Richard Feynman Quotes

[T]his rule explains several of the ordinary phenomena... such as angle of incidence equals angle of reflection, and , that light bends... from air to water, and travels in straight lines... It's all hidden in that one rule.

The probability of an event is always... the square of an amplitude... the size [area] of a circle corresponding to an arrow. An arrow is called an amplitude. For every event you calculate an amplitude (which is an arrow on a plane). The probability is the area corresponding to that arrow.

[T]he size of the arrow depends upon the... materials... [Y]ou make an arrow, and depending upon the time it takes for the light to get from the source to... where you... count it, you turn that arrow like a clock... round, round, depending on how much time it takes... every second it goes around... 1 followed by 15 zeros [<math>10^{15}</math>] times... It doesn't take light very long to get from the source... but it still turns a lot of times... It's like the roulette wheel and just the moment it hits the counter, it happens to be setting at some angle... It can look like a small angle when you're done, but you had to turn... like a clock hand after 25 years... it can start at 2:00 and end up at 2:15. ...That's ...the arrow for the first surface. Now the arrow for the second surface. Rule: same as the arrow for the first surface... [rotated] in the... opposite direction... When you go from air to glass it's one way... glass to air you change it around. ...You start this way for the second surface, and you turn this [arrow]... for the time, and when you get finished with this roulette wheel in the second one it comes out so. And now you add them together... and that's the laws of... light, and that will tell you whether it reflects or doesn't reflect.

For each reflection you make an arrow. This arrow... for the reflection from front surface, and this arrow... from the back surface... and... you tie the arrows together this way... [Y]ou put the tail of the other one on the head of that one... and you put these two arrows together by this rule, and you look at <nowiki>[</nowiki>the vector sum,] how far off you've come from the end... You count the number of beans you put in the barrel, I mean you make these pictures. ...[T]hen you ask, "How big is this circle [whose radius is the vector sum of the front and back arrows] in area?" And that area represents the probability... If the circle area is big, then you get a high probability, if... small, you get a small probability.

Amplify. ...[W]hen we have a device like this and we put it in the dark... it goes click, click... Every once in a while a light particle comes in: a photon. This is a particle in every sense. ...[I]f you have a very weak light... and... you put two cells out, and there's just a few... [photons] coming, then it goes on one or the other... the particle is either here or there. ...It is particles, in every way, whenever you can detect it. ...If we were ten times more sensitive to light, then in the dark, we would see... little flashes, little tiny... dots of light, the nerves would go off just like the photomultiplier, in spots. But the human eye is not quite that sensitive, and it takes 5 or 6 ...photons ...to make one nerve fiber go off. ...So we cannot detect, with the eye, light quite low enough to notice the fact that it comes in the form of rain drops.

If we make an instrument that can detect light, that's as sensitive as it can possibly be made. ...This ...is called a photomultiplier.

That's called monochromatic light, light of one color. ...I'm going to discuss all my phenomena for a while with light of one color, because it's simpler

I don't know about philosophy of Mayans. We have very little information due to the efficiency of the Spanish es and... mostly their priests, who burned all the books... hundreds of thousands of books, and there's three left... [O]ne of them has this Venus calculation... Just imagine our civilization reduced to three books... left by accident.

[I]n the years we have developed enormous abilities in mathematics and it takes a long time to train the students, and so they're very highly educated in that, but if you ask them why. Now we go back to the Mayans... [W]hy the rule? ...They don't know. They don't understand... The more accurately they can do it... adds nothing to their understanding... The student who is able to make these calculations of Venus... Mars, the Sun, the eclipses and everything else is a super priest, doesn't know why, any better. And if you were to explain that it was nothing but counting days, you would be reduced to the truth... and to an honest statement that he doesn't understand it.

What the students are taught ...now ...about physics ...The numbers are much bigger... so enormous you can't count them directly, and so we've invented a fantastic array of tricks and gimmicks for putting together the numbers... without actually doing it. ...We don't actually ...draw 7,000 arrows and find... the end point... just like we don't actually count 415 pennies... We do it by... the tricks of mathematics, and that's all. So... we're not going to worry about that. ...[Y]ou don't have to know about mathematics. All you have to know is what it is... tricky ways of doing something which would be laborious otherwise.

[T]he Mayan[s]... had a scheme for predicting... when Venus was a morning... or . ...[T]hey had a rule for... making corrections and... had a very good way of predicting when Venus was coming up. ...Suppose that the professors (the priests in those days) ...were giving a lecture ...to explain ... these wonderful predictions ...He would say, "What we're doing is counting the days, just like you're putting nuts in a pod." ...[The students] did not know a quick and tricky way to add 365 x 8. ...These students were learning ...the laws of arithmetic. Something... to us now, because we have public, free, general education, almost everybody has to... learn... by a tricky scheme... The waitress, just an ordinary person, in two minutes does that. How..? ...She's ...counting ...415 pennies ...then ...287 more ...and telling you how many pennies you would have got if you counted ...beginning to the end. But it's highly educated and very trained to... do that... quickly. ...In the 14th century [it was] mathematicians... who could do that.

That was the beginning and the idea seemed so obvious to me that I fell deeply in love with it. And, like falling in love with a woman, it is only possible if you don't know too much about her, so you cannot see her faults. The faults will become apparent later, but after the love is strong enough to hold you to her. So, I was held to this theory, in spite of all the difficulties, by my youthful enthusiasm.

One of the most important things in this 'guess — compute consequences — compare with experiment' business is to know when you are right. It is possible to know when you are right way ahead of checking all the consequences. You can recognize truth by its beauty and simplicity. It is always easy when you have made a guess, and done two or three little calculations to make sure that it is not obviously wrong, to know that it is right. When you get it right, it is obvious that it is right — at least if you have any experience — because usually what happens is that more comes out than goes in. Your guess is, in fact, that something is very simple. If you cannot see immediately that it is wrong, and it is simpler than it was before, then it is right. The inexperienced, the crackpots, and people like that, make guesses that are simple, but you can immediately see that they are wrong, so that does not count. Others, the inexperienced students, make guesses that are very complicated, and it sort of looks as if it is all right, but I know it is not true because the truth always turns out to be simpler than you thought.

Therefore psychologically we must keep all the theories in our heads, and every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics.

It is not unscientific to make a guess, although many people who are not in science think it is. Some years ago I had a conversation with a layman about flying saucers — because I am scientific I know all about flying saucers! I said “I don’t think there are flying saucers”. So my antagonist said, “Is it impossible that there are flying saucers? Can you prove that it’s impossible?” “No”, I said, “I can’t prove it’s impossible. It’s just very unlikely”. At that he said, “You are very unscientific. If you can’t prove it impossible then how can you say that it’s unlikely?” But that is the way that is scientific. It is scientific only to say what is more likely and what less likely, and not to be proving all the time the possible and impossible. To define what I mean, I might have said to him, "Listen, I mean that from my knowledge of the world that I see around me, I think that it is much more likely that the reports of flying saucers are the results of the known irrational characteristics of terrestrial intelligence than of the unknown rational efforts of extra-terrestrial intelligence." It is just more likely. That is all.