break the brick, you only see the
surface. That the brick has an inside is a simple theory which helps us
understand things better. The theory of electrons is analogous. So I began
by asking, "Is a brick an essential object?"
Then the answers came out. One man stood up and said, "A brick as an
individual, specific brick. That is what Whitehead means by an essential
object."
Another man said, "No, it isn't the individual brick that is an
essential object; it's the general character that all bricks have in common
-- their 'brickness' -- that is the essential object."
Another guy got up and said, "No, it's not in the bricks themselves.
'Essential object' means the idea in the mind that you get when you think of
bricks."
Another guy got up, and another, and I tell you I have never heard such
ingenious different ways of looking at a brick before. And, just like it
should in all stories about philosophers, it ended up in complete chaos. In
all their previous discussions they hadn't even asked themselves whether
such a simple object as a brick, much less an electron, is an "essential
object."
After that I went around to the biology table at dinner time. I had
always had some interest in biology, and the guys talked about very
interesting things. Some of them invited me to come to a course they were
going to have in cell physiology. I knew something about biology, but this
was a graduate course. "Do you think I can handle it? Will the professor let
me in?" I asked.
They asked the instructor, E. Newton Harvey, who had done a lot of
research on light-producing bacteria. Harvey said I could join this special,
advanced course provided one thing -- that I would do all the work, and
report on papers just like everybody else.
Before the first class meeting, the guys who had invited me to take the
course wanted to show me some things under the microscope. They had some
plant cells in there, and you could see some little green spots called
chloroplasts (they make sugar when light shines on them) circulating around.
I looked at them and then looked up: "How do they circulate? What pushes
them around?" I asked.
Nobody knew. It turned out that it was not understood at that time. So
right away I found out something about biology: it was very easy to find a
question that was very interesting, and that nobody knew the answer to. In
physics you had to go a little deeper before you could find an interesting
question that people didn't know.
When the course began, Harvey started out by drawing a great, big
picture of a cell on the blackboard and labeling all the things that are in
a cell. He then talked about them, and I understood most of what he said.
After the lecture, the guy who had invited me said, "Well, how did you
like it?"
"Just fine," I said. "The only part I didn't understand was the part
about lecithin. What is lecithin?"
The guy begins to explain in a monotonous voice: "All living creatures,
both plant and animal, are made of little bricklike objects called
'cells'..."
"Listen," I said, impatiently, "I know all that; otherwise I wouldn't
be in the course. What is lecithin?"
"I don't know."
I had to report on papers along with everyone else, and the first one I
was assigned was on the effect of pressure on cells -- Harvey chose that
topic for me because it had something that had to do with physics. Although
I understood what I was doing, I mispronounced everything when I read my
paper, and the class was always laughing hysterically when I'd talk about
"blastospheres" instead of "blastomeres," or some other such thing.
The next paper selected for me was by Adrian and Bronk. They
demonstrated that nerve impulses were sharp, single-pulse phenomena. They
had done experiments with cats in which they had measured voltages on
nerves.
I began to read the paper. It kept talking about extensors and flexors,
the gastrocnemius muscle, and so on. This and that muscle were named, but I
hadn't the foggiest idea of where they were located in relation to the
nerves or to the cat. So I went to the librarian in the biology section and
asked her if she could find me a map of the cat.
"A map of the cat, sir?" she asked, horrified. "You mean a zoological
chart!" From then on there were rumors about some dumb biology graduate
student who was looking for a "map of the cat."
When it came time for me to give my talk on the subject, I started off
by drawing an outline of the cat and began to name the various muscles.
The other students in the class interrupt me: "We know all that!"
"Oh," I say, "you do? Then no wonder I can catch up with you so fast
after you've had four years of biology." They had wasted all their time
memorizing stuff like that, when it could be looked up in fifteen minutes.
After the war, every summer I would go traveling by car somewhere in
the United States. One year, after I was at Caltech, I thought, "This
summer, instead of going to a different place, I'll go to a different
field."
