I was working in a sprawling used bookstore, full of paper dust and character. It was right around the time that I was working up to acknowledging that my "break" from college was a full-fledged drop-out. Nonetheless, I'd hardly given up the sublime sensation of figuring stuff out. There's always been an endless series of questions looming indomitable in the back of my head, hulking continents of uncertainty forming the horizons of my puddle of knowledge. Still, I gamely ply their shores with my tiny rowboat of a brain, delighting in the endless process of mapping and expanding the surface area of my ignorance.
At the beginning of our story, I was reading Feynman's book on quantum electrodynamics (puckishly titled "QED"), and feeling like I understood a great deal more than I probably truly did-- Feynman had a gift for conveying complex concepts in terms approachable even to the layman. Something in his arrow diagrams of particle paths resonated with my very hazy grasp of Einstein's "weights distorting a rubber sheet" representation of gravity. The illustration made sense on a gut level, but I'd never really been able to fit it into my understanding in any structured way. But with Feynman's undimensioned arrows as an example, I tried representing mass as a scalar on an axis perpendicular to the spacial dimensions, and incorporating this into simple force and motion equations... and promptly got a headache. I never finished freshman physics, you see. Bogged down in Calc II. The Nobel Committee is not in the habit of keeping my contact info up-to-date. Still, there was something interesting about this. So I set down QED (inspirational, but otherwise inapplicable) and cracked into a few textbooks. In a few weeks, with just a smidgen of linear algebra, I'd derived gravitation as an emergent vector completely consistent with all my earlier equations.
Of course I assumed I was re-inventing the wheel. Still, it was exciting to independently uncover the understandings I would've learned by rote and lecture had I remained in college. I decided to see how far I could go. Like everyone who's ever seen a scientist on television, I was familiar with "E=Mc2"; but the real nature of energy was still very much "Here There be Dragyns" territory for me. I used physics books only to reference the basic equations I was trying to balance; I wanted to see if I could get there on my own with what I had done so far. It took over a month, and a handful of additional dimensions before I found a system that held together. Mass and energy, vectors that could be translated across dimensions into one another with a tiny bit of math magic. Plug in values and constants, and the results held to the classical conversion equations across the board.
All this time, I kept my project to myself. I assumed that my more educated friends had no interest in re-hashing remedial topics in which I lacked even the basic vocabulary, and that my less-technically-inclined friends would find the entire exercise weird and wearying. And I wanted to see what I could accomplish on my own, with nothing more than my high-school background and the standard equations as a sort of answer key to check my results against. And... one other reason, one I wasn't willing to admit even to myself. When I flipped through the physics books, I wasn't finding anything like my method. Perhaps it meant I was using a longer and more circuitous route that usual deriving these relationships. Maybe, just maybe, I was working at a level above the target audience for my textbook. But... couldn't there be just a chance-- a tiny, insignificant chance, that I was doing something somewhat original? That by innocently applying an esoteric method of analysis, I was seeing familiar relationships represented in a novel way? And could this lead somewhere even more exciting?
After all, there isn't one unique set of "parent" vectors that interact to produce any given "child" vector. Even if we're restricted to parents that remain perpendicular to one another, you can find multiple solutions as long as you're allowed to add dimensions and reverse signs. Which meant that mathematically, gravity had multiple sources. It didn't need to rely on mass/matter, which is after all just a sign-restricted single vector in a system with many. Could this explain the missing matter in the observed universe? And could I explain the various paradoxes of irreversibility with this system? How did quantum effects factor in, if at all? What about... well. Suffice it to say that it was a time of ballooning giddiness, the precise sort of hope-against-hope that lets us happily plan what we're going to do with our hypothetical lottery winnings. Easily explained, and eminently human. Which is to say: stupid.
There is a class of brain teaser we first run across in elementary school, in which we're asked to choose a number, apply a bunch of simple arithmetic processes to it, and achieve a result predicted by the book. What's magic when we're 10 is inane only a few years later; these tricks are all just simple applications of distributivity, commutativity, and other elementary principles of algebra. The original number is factored out, and "predicting" the result is then unimpressive for anyone able to add.
