I've inadvertently cultivated a reputation among my peers as a math guy. The truth is, I didn't really become interested in mathematics beyond a necessary evil until about 2009, when I finally resolved that I would sit down and and just look at the anatomy of the field until I understood it.
When I identify something of value out in the wilderness, I, like many other people, tend to evangelize about it a little bit. For math, the reactions I've gotten have ranged from gee shucks I'm so bad with numbers
to important people like me don't have to understand propellerhead crap like that
, with precious little genuine interest. I'll address the indignation elsewhere, though I suspect it's just insecurity in disguise. As for numeracy, I'm no good with numbers either. I think in shapes.
When most people hear the word math, they appear to conjure up experiences from high school or their undergraduate program where they were traumatized by drill after mind-numbing drill of algebra, calculus or trigonometry. Clichéd questions abound:
What's it for? When am I ever going to use this?
Answer: These branches of mathematics are for building things. You would use them if you were planning to build a tool-shed or nuclear submarine. As rewarding as it is to build things, however, not everybody does it for a living—or even a hobby for that matter—so it isn't especially surprising that people don't encounter in the real world the math that they were forced to choke down in school. Aside from basic arithmetic, about the only school-compulsory math a non-engineer would find useful in their day-to-day life is statistics, which, frankly, everybody should understand in order to keep politicians and bureaucrats in check, and stay out of trouble with their bookie.
Before I started to really look at it, I thought of mathematics as a sprawling, arcane labyrinth, that existed objectively, like the hard sciences to which it is so often married. It was something of an epiphany to realize that every iota of mathematics was invented—rather than discovered—by a person, to solve some problem or other.
The field is also spectacularly egotistical, with its participants historically being men of leisure with plenty of time to play around with intellectual puzzles. Just about every mathematical concept beyond what the average person is exposed to is named after somebody or other, and there was considerable pressure for a mathematician to seal his notoriety early on in his career, superstitiously before his 30th birthday.
Contemplating mathematics from the point of view of a mathematician gave me a sense of empathy I didn't have before. Picture this: you're hard at work trying to get famous by beating out symbols on a blackboard. The people you're trying to impress are just like you. And there's a deadline. Of course your notation is going to be inscrutable: nobody else has to understand it.
It's quaint how the paragon of precision, order and certitude is codified as ad-hoc scribbles, indexed by last name. Knowing that makes me feel just how quirky and human the discipline of mathematics really is, and that it isn't so daunting after all.
Algebra, calculus and trigonometry are useful for engineering stuff, but a great deal of mathematics is designed for engineering thought. It is the mathematics of form rather than quantity, of structure, relationships and change. There's hardly any of the boring calculations you'd be accustomed to as math, and a mountain of it is directly applicable to so-called tech work.
Mathematical notation is optimized over centuries for writing very hastily by hand on a surface for which space is a premium. Symbols are chosen largely arbitrarily, or by tangential analogy, such that a given notation can have different meanings in as many contexts. The operations underpinning the symbols themselves are meant to be understood in advance and carried out ultimately in a person's head.
This is actually an argument for learning how to code. Not only do computers take care of the gruntwork of computation as the name suggests, the notation is actually an improvement over conventional math, being that it's far easier to compel a person to use a consistent grammar than design a computer to correctly interpret chicken scratch.
Of course, the act of programming is still very much centred around imagining in your head how the symbols are going to behave before you run them, then running them to see if your supposition was correct. This I believe is why even those who work so closely with information technology—and develop extreme proficiency—still don't take the last step into programming, even when they understand its value: the user experience is just too damn onerous.
Computers turn math into real-life actions. Whether we're hacking the Gibson on a command line or faux-fingerpainting on some jelly bean touch screen, it's all math under the hood. The more we understand, the more powerful we become. I'm suggesting it's time that we start demanding interfaces that expose and help us understand the underlying mathematical principles in ways that help us get our work done. I make them that way myself whenever I can. This isn't just for the non-programming contingency either. I use them too.