On intuition and learning, or, why art matters

Art loves chains

    –Nadia Boulanger


This little blurb is just a reflection on what I feel to be a completely underappreciated and mistunderstood facet of learning any subject. Sure, I admit it might be just peculiar to me but I've had such great and good success with it I thought I'd share. I've used this approach over decades of teaching martial arts and Mathematics at the university level. As with all things understand it if you choose and let me know if it jibes with your experience.

Three important definitions

What is art?

There are a few definitions in my dictionary. These are

The last one is what I think is the more important for what I'm writing about. However, the first with its inclusion of aesthetic value is important too. What I am trying to get here is the idea that one has skill that is acquired and an aesthetic sensibility for what is right and not.

Intuition and what it's not

Hand in hand with art as aesthetic-based skill goes intuition, which my dictionary defines: The more common use is that one 'just knows' something. We see this in the popular mindset all the time whereby someone has a hunch with no supporting facts or prior knowledge. This borders often on the supernatural. Since I managed to avoid being gifted in this way, I must plod on with reality as best I can. Crucial here is that intuition can be tutored, in other words you may work with something enough to be able to hop over much slower inference. This is one of the foundations of skill.

Talent, IQ and all that

I have to chat about talent, because attitudes about talent usually get in the way of acquiring skill. Moreover, IQ often surfaces too in strangely counterproductive ways. Here is what my dictionary says about talent: These are the definitions, but I don't buy into the idea of talent at all. I should warn you that I started out as a musician and was something of a child prodigy, so I am basing this on my experience. The key here again is that talent is something that is seen as being natural or innate. In truth, nobody I know of who is listed as talented in music gets by without having practiced a tremendous amount. The popular thinking is that music is just there and one has musical ability, much like being born with a pair of wings. Nobody has to teach a bird to fly. Many consider being called talented a great compliment. It is this attitude towards innate abilities that causes much grief and suffering because it confuses the complimented that hard work is not important and excuses the complimenter from having to try. Sure I've seen people who start some field of study or activity and excel at it almost immediately. In those cases there always one of two things going on. Either they have had some similar training elswhere so that there is a cross-training effect, or they are effective self-learners.

Talent really is not much more than liking something enough to do it repeatedly and therefore get better at it. I have to admit bitterness here, since I grew up in a rural school system which felt that talent was innate, so that there were no programs for me to develop. I was lucky since I was quite hostile to this attitude – I knew that I was practicing 4 to 6 hours a day and resented like Hell having that swept under the rug – and I made it a point of tracking down instructors at the local university to teach me those things I wanted to know. I started taking college-level instruction in the eighth grade in music theory and composition. I just want you to understand that what I write here is from the perspective of someone who was universally accorded that status of being "gifted".

So what about IQ? How does this fit in? Well, it doesn't, at least not in the way most folks want it to. This is usually the pseudo-scientific manifestation of talent. It was not always so. The first person to posit an intelligence quotient (IQ) was Alfred Binet at the end of the 19th century. I suggest strongly reading Stephen J. Gould's book "The Mismeasure of Man" for a more thorough and probing discussion.

Binet's original idea – and it is a good one – is that people who we consider impaired have a difficult time with mundane tasks. No mention of "gifted" people or geniuses was really there. As such, the first test was not to measure intelligence per se, but inability to do basic tasks. It really is a good measure of this. The idea caught one and got quite a life of its own and became the darling of the racists back in the early part of the twentieth century, where the distinctions were made to coincide with race (so a mongoloid was someone who was supposedly as stupid as a Mongol. Say, didn't they almost conquer the world once, and we were all saved from a nasty drubbing because they changed their minds?). American Science didn't really exist until after WW II (I don't know why everyone thinks this is classified material, but the US was about the last place anyone with brains would go up until the late 1930's), and Gould rightly points out that the dismally low levels of Science pre WW I is at least one reason such bad research got a foothold. Gould certainly does have his opinions, but he argues them quite well and the book is well worth a read.

A nice parallel (in Gould's book, as I recall, although I don't have it in front of me for reference), is measuring water in a bucket. If we measure the water repeatedly we should get the same result or there is something either seriously wrong with the bucket or our measuring device. But, giving a person the exact same IQ test everyday for a year would not do that. You'd see a rise in their supposedly immutable intelligence and by the end they'd be right up there with Einstein.

Soapbox: I am a Mathematician by profession and bristle when people try to introduce numbers into a discipline. Most of the time they rig it so it comes out the way they want and we are none the wiser for their efforts, so it is incumbent on a researcher to demonstrate that they really can introduce Math meaningfully. Gould nicely shows how IQ researchers masturbated with Statistics and went academically blind because of it.

In my experience, those people whom I find are the most intelligent all share a common attribute: They are gifted at teaching themselves. I think a better measure of intelligence, therefore, would be measuring how well people learn from others and how well they can self-instruct. To the best of my knowledge there is no such field of research for doing this.

All together now

Let's start with my bias: Art is the only proper human undertaking

The quote at the top of this page from Madame Boulanger is very important. She was one of the most noted teachers of music in the first half of the twentieth century and managed to list among her pupils Stravinsky, Copeland, Piazzolla and many others. Her comment was aimed squarely at those people who think that music just sort of happens all on its own. Her point is that it is only by completely and utterly controlling it as a medium that we can make it do what we want.  My music teacher, Anthony Newman was a pupil of hers as well.