Readers with an IT background may have been snickering at me at least four paragraphs back. Everyone else should start now. By using a branch of mathematics I understood just enough to get myself into trouble, I'd managed to consistently cancel out everything I was putting into my equations. Of course everything balanced. Things will do that when you drop equal amounts of crap on either side. And of course I got valid results when I plugged in constants and classical equations-- all of the garbage I was doing evaporated and left only the familiar, much less arduous relationships in place. I wasn't doing anything wrong per se. You can solve simple physical equations using vector spaces and linear combination. You can also balance your checkbook using quadratics. Textbooks don't provide examples of either approach*, presumably because only morons would attempt them and it's considered gauche in the academic world to give morons tools they'll only use to hurt themselves. I'd spent a few months effectively proving that the basic laws of mathematics continue to function even when wielded by chimps. Which is worth knowing, I suppose. But it wasn't quite what I set out to do.
Back in the bookstore, Mark (our resident Employee With An Actual Degree) would refer to one of our regular customers as "the original intellectual dilettante", with a certain amount of affectionate derision. Every week or two she'd be on a new topic, eagerly absorbing every scrap she could find and giddily sharing choice tidbits from her foraging. I found her delightful, if occasionally exasperating. There was another class of customers who compulsively shared their understandings of the world: invariably male, of a wizened middle age; lurching erratically in the midst of a miasma of public assistance, indifferent hygiene, and tightly-wound desperation. Eye contact was an all-or-nothing affair, and equally unnerving either way. They didn't seem to know one another, but they were united by a disdain for classical education and a fervent belief that they'd unknotted the secrets of the cosmos through fevered readings of popular science topics.
Whether they were disproving theism via their interpretation of Brownian motion's deeper implications, or appealing to chaos theory to advocate anarchy as the only just system of governance, the logic sounded flawless... unless one realized that words have multiple meanings, and metonyms are not magically real. Heisenberg's famous uncertainty applies to teleology only as overwrought literary metaphor, not as compelling argument. But the primary deficiencies of these walking Wittgensteinian straw men were not intellectual in nature. Their analytical engines were plenty powerful, if poorly tuned. Indeed, they demonstrated an interest and ability well above average in their explorations of the world's workings. Their failings were those of grounding: in the basic principles of their subject matter, certainly, but even more vitally they lacked grounding in a peer group-- people to touch base with, calibrate the scales of sanity and establish the base levels of essential concepts as they worked with them. The necessity of consensus is impressed upon us early, but hidden benefit of formal education is opportunity. The vocabulary, the background, and the socio-economic passcodes to maintain access to a group devoted (in effect if not always intent) to continuous cross-checking. Otherwise, as soon as we start fooling ourselves there's nothing to stop us from digging in deeper. Nobody to pull us out of the recursive loops of wishful thinking and self-reinforcing mistakes. These guys were crazy before they were alone, I'm sure. But I'm also sure that all the unchecked hours inside their own heads weren't doing them any favors.
I don't recall having much of a reaction when I realized that I'd wasted months testing (not even proving) whether or not a+b really equaled b+a. It was annoying, but I've always been able to laugh at my own ridiculousness. Eventually, though, I made the connection between my behavior and the bookstore's gutter philosophers. It... hit me hard. And some of the bruises still show. I could handle being another intellectual dilettante, useless but happy. She had partners, enthusiastically sharing her sense of wonder. The crazies had nothing but unwilling audiences for their rantings, and a yearning to be understood that was powerful enough to make them miserable but not enough to change their behavior.
It was ten years back that I figured this out. I never stopped learning, but I never quite lost myself like that again. Haven't finished QED either, come to think of it. I'm still not sure whether I'm more like her or like them. And I'm still not sure which way I'm headed. And that, unfortunately, is the only honest conclusion I've got for this rambling little confession. Check with me again in ten years and we'll see if I can do better.
*Okay, actually you'll see lots of mechanical problems solved with linear algebra, but what I was doing was representing spatial dimensions and physical properties as independent axes and deriving properties and relationships and interactions from them, which led to some really beautiful symmetries and startling possibilities when I included time as yet another axis ("fourth dimension" my ass) and damn it all I really was trying to avoid going on at length here about exactly how I built my imaginary cloud castles. Point being: I have some idea of how linear algebra can be usefully applied, and trust me, what I was doing was NOT it.