Mathematics is Only Patterns
Mathematics is Only Patterns
This is what Richard Feynman says about mathematics:
"I'm going to tell you what science is like by how I learned what science is like.
My father did it to me. ... When I was very young, my father would play a game with me after dinner, He had bought a whole lot of old rectangular bathroom floor tiles from somewhere in long Island City. We set them up on end, one next to the other, and I was allowed to push the end one and watch the whole thing go down.
Next, the game improved. The tiles were different colors. I must put one white, two blues, one white, two blues, and another white and then two blues - I may want to put another blue, but it must be a white.
Well, my mother, who is a much more feeling woman, began to realize the insidiousness of his efforts and said, "Mel, please leave that poor child put a blue tile if he wants to." My father said, "No, I want him to pay attention to patterns. It is the only thing I can do that is mathematics at this earliest level." If I were giving a talk on "what is mathematics?" I would have already answered you. Mathematics is looking for patterns."
He gives another example:
"I would like to report other evidence that mathematics is only patterns. When I was at Cornell, I was rather fascinated by the student body, which seems to me was a dilute mixture of some sensible people in a big mass of dumb people studying home economics, ect., including lots of girls. I used to sit in the cafeteria with students and eat and try to overhear their conversations and see if there was one intelligent word coming out. You can imagine my surpirse when I discovered a tremendous thing, it seemed to me.
I listened to a conversation between two girls, and one was explaining that if you want to make a straight line, you see, you go over a certain number to the right for each row you go up, that is, if you go over each time the same amount when you go up a row, you make a straight line. A deep principle of analytic geometry! It went on. I was rather amazed.
She went on and said, "Suppose you have another line coming in from the other side and you want to figure out where they are going to intersect." Suppose on one line you go over two to the right for every one you go up, and the other line goes over three to the right for every one that goes up, and they start twenty steps apart, ect. - I was flabbergasted. She figured out where the intersection was! It turned out that one girl was explaining to the other how to knit argyle socks."
To him, mathematics is nothing but the discovery of patterns.
On Feynman's discovery of pattern
The first paragraph in the preface of "Relativistic Quantum Mechanics' by Bjorken and Drell:
"The propagator approach to a relativistic quantum theory pioneered in 1949 by Feynman has provided a practical, as well as intuitively appealing, formulation of quantum electrodynamics and a fertile approach to a broad class of problems in the theory of elementary particles. The entire renormalization program, basic to the present confidence of theorists in the predictions of quantum electrodynamics, is in fact dependent on a Feynman graph analysis, as is also considerable progress in the proof of analytical properties required to write dispersion relations. Indeed, one may go so far as to adopt the extreme view that the set of all Feynman graphs is the theory."
"In addition to their value as a mathematical tool, Feynman diagrams provide deep physical insight into the nature of particle interactions. Particles interact in every way available; in fact, intermediate virtual particles are allowed to propagate faster than light. The probability of each final state is then obtained by summing over all such possibilities. This is closely tied to the functional integral formulation of quantum mechanics, also invented by Feynman."
From a wikipedia link:
"In their presentations of fundamental interactions, written from the particle physics perspective, Gerard 't Hooft and Martinus Veltman gave good arguments for taking the original, non-regularized Feynman diagrams as the most succinct representation of our present knowledge about the physics of quantum scattering of fundamental particles. Their motivations are consistent with the convictions of James Daniel Bjorken and Sidney Drell:"
Created on 05/02/2009 10:16 AM by admin
Updated on 02/25/2017 11:55 PM by admin