Beauty is truth, truth beauty, that is all
Ye know on earth, and all ye need to know. —John Keats

Nonsense and beauty have close connections. —E. M. Forster

When two texts, or two assertions, perhaps two ideas, are in contradiction, be ready to reconcile them rather than cancel one by the other; regard them as two different facets, or two successive stages, of the same reality, a reality convincingly human just because it is complex. —Marguerite Yourcenar

The ultimate fate of the successful revolutionary is to become an icon. By "revolutionary" I don't simply mean the usual suspects like Vladimir Lenin, Mao Zedong, and Che Guavera; instead, I intend for "revolutionary" to include the likes of Albert Einstein, Pablo Picasso, Elvis Presley, the early Catholic Church, and the cockroach. Each of these revolutionaries started out on the fringe, succeeded in redefining the norm (thereby changing their environment), and eventually came to be archetypes for something broader than the niches that they originated.

History also shows us that for every successful revolutionary, there are a thousand failures. Succeeding as a revolutionary certainly requires some luck, but it also demands a certain amount of innovation. The trick seems to be in introducing an innovation that the rest of world is ready to adopt. Should the world not be ready, or should the innovation not really be all that relevant or innovative, then revolutions fail before they ever really begin.

Observers of this game can't possibly focus attention on all would-be revolutions. There are simply too many and only so much information that any single person, animal or art critic can process. When a candidate revolution surpasses some threshold for critical mass, only then do we pay attention; yet most failed revolutions go unobserved.

On the other extreme, with enough time icons also fade to invisibility. Usually they become backdrops by which other things are defined or simply become accepted as truisms or even cliches.

The end result is that we naturally tend to focus on things in the middle. Nature does as well. To do anything else would be counter-productive for these are the only things that have relevance to the current context. They are neither mundane nor arcane, but fall somewhere in between. And on the border, just at the transition between revolution and the norm is where all of the interesting things reside: invention, humor, discovery, creativity, novelty, and beauty. Especially beauty.

My copy of Merriam-Webster defines beauty as the "the quality or aggregate of qualities in a person or thing that gives pleasure to the senses or pleasurably exalts the mind or spirit." In a nutshell, this definition suggests that beautiful things are things which positively push our emotional buttons, be it a sunset, baby, swimsuit model, building, lion, tree, equation, cart wheel, or even the occasional beautiful bottle of beer. Clearly, the existence of such a wide array of beautiful things reflects the fact that "beauty" is semantically loaded and with meanings that dramatically differ between contexts. In other words, beautiful babies will usually have vastly different defining characteristics than beautiful trees. What they share, however, is a relative rank on a scale of emotional pleasure: all things being equal beautiful babies are emotionally preferable to ugly babies, as are beautiful trees to ugly trees.

Looking at beauty as an emotional yardstick, not only does it bend itself in different ways from one beholder to another, but it also warps itself when applied to different objects. That said, how is it possible to defend notions of objective beauty? Here is the short answer: beauty is not a stateless attribute, but a function of the beholder, the object, and the context. While it may be hopeless to speak objectively as to the relative beauty of a particular object, I believe that we can objectively talk about beauty as a function and perhaps even talk objectively about certain instantiations of beauty

As a function, beauty is not without reason but instead reflects very subtle agreements between the beholder's internal state and the change in context introduced by an object. Each of us has a set of expectations and desires for how the world works or how the world should be. Depending on the person, success can be idealized in many different ways: a trophy wife, the luxury of a lazy day, many children, opulent wealth, feeling understood, or simply finding the perfect taco.

When we find something beautiful, I claim that the beautiful object is exceeding our expectations in some manner. When expectations related to emotion are exceeded, there is a hint of novelty and even surprise. As such, I will argue that "interestingness" is intimately related to beauty in that both are found when our internal models are slightly overwhelmed. Thus, in order to truly understand beauty as a function, we must understand the mathematical process of modeling and how it pertains to novelty.

