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Look Up (and Other Study Tips)

Faculty member Andrew McIntyre's Convocation Speech

 

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Facts Are Not Enough

 

If I list everyone I should greet, I'm bound to leave someone out, so let me just say, "Hey, everybody. Welcome to Bennington!" It's an honor to be asked to speak at this convocation.

I love this time of year — for me, September first is the new year. And I love being here, at Bennington. This begins my fourth year here, and I am excited to be part of this college, this community. One thing I love in particular is the refreshing strangeness of this place.

I have three points I want to make, and I actually have a theme, and even a title, for this address, but I want to put off telling you the title until later, and start with this experience of "strangeness." Of what does strangeness consist? It happens when expectation and experience conflict. Two of the three points I want to make are hidden in that statement.

The first is "expectation." Before coming to Bennington, I had never attended a convocation, I wasn't even entirely sure what the word meant. So I was coming into this with no expectations. Then the ceremony started with human heartbeats over the loudspeakers, and an evidently mildly crazed man stood up, drawn to dance with the beat — in that moment, I realized that I did have an expectation, and that this wasn't it. What I'm interested in right now is the hidden quality of this expectation.

Let me give a couple of other examples. Starting a new year, maybe many of you have visited IKEA? They have this marvelous selection of rugs and geegaws, cutlery... Imagine that you have bought a box of cutlery. Picture opening the box, and inside you find — five forks. Now, there's a mistake, right? You're missing a fork. Or you have an extra. Forks always come in fours, sixes, twelves — never fives. If you think about this for a second, though, there is no logical reason to prefer four or eight forks over five or nine. This isn't like eggs, which you might need to share with a neighbour. In fact, in much of the world, things tend to come packaged in odd numbers rather than even. This expectation, that things should come in even numbers, may have been hidden to you until this moment. And you may know that all of us got this assumption, indirectly, from an obsessive-compulsive Greek that lived two and a half thousand years ago, who associated even numbers with stability.

Another example. This is an old science chestnut (pardon the pun): from what is a tree made? If this was a science class, some smartass would say "wood." What I mean is, where does the mass of the tree come from? If I tell you that the majority of the mass of the tree is air — and the remainder is water, the exact percentages depend on the tree and on how you do the bookkeeping — if you haven't heard this before, this probably seems strange. It counters your expectation. Yet, I don't know about you, but before I heard this, I had never thought about what a tree was made from before. I wasn't aware I had any expectation. It wasn't until I was surprised at the answer that I realized there was a hidden expectation there. I don't know if the expectation is there, waiting, or if it comes into being when I am asked the question, but either way it is unconscious until that moment.

That's my first point, the hidden quality of expectation. My second point is the other element of the experience of strangeness, the quality of the experience with which expectation conflicts. If someone sends you a picture of a cat pushing a watermelon out of a lake, that's strange, it's funny, but that is all. The experiences of strangeness in which I am interested here are those which are not just nonsensical, but those that hint at a different sense, an unfamiliar order. If the music Bruce Williamson plays is not what you usually listen to, it may seem odd, but I hope it is at least clear that it is not strange for the sake of being strange — it's not like he's trying to be Kenny G, but failing — rather it seems strange because it is following a different set of weights and measures and priorities than we're used to. It is a hint of a doorway to a different world.

When I first went to college, I actually went for physics, and I thought I had mathematics pretty figured out. Not that I knew everything, but I had a sense of the boundaries. I knew all the math books in the public library — there were like half a dozen of them. Then I arrived at university, and the math and physics library alone was the size of Crossett. Not filled with finer and finer distinctions, but each book a whole new world — math has its Bach, its Beethoven, its Stravinsky, its baroque and jazz and serialism. The size of the unknown is bigger than it ever was. Unfortunately, the great strangenesses of mathematics take a while to explain, so I am going to instead take my examples of expansive strangeness from this physical, material world that we share. Where did we come from? What are we made of? Where are we?

You may know that agriculture is about twelve thousand years old. Cities, and most of what we call civilization, also dates from that time, the end of the last ice age. Certainly recorded history goes back no further. What I want to impress on you is what a short time this is. Look to your left, and imagine that the person sitting next to you is your mother. For the purposes of this exercise, imagine that she is the age you are now. Now, sitting next to her, imagine her mother, your maternal grandmother, again the same age you are now. Then sitting next to her, her mother, and so on. Continue until you have filled this entire hall. The last woman you place in a seat lived about ten to twelve thousand years ago, at the dawn of agriculture. (Actually, due to a quirk of the statistics of these things, at this point many of us are probably picturing the exact same woman.) Those five or six hundred women form a chain that led you here, and they have been witness to the whole of human history, everything, Babylon and Egypt, Greece, Rome, China, the French Revolution, everything humans have ever built or said or done.

