In a previous post I spoke about the importance of feedback loops in creative processes, including programming. Here’s a talk and an essay where Bret Victor explores this issue in more depth.

Victor not only identifies the importance of the feedback loop in determining search speed and enabling discovery, but also notes that the intelligibility of the trial-result relationship is as critical. Understanding the trial-result relationship allows the creator to focus on the productive areas of the search space, ignoring bad solutions and thus avoiding unnecessary trials. This aspect, the learnability of the trial-result relationship in programming, is the focus of his essay Learnable Programming.

When writing up the post on regularity I was looking for an image that would match the content. As you can see if you go back to that entry the image shows a regular structure, a fragment of architecture. I was quite happy with it, but what turned out to be even more interesting was the article I lifted it from, which I did not look at until now.

It happens that in that post the author explores some of the same ideas I’ve considered when attempting to apply concepts from information theory[1] to yield an interpretation of artistic experience as a learning process. The notions of monotony and complexity are also given a similar (tentative) mathematical formalization in terms of algorithmic information theory, which is how we have just discussed regularity in the previous entry.

Of special interest is the hypothesis of how monotony (at the low complexity end of the spectrum, see below on AIC) is not only boring but in fact distressing, due to a mismatch between what our neural system is tuned to observe and what is actually observed

why is human neurological response actually negative? Some insight into the effect comes from the notion of Biophilia, which asserts that our evolution formed our neurological system within environments defined by a very high measure of a specific type of coherent complexity. That is, our neurological system was created (evolved) to respond directly and exquisitely to complex, fractal, hierarchical geometric environments. When placed in environments that have opposite geometrical features, therefore, we feel ill at ease.

In my brief essay on the matter I mentioned hierarchical nature of processing in the visual cortex, which is reflected in machine learning approaches using recurring neural networks such as HTM’s and deep learning. The hierarchical nature of the processing, as well as the dual top-down and bottom-up flow of information are well established in neuroscience. However, it remains to be seen if there is a neurological explanation for the observation that “we feel ill at ease” with, for example, monotonous geometry.

In any case, all this led me to to try to extend my information-theoretic picture of artistic expression and experience with a grounding in neurological processes. In particular, how does the brain deal with regularity and novelty as relates to learning and satisfaction/pleasure. Knowledge from neuroscience points to dopamine as both related to pleasure and reward and, critically, learning (temporal difference learning).

I’m still thinking many of these ideas through, but I’m going to try to summarize some of them in their crude form[6] so I can return to this as reference, please excuse the lack of polish.

Here are the main points:

* Artistic expression can be characterized in terms of its position in a spectrum whose extremes are the obvious/boring on one side and the unintelligible on the other. This spectrum corresponds to the algorithmic information content of the expression.

* Artistic experience is a learning process where regularities are extracted and predictions are made according to those regularities

* Novelty is the mismatch between prediction and observation, novelty is a departure from regularity

* Novelty, either as reward-prediction error, or as an intrinsic reward (indirect indicator of reward) motivating exploration[2], activates dopamine in the brain. In the latter case, this is related to the exploration vs exploitation aspect of reinforcement learning[3].

* Different dopamine response profiles yield different levels of sensation-seeking in individuals[4], which may partially account for different taste in terms of desired optimum points on the AIC spectrum

* The optimum balance between insufficient and excessive complexity in the AIC spectrum parallels the requirement of balance between task difficulty and skill in flow

* Artistic satisfaction/pleasure is an interplay between novelty and regularity[5], it may be possible to explain this within some model of reward mediated by dopamine[6]

Notes/References

[1] Perhaps the canonical example of this line of work is Jurgen Schmidhuber’s treatment

[6] In particular, it is unclear whether a dopaminergic model is applicable to standalone perception which is the case for artistic experience, since actions and explicit reward are absent, and the timescales may be too small to be compatible with such a model.

I’ve spokenbefore of regularity, but haven’t defined it exactly. But before going into that, let’s first consider the intuitive notion that comes to mind. By regularity we mean something exhibiting pattern, repetition, invariance. We say something is regular if it follows a rule. In fact, the word’s etymology matches this, as regular is derived from the latin regula, rule. Repetition and invariance result from the continued applicability of the rule, over time and/or space, to that which is regular. For example

1, 3, 5, 7, 9, 11, 13, 15….

we say this sequence is regular because it follows a rule. The rule is

each number is the result of adding 2 to the number before it

As per our scheme above, the rule is applicable throughout the sequence, the +2 difference repeats, and it is invariant.