And so it goes with all fields of endeavor. Our great claim to fame as human beings is that we are thinking and learning machines. We don't sprout fur when it gets cold, we think about fluid dynamics and thermodynamics then invent the Jacuzzi. If the sabre-toothed tiger threatens you, invent the uzi. My point here is that the way people actually function is by acquiring skills and internalizing them. This builds the intuition needed. Then there is an aesthetic sense of what is right and wrong that goes hand in hand with this.

The way that prople operate on a day to day basis is this way. Consider how the Sciences are done. There is no such thing as sitting down and ploughing straight through a serious research problem from start to finish. That only occurs in very carefully contrived textbook problems.

A rant. Mathematicians often harp on 'proofs' of results but do not explain that to the laity in any meaningful way. When one lives with a hard problem for an extended time, gradually convincing oneself of the rightness or wrongness constitutes the actual proof. However, since books could be written about that, the convention has evolved that very carefully controlled prose with highly mannered stylism, called technical prose, is used to give a condensation of this. Including a comment that "I'd just finished a huge meal and during my constitutional I got to thinking about the way that the main course was sliced which in turn hinted that I might want to take whatever the current bane of my existence was and slice it up similarly, leading to the result that..." would be forcibly struck by any editor worth his salt. The condensed version is the proof you get to read in a book. Students always read a proof and flatly state they have no idea of how to write one and they are correct. Mathematicians should put their money where their mouths are and offer courses in how to do proofs and then write them up, rather than just sort of picking it up from the ether and begrudging students for their stupidity.

In reality, one looks for patterns and these shifting patterns eventually trigger associations. Jacques Hadamard was a famous Mathematician and wrote a very interesting book called "Psychology of Invention in the Mathematical Field." There are an awful lot of cognitive theories of learning and I've yet to find many that I really think of as credible. Hadamard's thesis is still rather controversial. Essentially, he chatted up his friends and found that the way he and they operated was along the following lines. Human thinking is not hierarchical = arranged with some overarching organizational scheme, like a table of contents or an index, but heterarchical = arranged as a network, like the World Wide Web. There are many ways of linking or interconnecting bits of information and the actual way that the network is organized varies by person. A good example of this is people who can memorize extremely long numbers at a glance (such as the first few hundred digits of pi). One person who was particularly good at this said that he did this by having a story he remembered that led him from one digit to another. There was nothing even slightly mathematical about his process. In this case the first part of Hadamard's thesis has one insinuating the facts into the network and building in the sorts of links to this information that allows for recall. Intuition is then built and then one may let the patterns and associations interact. It is indisputable that human brains are excellent pattern recognition machines and the musings phase lets that run full tilt.

As Nietzsche pointed out, thinking is not a faculty such as vision. We have full control of vision and if there were an instance when we couldn't see some shape, even briefly, we'd hot foot it to the doctor. On the other hand, this is exactly what happens in thinking. How often do we know some fact but can't quite seem to recall it at the instant we need it? Or there is some bit of logic that escapes us for the moment? There are far too many variables that affect thinking such as being tired, hungry, grumpy, etc. Consequently part of education is also learning the discipline to counteract this, at least a bit.

Yet another bias is on the role of a good education. Just willy-nilly learning facts as is in vogue in much education is the worst way to learn. Part of learning a subject is doing so in a way that the links are usable and make sense for the topic. This is what the role of a good teacher is. Hate to sound like an old fogey, but wisdom is the crucial element for a good education and the reductionist attempt to transform all branches of learning into facts simply makes it easy to crank out idiot experts, which is really what the US higher education system has perfected. Facts are easily quantifiable on tests but wisdom is not, therefore facts are what is taught. Another bias of mine is that a good classical education is crucial, not e.g., because you will have to quote Shakespeare to get a job, but because it acquaints you with the best of the best in human thinking. Human beings are raised while homo sapiens are born.

A good model for all learning is human language. It is, I think, the natural model since humans do learn languages as a matter of course from birth, although I am not a linguist (nor a psychologist). One does not laboriously form sentences but takes several years of familiarization and pattern internalization and then the thought comes and the sentence is there (and perhaps even it is out of out mouths sooner than we would like...) This is the way, I have come to believe, all human activities function, be it Music, the Sciences, martial arts or any other discipline. Of course, some activities, such as Music, do require a certain modicum of muscle memory, but that is not what I'm talking about. Before I hear a yelp that Mathematics is logical I am not disputing that. I just maintain Mathematicians aren't. We don't require that Botanists photosynthesize, do we? In the case of Mathematics, intuition has gotten us into trouble in the past with things that were supposedly obvious. Now we have an enormously sophisticated model of thought, Logic, to helps us not shoot ourselves in the foot. "It is by intuition we discover and Logic we prove" is a quote I heard in graduate school that has stuck with me through the years.

So here is the moment you've been waiting for. No matter what field you decide to study, aim for art in it. That is to say, practice it until it is second nature, tutoring your new intuition, but be mindful of the style since that will be the easiest way to know right from wrong. Seek the wisdom for the subject since it is there that you will understand it in a profound way. I am a notoriously quick study and what I have outlined here is just what I do. There is an old samurai maxim: "He who masters one art shows it in all he does". Of course art here meant war art, such as swordsmanship, but the point is well taken. The Japanese have this as a cultural concept. The idea was that one pursued the Way of a given discipline and strove for mastery, refinement and elegance.