If you look at the history of multicellular animal life — imagine that you give a course on animal life, and you give each epoch time proportional to its length. So for example dinosaurs lasted about 160 million years, about a quarter of the time animal life has existed on earth, so they would get a quarter of the term, six or seven classes. Tool use and fire would appear on the last day of class, in the last five minutes, anatomically modern humans in the last minute, and the last ten thousand years would get the final three seconds of the last class.

What are we made of? Everyone knows this, but I think it is not enough appreciated: 99.99% of the human body is made up of eleven repeated elements, over and over; 99% of it is just six repeated elements, oxygen, carbon, hydrogen, nitrogen, calcium, phosphorus. We know now that every two carbon atoms are exactly identical, not identical like two regulation baseballs, but identical like two number twelves, mathematically identical. Everything you are experiencing right now, your fingers, your skin, your liver, your most embarrassing moment in high school — the memory you are having of that moment right now — all of it consists only of a dozen exactly repeated elements — just organized.

One last example, and then I'll get to my third and final point. Imagine this marble is the Earth. Everything we know about happened here — all humanity, every dictator, every empire, every lover and mother and child, as far as we know every living thing ever. Now, on a scale model, how big is the sun, and where is it? Many people would say maybe yay big, at the other end of the room... in fact, this would be the sun here, to scale. To put it in the right place, I'd have to place it out in commons lawn. This scale model is a bit unwieldy, so let's scale it down; now, this here will be the sun, and the earth is an invisible mote of dust, about here. There are other planets, out in the audience, which we have visited with probes. Where is the nearest star? Most people would put it at the other end of the hall, maybe the other end of campus, right? In fact, to scale, the nearest star to us would be in Boston.

You probably know that we live in a galaxy of stars, one hundred billion of them. If everyone in this room devoted their lives full time to counting them, one per second, it would take us forty years working together to count them all. It is a flat disc, with spiral arms — let's imagine a scale model, stretching across this room. It would be a disc about this thick, a bigger bulge in the center — our sun is of course invisibly small in this model, and the distance from us to the nearest star, that distance from here to Boston: that distance in this model would be about the width of a human hair. This is not the only galaxy; galaxies themselves number in the tens of billions.

This is the actual world we live in. That is the earth on which this room is rooted. I find it remarkable that in all this immense history, no human has known how long we've been here, what we are made of, where we are, until now, until the last two or three women out of these five or six hundred. We live at an extraordinary time, in an age of extraordinary intellectual adventure.

Now I can reveal the title of my address. The title is: "Bennington Study Tips". That's not a joke. I was thinking about this talk, and I thought, if I can't be entertaining, I can at least be useful. There are many books written on study tips for college. Looking at them, what strikes me is that all the advice is solitary: schedules, organization, memorization; and all placing you as a passive receiver of books and lectures. It is important to get the facts straight and get shit done on time. If college was only books and lectures, though, you could do it alone. Where Bennington excels — and where it confuses new students — is in focusing on creative and responsive encounters between you and faculty, between you and other students, between you and the material. So, study tips:

First point, watch for hidden expectations: I gave examples of little ones; the big ones can be a barrier to learning. They affect your behaviour, they affect the way you understand things, but they live in your blind spot and are hard to find on your own. If you've ever sat in a class and thought, "I can follow all the steps, but it still doesn't make sense", then you were probably struggling with one of these invisible demons. These are demons which lose their power when named.

Second point, watch for expansive strangeness: This is also hard to see on your own, because  each of us has a powerful tendency to order all our experiences into our own existing framework. Generally this is a good thing but it can blind you to possibilities. If you have dismissed some classes or pursuits as pointless or silly or boring, that may be a hint. Some of your faculty and fellow students may seem like we come from different planets. That's because we do. Some of these planets are pleasant. Consider visiting.

