New York wise-guy genius.



"One day at Princeton I was sitting in the lounge and overheard some mathematicians talking about the series for e, which is 1 + x + (x)(x)/2! + (x)(x)(x)/3! Each term you get by multiplying the preceding term by x and dividing by the next number. For example, to get the next term after (x)(x)(x)(x)/4! you multiply that term by x and divide by 5. It's very simple.

When I was a kid I was excited by the series, and had played with this thing. I had computed e to any power using that series (you just substitute the power for x).

'Oh yeah?' they said, 'Well, then, what's e to the 3.3?' said some joker - I think it was Tukey.

I say, 'That's easy. It's 27.11'

Tukey knows it isn't so easy to compute all that in your head. 'Hey! How'd you do that?'

Another guy says, 'You know Feynman, he's just faking it. It's not really right.'

They go to get a table, and while they're doing that, I put on a few more figures: '27.1126,' I say.

They find it in the table. 'It's right! But how'd you do it!'

'I just summed the series.'

'Nobody can sum the series that fast. You must just happen to know that one. How about e to the 3?'

'Look,' I say. 'It's hard work! Only one a day!'

'Hah! It's a fake!' they say, happily.

'All right,' I say, 'It's 20.085.'

They look in the book as I put a few more figures on. They're all excited now, because I got another one right.

Here are these great mathematicians of the day, puzzled at how I can compute e to any power! One of them says, 'He just can't be substituting and summing - it's too hard. There's some trick. You couldn't do just any old number like e to the 1.4.'

I say, 'It's hard work, but for you, OK. It's 4.05.'

As they're looking it up, I put on a few more digits and say, 'And that's the last one for the day!' and walk out.

What happened was this: I happened to know three numbers - the logarithm of 10 to the base e (needed to convert numbers from base 10 to base e), which is 2.3026 (so I knew that e to the 2.3 is very close to 10), and because of radioactivity (mean-life and half-life), I knew the log of 2 to the base e, which is .69315 (so I also knew that e to the .7 is nearly equal to 2). I also knew e (to the 1), which is 2.71828.

The first number they gave me was e to the 3.3, which is e to the 2.3 - ten - times e, or 27.18. While they were sweating about how I was doing it, I was correcting for the extra .0026 - 2.3026 is a little high.

I knew I couldn't do another one; that was sheer luck. But then the guy said e to the 3: that's e to the 2.3 times e to the .7, or ten times two. So I knew it was 20.something, and while they were worrying how I did it, I adjusted for the .693.

Now I was sure I couldn't do another one, because the last one was again by sheer luck. But the guy said e to the 1.4, which is e to the .7 times itself. So all I had to do is fix up 4 a little bit!

They never did figure out how I did it."

FROM: "Surely You're Joking, Mr. Feynman!", by Richard P. Feynman, Norton, 1985, pgs. 192-193.

"It is a great adventure to contemplate the universe, beyond man, to contemplate what it would be like without man, as it was in a great part of its long history and as it is in a great majority of places. When this objective view is finally attained, and the mystery and majesty of matter are fully appreciated, to then turn the objective eye back on man viewed as matter, to view life as part of this universal mystery of greatest depth, is to sense an experience which is very rare, and very exciting. It usually ends in laughter and a delight in the futility of trying to understand what this atom in the universe is, this thing - atoms with curiosity - that looks at itself and wonders why it wonders. Well, these scientific views end in awe and mystery, lost at the edge in uncertainty, but they appear to be so deep and so impressive that the theory that it is all arranged as a stage for God to watch man's struggle for good and evil seems inadequate."

FROM: "The Meaning of it All", by Richard P. Feynman, Addison-Wesley, 1998, pg. 39.

When Feynman was 17 or 18 he worked one summer in a hotel run by his aunt. Here is one of the observations he made:

"Among the desserts there was some kind of coffee cake that came out very pretty on a doily, on a little plate. But if you would go in the back you'd see a man called the pantry man. His problem was to get the stuff ready for desserts. Now this man must have been a miner, or something - heavy-built, with very stubby, rounded thick fingers. He'd take this stack of doilies, which are manufactured by some sort of stamping process, all stuck together, and he'd take these stubby fingers and try to separate the doilies to put them on the plates. I always heard him say, 'Damn deez doilies!' while he was doing this, and I remember thinking, "What a contrast - the person sitting at the table gets this nice cake on a doilied plate, while the pantry man back there with the stubby thumbs is saying, 'Damn deez doilies!'" So that was the difference between the real world and what it looked like."

FROM: "Surely You're joking, Mr. Feyman!", by Richard P. Feynman, W.W. Norton, 1985, pg. 26.

"If you are interested in the ultimate character of the physical world, or the complete world, and at the present time our only way to understand that is through a mathematical type of reasoning, then I don't think a person can fully appreciate, or in fact can appreciate much of, these particular aspects of the world, the great depth of character of the universality of the laws, the relationships of things, without an understanding of mathematics. I don't know any other way to do it, we don't know any other way to describe it accurately ... or to see the interrelationships without it. So I don't think a person who hasn't developed some mathematical sense is capable of fully appreciating this aspect of the world - don't misunderstand me, there are many, many aspects of the world that mathematics is unnecessary for, such as love, which are very delightful and wonderful to appreciate and to feel awed and mysterious about; and I don't mean to say that the only thing in the world is physics, but you were talking about physics and if that's what you're talking about, then to not know mathematics is a severe limitation in understanding the world."

FROM: "The Pleasure of Finding Things Out", by Richard P. Feynman, Helix Books, 1999, pg. 15.

"I am Professor Feynman, in spite of this suit-coat. I usually give lectures in shirtsleeves, but when I started out of the hotel this morning my wife said, "You must wear a suit." I said, "But I usually give lectures in shirtsleeves." She said, "Yes, but this time you don't know what you're talking about so you had better make a good impression ..." So I got a coat."

FROM: "The Pleasure of Finding Things Out", by Richard P. Feynman, Helix Books, 1999, pg. 97.

"There is an infinite amount of crazy stuff, which, put another way, is that the environment is actively, intensely unscientific. There is talk of telepathy still, although it's dying out. There is faith-healing galore, all over. There is a whole religion of faith-healing. There's a miracle at Lourdes where healing goes on. Now, it might be true that astrology is right. It might be true that if you go to the dentist on the day that Mars is at right angles to Venus, that it is better than if you go on a different day. It might be true that you can be cured by the miracle of Lourdes. But if it is true, it ought to be investigated. Why? To improve it. If it is true, then maybe we can find out if the stars do influence life; that we could make the system more powerful by investigating statistically, scientifically judging the evidence objectively, more carefully. If the healing process works at Lourdes, the question is how far from the site of the miracle can the person, who is ill, stand? Have they in fact made a mistake and the back row is really not working? Or is it working so well that there is plenty of room for more people to be arranged near the place of the miracle? Or is it possible, as it is with the saints which have recently been created in the United States - there is a saint who cured leukemia apparently indirectly - that ribbons that are touched to the sheet of the sick person (the ribbon having previously touched some relic of the saint) increase the cure of leukemia - the question is, is it gradually being diluted? You may laugh, but if you believe in the truth of the healing, then you are responsible to investigate it, to improve its efficiency and to make it satisfactory instead of cheating. For example, it may turn out that after a hundred touches it doesn't work anymore. Now it's also possible that the results of this investigation have other consequences, namely, that nothing is there."

FROM: "The Pleasure of Finding Things Out", by Richard P. Feynman, Helix Books, 1999, pgs. 106-107.