[taos-glug] new reading goals; Exercise 1.13-1.15

Personally, I'm trying to cover about 25 pages per
week in the printed version of SICP.

That would put me at the end of Chapter 1 by
July 28 (i.e., through Exercise 1.46), and more-or-less
through the end of Chapter 2 by Labor Day.

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Exercise 1.13

Does anybody remember how to do a proof by induction?  Once upon a time I could 
do it, but . . .

Exercise 1.14

I more-or-less arbitrarily skipped Exercise 1.14.   Did anybody do it or find 
it interesting?

Exercise 1.15

Part A.  My answer is that the procedure p is applied one fewer times
than sine, which means 5 (when calculating (sine 12.15).

Why 12.15?   It doesn't seem to me to be a particularly interesting or 
meaningful value.

How did I determine my answer?  Empirically at first, by defining
a global counter and printing it out at the end.   This is not very cool.

But it does seem demonstrable that p is applied one fewer times than sine.

Part B.  Damned if I know.   The number of calls to procedure p
does increase as 'a' in (sine a) gets larger, but not proportionally.
Again, I determined this empirically.

a        calls to p
--       -
0        0 
pi       4 
2pi      4 
3pi      5 
4pi      5 
40pi     7

But I don't have any idea how to figure its "growth in space."

My opinion is that the "orders of growth" discussion is inadequate.  Probably 
it assumes the reader
knows some math that I, at least, don't in fact know.

But even the authors admit there is something bogus about it.  As they say in
footnote 36, "These statements mask a great deal of oversimplication."   They 
also call orders of
growth a "crude description of the behavior of a process."

For this exercise, I guess I would have liked the help of a math teacher to 
explicate the trigonometric
theorems.   Does anybody know one?   Maybe if I understood the mathematical 
strategy, I'd be able to guess
what kind of processes were probably going to be generated.

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