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Rudolf Arnheim and Bayesian Aesthetic Meta-Uncertainty

Updated: Jan 22, 2021

In his book "Art and Visual Perception" Arnheim considers one of the most minimal artworks, a circle on a piece of paper (although a dot would have been more minimal because it can be specified by two parameters instead of three). Imagine a strictly defined art form which only allows one dot on a square. Where would the best place to put the dot be and why?

He writes "The disk in Figure I is not simply displaced with regard to the center of the square. There is something restless about it. It looks as though it had been at the center and wished to return, or as though it wants to move away even farther. And the disk's relations to the edges of the square are a similar play of attraction and repulsion... For any spatial relation between objects there is a "correct" distance, established by the eye intuitively" He refers to psychological forces with the disk being at rest when it is in the center of the square. If people are asked which way the disk wants to go they will give answers that are not random, they have priors about stability, the disk being most stable in the center or on the symmetric diagonals or central horizontal or vertical lines that bisect the square.

Let us try a Bayesian model selection explanation based on the automatic Occam's razor. If the game is to maximize the probability of a disk being in a position conditioned on a generative probabilistic model, then the simplest model that can explain the position of the disk would be the one where the disk was in the middle of the square because it requires the least information to specify. A more complex model is one where we say that the disk is on one of the symmetric bisecting lines of the square. Under this slightly more complex model, there is still quite a high probability that the disk's position is explained by the model. A more complex model still is one where the position of the disk is homogeneously drawn from a grid of points on the disk. In this case the disk being in any one position will be less probable than will the disk's probability according to either of the other two simpler models. We can say we understand the disk's position well if we can invent in our heads an explanation for its position which is of high probability. The simpler the explanation the more satisfying in a sense.

However, the simplest explanation may not be the most interesting. An interesting explanation I think is one which makes us most uncertain about whether a simple explanation or a complex explanation is the right one. We're meta-unsure, whether the simple explanation is right, or the complex explanation is right. So here I have hypothesized a high level and general aesthetic principle which I will call "Aesthetic Meta-uncertainty". An image is interesting to the extent that using our internal models, we're not sure whether a simple model or a complex model is the most appropriate to explain the image.

This is related to what has been said previously that an image is interesting if it is neither too simple nor too complex, but is on the edge of understanding. We wish to look at such images more, in the hope of understanding them. We cannot fall in love with the standard kettle, it is too simple. Neither can we fall in love with a random image, it is too complex. We like images that are on the interface of understandability. Such a principle is clearly going to be useful to a child who must decide what to attend to. There is no point attending to the overly simple or the overly complex. A similar intuition is described by others but in the form of Maximization of Learning Progress. We may like images that we can learn now things about most rapidly. An image that we are always learning something new about may be the most interesting image. As with all these grand general aesthetic statements, the hard part is in formulating them explicitly in mathematics and making them work in a real-life situation.

This approach is related to Paul J Silva's work on knowledge emotions such as surprise, confusion, and awe, which falls within the appraisal theory of emotion, something I've looked at in some detail elsewhere in terms of artificial emotions and simulating them.

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