squashed:

In the smoking aftermath of the Robot Wars, we’ll look back and wonder why we couldn’t get along with our creations. Didn’t we program them to love us?

I think it will be because we’re bad at math. At least, we’re bad at the kind of math computers are good at. While we may not be irrational, we don’t always think in terms of precise numbers. If I set my coffee maker to make coffee at 8:00, it makes coffee at exactly 8:00. If I make coffee at 8:00 in the morning, I make it at approximately 8:00. If I start brewing the coffee at 8:02, it’s essentially 8:00 to me because the two times are about the same. To the coffee maker, on the other hand, 8:02 is a different time than 8:00—and no more like 8:00 than it is like 12:37. We’re much better at analogy than we are with manipulating numbers.

It wouldn’t be too hard to program a computer to ace the math portion of the SAT. The biggest difficulty would be input. But could the computer manage the analogies on the verbal section? Tree is to timber as sheep is to a) mailbox b) mutton c) stable d) goat. It’s easy for us—but programming a computer to manage that is incredibly difficult. We are much better at thinking by  analogies than we are mathematically.

This is one of the difficulties neoclassical economics runs into. Value is caluculated numerically. While we’re capable of doing this—we usually don’t. If we buy a $5 drink and absolutely hate it, we might insist on drinking it because we paid for it. If $5 falls out of our pocket, we might spend the entire day being upset about it.

Okay, the math teacher in me bites.

1) “We’re much better at analogy than we are at manipulating numbers.”

Is that true?  It concerns me for two reasons.  (But let me first say that NEITHER of the two reasons is that I place a greater value on manipulating numbers than I do on analogy — I don’t.)

First, a great deal of number manipulation is a matter of training and practice — algebra was invented specifically because it is so procedural that you can do it, and get the right answer, without thinking.  Human beings are actually very, very good at learning habits and routines.

Second, I agree that a lot of our thinking uses analogy, but it seems to me that we misuse analogies almost as often as we use them appropriately, and almost as often as we misuse numbers.  Every time you start your coffee at 8:02 instead of 8:00, someone somewhere is using a terribly loose and inaccurate analogy to characterize what’s wrong in his or her marriage, business, classroom, etc.

2) “It wouldn’t be too hard to program a computer to ace the math portion of the SAT.”

It would be incredibly hard.  As much as it kills me to say it, the math portion of the SAT actually does an admirable job of going beyond mere procedural “number manipulation”.  Rather than the numerical answer to a problem, it’s actually the procedures, formulas, rules, etc. that are the true end products of mathematical reasoning.

Again: the point of the procedures, rules, and formulas is to allow you to compute without thinking.  The reasoning involves interpreting a problem and deciding which procedure to use; or deriving a new rule that will work in this situation; or generalizing a few examples into a formula.  (After this, you usually have to actually crunch the numbers, but by that point, the reasoning is mostly over.)   Mathematical thinking is actually extremely verbal, and the problems on the SAT actually do a pretty good job of focusing on this rather than mere computation.

Computers are no better at mathematics than they are at poetry.  Humans are pretty damn amazing at both.