I like to think of my dogs as applied scientists. I throw a stick, they try to anticipate where it will land, they bring it back, and the game begins anew. Most of the fun for my dogs seems to be in the anticipation, which is also where the applied science comes into play. While my dogs have never taken a calculus or physics course, they nevertheless "know" calculus and physics in the sense that they do a pretty good job at mentally solving the equations of motion for how sticks fly through the air. Moreover, they also demonstrate proficiency in applied human psychology when they read subtle cues that indicate that a throw will actually be a feint.

My dogs demonstrate an ability to form mental models for how the world works. Of course, humans do this as well. We have hard-wired models that derive from evolutionary sources that influence our taste in food and even affect which sounds we find pleasurable or annoying. We are culturally influenced by standards of beauty that affect our choice in an ideal mate. And over the course of a lifetime, we constantly adapt our vision of success to mesh with a maturing set of values.

While it is clear that humans contain many implicit models from evolutionary and cultural sources that are common to nearly everyone, our explicit models are much more interesting because of the relatively rapid rate in which adaptation occurs. Rapidly adapting models that coexist must recursively account for one another, much like how my dogs will adapt to my misleading cues for when and where I will throw a stick. Both canines and humans form models for the other's behavior, and these models often have circularity in that they take themselves into account. These are smart dogs, after all.

But as impressive as they are, the mental models of my dogs pale in comparison to the amazing array of mental models at work in the typical human brain. For example, two humans engaged in a conversation must consider (at a minimum) the social norms of speaking, shared cultural assumptions, facial cues, anticipation of trigger words and phrases, word ambiguity, and the actual content of the conversation. The content of a conversation, alone, may demand that participants exercise even more mental models. In conversations based on disagreement (such as an argument or debate), participants must consider complexities related to building first-order models of one another (what I think your words meant), second-order models (what I think you will think about these words), and even third-order models (what I think that you think that I thought about your words). With all of these intricacies at work, it is a miracle that two people can talk about the weather, let alone discuss and resolve deep issues.

How we are able to communicate content to one another may be intimately related to the complexity of our mental models. Being either too simple or too complex diminishes one's ability to communicate. To see why, consider a simplified form of communication that requires you to consider another person's statement about the world, and to use that information to potentially alter your view of the world. More concretely, consider the simple task of choosing a book to purchase and read. Your goal is to find a book that you will enjoy and your decision is to be made solely by reading reviews from three reviewers known to you:

• Reviewer A has very simple tastes in that he likes children's literature and nothing else. Moreover, the praise that Reviewer A gives to a book is directly related to its ratio of pictures to words.
• Reviewer B likes science fiction that is not too speculative, has more dialogue than description, and casts the future of humanity in a positive light. If prompted, she can spontaneously give a dissertation on why science fiction should be given more respect by serious critics. She also has a liking for classic horror reminiscent of Lovecraft, Poe, and the Brothers Grimm, but is less appreciative of modern horror writers. She has a supreme respect for Thomas Pynchon and James Joyce, but acknowledges that there's a lot going on with these two that she just doesn't get. Finally, she considers spy novels to be a guilty pleasure and absolutely despises romance novels.
• Reviewer C has never given a clear and decisive review for any piece of literature or even any single author or genre. When inspired, he heaps both praise and criticism for the same work. In fact, every review he has ever written contradicts many of his other reviews. However, when pressed he will admit that he enjoys many of the books that he reads.

Now the question is: which reviewer will supply you with information from which you can make an informed decision as to which book to buy? Reviewer A is of little value to you as a reader because his model of literature is one-dimensional. Similarly, Reviewer C is also of little value but for opposite reasons; his tastes are so complex as to be indistinguishable from a random process. There may be some hidden method by which he bases his decisions, but for the most part they appear to be indistinguishable from the toss of a coin. As a result, we have an inability to model Reviewer C's preferences, while Reviewer A is trivial to model.

Reviewer B is a mixture of simplicity and complexity. You and I may disagree with her opinions on various topics, but she is transparent in the sense that we can build a fairly accurate model for what she likes and why. Moreover, we can also discover where our interests overlap with her's, which means that even when we disagree with her, we can use her reviews to make an informed decision.

