When I was a little kid in elementary school, I was fascinated by the space program. I didn't want to be an astronaut just to fly in space, though. I wanted to be a space scientist. Somehow, I deduced that space science involved Einstein, and to understand Einstein, you had to know algebra. So I went to the library to see if I could figure it out.
I could not make any sense of it at all based on what I saw in the odd textbook or two that was there. The technical books were either far too simple, and said nothing except ‘algebra is very complicated, so we will discuss physics without it’ or were so filled with symbols that seemed to never be defined anywhere. I’m not sure, at this tender age, that I understood that such symbols indeed needed to be defined- I just caught on quickly that I was no Einstein, because I could not just pick up any page of deep mathematics and understand it, completely free of context. I was no genius, apparently, and so doomed to never be a ‘great’ scientist.
Still, with this sobering fact still stinging in my mind, I did resolve that I would understand what these symbols meant, someday. While I shoveled coal on a train or something.
As I look around, I see on top of my computer a page of derivations that I have been working through from Jose’ and Saletan’s Classical Dynamics. I include it here as a scan. It’s really pretty run-of-the-mill calculus; partial derivatives scattered across the page scare some people that know a little calculus, but I think this is something students learn by third semester of college calculus (in the spirit of righting the wrongs I suffered as a child, take a look at the little ‘backward 6’ things- I’ll tell you what they mean because no one would tell me years ago: it is a way of watching the change in one quantity as you vary another, while keeping any others involved constant. There are details to flesh out before you can do it yourself, but this is what it means). Clearly, somewhere between being the child in my hometown library and now, as a mature adult, I figured out what those and many other symbols mean. I want to think back to how this happened.
It wasn’t school. By third grade, I was so horrified and brutalized by school that I dispaired of ever getting anything out of it. I hated school, and it hated me. I got paddled a lot, for offenses as trivial as having an untied shoe. This was not some authoritarian Catholic reeducation camp, or military boarding school, mind you, but the benevolent little public school down the street from where I lived. So I gave up on school.
I learned almost nothing of math in middle school. Not long division or mixed fractions or any of that. Nothing. But I kept reading about how I needed to know differential equations and tensors to understand the important parts of physics. All my favorite authors said so- Carl Sagan, Isaac Asimov, Freeman Dyson, George Gamow- but none of them really offered much help in getting there.
Around thirteen, I got mixed up in booze and pot and self-hatred. Thankfully, just as suddenly, I snapped out of it. I really got in a heap of trouble at school- I routinely antagonized teachers, I slacked and malingered and wasted time. But, ironically enough, the crisis came when the vice-principal of the school thought he would get rid of me by claiming I had been ‘selling pills’.
Absolute nonsense. I had drank a pint of cherry flavored vodka in one sitting at 13, and I had smoked some of the nastiest ditchweed marijuana you have ever seen, but I never sold anything (except hits off a 64oz beer a guy on my paper route gave me in lieu of payment once, but that was outside of school). But I never sold any pills, nor did I take any. It just wasn’t the redneck punk kid idiom then. Dope and liquor. Lynard Skynard and ZZ Top. Pills seemed kinda queer. I think I heard about people taking Quaaludes, but I had no idea what they were, and they didn’t seem appealing.
The moment of truth came and went, because the vice principal could not produce any evidence, nor did he seem to have a clear idea of what he wanted to do. But I got sent to a new school on the initiative of myself and my parents. One with a rough reputation.
To be honest, I cannot remember a thing about it. I certainly didn’t have any mathematical or scientific epiphany then, with the exception that I had discovered chemistry was good for making explosives. This is a story in itself that I will tell later, but is, at its heart, why I am a chemist and not a physicist, and why, though I am deeply attracted to theory, I will always be an experimentalist. Nearly blowing yourself up scares you, certainly, but it is an integral part of the formation of many chemists I know.
I had a short time to reflect, though, about the fact that I was headed nowhere. I laid off the vices- not that I didn’t drink the occasional beer in high school, and I smoked a joint again at 14, but the hardcore self-destruction stopped before it ever got started. I could just see, in that brief interlude, that it led to oblivion.
I went back into the school system that I had escaped- my first year of high school, I figured out quickly that I was right about my assessment of where my old friends were headed (and to a man, they all crashed hard and never really recovered the promise they showed).
By contrast, as my childhood buddies from elementary school went on to high school, they fell in with kids that knew that they wanted to go to college and be something.
I sort of thought that this was bullshit, but as I hung out with them, and transferred back into the better school system (with the rough reputation), I just naturally started to act more like them. I started to want my path to be like theirs. I started to believe that I could do it. They seemed sure they could, and I was frankly sure that I was at least their intellectual equal. I began to regret all the goofing off. I hoped that it wasn't too late to turn around. I feared that my bad grades in high school might keep me out of college. Back to shoveling coal on the train. I really wanted to avoid that.
In ninth grade, algebra had been a bit of a muddle, because I had not paid attention, and figured my chance at being a prodigy was spent, so I’d never be a scientist, so who cared. I could be a ne'er-do-well and badass and maybe still avoid being a coal-shoveler, if not an inmate. All these worries about not being able to be a scientist because I was no Einstein were stupid thoughts, in retrospect. I have met real prodigies since then. Some did well as professional scientists, and some did not at all.
But being a prodigy or genius certainly isn’t a prerequisite for being a scientist, and the horrible hagiographic biographies of great scientists have done a lot of harm by making it seem so. Hell, even Einstein was not the Einstein I imagined when I was a kid, and this is not to diminish any of his awesome accomplishments. Einstein is an important scientist, but not the only one. Not every mathematician has to be Gauss to be good and productive, either.
