Math 162B/C
Calculus II
Spring, 2007

Math 161 F
Reading Assignment #2

1. Would it be fair to say Professor Feynman is acknowledging that there are a fair number of physical phenomena physicists study but of which they have no deep conceptual understanding apart from the mathematical description of the phenomena? Support your answer, drawing on material in the three paragraphs beginning on p. 170 with “Suppose that in the world ...”. Why should it be troubling to scientists if their understanding of physical entities were inseparable from mathematical descriptions of the behavior of those entities?
2. In what ways is mathematics a language? Give an example from your own experience in which you are using mathematics as a language. In what ways is it more than a language? What example does Feynman give that it is more than a language?
3. 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. (SOHCAHTOA), 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. Would this be an example of what the author calls Babylonian mathematics or an example of Greek mathematics?
4. 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?
5. 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?

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Thomas L. Scofield
Department of Mathematics and Statistics
Calvin College