Valuable reviewers have the property that they are not too simplistic and not too complex. They provide information but in a way that can be understood. Using an analogy from programming, a valuable reviewer can be used as a "subroutine" to more compactly represent our own tastes. For example, to enumerate the defining characteristics of all of your favorite books you could write down thing such as "if mystery genre, then ending must be a surprise, be consistent with the earlier events in the story, and not involve a guilty butler," or "if poetry, never iambic pentameter, but haikus with water imagery are okay." Such a rule set is likely to be tremendously complex, especially if it accurately captures your preferences. However, this daunting task can be simplified by making reference to a reviewer that has significant overlap with your own tastes. You could simplify your rule set by supplanting complex rules with less complicated ones such as "if science fiction and author is not Asimov, then accept what reviewer B says." In this way, the complexity in describing your own tastes can be abstracted away by making reference to a reviewer.

In a nutshell, the value of a reviewer seems to be proportional to how he or she allows us to compress descriptions of or own preferences. This basic idea has several corollaries:

• A valuable word allows us to express many sentences more compactly.
• A valuable scientific theory allows us to more compactly express the rules of the universe.
• A valuable mathematical theorem can be used to prove many more theorems.
• A valuable idea clarifies other concepts.
• A valuable piece of art inspires thoughts and feelings that are otherwise difficult to express.

In each case, the value of an object is related to it's ability to more compactly represent similar objects in a well-defined domain. Thus, an object's value is a function of the object's attributes as well as its environment. In some cases, the domain and environment are globally encompassing and invariant (such as in the case of science and mathematics). But in many other cases, value is entirely relative to the context as, for example, when we shift the environment from one individual to another.

I once knew a musician that liked to test the limits of what people would tolerate. In one extreme experiment, he took a Unix operating system kernel (a large binary file that is essentially the master program of a Unix machine), compressed it, then burned the resulting sequence of zeroes and ones onto an audio compact disk. He labelled the resulting CD "computer music," listed himself as the composer, and distributed copies to friends, family, and acquaintances. I was among the last group, and my copy of the CD spent most of its life as a coaster for my coffee mug.

While my musician acquaintance found some value in producing a CD that is the musical equivalent to white noise, most of us don't like listening to static, and very few of us like to listen to random notes. I suspect that the value my acquaintance placed on his CD had more to do with making a social statement or in being ironic, and that's all well and good, but his CD would fail virtually all reasonable tests of value based on musical standards.

Like, Reviewer C, random sounds are arguably rich with information (because they cannot be compressed), yet fail to hold any relevance to the intended audience. On the other extreme, a metronome beat, being the epitome of acoustic simplicity, has almost no musical value at all. As such, a metronome beat and musical scales are analogous to Reviewer A in that both hold very little relevance in terms of characterizing what moves or interests us.

Good music, by any standard, has a mixture of familiarity and surprise. So do good movies, stories, paintings, and jokes. To a certain degree, creative, novel, and interesting things break our internal models—but just barely. If something is easily explained by our internal models, then we are left feeling underwhelmed and with a sense of "hell, I could of done that." If something flies way beyond the our internal models, it may seem alien, extreme, or just plain weird. All of this is to say that creativity has everything to do with stretching a boundary within an existing framework.

Supreme Court Justice Potter Stewart wrote that while he would not attempt to define pornography explicitly, "I know it when I see it." He could have been talking about beauty. Generating creative things—by definition—means avoiding the derivative and formulaic, which is why it is far easier to be a critic than a creator. Marvin Minsky once made a similar observation when he wrote that we have an exceedingly firm grasp on the non-beautiful but only a tenuous grasp of the beautiful:

In order to establish an individuality, a creative modern artist must also generate some unconventional alternatives. Doing that may also involve unsuppressing some conventional censors. In any case, from the negative knowledge point of view, we might argue that often beauty is neither in the eye, nor even in the mind of the observer, but precisely the opposite: it may lie in the power to inactivate many of that observer's internal critics.

