Sunday, February 21, 2010

thinking in math

Last week an artist asked me what exactly I meant when I said I "see the world in math**," something her husband apparently also says but can't explain. I tried to explain but I can't really comprehend any other way of thinking (it's just very obvious from some conversations that it's not universal...) so the best I could do was more of an answer to how to think like an economist (automatically fitting observations into formulaic incentive-driven laws of behavior and nature, etc).

But this article reminded me what the real difference is. To people who see the world in math, they see things in terms of mathematical concepts. To people who... I dunno what the opposite would be, understanding poetry?... math is a mechanical set of tools of manipulation to get some particular answer. Fractions and decimals and percentages are different things entirely with complicated rules for converting between them, not different ways of representing the same thing that vary only by convenience. Algebra involves manipulating symbols according to particular sets of permitted actions, not logical deduction. Cross-multiplication is a magical trick to figure out which fraction is bigger, not a trivial consequence of multiplication. FOIL is a rule you have to memorize when you learn polynomials, not a meaninglessly particular application of the distributive property. Quadratic equations are impossible to solve unless you have the formula memorized, not something you can logically derive as needed, just like every other expression that doesn't happen to fit the quadratic mold.

And the product of this type of thinking is the endless discussion in the comments of the article above, which makes my brain hurt by its insanity/inanity much more than division ever did (and makes me giggle a lot.)

I'm so out of touch with the mechanical way of thinking about math that I completely forgot that I ever learned how to manipulate fractions into decimals and into percentages until I visited my 4th grade teacher in college when she was giving that lesson and it blew my mind to watch her break the concept into so many separate mechanical pieces (yes this and many other reasons add up to me being a very horrible teacher when the day comes that I can no longer avoid it...) Sure, part of it is just the curse of knowledge, and I can't remember what it as like not to know how to solve equations, but mostly it's the difference between seeing a logical flow and seeing miscellaneous puzzle pieces with memorizable, disconnected algorithms for assembly.

Anyway, I don't mean to make it a point of conceit, but frankly the point of this post is that for those of us who see the world in math (which in any case is about everyone who will ever read this...) the fact that the New York Times can run a piece elaborating a fourth grade arithmetic lesson that was trivial to begin with is hilarious, mind-boggling, etc. I laughed a lot and wanted to share =)

**Which was actually just my way of saying I was baffled by her occupation and incapable of making conversation about it, so please have mercy and enlighten me or change the subject. When it comes to art and literature and all that I'm as intellectually disabled as the Verizon call representative who insisted that .02 cents per minute was a meaningless, impossible quantity...