So in 2nd year algebra, things started poorly. I got D’s several periods. I started off never doing my homework, which is why I got D’s, but I started paying attention. I made a couple of brainy friends, and we got to where we competed at doing the homework. One kid really shone, and I set my sights on him. It became fun. I got good at it. I started thinking about it a lot, asking teachers for extra stuff. I started to wonder about it, to vaguely realize how deep and interesting it is.
My good crowd let me know that I had to take geometry and Algebra 2 at the same time to make it to calculus. Calculus- the word alone was enough to fill most kids with dread. But I needed calculus. I had decided I would be a physicist. I was still getting D’s in math, but I knew that this was not indicative of what I could do. I knew the D's would go away once I started to engage, and they did. Geometry was fascinating, and exposed me to logic in a way that forever changed my way of looking at the world. I could chain ideas together. I could actually, definitively prove some things. There was a certainty to the world that I had never recognized.
I also took intro physics my sophomore year from a kind and gentle man, one so pliant and easy going that we barely got into the subject at all. He seemed, in a way, unwilling to make us learn it. But I asked him about the difficult and mysterious world of differential equations, and he lit up. He gave me a copy of his college calculus book. I looked in it, and with my budding mathematical skills, I knew that I could figure this stuff out. I still have the book- it is still one of my most prized possessions.
The summer between sophomore and junior year, I carried the calculus book around a lot. It was going to solve some of the childhood mysteries for me. First, I was able to decipher a hieroglyphic that had filled me with shame at my ignorance as an elementary school student, the mysterious sigma, the greek letter that looks like a weird E or something.
To hardcore mathies, this has to sound a little stupid. But as a kid, literally no one I encountered had any idea what this thing meant. It might come as a surprise to engineers and scientists that almost none of the nontechnical people they encounter has any idea. I didn’t grow up around engineers or scientists, just good, working-class people that thought I was a little weird but loved me anyway.
The revelation that sigma means to sum, to add up a string of values using some rule specified by what follows it, was like Champollion sitting down with the Rosetta stone and knowing for the first time what was written in Egyptian tombs. I was giddy, and felt oddly powerful, like an initiate into a secret society. I knew something that most of my friends, even those that would eventually become fluent in mathematics, found inpenetrable. I wanted to tell them, but found out quickly that nothing kills a party like a math nerd trying to explain something ‘cool’ they figured out. Mathematics is, alas, often a solitary meal. Still delicious, though. Then, there on page 201, where scribbling from those days when I was not yet 16 still linger, I figured out the fundamental theorem of calculus. I knew what it meant. I wasn’t good at calculus yet, I couldn’t apply it, but I understood what it meant. I understood the proof, and would for ever after know what calculus was about.
I can still remember the surprise in my mind, that I understood. It was afternoon, sometime in the summer, and I had taken another stab at figuring things out. As these things go, there was some critical insight that I had been missing- I have no idea what it was now, but I still go through the same sequence to this day as I struggle with new science and math. With proper tutoring, I would have no doubt sped right past whatever it was that was hanging me up, but I would have been robbed of the joy of having the parts snap together suddenly in my mind. I may have even hugged the book. I let myself have the rest of the day away from the book, just to relish the feeling. I went through a lot more of the book that summer, mainly the sections on applications of single variable calculus.
Junior year was trigonometry for math, and chemistry for science. I fell in love with chemistry. I still had a machismo thing that made physics and math seem like the only subjects worthy of a math-jock like me (sometimes, I still indulge in this, though I know it is patently untrue. I keep the math and physics dusted off to abuse my chemist friends, and for fun. But I have seen what I think of as simple chemistry absolutely dumbfound bright physicists. It requires a different way of thinking. I hope to get into that another day). But chemistry was fun. Trig was fun. I knew where this was all headed the next year in calculus, so none of it seemed pointless. Some of the brainy kids from algebra seemed to fall by the wayside as math required more than the gymnastic skill algebra demands, and began to become deep conceptually. When we talked about infinite series, and imaginary numbers (you use them in algebra, but as a formal thing. Not as a concept.) some never really recovered. I got decent grades for the first time in my life. I began to think about where to go to college more than if I would go.
Senior year calculus was a breeze. I got mainly A’s, even one semester of straight A’s to prove to my girlfriend that I could do it. I whipped several ‘good scholar’ kids in the community at a Math Science League in chemistry. It outraged some of them that a C average kid was even there. It galled the hell out of the principal to have to give me an award for winning. I came in third in math, but I am fairly sure that this is because my computational skills were still developing. I still had trouble with long division and mixed fractions, and was wont to drop a negative sign here and there. Bad habits from my slacking days.
College did not go so smoothly, but I will leave that story for another time, except to catch up to the present, and to say that ultimately, it was a triumph, though circuitous. I have a BS in Chemistry, enough hours in Physics for a BS in physics, a minor in Math, and a PhD in Chemistry. I did a post doc at a physics lab, and have a great job doing industrial research where I get to use a little of all of it, plus a little engineering here and there.
The moral of the story is that the road was personal, and I did what I started out to do as a little kid, though I dispaired of getting to the end of it many times along the way. I owe what I have accomplished to my parents teaching me that I could do whatever I decided to do (deciding being the hard part) and to my grandmother, who told me to never let anyone beat me out of an education, including myself. I wish I had put money on it in third grade when they told me I’d never be a scientist because I had no mathematical ability. Now, I need to stop. I have some differential geometry to study.