It was right after Watson and Crick's discovery of the DNA spiral.
There were some very good biologists at Caltech because Delbrück had his lab
there, and Watson came to Caltech to give some lectures on the coding
systems of DNA. I went to his lectures and to seminars in the biology
department and got full of enthusiasm. It was a very exciting time in
biology, and Caltech was a wonderful place to be.
I didn't think I was up to doing actual research in biology, so for my
summer visit to the field of biology I thought I would just hang around the
biology lab and "wash dishes," while I watched what they were doing. I went
over to the biology lab to tell them my desire, and Bob Edgar, a young
post-doc who was sort of in charge there, said he wouldn't let me do that.
He said, "You'll have to really do some research, just like a graduate
student, and we'll give you a problem to work on." That suited me fine.
I took a phage course, which told us how to do research with
bacteriophages (a phage is a virus that contains DNA and attacks bacteria).
Right away I found that I was saved a lot of trouble because I knew some
physics and mathematics. I knew how atoms worked in liquids, so there was
nothing mysterious about how the centrifuge worked. I knew enough statistics
to understand the statistical errors in counting little spots in a dish. So
while all the biology guys were trying to understand these "new" things, I
could spend my time learning the biology part.
There was one useful lab technique I learned in that course which I
still use today. They taught us how to hold a test tube and take its cap off
with one hand (you use your middle and index fingers), while leaving the
other hand free to do something else (like hold a pipette that you're
sucking cyanide up into). Now, I can hold my toothbrush in one hand, and
with the other hand, hold the tube of toothpaste, twist the cap off, and put
it back on.
It had been discovered that phages could have mutations which would
affect their ability to attack bacteria, and we were supposed to study those
mutations. There were also some phages that would have a second mutation
which would reconstitute their ability to attack bacteria. Some phages which
mutated back were exactly the same as they were before. Others were not:
There was a slight difference in their effect on bacteria -- they would act
faster or slower than normal, and the bacteria would grow slower or faster
than normal. In other words, there were "back mutations," but they weren't
always perfect; sometimes the phage would recover only part of the ability
it had lost.
Bob Edgar suggested that I do an experiment which would try to find out
if the back mutations occurred in the same place on the DNA spiral. With
great care and a lot of tedious work I was able to find three examples of
back mutations which had occurred very close together -- closer than
anything they had ever seen so far -- and which partially restored the
phage's ability to function. It was a slow job. It was sort of accidental:
You had to wait around until you got a double mutation, which was very rare.
I kept trying to think of ways to make a phage mutate more often and
how to detect mutations more quickly, but before I could come up with a good
technique the summer was over, and I didn't feel like continuing on that
problem.
However, my sabbatical year was coming up, so I decided to work in the
same biology lab but on a different subject. I worked with Matt Meselson to
some extent, and then with a nice fella from England named J. D. Smith. The
problem had to do with ribosomes, the "machinery" in the cell that makes
protein from what we now call messenger RNA. Using radioactive substances,
we demonstrated that the RNA could come out of ribosomes and could be put
back in.
I did a very careful job in measuring and trying to control everything,
but it took me eight months to realize that there was one step that was
sloppy. In preparing the bacteria, to get the ribosomes out, in those days
you ground it up with alumina in a mortar. Everything else was chemical and
all under control, but you could never repeat the way you pushed the pestle
around when you were grinding the bacteria. So nothing ever came of the
experiment.
Then I guess I have to tell about the time I tried with Hildegarde
Lamfrom to discover whether peas could use the same ribosomes as bacteria.
The question was whether the ribosomes of bacteria can manufacture the
proteins of humans or other organisms. She had just developed a scheme for
getting the ribosomes out of peas and giving them messenger RNA so that they
would make pea proteins. We realized that a very dramatic and important
question was whether ribosomes from bacteria, when given the peas' messenger
RNA, would make pea protein or bacteria protein. It was to be a very
dramatic and fundamental experiment.
Hildegarde said, "I'll need a lot of ribosomes from bacteria."
