I remember once my dad told me how as a lad he had constructed a sort of weather vane in the shape of an aeroplane, complete with two propellers which could spin, and fastened it to a fencepost 'round the ol' homestead. One day when the wind was blowing fairly strong and steady, both of those propellers were just a-spinnin' as fast as can be. Watching this, my dad turned to my granddad and wondered to him why what with those propellers spinning so fast, that aeroplane couldn't just take off and fly away? Granddad reportedly replied that it just couldn't. He may have been at a loss to clearly explain the underlying physical principles, or he may not even really have understood why not for himself. But that's all he said, anyway.
My dad since went on to get a PhD in Civil Engineering, and now not only understands clearly why the aeroplane couldn't take off, but also has both intellectual and intuitive understanding of esoteric concepts ranging from the buckling properties of structural materials to the neutron-absorption cross-sections of fissile ones, and of course such things as Special Relativity, fluid dynamics, aerodynamics, and other domains to which my grandfather might have appealed to illuminate his rather terse response in the foregoing "aeroplane incident."
As a child of the early '70s, I watched a lot of Sesame Street, Schoolhouse Rock, and The Electric Company, but apparently those fonts of wisdom fell short of slaking my thirst for erudition. The Sesame Street graduate, for instance, can count as far as twenty (maybe in both English and Spanish!), but no further. The number systems of many European languages being more or less irregular up through 100, and given no rules for construction, the Sesame Street scholar, like some pre-adolescent Blackjack player, is stuck on the verge of twenty-one, or is compelled to invent. My name for forty was "twenty-twenty" (thirty was "twenty-ten"). These names seemed somehow ridiculous to me, and so I gave it up and resigned myself to the hope that someday I would somehow just know better. Had I lived in Roman times, perhaps I would not have been so easily daunted. But then again tele-vision would have existed in name only, and I probably wouldn't have gotten to watch Via Sesamem at all.
I remember always having been interested in and hungry for the idea of Mathematics, but at the same time knowing little or nothing about any part of it. In gradeschool, I played the swine before which such pearls as numbers like pi and formulae like E = mc2 might be cast -- magical scriptures whose meaning I understood but little, and whose use not at all. I was a young "Mathematics groupie", and longed to add some kind of solidity to my vague yearnings. I had a peculiar interest in graphs and plots of data. Orderly statistical data not being abundant in the world of a pre-teen, I would invent some. One of my more promising schemes was to categorize my various activities, e.g., watching TV, eating, sleeping, other, etc., and then carry a little notebook around for a week and note how I spent each day. At the end of the week I would produce seven pie-charts, showing how and when my time was spent each day, colour-coded and done in pencil and crayon with ruler and compass. This I did on a few separate occasions.
At one point, my dad gave me a little olive-green book, promisingly entitled, A Manual of Useful Data, filled with tables of quantities no doubt useful to the practicing engineer, the last few pages containing diagrams and formulae for calculating areas and volumes of certain basic shapes and solids. Further armed with the gift of a Sharp scientific calculator, I spent hours drawing geometrical spaceships, and, after selecting dimensions, calculated their volumes, masses, etc. I have since learned (and again forgotten, I'm afraid) how to derive these very formulae from base principles. Ah, multiple integration in non-Cartesian coordinates is a many-splendored thing! I also learned how Einstein's most famous formula may be derived from familiar Newtonian physics formulae by the addition of Lawrencian transformations, as opposed to being some inspiration dropped from the skies as The Far Side's Gary Larson and other cartoonists might have us suppose.
But I had to wait until almost my twenties to learn it. I had wanted to know those sorts of things since I was five or six. At around that age, having heard that one plus one are two, and knowing that zero came just before one, I once wrote 0 + 0 = 1 on a paper and proudly showed it to my parents. Like my grandfather before, they just said flatly that it was wrong, and would hear no protests. They may have said that zero plus zero were in fact zero, but no explanations of any length were given, and I remained confused and unsatsified. The numbers continued jealously to guard their shroud of mystery. It wasn't until the end of High School, when I came back from a summer of study at college, which included Calculus, that my dad said, "Now I finally have somebody I can tell this joke to!" and he wrote out symbolically: integral with respect to CABIN of one over CABIN equals what? And yes, faithful reader, my first Calculus teacher had done his job well enough, and with only slightly trembling fingers I grasped the pencil and held up my side of the equation, so to speak, with the answer, LOG CABIN. My dad's lonely 16-year vigil had not been in vain.