Analysis vs Algebra predicts eating corn?

I like learning about odd connections between disparate things. This probably is the oddest example that I know.

Broadly speaking, mathematicians can be divided into those who like analysis, and those who like algebra. The distinction between the two types runs throughout math. Even those who work in areas that are far from analysis or algebra are very aware of the difference between them, and usually are very clear on which their preference is. I'll delve into this in more depth soon, but for now let's just take it for granted that this is a well-known distinction, and it has meaning for mathematicians.

Back when I was in grad school there was a department lunch with corn on the cob. Partway through the meal one of the analysts looked around the room and remarked, "That's odd, all of the analysts are eating corn one way and the algebraists are eating corn another!" Everyone looked around. In fact everyone was eating the corn in one of two ways. One way was to munch over the length of the corn in a straight line, back up, turn slightly, and do another row across. Kind of like how an old typewriter goes. The other way was to go around in a spiral. All of the analysts were eating in spirals, and the algebraists in rows.

There were a number of mathematicians present whose fields of study didn't make it clear whether they were on the analysis or algebra side of things. We went around and asked, and in every case the way they ate corn matched their preference. Since then I've made a point of amusing myself by asking mathematicians I meet whether they prefer algebra or analysis, and then predicting which way they will eat corn. I'm probably up to 40 or so by now, and in every case but one I've been able to correctly predict how they eat corn. The one exception was a logician who claimed to be exactly on the fence between the two. When I explained the corn thing to him he looked surprised, and said that he had an unusual way of eating corn. He went in loose spirals! In other words he truly was a perfect combination of algebra and analysis!

If you have even a passing familiarity of probability, it is clear that despite how unbelievable it initially is that the type of mathematics you prefer is connected to how you eat corn, it is pretty much certain that there actually is a very strong connection. If you believe, as I do, that this difference is connected to how we think about other things, then there must be some odd connection between how we like to understand the world and how we eat corn. Why is another matter.

How do I explain the distinction between algebra and analysis? Well the best way to understand it is to ask you to study advanced mathematics. You will have to take many courses with the word "algebra" in the name, and others with "analysis" in the name. By the time you're done you'll have experienced the difference, and you'll be clear on which you prefer. Odds are you won't do that, but that is the most reliable way to come to understand it.

If I have to wave my hands and explain it, I would explain it like this. In algebra there are sequences of operations which have proven to be important and effective in one circumstance. Algebraists try to reuse these operations in different contexts in the hopes that what proved effective in one situation will be effective again. By contrast an analyst is likely to form an idiosyncratic mental model of specific problems. Based on that mental model you have intuitions that let you carry out long chains of calculations that are, in principle, obviously going to lead to the right thing. Typically your intuition is correct to within a constant factor, and you're only interested in some sort of limiting behavior so that is fine.

If you don't know any advanced math, the odds are about equal that my explanation is going to mislead you as to give you an idea what I am talking about. You'd be better off figuring out your preference by looking at how you eat corn. That said, the distinction carries through into other subjects that I've learned about. But not in a clear and obvious way.

For instance I've noticed the difference cropping up in programming. The distinction is often hard to explain. There are a wide variety of programming techniques, and most programmers have only really learned a few. Some of those techniques appeal to analysts, and others to algebraists. But if you've only been exposed to techniques that are a good fit for one, then how do you know which you'd prefer? Worse yet, when two programmers talk and have different experience bases, how can they tell whether their natural intellectual tastes are similar or different?

Let me give some examples. Upon my first encounter it was clear to me that object oriented programming is something that appeals to algebraists. So if you're a programmer and found Design Patterns: Elements of Reusable Object-Oriented Software to be a revelation, it is highly likely that you lean towards algebra and eat your corn in neat rows. Going the other way, if the techniques described in On Lisp appeal, then you might be on the analytic side of the fence and eat your corn in spirals. This is particularly true if you found yourself agreeing with Paul Graham's thoughts in Why Arc Isn't Especially Object-Oriented. There was a period that I thought that the programming division might be as simple as functional versus object oriented. Then I encountered monads, and I learned that there were functional programmers who clearly were algebraists. (I know someone who got his PhD studying Haskell's type system. My prediction that he ate corn in rows was correct.) Going the other way I wouldn't be surprised that people who love what they can do with template metaprogramming in C++ lean towards analysis and eating corn in spirals. (I haven't tested the last guess at all, so take it with a grain of salt.)

Going out on a limb, I wouldn't be surprised to find out that where people fall in the emacs/vi debate is correlated with how they eat corn. I wouldn't predict a very strong correlation, but I'd expect that emacs is likely to appeal to people who would like algebra, and vi to people who like analysis.

And now to wrap up, why would how we eat corn say something how we think? Here is what I think.

When you pick up a piece of corn on the cob, you have two cues for how to eat it. The first is that the corn is laid out in very nice rows. How can you not follow the lines that are laid out for you? The other is that as you eat, your teeth scrape down the corn. If you twist your wrist, you'll eat more efficiently. Why would someone want to eat inefficiently?

My best guess is that the cue you notice and follow reflects a natural tendency about how you tend to think in general. And this tendency is tied to such things as what kind of math you prefer or what programming techniques would prove interesting for you.