Meselson and I had extracted enormous quantities of ribosomes from E.
coli for some other experiment. I said, "Hell, I'll just give you the
ribosomes we've got. We have plenty of them in my refrigerator at the lab."
It would have been a fantastic and vital discovery if I had been a good
biologist. But I wasn't a good biologist. We had a good idea, a good
experiment, the right equipment, but I screwed it up: I gave her infected
ribosomes -- the grossest possible error that you could make in an
experiment like that. My ribosomes had been in the refrigerator for almost a
month, and had become contaminated with some other living things. Had I
prepared those ribosomes promptly over again and given them to her in a
serious and careful way, with everything under control, that experiment
would have worked,, and we would have been the first to demonstrate the
uniformity of life: the machinery of making proteins, the ribosomes, is the
same in every creature. We were there at the right place, we were doing the
right things, but I was doing things as an amateur -- stupid and sloppy.
You know what it reminds me of? The husband of Madame Bovary in
Flaubert's book, a dull country doctor who had some idea of how to fix club
feet, and all he did was screw people up. I was similar to that unpracticed
surgeon. The other work on the phage I never wrote up -- Edgar kept asking
me to write it up, but I never got around to it. That's the trouble with not
being in your own field: You don't take it seriously.
I did write something informally on it. I sent it to Edgar, who laughed
when he read it. It wasn't in the standard form that biologists use --
first, procedures, and so forth. I spent a lot of time explaining things
that all the biologists knew. Edgar made a shortened version, but I couldn't
understand it. I don't think they ever published it. I never published it
directly.
Watson thought the stuff I had done with phages was of some interest,
so he invited me to go to Harvard. I gave a talk to the biology department
about the double mutations which occurred so close together. I told them my
guess was that one mutation made a change in the protein, such as changing
the pH of an amino acid, while the other mutation made the opposite change
on a different amino acid in the same protein, so that it partially balanced
the first mutation -- not perfectly, but enough to let the phage operate
again. I thought they were two changes in the same protein, which chemically
compensated each other.
That turned out not to be the case. It was found out a few years later
by people who undoubtedly developed a technique for producing and detecting
the mutations faster, that what happened was, the first mutation was a
mutation in which an entire DNA base was missing. Now the "code" was shifted
and could not be "read" any more. The second mutation was either one in
which an extra base was put back in, or two more were taken out. Now the
code could be read again. The closer the second mutation occurred to the
first, the less message would be altered by the double mutation, and the
more completely the phage would recover its lost abilities. The fact that
there are three "letters" to code each amino acid was thus demonstrated.
While I was at Harvard that week, Watson suggested something and we did
an experiment together for a few days. It was an incomplete experiment, but
I learned some new lab techniques from one of the best men in the field.
But that was my big moment: I gave a seminar in the biology department
of Harvard! I always do that, get into something and see how far I can go.
I learned a lot of things in biology, and I gained a lot of experience.
I got better at pronouncing the words, knowing what not to include in a
paper or a seminar, and detecting a weak technique in an experiment. But I
love physics, and I love to go back to it.
--------
Monster Minds
While I was still a graduate student at Princeton, I worked as a
research assistant under John Wheeler. He gave me a problem to work on, and
it got hard, and I wasn't getting anywhere. So I went back to an idea that I
had had earlier, at MIT. The idea was that electrons don't act on
themselves, they only act on other electrons.
There was this problem: When you shake an electron, it radiates energy,
and so there's a loss. That means there must be a force on it. And there
must be a different force when it's charged than when it's not charged. (If
the force were exactly the same when it was charged and not charged, in one
case it would lose energy, and in the other it wouldn't. You can't have two
different answers to the same problem.)
The standard theory was that it was the electron acting on itself that
made that force (called the force of radiation reaction), and I had only
electrons acting on other electrons. So I was in some difficulty, I
realized, by that time. (When I was at MIT, I got the idea without noticing
the problem, but by the time I got to Princeton, I knew that problem.)
