From Cell Membranes to Computational Aesthetics: On the Importance of Boundaries in Life and Art

by Yohan J. John

6a019b010d0685970b01a511a3baa9970c-320wiNo one knows exactly how life began, but a pivotal chapter in the story was the formation of the first single-celled organism — the common ancestor to every living thing on the planet. I like to think of the birth of life as the creation of the first boundary — the cell membrane. That first cell membrane enclosed a drop of the primordial soup, creating a separation between inside and outside, and between life and non-life. Through this act of individuation the cell could become a controlled environment: a chemical safe zone for the sensitive molecular machinery needed to maintain integrity and facilitate replication. The game of life consists in large part of perpetuating the difference between inside and outside for as long as possible. Death, then, is the dissolution of difference. But the paradox at the heart of life is that the inside cannot survive without the outside. The cell requires raw materials — nutrients and energy — to sustain itself and to reproduce, and these must be sought outside the safe zone, in the wild and unpredictable outside world.

The cell membrane has a dichotomous role. It must preserve the cell’s identity as an entity that is distinct from everything outside it, but it must not be an impenetrable wall. It must be a gateway through which the cell can absorb raw material and eject waste, but it cannot allow the inside to become inundated by the outside. It fulfills this challenge by being selectively permeable, carefully overseeing the traffic between the inside and the outside. The cell membrane must also be flexible, because it serves the roles of locomotion and consumption. In a single-celled organism, the cell membrane is therefore a primitive sense organ, a transportation system and a digestive system, all rolled into one.

The birth of life was a moment of cleaving: when the first cell membrane enveloped its drop of primordial ooze, it cleaved the inside from the outside, but it also became the conduit through which the inside could cleave to the outside. Like Janus, the two-faced Roman god of beginnings and endings, of doors and passageways, the cell membrane is a sentry looking in two directions simultaneously. Given its role in cellular transaction, transition and transformation, the cell membrane’s function might even be described as a precursor to intelligence.

The connection between boundaries and intelligence may run quite deep. In multicellular organisms like humans, the skin is the boundary between inside and outside. Skin cells, as it turns out, are related to neurons. During embryonic development, cells in the ectoderm, which is the outermost layer of the embryo, gradually differentiate to become the cells of the skin and the nervous system. (Researchers have recently found ways of turning skin cells into neurons, suggesting that the line between these two kindred cells may be somewhat permeable.) The skin of a multicellular organism is much like the cell membrane of a single cell: it separates inside from outside, providing a physical boundary for the organism. But the inkling of intelligence in that first semipermeable membrane finds its full expression in the nervous system, which patrols a very different sort of boundary: the line between predictable and unpredictable, between known and unknown.

Life is an obstacle course full of things an organism needs or desires, like food and shelter, and things it would prefer to avoid, like predators or foul weather. Maximizing the good while minimizing the bad requires being able to use patterns in the environment to anticipate what is going to happen. Plants must be sensitive to the rhythmic pattern of the seasons. Animals in turn must predict the patterns of plants and other animals. The evolution of the central nervous system — the brain and the spinal cord — was a great leap forward in the pattern-recognition capabilities of living things. The ability to recognize and categorize the patterns in nature and use them to survive and thrive is central to intelligence. It allows living things to find (and create) islands of order and stability in a swirling sea of change and uncertainty.

But it’s dangerous to just stay put once you’ve found an island of order. Resources are limited and change is the only constant — the boundary between the solid ground of reliable knowledge and the encircling sea of unpredictability is in a state of flux. Nature seems to always find a way of casting us out of the gardens of Eden we create or discover [1]. A pattern-seeker must be vigilant, staying on the lookout for unforeseen dangers and new opportunities. This vigilance takes the form of exploration, and even very simple animals do it. Insect colonies have specialized scouts that search for fresh sources of food. Introduce a new object into the cage of a lab rat, and the first thing it does is investigate it thoroughly.

