Prizefighter Muhammad Ali ^{Note 1} was teased by reporters in 1964, after failing the U.S. Armed Forces qualifying test due to poor writing and spelling skills. He responded by saying, "I said I was the greatest; I never said I was the smartest." I laughed at the time, wondering how anyone could consider himself great if he wasn't smart. But then I gave it some thought, and realized that being smart was not necessarily as important to everyone else as it was to me. There are many other ways one can be "great".

I'm smart. You may think I'm being immodest if I say it outright like that, but I'm not sure why. It doesn't represent any accomplishment on my part, but rather is largely an accident of heredity. Were I two meters tall (six foot five), nobody would think it boastful of me if I were to say, "I'm tall". It would just be a statement of fact.

Well, I'm not tall (far from it), but I am smart, and that's always been my most defining characteristic, my identity. My father was always very proud of my intelligence, but I think it initially impressed my mother less. Although like my father she was proud of my being smart, she might have preferred me to be tall. Talking to Margie one day after she and I were married, my mother emphasized how smart I was. Margie agreed, but said that wasn't really the main reason she loved me. My mother said something that Margie interpreted at the time as implying that being smart was my major strong point. But perhaps my mother was just prompting Margie to recite my other good qualities.

I didn't start out well in mathematics in elementary school. Well, they call it mathematics, but it's actually just arithmetic. The problem was that in the fourth grade, I refused to memorize my multiplication tables (in those days, they were taught up through 12 times 12). I have an excellent rote memory (more auditory than visual), but I've always had trouble memorizing things that don't need to be memorized because you can just figure them out from first principles (see my blog entry "Dan and the moon"). And since the answer to multiplication problems with multiplicands of 12 or less can be easily figured out, I didn't see any need to memorize the answers. ^{Note 2}

My difficulties with arithmetic were one reason why, as a child, I myself didn't think I was particularly smart. In school, once I got beyond basic arithmetic, I always got A's in my math and science courses, but hey, that was math and science - they were easy. And as noted above, my parents clearly thought I was smart, but don't parents always think that?

So I didn't take notice until late in high school, when my scores on the "College Board" SAT (Scholastic Aptitude Test) came in, all well above 700 (800 was the maximum possible score). They also included a perfect score of 800 on the afternoon Advanced Mathematics test. But I was particularly stunned, as was everyone else, by an 800 in the English Achievement test. I had been getting C's in English for years, and wasn't very interested in my English courses. My parents were friendly with Jack Fields, a Great Neck English teacher, and years later he bemoaned the fact that I had never been in one of his classes - he thought he would have been able to get me interested in the subject. I didn't quite hit 800 on my Advanced Physics test - if only Mr. Lusch had been a more inspiring teacher.

It was these SAT scores, particularly in Advanced Math, that got me into MIT (being barely in the top 20 percent of my high school class, I'd never be admitted today). And I coasted through my undergraduate years at MIT without working very hard at all. My fellow students thought of me as a "tool" (MIT slang for someone who studies all the time), because I was getting very good grades (virtually straight A's). But in fact, although I always attended all my classes and did all my homework assignments, I didn't actually find it very difficult.

Being smart had at least one negative effect on me: I think it contributed to making me lazy. Things came to me too easily. In a much-cited statement, Calvin Coolidge said,

Nothing in this world can take the place of persistence. Talent will not; nothing is more common than unsuccessful people with talent. Genius will not; unrewarded genius is almost a proverb. Education will not; the world is full of educated derelicts. Persistence and determination alone are omnipotent. The slogan "press on" has solved and always will solve the problems of the human race.

I've always retained a great deal of factual information, despite seldom setting out to explicitly memorize it. As I noted in my earlier-cited blog entry "Dan and the moon", I recently discovered that some people at the Kronos Corporation, where I worked for nearly 25 years, played a game called "Stump the Krak", to see if they could find a scientific or mathematical question that I couldn't answer. Members of my family sometimes seem to think I know everything. I don't, of course, far from it, but see my sister's first "guest blog entry", "Ask Larry".

