Commentary: What if math is really sloppy and inaccurate?

The computer game Civilization IV quotes a compelling thought: "If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics." -Roger Bacon (Opus Majus, bk.1, ch4.).

I was thinking about this when a foundation head asked me the other day, how would I use sims to teach math?

Play Cisco's [Binary Numbers] game.

To answer that question, one first has to ask oneself, what is math, anyway? (And by the way, I use math everyday, quite a bit, and it is essential to create most simulations.)

And maybe the second part of the question is, as the Bacon quote suggests, is math perfect? After all, 1 + 1 always equals 2. And 5! always equals 120. Isn't that perfection? It seems like it.

Except, what if the symbols and numbers of math is a form of pedagogy (including taxonomies, graphs, and abstractions)? What if math is best seen as a layer of content on top of, and to augment, real experiences? (If someone throws a ball, using math I can figure out where and when it is going to land. If someone is spending X dollars, I can tell when they will run out.) In that case, the question of the "perfection" of math rests not just on the self-referential math-to-math manipulations (where math becomes a bubble-world), but also the real life-to-math, or math-to-real life transitions.

Here's a simple example: if I drive 60 miles per hour for 3 hours, I will have travelled 180 miles. That is a perfect statement. But does that perfectly translate to real life? Probably not, because no one drives exactly 60 miles per hour, and, perhaps, few people drive for exactly three hours. The math is sloppy and inaccurate, but good enough to be pretty helpful.

Or a simpler example: If I combine two piles of hay, what do I get? One pile of hay!

So, beneath a faux, self-defined perfection, in fact, math is sloppy and inaccurate, if asked to on- and off-ramp to the real world. Likewise, in an academic setting, the learning about math requires the systematic stepping back from, even refudiation, of reality.

What's the Point?

Is there a point to the math observation? Maybe.

Only if math is better defined as a tool for improving our relationship with the real world, not just as the rules of an insular, perfect little pocket-world, then we can create simulations to make people great at using math, instead of creating simulations that helps people become great at knowing math.

Furthermore, multiple levels of self-referential systems ("the point of second grade is to prepare a student for third grade," or "the stock market will go up because it has gone up," or "if you beat the simulation, you know how to use the skill in the real world") are the signs of a fall.

But breaking the perfect pocket world requires a view of math that is at odds with current schools, text books, standardized testing, and in fact entire philosophy of being. The odds of changing all of that are not so good. Especially because, quoting Roger Bacon, math is perfect.

As Yogi Berra would have said, "It's the Big Skills redux all over again."