What I thought was: I'll shake this electron. It will make some nearby
electron shake, and the effect back from the nearby electron would be the
origin of the force of radiation reaction. So I did some calculations and
took them to Wheeler.
Wheeler, right away, said, "Well, that isn't right because it varies
inversely as the square of the distance of the other electrons, whereas it
should not depend on any of these variables at all. It'll also depend
inversely upon the mass of the other electron; it'll be proportional to the
charge on the other electron."
What bothered me was, I thought he must have done the calculation. I
only realized later that a man like Wheeler could immediately see all that
stuff when you give him the problem. I had to calculate, but he could see.
Then he said, "And it'll be delayed -- the wave returns late -- so all
you've described is reflected light."
"Oh! Of course," I said.
"But wait," he said. "Let's suppose it returns by advanced waves --
reactions backward in time -- so it comes back at the right time. We saw the
effect varied inversely as the square of the distance, but suppose there are
a lot of electrons, all over space: the number is proportional to the square
of the distance. So maybe we can make it all compensate."
We found out we could do that. It came out very nicely, and fit very
well. It was a classical theory that could be right, even though it differed
from Maxwell's standard, or Lorentz's standard theory. It didn't have any
trouble with the infinity of self-action, and it was ingenious. It had
actions and delays, forwards and backwards in time -- we called it
"half-advanced and half-retarded potentials."
Wheeler and I thought the next problem was to turn to the quantum
theory of electrodynamics, which had difficulties (I thought) with the
self-action of the electron. We figured if we could get rid of the
difficulty first in classical physics, and then make a quantum theory out of
that, we could straighten out the quantum theory as well.
Now that we had got the classical theory right, Wheeler said, "Feynman,
you're a young fella -- you should give a seminar on this. You need
experience in giving talks. Meanwhile, I'll work out the quantum theory part
and give a seminar on that later."
So it was to be my first technical talk, and Wheeler made arrangements
with Eugene Wigner to put it on the regular seminar schedule.
A day or two before the talk I saw Wigner in the hall. "Feynman," he
said, "I think that work you're doing with Wheeler is very interesting, so
I've invited Russell to the seminar." Henry Norris Russell, the famous,
great astronomer of the day, was coming to the lecture!
Wigner went on. "I think Professor von Neumann would also be
interested." Johnny von Neumann was the greatest mathematician around. "And
Professor Pauli is visiting from Switzerland, it so happens, so I've invited
Professor Pauli to come" -- Pauli was a very famous physicist -- and by this
time, I'm turning yellow. Finally, Wigner said, "Professor Einstein only
rarely comes to our weekly seminars, but your work is so interesting that
I've invited him specially, so he's coming, too."
By this time I must have turned green, because Wigner said, "No, no!
Don't worry! I'll just warn you, though: If Professor Russell falls asleep
-- and he will undoubtedly fall asleep -- it doesn't mean that the seminar
is bad; he falls asleep in all the seminars. On the other hand, if Professor
Pauli is nodding all the time, and seems to be in agreement as the seminar
goes along, pay no attention. Professor Pauli has palsy."
I went back to Wheeler and named all the big, famous people who were
coming to the talk he got me to give, and told him I was uneasy about it.
"It's all right," he said. "Don't worry. I'll answer all the
questions."
So I prepared the talk, and when the day came, I went in and did
something that young men who have had no experience in giving talks often do
-- I put too many equations up on the blackboard. You see, a young fella
doesn't know how to say, "Of course, that varies inversely, and this goes
this way..." because everybody listening already knows; they can see it. But
he doesn't know. He can only make it come out by actually doing the algebra
-- and therefore the reams of equations.
As I was writing these equations all over the blackboard ahead of time,
Einstein came in and said pleasantly, "Hello, I'm coming to your seminar.
But first, where is the tea?"
I told him, and continued writing the equations.
Then the time came to give the talk, and here are these monster minds
in front of me, waiting! My first technical talk -- and I have this
audience! I mean they would put me through the wringer! I remember very
clearly seeing my hands shaking as they were pulling out my notes from a
brown envelope.
