Math 161 D
Calculus I
Fall 2000

Reading Assignment

The Relation of Mathematics to Physics

1. Feynman begins by giving three examples of what he is not going to be talking about: the action of a virus, checkers played on an enormous board, and computer circuitry.
   • What do these 3 examples have in common?
   • How are these situations different from what Feynman calls the {\em fundamental laws of physics}?
2. What important difference between Feynman's next two examples -- electrolysis and Newton's law for gravitation -- does he want the reader to understand? [In other words, why is electrolysis not an example of the kind of thing he wants to talk about in the remainder of the article?]
3. Explain briefly the ``particle-model'' explanation of gravity. Why doesn't it work?
4. Feynman makes a number of statements that indicate something about his view of the nature of mathematics.
   1. List three such statements.
   2. Does he think about ``mathematics'' the same way you do (or did in high school, if your view of mathematics is changing)? If there is a difference, describe a feature of that difference.
5. What distinction does Feynman make between "Babolonian" and "Greek" mathematics?
6. Suppose, by way of trigonometry, that all the facts you can remember are
   • the Pythagorean Theorem,
   • the definitions of the trigonometric functions as they pertain to a right triangle — that is, that sine of an acute angle is opposite over hypotenuse, etc. (SOH-CAH-TOA), and
   • the reciprocal relationships: sin x = 1/csc x, cos x = 1/sec x, tan x = 1/cot x.
   Can you deduce the following (other) facts (at least, for acute angles): that
   • tan x = sin x/cos x, cot x = cos x/sin x, and
   • sin²x + cos²x = 1, 1 + tan²x = sec²x, 1 + cot²x = csc²x?
   Show how you would deduce them. (Pick one as an example.) Would this be an example of "Babylonian mathematics" or an example of "Greek mathematics"?
7. How does the author justify saying that mathematicians “do not even need to know what they are talking about, or ... whether what they say is true”? Would the same be true of physicists (or other physical scientists)? Is this a deficiency of mathematics?
8. Why should it be troubling to scientists if their understanding of physical entities were inseperable from mathematical descriptions of the behavior of those entities?
9. Feynman quotes Jeans: ``the Great Architect seems to be a mathematician.''
   1. Does Feynman agree? Why do you think he agrees or disagrees with Jeans?
   2. Do you agree? (Offer some additional or counter-balancing evidence.) What does your answer say about the nature of God?
10. What would you say to a friend who is frustrated over the difficult math courses he has to take along the way to getting a degree in a scientific field?

Thursday, 11-Jan-2001 16:03:12 EST

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