We tend to describe the behavior of animals behavior in purely utilitarian terms. The exploratory behavior of rats, or birds, or bees, is just a combination of foraging for food, looking for mates, and keeping an eye out for predators. When it comes to human culture, however, utilitarianism can often seem like a bit of a stretch. Is it fear or hunger that drives people to investigate the depths of the ocean, or the far reaches of space?

We humans get bored on our islands of order, even though we need them for our survival and sanity. We also like to sail off into the unknown from time to time. What constitutes the unknown varies from person to person — it’s not just scientists or philosophers that contend with it. Only a fraction of the world’s population has the inclination and the good fortune to experience first hand the outer limits of scientific knowledge, but a far larger number of people can contend with the boundaries of their worldviews in the domains of art and culture. The edge is where the action is — on the beach where the chaotic sea meets the tranquil beach. But what is it that drives us to the experiential edge in the first place? And does it have anything in common with the forces that drive living things out of their comfort zones in search of sustenance?

The difference between a desire and a drive is that a desire subsides when the goal is reached, whereas a drive is independent of the attainment of the goal — the act of striving becomes pleasurable in itself. Living beings have a variety of desires that can be temporarily satiated, but the lust for life is a drive, not a desire. In the long run life appears to revel in the very attempt to perpetuate itself. Intelligent beings, meanwhile, seem to revel in the attempt to expand their islands of order, fighting back the lapping waves of the unknown.

We have a name for the drive towards the unknown — it’s called curiosity. Jürgen Schmidhuber, an artificial intelligence researcher, has a theory of “computational aesthetics” that offers us a vivid mathematical analogy for curiosity. The theory can be summed up in one bold assertion: that interestingness is the “first derivative” of beauty. Readers who detect a whiff of scientific imperialism will hopefully bear with me as I unpack this idea, which need not be taken as anything more that playful speculation. I admit, colloquial and intuitive concepts like “beauty” or “interestingness” often get bent out of shape a bit when scientists examine them, but this is not necessarily a bad thing. Sometimes we need to distance ourselves from our intuitions to discern their outlines more clearly.

According to Schmidhuber’s computational theory of aesthetics, the subjective beauty of a thing is defined as the minimum number of bits required to describe it. Since descriptions vary from person to person, beauty is in the eye of the beholder. A definition of beauty based on bits of information is not in itself particularly alluring, but it can be improved if we see it as an attempt to capture subjective simplicity or elegance. It is perhaps unsurprising that a scientist’s definition of beauty has much in common with Occam’s Razor. [2]

However, beauty is not necessarily interesting. We also seek the shock of the new, the excitement of the unusual. So Schmidhuber goes on to define interestingness as the rate of change of beauty — the time-derivative of the subjective description length. A derivative measures the rate of change of one thing with respect to something else. The time-derivative of distance is speed (the rate at which your distance from some point changes), and the time-derivative of speed is acceleration (the rate at which your speed changes). For something to be interesting then, the observer’s ability to describe it must change with time. So interestingness is a dynamic quality, whereas a thing can be beautiful even if it never changes.

Some examples will help us understand what this means. Most people will agree that staring at a blank screen is quite a boring experience. A blank screen is extremely simple from an information-theoretic perspective, and so its description length will be very short. The description might be something like “Every pixel is black”. There is clearly a pattern, but it’s trivially simple. The information on a blank screen can be easily compressed. White noise sits at the other extreme. Somewhat counter-intuitively, information theory tells us that random noise is rich in information, so it’s description length is extremely long. Totally random information cannot be compressed. An accurate description of white noise on a screen would require specifying what is happening in each and every pixel. If a pattern is something that has structure and internal coherence, then randomness is the absence of pattern. Most people find random white noise boring too. What people find interesting lies somewhere in the middle — between what is too easily compressed, like a blank screen, and what is totally incompressible, like white noise. We like patterns that are simple, but not too simple; complex, but not incomprehensibly so.