Thus, to Minsky, beauty is a double-negative. When we consider the beauty of something, our minds perform the test "is this non-beautiful?" A negative answer to the negative test yields an affirmative answer. Thus, beautiful things overwhelm us by exceeding our expectations. Moreover, beautiful things have value to us because they yield a means of expressing emotions that are valuable to us, or are difficult to express.

To rehash, I claim that beauty is a function of the object, the beholder, and the context. Beautiful things allow the beholder to more accurately express emotional ideals within a given context. While this definition can be mathematically formalized, the basic idea is intuitive because it is so familiar to our everyday experience. In fact, I suspect that a definition for beauty may seem elusive precisely because the fundamental ingredient—facilitating expressions of our emotional ideals—is also fundamental to how our mind works. The very act of seeking more accurate and compact means of understanding the world actually makes us blind to the very phenomenon that is at work.

Like most interesting things, the notion of beauty is a great source of contention. When we claim that something is beautiful, we are revealing our values, goals, and ideals. It is no wonder, then, that beauty and beautiful things are ascribed with so many conflicting characteristics: exotic versus ordinary, simple versus complex, objective versus subjective, or timeless versus transient.

In all of these cases, the discrepancies seem to reside in the hidden variable of beauty: context. Context implies more than just a current situation; it also embodies the history leading up to an event as well as the scope by which an evaluation is made. Context also contains hidden assumptions that may not be shared between individuals. Hence, the difficulty we find in trying to communicate why we find something beautiful is there because it is the same problem of trying to communicate our emotional ideals. Trying to justify why you find something beautiful, in the most extreme case, is akin to trying to define a word with very subtle meaning and with no known synonyms; without making reference to the beautiful object, we may lack the language to express our emotional ideals. Moreover, the context in which we evaluate the relative beauty of an object will often consist of other known objects. This is why derivative works, off-shoots, and look-a-likes rarely have the appeal of an original.

I began this essay by stating that successful revolutionaries ultimately become icons. Generally speaking, this phenomenon is an artifact of how information and ideas slowly diffuse through a population, almost in a trickle-down manner. Humans have the unique and privileged position of being able to watch the coming and going of revolutions on many different time scales. Not only do we perform postmortems on the historical record to dissect revolutions in biology, culture, and economics, we also actively watch, anticipate, and predict were future revolutions will emerge and take us. The reason why is simple: survival and influence. Those at the head of an emerging revolution hold a powerful position that manifests itself in the ability to steer the whole world—at least for a while.

On the border between revolution and the norm is a phase transition. Committing to a revolution prior to it being a full-blown success is a lot like buying into an IPO in a troubled market. The trick is to buy low and sell high, as they say, and the market of ideas works much the same, as academics and artists often build careers on simply being an early advocate of a novel notion. Those academics and artists most adept at this game also know when to cash out and move on to the next opportunity. And the best at anticipating major shifts also may gain a reputation for knowing where future trends lie; as a result, they can influence events just by force of personality—sort of like a celebrity stock analyst talking up a flawed company.

Perhaps this is why humans value newness so much. All things being equal, we almost instinctively place a premium on the new over the old in anticipation of the new gaining even more ground. At its worse, this phenomenon is responsible for the "one hit wonders" that most of us would like to forget. But at its best, our preference for the new primes us to more quickly recognize new innovations and to, perhaps, step up to the plate and start our own revolutions.

For all of these reasons, as a society we have cultural tastes that shift over time. Beautiful things—those things that permit a more accurate expression of an emotional ideal—often reside at the vanguard because they are effectively the newest means of emotional expression. And yet, things that retain their value of expression because they have no fungible substitute manage to persist as well.

None of this is to say that notions of beauty are arbitrary—on the contrary, I am claiming that beauty is anything but arbitrary. What we find beautiful reflects the subtleties of our emotions and values and reveals who we are. In this sense, beauty is truth. But in the sense that what we value uniquely defines us as individuals, beauty is nonsense because of the incomparable nature of human individuality. In either case, beauty is a mirror in that it reveals as much about the beholder as it does about the object.

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