But then a miracle occurred, as it has occurred again and again in my
life, and it's very lucky for me: the moment I start to think about the
physics, and have to concentrate on what I'm explaining, nothing else
occupies my mind -- I'm completely immune to being nervous. So after I
started to go, I just didn't know who was in the room. I was only explaining
this idea, that's all.
But then the end of the seminar came, and it was time for questions.
First off, Pauli, who was sitting next to Einstein, gets up and says, "I do
not sink dis teory can be right, because of dis, and dis, and dis," and he
turns to Einstein and says, "Don't you agree, Professor Einstein?"
Einstein says, "Nooooooooooooo," a nice, German-sounding "No," -- very
polite. "I find only that it would be very difficult to make a corresponding
theory for gravitational interaction." He meant for the general theory of
relativity, which was his baby. He continued: "Since we have at this time
not a great deal of experimental evidence, I am not absolutely sure of the
correct gravitational theory." Einstein appreciated that things might be
different from what his theory stated; he was very tolerant of other ideas.
I wish I had remembered what Pauli said, because I discovered years
later that the theory was not satisfactory when it came to making the
quantum theory. It's possible that that great man noticed the difficulty
immediately and explained it to me in the question, but I was so relieved at
not having to answer the questions that I didn't really listen to them
carefully. I do remember walking up the steps of Palmer Library with Pauli,
who said to me, "What is Wheeler going to say about the quantum theory when
he gives his talk?"
I said, "I don't know. He hasn't told me. He's working it out himself."
"Oh?" he said. "The man works and doesn't tell his assistant what he's
doing on the quantum theory?" He came closer to me and said in a low,
secretive voice, "Wheeler will never give that seminar."
And it's true. Wheeler didn't give the seminar. He thought it would be
easy to work out the quantum part; he thought he had it, almost. But he
didn't. And by the time the seminar came around, he realized he didn't know
how to do it, and therefore didn't have anything to say.
I never solved it, either -- a quantum theory of half-advanced,
half-retarded potentials -- and I worked on it for years.
--------
Mixing Paints
The reason why I say I'm "uncultured" or "anti-intellectual" probably
goes all the way back to the time when I was in high school. I was always
worried about being a sissy; I didn't want to be too delicate. To me, no
real man ever paid any attention to poetry and such things. How poetry ever
got written -- that never struck me! So I developed a negative attitude
toward the guy who studies French literature, or studies too much music or
poetry -- all those "fancy" things. I admired better the steel-worker, the
welder, or the machine shop man. I always thought the guy who worked in the
machine shop and could make things, now he was a real guy! That was my
attitude. To be a practical man was, to me, always somehow a positive
virtue, and to be "cultured" or "intellectual" was not. The first was right,
of course, but the second was crazy.
I still had this feeling when I was doing my graduate study at
Princeton, as you'll see. I used to eat often in a nice little restaurant
called Papa's Place. One day, while I was eating there, a painter in his
painting clothes came down from an upstairs room he'd been painting, and sat
near me. Somehow we struck up a conversation and he started talking about
how you've got to learn a lot to be in the painting business. "For example,"
he said, "in this restaurant, what colors would you use to paint the walls,
if you had the job to do?"
I said I didn't know, and he said, "You have a dark band up to
such-and-such a height, because, you see, people who sit at the tables rub
their elbows against the walls, so you don't want a nice, white wall there.
It gets dirty too easily. But above that, you do want it white to give a
feeling of cleanliness to the restaurant."
The guy seemed to know what he was doing, and I was sitting there,
hanging on his words, when he said, "And you also have to know about colors
-- how to get different colors when you mix the paint. For example, what
colors would you mix to get yellow?"
I didn't know how to get yellow by mixing paints. If it's light, you
mix green and red, but I knew he was talking paints. So I said, "I don't
know how you get yellow without using yellow."
"Well," he said, "if you mix red and white, you'll get yellow."
