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Mathematics. We all have our personal sums and divisions. I was once 20; I am now 70. The years have added up, and what is left is now a fraction. 

When I entered college in 1966, I was just over half the age of the professor who had the most influence on me. He is now 85 and have become exactly 14/17ths his age. I am catching up. The ratio has narrowed. 

(If we both live long enough, I calculate by my birthday in 2025, I will be older than him by seven months.) 

There was once a great difference in our ages and in our wisdom; now we are roughly equal. The piling of years does that; the gathering of experience. 

I have spent my life learning. It is the basic drive, like women for Don Giovanni, or gathering corporate acquisitions for Warren Buffett. But more math: Every time I increase what I know by 2 percent, I double what I don’t know. I learn arithmetically, I become ignorant exponentially. It is as if I am splashing in an inflatable wading pool on the beach next to the ocean.

When I was young, I was a complete idiot, and my ambition in life was to know everything. Seriously: everything. I suppose underneath the surface, I understood that was impossible. But you have to have some kind of aspiration. 

But back then, being an idiot, I still thought being intelligent meant knowing a lot of stuff. And I knew a lot of stuff. Piles of facts and factoids. I could explain the Defenestration of Prague in 1618: the shifting taxonomy of lions from Felis leo to Panthera leo to Leo leo; the use of the Neopolitan sixth chord as the subdominant in a minor key. And perhaps I showed off a bit too much. But now I understand that knowing stuff is mere accumulation. Nothing to take credit for: These things stuck in my mind because my brain is gummy. 

Besides, the more you learn, the more you discover that what you once took to be fact has either been superseded by later research, or been misunderstood, or turned out to be canard and cant. I.e., Cliff Clavinism. 

I have a pile of books and music scores that keep me going, and I add to that all the things of the real, the physical world, that I observe — the seasons changing on the trees, the birds chirping, the clouds ranging over the skies.

I am hungry to take it all in. 

But there is another delusion: that being intelligent somehow means being rapid of apprehension. Quick. Sharp. Fast on the uptake. While it is true that a fast comprehension comes with intelligence, it is, as they say, necessary but not sufficient. 

People who know they are smart tend to sort things very quickly into their silos, eager like tennis pros, to volley the next shot back. C’mon, you can bring’em faster than that! But sorting isn’t intelligence. Quickness of wit is fine; it is fun, it is exhilarating, but it doesn’t get us to the core of things. 

This is something I have come to understand over many years. Two people, more than any others, more than any book or class, taught me what to value in whatever mote of intelligence I possessed. 

The first was my wife. She was the most intelligent person I ever knew, although, on first hearing her, you might be confused over that issue. She could say the most surprising things: “Andrew Wyeth is more abstract than Jackson Pollock” or “You can fall into blue.” (We once argued over that last one for three full days and nights, before I capitulated. I always gave in. She was always right, although you had to think sideways or give up long-held unreflected prejudices. Wyeth is abstract in the sense that he abstracts a visual essence from the world and flattens it into an image made of blurts and squiggles, while a Pollock painting is no abstraction: It is palpably and solely a painting; it is what it is and nothing else. As for blue, I have been drowning in it since that fight.)

What she had was complete and utter openness to input. A failure to plop input into those silos. She didn’t so much think outside the box, but was unaware there was a box. I marveled at her insight, which she was basically oblivious to. It just was. 

It led me to my doctrine of volitional ignorance. That is, to approach any subject from the point of view of complete innocence. Forget what you think you know and just take in the new experience. 

The second person, and earlier lesson came from that professor, now frail and failing, who forced me to engage with the material. 

When I first got to college, I knew I was bright, and I responded to classes by doing what I had always done: giving the teacher what he or she wanted. I was good at that. But in my class of English Romantic Poetry, I handed in my first paper, saying exactly what I knew my professor wanted me to say and he gave me back my paper with a big, red “D” on it. (Technically, it was a D-plus). I was dumbfounded. There was nothing in the paper that didn’t repeat what he had said in his lectures. It couldn’t have been that far wrong.

But what he wanted from me was not what I thought he wanted. He wanted me to engage with the material. To know something, not to know about something. There is a difference, not just in magnitude, but in kind between knowing about and knowing. 

That is where engagement comes in. Paying attention. Not sorting to be done with, but holding something between your thumb and fingers, twirling it around, seeing it from all sides, squeezing it to see how hard it is, cutting it open to see what’s inside. 

You must start from the simplest things. Looking at a painting, do not decide what the subject is or means, but first look. Long and hard. Describe everything you see, however slight. Don’t forget the corners, what is hidden in the shadows, describe the exact color of the blank parts of the background, what the fingers of the subjects left hand is doing. Get all the bits in first. Take time. I once spent seven hours in front of a single painting. It takes time and commitment. It takes engagement.

Only when you have spent all the time you need should you then essay to understand what the art might be about. Ingest it first, digest it second. 

Fifty years ago, my professor forced me to engage with the material. I wasn’t there to learn facts about Shelley, but to engage with the work and see what it might teach me. I have been attempting that ever since. It is a hard practice to keep up: so much easier to categorize and dispense and move on to the next. More efficient. Gets things done. 