My third and final point: if facts are not enough, what else is there to learning? If expertise consisted only of facts, then our easy access to facts would make expertise obsolete. Learning everything Bruce Williamson knows about music won't get you much closer to playing like Bruce Williamson; I think we recognize this about arts of performance, but the same is true of math, biology, political science, anything. Facts are important, but they are easy; at Bennington we tend to concentrate on the hard part. If you think learning is only facts, you can come away from your first classes feeling like we aren't "covering" anything.

So what is the hard part? What makes expertise different from just having a pile of facts? In talking to people about this, I have called it a framework, or a way of seeing, but that is too vague to be useful. To explain it, I wanted something more specific. Not a whole explanation of expertise, only a helpful image or metaphor.

Here is what I came up with: imagine you have twenty-five things. They could be twenty-five people in a class, or twenty-five ideas; or, if you want to be concrete, imagine sewing twenty-five buttons onto a pillow, five rows of five. I want to imagine that some of these things are connected to each other: some people know each other, some ideas are connected, or you can imagine connecting some pairs of buttons with pieces of string. For simplicity I imagine that each pair is either connected or not, yes or no. Between those twenty-five things, there are three hundred possible pairs, three hundred possible connections that could, or could not, be made. How many patterns of connections are there? That is, in how many ways could the web of relationships of twenty-five people be strung? How many patterns of string can you make on this pillow by connecting the buttons in pairs? The number is not difficult to find, but no computer now existing, or that will ever be built, can list all the possibilities. I can say that with absolute certainty because the number of patterns is not only bigger than the number of stars in the galaxy, in all the galaxies, but it is far bigger than the number of atoms in all the stars in all the galaxies. We would have to convert the whole earth, and the sun, and all suns, into computers just to start having enough computer memory to write down the answer — and still we would get nowhere close. And that's only twenty-five things.

I think this image, and the vastness of this number in particular, helps explain, a little bit, the nature of learning. I do not think it is exactly right, but it is helpful. To be a great mathematician, or writer, or dancer, it is not enough to have specific facts or elements; expertise consists of this web of connections between them. Forming these connections must necessarily be non-verbal, because there are literally too many for words. The large numbers involved mean that these connections must be made unconsciously, like the way we process a vast amount of visual information without conscious input or awareness. I think this is why we can have expectations of which we are not consciously aware — the connections have formed spontaneously. I think it is why we can be very intelligent yet blind to some things: we can agree on the words and facts, but there is a lot of room for the connections to be different. New facts make sense to us only if they fit.

And I think this is why teaching, and learning, are so difficult. Anyone with expertise has an intricate network of connections formed through years of effort. If I want to give you that expertise, I can't give that network to you directly. I can only communicate in words, in discrete facts. In my mind, the theory of vector spaces — it's not important what that is — is a robust, tightly interconnected web of ideas. Its power comes from the form of the interconnections, and its connections to other things, not the component parts. I can't give it to you whole, much as I'd like to. To transmit it to you, I have to disconnect it, disassemble it, and give you the pieces, in an order that I hope will allow it to spontaneously assemble in your mind in the correct form.

This process is highly individual, because this structure has to be anchored to your existing connections. As in architecture, one building plan can end up having two quite different realizations in two different sites. The process is also individual because no two people put the pieces together in exactly the same way, which is why I can still be surprised by your ideas after years of experience.

A curious thing about these connections is that they have to come from you to be solid — if I tell you, "glue these two here," you'd think that would make the process faster, but not only does that create a weak bond, but the bond is forever weak; it forms a potential mental block. As a teacher I have to create conditions and then resist the urge to meddle too much. I can't see directly if the web of connections is growing healthily — I have to sample the web in your mind by asking discrete questions, like sonar pings, and try to gauge the shape of the unseen structure by the answers. If there is a rattly spot, it might be caused by a faulty, hidden assumption; we have to locate the assumption and break it so the structure can grow correctly. If the growth is jammed, we need to find the right piece to break the bottleneck.

Misunderstandings can happen if you think classes are just about facts. You might think a faculty member is withholding a fact just to make you work, or asking you questions just to try to catch you out. In fact, we are doing our best — not always perfectly, but we are trying — to allow this structure — your understanding and ability — to form as quickly and solidly as possible.

So those are my Bennington study tips. One last thing. Another thing I love about Bennington is the lack of light pollution. If you stand out at the end of world tonight and look up, you will see the disc of our galaxy, (edge on since we are inside it), starting just to the right of commons and stretching almost directly overhead, with the central bulge being just below the horizon. Thanks, and good luck.