Somewhere around 50 years late? *sigh*
OK, I was a fairly bright (never so-called “genius” level bright, but not intellectually dim, either) teenager. Oh, I was completely clueless, ignorant and could almost be classed as a zombie in all regards except for intellectual curiosity. A genuine nerd before such things were so labeled. An Odd, if ever there were one. I did have friends, but that’s ALL due to their friendliness (well, perhaps save for another Odd I connected with due to his parents’ long-standing friendship with my parents, and their awareness of our similar Odd-ness *heh*).
So, there I was at fourteen pitching the idea that my parents spend some of “my” money (long story involving an insurance settlement for injuries directly and completely caused by a neighbor’s stupidity and paid for by their car insurance) to buy a set of The Great Books of the Western World. Sold it. They bought the set. It thereafter “lived” by my bed until I got married, its authors works my constant companions.
Slide ahead a year from the purchase. I had just about completed a recovery and rehabilitation from the damage done me by “New Math”–said rehabilitation at the hands of a great math teacher (thank you, Mrs. Heinz, wherever you are!) via a year of high school geometry. Maths became enjoyable again. And then. . . Newton’s Principia Mathematica, though not in Latin (a language I still have no real facility with). Why not? It was really just an extension of geometry, since ALL Newton’s development of calculus in it were geometrically-inspired, driven, and derived. Oh, I won’t say I mastered Newton’s developments as an autodidact at the age of fifteen. No, I certainly did not, but. . .
Fast forward to my first year of calculus class. The teacher drew me apart after the first exam and required me to retest on the material, using different test problems, because I had scored 100% without writing in any of the intermediate steps between problem and answer, and I could offer nothing except, “Well, it seems obvious.”
So, retest. Same results. Puzzled him, and even I was puzzled as time went on and I saw other students I knew were brighter than I was have to work through the steps.
Just this evening, prompted by a mention of Newton’s approach to calculus in a novel, I recalled how much fin working through Principia had been a couple of years before that calculus class and the light dawned: I wasn’t just “seeing the answer” through some sort of intuitive insight. No, it was just the echo of having played around with Newton a couple of years before.
Now, I’m not as mentally sharp in intellectual pursuits as I was when I was a teenager, but I still enjoy working through concepts, and yes, even maths, to arrive at new and interesting ideas or learn new things about, well, just about anything. I’m still curious and enjoy poking the bear of my ignorance, prodding it into learning something new, so at least I still have that. No, I don’t learn languages as easily as I once did, and yes new concepts take a wee tad more effort to work out than I recall once being the case, but such things are still fun.
Still, why the heck did it take something like 50 years for me to make the connection between playing with Principia and the way calculus seemed so easy? Cluelessness. *heh* I still got it!