Despite my high intelligence, and perhaps to some extent due to my laziness, I can't say I accomplished anything in my life that will be remembered by the world at large. But I did have a successful engineering career based largely upon being smart.

Since my father seemed to be so proud of my intelligence, I'll close with a particular incident that stands out in my memory, although it's a rather long story. I recall listening to my father telling this story to my mother:

My uncle Milton took our two families fishing one day, and the first step was to catch minnows to use as bait. We fished for them in a rural stream, using very small hooks baited with compressed wet bread. We didn't all have real fishing rods, so many of us just used fishing line attached to long sticks.

I noticed that Milton was pulling out minnows almost as fast as he could bait the hooks and throw them into the water, while I was getting virtually none. It seemed to me that I ought to be able to observe what the difference was between what the two of us were doing. After all, he couldn't have any magic aura around his hook that attracted minnows. If he was consistently getting a different result, it must have been for a reason.

Was he jiggling his hook in a particular way? I watched carefully, and tried to duplicate his motions. Was he using larger, or smaller, balls of bread for bait? I carefully duplicated his amounts. No effect.

Finally, I decided that he must have been placing his hook in a better spot, more in the center of the stream. He was, after all, using a real fishing rod, which was considerably longer than my wooden stick. I lengthened my line, and tried casting it out into the center of the stream, but couldn't reach it.

I set off into the woods a bit, and located a longer stick. I stripped off its branches, and re-tied my line at the end. It didn't do the job, but I noted that I was still not getting my hook as far out in the stream as Milton was.

So I went deeper into the woods, and eventually found a much longer stick. I prepped it as before, and it was finally as long as Milton's rod, and I could reach the center of the stream.

And that did it. The next thing I knew, I was pulling in as many minnows as Milton.

I later recounted this story to my father, and he seemed to be ecstatic. He dragged me over to my mother, and told me to repeat it to her, as he added his own commentary.

I looked to see what Milton was doing differently. "Observation!" said my father.

I reproduced various differences in Milton's technique. "Experimentation!"

I cut a longer stick. "Action!"

I cut an even longer stick. "Persistence!"

I was disappointed to find that my mother seemed unimpressed.

Note 1:   Muhammad Ali was born Cassius Marcellus Clay, but changed his name to Muhammad Ali in 1964, when he joined the Nation of Islam. That was the same year he uttered the words I cited, and I'm not sure whether it was before or after he announced his name change. Thus I wasn't sure which name to put under the quote.

A tireless self-promoter, Ali was renowned for repeatedly exclaiming, "I'm the greatest."   [return to text]

Note 2:   The two-times table is trivial - I've always found it easy to double in my head (that is, 2 X 8 is just 8 + 8). For 4, you just double twice, and for 8 you just double three times.

Three's a little harder - you have to double, and then add the original number. For six, multiply by three as described, and then double again.

The pattern for five is obvious: 5, 10, 15, 20, 25, ... and so on. Five times N is just ten times N divided in half.

Nine times is easy, since 9N = 10N - N. That is, 9 X 7 = 70 - 7 = 63. In fact, the pattern is simple: the first digit of the result is one less than the number you're multiplying by nine, and the second digit is the "tens complement" (the number subtracted from 10).

Ten times is obvious, just add a zero. To multiply by 11 (up through 11 X 9), just double the digit (11, 22, 33, 44, 55, etc). And to multiply by twelve, double the number and add it to itself shifted left (12N = 10N+2N).

So we're left with the seven-times row as the only row in the multiplication table having no particular "trick". But since 7 times N is the same as N times 7, you can always just turn the product around, and then use the other tricks described above. Unless it's seven times seven, but that's a perfect square - I knew them all by heart just from frequent use.

OK, one day, under duress, I memorized the seven-times table. My father made me do it while driving me somewhere, and it only took me about fifteen minutes to memorize it permanently, which shows you just how lazy I actually was. And on a subsequent drive, he made me learn the three-times table as well.

Still, when the class was divided into two lines, and a multiplication problem on a "flash card" was exposed to the two front people in each line, I always lost the race to give the answer. When I was in the fourth grade, nobody would have predicted that one day I would find calculus at MIT to be a breeze.  [return to text]