work of art can sometimes convey clear information, and sometimes very ambiguous information. But a good work, I think, lives somewhere between the two extremes, carrying just the right entropy for its intended audience.

I don’t know whether anyone has tried to measure the entropy of a work of art. But if we could measure it and base our evaluations on a quantitative value, might it narrow the gap between critics and the public, even a little? An outlandish thought to entertain.