Schmidhuber’s theory is couched in the language of computer science and artificial intelligence, which is why the concept of data compression plays such a prominent role. We don’t really know if the brains of humans and animals compress experience in the same sense that a computer algorithm does. But we do know that living things use pattern-recognition to make useful predictions about their environments. We compare the patterns we’ve encountered in the past with our present experience, and try to anticipate the future. We categorize the patterns we encounter — poisonous or edible, sweet or bitter, friend or foe — so that if we encounter them again, we know how to react. Rather than compressibility per se, perhaps what we find interesting is the possibility of enhancing our categories so they encompass more of our experiences. Knowledge consists of having comprehensive categories for as many experiences as possible, and knowing how to respond to each category.


A toy model that displays a burst of interest.

What might interestingness look like? Let me describe a toy system that is confronted by something unexpected, and shows a spurt of interest. Let’s say we have a system that is experiencing something beautiful. The subjective beauty “B” can change over time. In the diagram above, beauty is the blue line, and it stays boringly constant for a while, but at the halfway point it suddenly changes. Imagine a pleasant but predictable movie that suddenly becomes unpredictable in the middle. The beauty increases! The system has an expectation “E” which in our toy system is a memory of the past value of B. The red line in the diagram is the expectation. The green line represents the interest level “I”, which depends on the difference between the beauty and the expectation. When expectation and reality don’t line up, the value of E is different from B, so the system’s interest level shoots up. But eventually E gets accustomed to the new value of B, and the interest level goes back to zero. If the system had perfect expectations and could perfectly predict the change to the value of B, then there would be no increase in the interest level. A curious system is addicted to these bursts of interest, and actively seeks them out. [3]

As it turns out, the brain’s dopamine neurons fire in bursts of this sort when something unexpectedly good happens. Researchers call this a “reward prediction error” signal, and it is one of the reasons many people think of dopamine as the “pleasure chemical”. But this misses a subtlety — if the pleasure is completely predictable, the dopamine cells don’t fire. This dopamine cell pattern is more of a novelty signal than a pleasure signal. (There seem to be several other things that dopamine does, so even calling it a novelty chemical is an oversimplification.) Neural network theorists often employ the dopamine burst as a “reinforcement signal” that allows a network to learn from experience and improve its ability to categorize and predict. [4]

As we simplify, expand and refine our categories we push forward the boundary between what we understand and what we still don’t quite have a handle on. We expand our islands of order, reclaiming land from the sea of unpredictability. Many of the categories humans obsess about have little or nothing to do with the struggle to survive. Curiosity pushes us to proliferate our aesthetic categories — and in extreme cases it leads to the infinitessimal parcellations of genre and sub-genre that the internet so effectively reveals and encourages. (I invite the reader who does not know what I am talking about to examine the various sub-genres of heavy metal music.)

Curiosity is the drive towards interestingness, and it brings us to the boundaries of what we understand. A trip to a modern art museum should adequately establish that we don’t just find any baffling experience interesting. We seek experiences that are in the sweet spot — not totally predictable and monotonous, but not random and formless either. During an interesting experience we don’t know exactly what is going on, but we get the feeling that meaningful resolution is but a few moments away. So a Hollywood blockbuster that is too formulaic and predictable is not very interesting, but an experimental art film with no formula at all can bore us to tears too. We like movies with a few twists — but in order to recognize them as twists we have to have some expectation of what normally happens. A really interesting movie flirts with the boundary between what we know well enough to anticipate, and what surprises and confounds us.

So how does curiosity help us “compress” or improve our categories? Think of the concept of genre. In order to get a subjective sense of what a genre is, you need to experience many examples. Curiosity is what draws you towards this experience. Even if you go to Wikipedia or and read up on the conventions of a given genre, you still need first-hand experience to understand how those conventions manifest themselves. You need to listen to several blues songs before you can be sure you know what the basic blueprint is. And the more you listen, the more musical structure you can perceive and predict. Once you understand the conventions — once you know what to expect — you can experience a burst of interestingness when someone subverts those conventions and confounds your expectation. A blues aficionado is well placed to appreciate the way a band like Led Zeppelin reinterprets the genre’s conventions. In the experience of such aesthetic subversion, you are once again confronted by what is strange and unpredictable, and the curiosity engine becomes fired up once more.

