No phenomenon directly involving a frequency has yet been detected above approximately 10^12 cycles per second. We only deduce the higher frequencies from the energy of the particles, by a rule which assumes that the particle-wave idea of quantum mechanics is valid.

You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!

From a long view of the history of mankind — seen from, say, ten thousand years from now — there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.

Finally, I must tell you what the arrow is for the net result. When a thing can happen in alternative ways you do what we call "add the arrows"... I know how to add numbers. How do you add arrows? The rule is... you simply put one arrow head on the tail of the other... I just draw the second arrow off from the first one... exactly parallel... it's drawn the same, but it's centered, it's moved... it's tied one onto the other, head to tail, and the result, it's supposed to be the sum. The adding is this net arrow that you would get, from where you started [from the beginning of the first arrow] to where you ended [at the end of the second arrow]. The way of thinking of it, that is rather nice, is to think of each arrow as indicating the direction of a step to be taken. If we take a step, on this plane, this way [the distance and direction of arrow #1] and then take a step that way [the distance and direction of arrow #2] and we say, where did we actually move? We could have done it all in one step, this one [from the beginning of arrow #1 to the end of arrow #2]. So this is the one step which is the equivalent of the succession of the other steps. Adding means putting together steps... The square of the [summation] arrow determines the probability of the reflection.

Whenever you see a sweeping statement that a tremendous amount can come from a very small number of assumptions, you always find that it is false. There are usually a large number of implied assumptions that are far from obvious if you think about them sufficiently carefully.

There has never been a satisfactory model of the very simple process of reflection of light from thin surfaces or... for any other phenomenon. Satisfactory in the old fashioned classical view. A logical hocus-pocus has to be done quantum mechanically in order in order to describe these things... This is another example of the type of difficulty when you try to reason in a straight forward... in a classical way about a simple phenomenon.

Mathematics is not just a language. Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning. It's, in fact, a big collection of the results of some person's careful thought and reasoning. By mathematics, it is possible to connect one statement to another.