This way of looking at regularity matches the language we’ve used previously when defining the key aspect of learning as the extraction of generally applicable knowledge from specific examples. In this case the specific examples would be any subset of the sequence, the general case is the sequence in its entirety, and the extracted knowledge is the rule “+2”.

We can take this further and try to formalize it by realizing one consequence of the repetition characteristic. And it is that something that repeats can be shortened. The reason is simple, if we know the rule, we can describe the entire object[1] by just describing the rule. The rule, by continued repetition, will reproduce the object up to any length. We can use the example before, and note how the sequence can be described succinctly as

f(x) = 2x + 1

which is much shorter than the sequence (which can be infinite in fact). So we can think of the rule as a compression of the object, or from the other point of view, the object is the expansion of the rule. Here’s another example

In this case, the object is a fractal, which can be described graphically by a potentially infinite set of points. The level of detail is infinite in the sense that one can zoom-in to arbitrary levels without loss of detail. This is why the description at a literal level (ie pixels) is infinitely long. However, like all fractals, the Mandelbrot set can be compactly described mathematically. So we say the set is highly regular by virtue of the existence of a short description that can reproduce all its detail. Here’s the short (formal) description for the Mandelbrot set

In mathematics the length of what we have called short description is known as Kolmogorov complexity, or alternatively, Algorithmic Information Content. It is a measure of the quantity of information in an object, and is the inverse of regularity as we have discussed it here[2]. We say that something with a comparably low AIC exhibits regularity as it can be compressed down to something much shorter.

I’ll regularly return to the concept of regularity as it is a fundamental way to look at pretty much everything, and is thus a very deep subject.

[1] For lack of a better word, I’m using the word object to refer to that which can house regularity, which is basically anything you can think of

[2] Note that this is not the only way to look at regularity, but rather one of two main formalizations. What we have seen here is the algorithmic approach to complexity (and regularity), but there is also a statistical view that is more suited to objects that do not have a fixed description, but rather a statistical one.

I have described rationality as the ability to represent the world correctly (in a brain). Correct representation allows for correct predictions. Predictions in turn allow choosing those actions that will attain goals; an intelligent agent can predict the result of its actions and develop plans accordingly. It sounds complicated but it’s really a routine process. Here’s a pigeon doing something like it.

Without the ability to develop plans (and during learning stages) an agent is limited to trying every possibility and seeing what happens. But trying everything out in the real world can be slow and even dangerous. So intelligent agents simulate the outside world internally to carry out the trial and error process much more quickly, and safely. This trial and error process is a loop.

A creative process can also be seen as a search containing a trial and error loop. I’m using the term creative process loosely and inclusively. It applies to any process where we are creating something with some specific intent and criterion. Call the result art if you like. It can be a painting, a computer program, a piece of music or the design for a bridge. There are many manifestations, but they can all be interpreted as a search for a solution in a large space of possibilities; finding good solutions is not trivial.

This is why trial and error is necessary. It cannot be known ahead of time what the best solution will be, nor how good a particular solution is, except by trying them out. During such trials the creator evaluates a solution. This evaluation then propagates information back to the search for other solutions, establishing a feedback loop.

Does this view of the creative process offer any insights as to how to best carry it out?

First, it is clear that, all other things being equal, the more possibilities are considered the higher the quality of the final solution will be. So speeding up the feedback loop can dramatically improve the outcome; removing barriers and delays between creation and evaluation. It turns out that the speed of the feedback loop is very sensitive to advances in technology, here are a few examples:

All these advances and many others can be interpreted as a tightening of the feedback loop, accelerating the creative process and thus exploring more possibilities. A straightforward example above is digital photography. By eliminating chemical processing the time between taking a shot and judging the result is drastically reduced (including reductions due to limited film etc). There are potential pitfalls, a faster feedback loop may also encourage a less disciplined and principled approach. But this is more a side effect of the advance than a property of the advance itself, which ceteris paribus is usually a net gain.

And another point can be made. When searching for solutions, the creator will inevitably be limited to a fraction of the search space. And the quality of the final solution can only be as high as that present in that space. There’s a tradeoff, if the space is too large, the search will be bogged down in the filtering of many low quality results. But if it’s too small, the quality of the best solution present in the examined space will be bounded, producing stagnation.

So the second insight is that adding a random element to a creative process allows the search space to be expanded beyond that which would be possible otherwise. This is the role of accident in art. It allows the creator to transcend his/her limits in exchange for more labor or a possibly worse outcome.

Notes

Additional interpretations are possible in terms of search and search spaces, for example

– The role of knowledge and expertise as a search heuristic