"Are you sure you don't mean pink?" "No," he said, "you'll get yellow"
-- and I believed that he got yellow, because he was a professional painter,
and I always admired guys like that. But I still wondered how he did it.
I got an idea. "It must be some kind of chemical change. Were you using
some special kind of pigments that make a chemical change?"
"No," he said, "any old pigments will work. You go down to the
five-and-ten and get some paint -- just a regular can of red paint and a
regular can of white paint -- and I'll mix 'em, and I'll show how you get
yellow."
At this juncture I was thinking, "Something is crazy. I know enough
about paints to know you won't get yellow, but he must know that you do get
yellow, and therefore something interesting happens. I've got to see what it
is!" So I said, "OK, I'll get the paints." The painter went back upstairs to
finish his painting job, and the restaurant owner came over and said to me,
"What's the idea of arguing with that man? The man is a painter; he's been a
painter all his life, and he says he gets yellow. So why argue with him?"
I felt embarrassed. I didn't know what to say. Finally I said, "All my
life, I've been studying light. And I think that with red and white you
can't get yellow -- you can only get pink."
So I went to the five-and-ten and got the paint, and brought it back to
the restaurant. The painter came down from upstairs, and the restaurant
owner was there too. I put the cans of paint on an old chair, and the
painter began to mix the paint. He put a little more red, he put a little
more white -- it still looked pink to me -- and he mixed some more. Then he
mumbled something like, "I used to have a little tube of yellow here to
sharpen it up -- a bit -- then this'll be yellow."
"Oh!" I said. "Of course! You add yellow, and you can get yellow, but
you couldn't do it without the yellow."
The painter went back upstairs to paint.
The restaurant owner said, "That guy has his nerve, arguing with a guy
who's studied light all his life!"
But that shows you how much I trusted these "real guys." The painter
had told me so much stuff that was reasonable that I was ready to give a
certain chance that there was an odd phenomenon I didn't know. I was
expecting pink, but my set of thoughts were, "The only way to get yellow
will be something new and interesting, and I've got to see this."
I've very often made mistakes in my physics by thinking the theory
isn't as good as it really is, thinking that there are lots of complications
that are going to spoil it -- an attitude that anything can happen, in spite
of what you're pretty sure should happen.
--------
A Different Box of Tools
At the Princeton graduate school, the physics department and the math
department shared a common lounge, and every day at four o'clock we would
have tea. It was a way of relaxing in the afternoon, in addition to
imitating an English college. People would sit around playing Go, or
discussing theorems. In those days topology was the big thing.
I still remember a guy sitting on the couch, thinking very hard, and
another guy standing in front of him, saying, "And therefore such-and-such
is true."
"Why is that?" the guy on the couch asks.
"It's trivial! It's trivial!" the standing guy says, and he rapidly
reels off a series of logical steps: "First you assume thus-and-so, then we
have Kerchoff's this-and-that; then there's Waffenstoffer's Theorem, and we
substitute this and construct that. Now you put the vector which goes around
here and then thus-and-so..." The guy on the couch is struggling to
understand all this stuff, which goes on at high speed for about fifteen
minutes!
Finally the standing guy comes out the other end, and the guy on the
couch says, "Yeah, yeah. It's trivial."
We physicists were laughing, trying to figure them out. We decided that
"trivial" means "proved." So we joked with the mathematicians: "We have a
new theorem -- that mathematicians can prove only trivial theorems, because
every theorem that's proved is trivial."
The mathematicians didn't like that theorem, and I teased them about
it. I said there are never any surprises -- that the mathematicians only
prove things that are obvious. Topology was not at all obvious to the
mathematicians. There were all kinds of weird possibilities that were
"counterintuitive." Then I got an idea. I challenged them: "I bet there
isn't a single theorem that you can tell me -- what the assumptions are and
what the theorem is in terms I can understand -- where I can't tell you
right away whether it's true or false."