But if you really want to partake in this life, be embedded in the world into which you have been dropped, it is essential to pay attention, to know in your bones how little you truly understand.  

 For the world is infinitely complex and can obey no schema you toss over it. Engage with it on any level and extract whatever you can. Savor it.  

square into skull

If you want to be really smart, you have to learn to be stupid. 

Now, I don’t consider myself to be particularly intelligent, but I have noticed when other people are, there are a few things they have in common. One of them is the ability to be blunt pig-iron stupid. 

What I mean is that intelligence can best be found in ”volitional ignorance,” or a willed erasure of everything you know. I am certain of this: What you know prevents learning. 

People create for themselves a model of reality, or more accurately, many models. These models derive from experience. When anything new makes itself felt, it is immediately tested against the model most appropriate. 

If no model is right, the new fact can be dealt with in one of two ways. More commonly, it is squeezed into the model like a square peg hammered into a round hole. The new is shaved and jiggered until it conforms with what we already know. In the end, we have learned nothing; we may only have renamed what we already knew. Unless the square is a brownie and the round hole is a mouth. eating a brownie

But intelligence is what makes us throw out the old category rather than mangle the nonconforming fact. And those who are genuinely brilliant throw out the categories before even considering the new fact. This is what I mean by volitional ignorance. It forces us to reinvent the wheel every single time and is the only way to discover anything genuine about the problem of wheels. 

It means you accept the experience fresh and start for yourself rather than relying on the culturally accepted model. 

I was talking of this with someone recently and he said, ”You mean, like coloring outside the lines,” and because I am not particularly quick of mind, I agreed. 

This worried me later. For it is not like coloring outside the lines, not at all. When he said that, he was in fact squeezing my square peg into his mental round hole, translating what I was saying into something he already understood. 

We all do this constantly, and I am not criticizing him for it. I am frequently guilty of the same thing. In fact, we cannot do otherwise without becoming yammering idiots. A certain amount of structure is needed to function in our daily lives: We cannot question the egg at every breakfast. 

But still, intelligence is the ability to get past the quotidian. I call the ignorance ”volitional” because it is something I make a choice about. Those who have no choice and are forced to see everything fresh at every second of their lives are called schizophrenic; they cannot edit the information coming into their brains. 

Yet, we need to be able to allow ourselves to enter that state on cue if we are ever to learn anything new and genuine. 

Coloring outside the lines implies a disregard of the structure of the drawing we are coloring. Intelligence doesn’t mean the mere disregard of structure, but the discovery of yet another structure, as if, looking up at the night sky, we were able to ignore all the constellations and create new ones, entirely our own, and what is more, that the ones we create are better and truer than the old ones, just as the Big Dipper is easier to see than the Great Bear. 

There are also several other aspects of intelligence that need mentioning, I think, although they are all related. 

First is that intelligence can apprehend the similarities of disparate things. It recognizes in what way the horse is the same as the fork. It makes us transcend the accepted categories of things and redefine the categories. Perhaps, instead of thinking of the categories ”mammal” and ”silverware,” we might discover that through human history, both horse and fork have been used as parts of the common category ”tool.” 

Or we might compare four legs with four tines. 

I remember a segment on Sesame Street where they played the game, ”Three of these things are kind of the same,” where they show us four items and ask which doesn’t belong, and which three do belong. 

In this case, they had a red ball, a tomato, a green apple and a ruddy pear. Well, there are four different answers: The ball is different because it is inorganic; the pear is different because it is not round; the apple is different because it is not red; the tomato is different because it is soft. 

The ability to see multiple answers is another sign of intelligence. Intelligence is not afraid of ambiguity. 

And finally, intelligence understands things metaphorically, that is, it thinks in images and discovers in them reductions of complex thoughts in small, understandable packages that resonate emotionally. 

Einstein first discovered his theory of relativity not in a mathematical equation, but in a mental picture. It gave him the insight he needed to later forge the math proving his insight. But the picture came first. 

Speaking of one thing while meaning another is the heart of intelligence. This is not a game, merely substituting one thing for another as in a rebus, but rather it is the recognition that our vocabulary is limited by what we know already. When we confront something genuinely new, we cannot speak of it in language we already have, we must speak of what it is ”like.” 

As for instance: Human love is infinitely complex. When we feel it, we almost always decide the word ”love” is inadequate to describe what we feel. We can either do what Woody Allen does in one of his films, and try to invent a new word: ”I glom you, I snorfle you,” but such a course is meaningless to anyone else. 

Or we can make a metaphor and say, ”My love is like a red, red rose that’s newly sprung in June,” or ”Love is the valence of pheramones.” 

In each case, we are trying to convey something of the complexity and subtlety of what we feel, not allowing it to die the death of the normal, the bland, the banal. We are insisting that the particular emotion be understood and felt by the stranger to whom we are talking. We want exactness in our language, and we can reach it only through inexactness. Metaphor is the means of doing it. 

All our highest and best thoughts are metaphorical. All the most banal come straight from the dictionary. 

The more precise a word is, the less it describes. Meaning depends on ambiguity. 

Intelligence is the lightning bolt that arcs from one thought to another, fusing them together like glass. 

All intelligence is a form of recognition.