What drives people to police their subjective aesthetic boundaries so zealously? What makes people so concerned with questions of authenticity or originality in art and music? I think going back to the cell membrane might give us some ways to think about such questions. The cell membrane separates inside from outside, mediating interactions between the two. In maintaining a chemical difference between the inside and the outside, it preserves the identity of the cell as an entity that is distinct from the environment. Perhaps aesthetic boundaries — and mental boundaries more generally — are central to our notions of identity. To carve out a distinct identity is to maintain a difference between an in-group (which could be just one person) and an out-group. Just as the cell membrane defines the contours of the cell, artistic and intellectual boundaries may define the contours of a personality, or of a community. For people whose identities are wrapped up in difference, to merge with the mainstream might seem a kind of cultural death: a dissolution of the boundary that sustains individuality and identity.

Staying on the boundaries of what is familiar in order to find sweet spots of interestingness allows us to expand our experiential horizons and reaffirm our existences as distinct individuals. But this can also be quite a tiring experience. What is true for a cell is true for an individual, and perhaps even for a culture — maintaining a boundary takes energy! Most of us aren’t critics — we can’t spend all our time refining our categories of experience, or sustaining idiosyncratic differences of taste and opinion. Sometimes we need to return to our comfort zones and replenish our supplies. Visiting a museum, for instance, is an experience that can be simultaneously interesting and mind-numbing. (In this age of endless online novelty, I can’t be the only one who seeks out tried and tested experiences — comfort food, old familiar songs, trashy television — as an antidote to too much interestingness!) Perhaps merging with the mainstream from time to time is not such a bad thing.

Individualism is taken as a self-evident virtue in modern liberal societies. But given all the effort involved in maintaining the boundary between inside and outside, between the Self and the Other, the opposite movement can be an act of liberation: dissolving the Self by forgoing, for a time, the maintenance of difference. Consider those moments during a sporting event (like a Wave) or a musical gathering (like a Rave) when everyone is moving in unison. It seems as if there is a kind of ecstasy in this voluntary surrender of individuality and difference.

Aesthetic experience, then, is a twofold process. On the one hand, it leads us to curiosity and wonder, which draw us away from our islands of certainty, transforming the contours of our selves. On the other hand, it offers us dissolution and union, which pull us back from the margins, towards community and commonality. Perhaps the dance of aesthetic experience is a microcosm of the great dance of life — a dance that began with the undulations of that first cell membrane. We sway in the direction of the unknown, and then drift back to the comfort of the known.


Notes and References

[1] The Genesis story of the fall from grace tells of how man and woman were cast out from the Garden of Eden. In The Power of Myth, Joseph Campbell interprets the story as follows: “Whenever one moves out of the transcendent, one comes into a field of opposites. One has eaten of the tree of knowledge, not only of good and evil, but of male and female, of right and wrong, of this and that, and of light and dark.” Campbell’s “field of opposites” is where pattern-recognition and categorization happen — it is the field of boundaries and differences, and also of self-consciousness. And this field is no paradise, because it is constantly threatened by the unfamiliar and the unpredictable.

[2] Jürgen Schmidhuber summarises his theory of aesthetics in a paper entitled “Driven by Compression Progress: A Simple Principle Explains Essential Aspects of Subjective Beauty, Novelty, Surprise, Interestingness, Attention, Curiosity, Creativity, Art, Science, Music, Jokes”.

[3] The diagram shows the results of a little simulation I coded up in Python. It’s a rudimentary “differentiator” that compares the present reality (B) with the recent past (E), and constantly updates its expectations (E). The burst of interest (I) happens during the transient period when reality exceeds expectation (when B > E). Many simple models of dopamine cells use a similar principle. Similar mechanisms can also be employed for edge-detection in a visual image, a crucial stage in object recognition. The system I demonstrate is pretty rudimentary — it just expects the present to resemble the recent past. You could say that a major goal of artificial intelligence and computational neuroscience is to create systems that have refined, flexible expectations with which to anticipate reality.

[4] Perhaps the hype cycle represents a burst of curiosity at the societal level. And perhaps social media frenzies are the dopamine bursts of the internet’s hive mind?


The Hype Cycle. Image from Wikipedia.