It often went like this: They would explain to me, "You've got an
orange, OK? Now you cut the orange into a finite number of pieces, put it
back together, and it's as big as the sun. True or false?"
"No holes?"
"No holes."
"Impossible! There ain't no such a thing."
"Ha! We got him! Everybody gather around! It's So-and-so's theorem of
immeasurable measure!"
Just when they think they've got me, I remind them, "But you said an
orange! You can't cut the orange peel any thinner than the atoms."
"But we have the condition of continuity: We can keep on cutting!"
"No, you said an orange, so I assumed that you meant a real orange."
So I always won. If I guessed it right, great. If I guessed it wrong,
there was always something I could find in their simplification that they
left out.
Actually, there was a certain amount of genuine quality to my guesses.
I had a scheme, which I still use today when somebody is explaining
something that I'm trying to understand: I keep making up examples. For
instance, the mathematicians would come in with a terrific theorem, and
they're all excited. As they're telling me the conditions of the theorem, I
construct something which fits all the conditions. You know, you have a set
(one ball) -- disjoint (two balls). Then the balls turn colors, grow hairs,
or whatever, in my head as they put more conditions on. Finally they state
the theorem, which is some dumb thing about the ball which isn't true for my
hairy green ball thing, so I say, "False!"
If it's true, they get all excited, and I let them go on for a while.
Then I point out my counterexample.
"Oh. We forgot to tell you that it's Class 2 Hausdorff homomorphic."
"Well, then," I say, "It's trivial! It's trivial!" By that time I know
which way it goes, even though I don't know what Hausdorff homomorphic
means.
I guessed right most of the time because although the mathematicians
thought their topology theorems were counterintuitive, they weren't really
as difficult as they looked. You can get used to the funny properties of
this ultra-fine cutting business and do a pretty good job of guessing how it
will come out.
Although I gave the mathematicians a lot of trouble, they were always
very kind to me. They were a happy bunch of boys who were developing things,
and they were terrifically excited about it. They would discuss their
"trivial" theorems, and always try to explain something to you if you asked
a simple question.
Paul Olum and I shared a bathroom. We got to be good friends, and he
tried to teach me mathematics. He got me up to homotopy groups, and at that
point I gave up. But the things below that I understood fairly well.
One thing I never did learn was contour integration. I had learned to
do integrals by various methods shown in a book that my high school physics
teacher Mr. Bader had given me.
One day he told me to stay after class. "Feynman," he said, "you talk
too much and you make too much noise. I know why. You're bored. So I'm going
to give you a book. You go up there in the back, in the corner, and study
this book, and when you know everything that's in this book, you can talk
again."
So every physics class, I paid no attention to what was going on with
Pascal's Law, or whatever they were doing. I was up in the back with this
book: Advanced Calculus, by Woods. Bader knew I had studied Calculus for the
Practical Man a little bit, so he gave me the real works -- it was for a
junior or senior course in college. It had Fourier series, Bessel functions,
determinants, elliptic functions -- all kinds of wonderful stuff that I
didn't know anything about.
That book also showed how to differentiate parameters under the
integral sign -- it's a certain operation. It turns out that's not taught
very much in the universities; they don't emphasize it. But I caught on how
to use that method, and I used that one damn tool again and again. So
because I was self-taught using that book, I had peculiar methods of doing
integrals.
The result was, when guys at MIT or Princeton had trouble doing a
certain integral, it was because they couldn't do it with the standard
methods they had learned in school. If it was contour integration, they
would have found it; if it was a simple series expansion, they would have
found it. Then I come along and try differentiating under the integral sign,
and often it worked. So I got a great reputation for doing integrals, only
because my box of tools was different from everybody else's, and they had
tried all their tools on it before giving the problem to me.
--------
Mindreaders
My father was always interested in magic and carnival tricks, and
wanting to see how they worked. One of the things he knew about was
mindreaders. When he was a little boy, growing up in a small town called
Patchogue, in the middle of Long Island, it was announced on advertisements
posted all over that a mindreader was coming next Wednesday. The posters
said that some respected citizens -- the mayor, a judge, a banker -- should
take a five-dollar bill and hide it somewhere, and when the mindreader came
to town, he would find it.
When he came, the people gathered around to watch him do his work. He
takes the hands of the banker and the judge, who had hidden the five-dollar
bill, and starts to walk down the street. He gets to an intersection, turns
the corner, walks down another street, then another, to the correct house.
He goes with them, always holding their hands, into the house, up to the
second floor, into the right room, walks up to a bureau, lets go of their
hands, opens the correct drawer, and there's the five-dollar bill. Very
dramatic!
In those days it was difficult to get a good education, so the
mindreader was hired as a tutor for my father. Well, my father, after one of
his lessons, asked the mindreader how he was able to find the money without
anyone telling him where it was.
The mindreader explained that you hold onto their hands, loosely, and
as you move, you jiggle a little bit. You come to an intersection, where you
can go forward, to the left, or to the right. You jiggle a little bit to the
left, and if it's incorrect, you feel a certain amount of resistance,
because they don't expect you to move that way. But when you move in the
right direction, because they think you might be able to do it, they give
way more easily, and there's no resistance. So you must always be jiggling a
little bit, testing out which seems to be the easiest way.
My father told me the story and said he thought it would still take a
lot of practice. He never tried it himself.
Later, when I was doing graduate work at Princeton, I decided to try it
on a fellow named Bill Woodward. I suddenly announced that I was a
mindreader, and could read his mind. I told him to go into the "laboratory"
-- a big room with rows of tables covered with equipment of various kinds,
with electric circuits, tools, and junk all over the place -- pick out a
certain object, somewhere, and come out. I explained, "Now I'll read your
mind and take you right up to the object."
He went into the lab, noted a particular object, and came out. I took
his hand and started jiggling. We went down this aisle, then that one, right
to the object. We tried it three times. One time I got the object right on
-- and it was in the middle of a whole bunch of stuff. Another time I went
to the right place but missed the object by a few inches -- wrong object.
The third time, something went wrong. But it worked better than I thought.
It was very easy.
Some time after that, when I was about twenty-six or so, my father and
I went to Atlantic City, where they had various carnival things going on
outdoors. While my father was doing some business, I went to see a
mindreader. He was seated on the stage with his back to the audience,
dressed in robes and wearing a great big turban. He had an assistant, a
little guy who was running around through the audience, saying things like,
"Oh, Great Master, what is the color of this pocketbook?"
"Blue!" says the master.
"And oh, Illustrious Sir, what is the name of this woman?"
"Marie!"
Some guy gets up: "What's my name?"
"Henry."
I get up and say, "What's my name?"
He doesn't answer. The other guy was obviously a confederate, but I
couldn't figure out how the mindreader did the other tricks, like telling
the color of the pocketbook. Did he wear earphones underneath the turban?
When I met up with my father, I told him about it. He said, "They have
a code worked out, but I don't know what it is. Let's go back and find out."
We went back to the place, and my father said to me, "Here's fifty
cents. Go get your fortune read in the booth back there, and I'll see you in
half an hour."
I knew what he was doing. He was going to tell the man a story, and it
would go smoother if his son wasn't there going, "Ooh, ooh!" all the time.
He had to get me out of the way.
When he came back he told me the whole code: "Blue is 'Oh, Great
Master,' Green is 'Oh, Most Knowledgeable One,'" and so forth. He explained,
"I went up to him, afterwards, and told him I used to do a show in
Patchogue, and we had a code, but it couldn't do many numbers, and the range
of colors was shorter. I asked him, 'How do you carry so much information?'"
The mindreader was so proud of his code that he sat down and explained
the whole works to my father. My father was a salesman. He could set up a
situation like that. I can't do stuff like that.
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The Amateur Scientist
When I was a kid I had a "lab." It wasn't a laboratory in the sense
that I would measure, or do important experiments.
Instead, I would play: I'd make a motor, I'd make a gadget that would
go off wh