IJ footnotes

[Adam Lou Stephanides]

On Tue, 19 Mar 1996, Paul Mackin wrote:

> One footnote that intrigued me was 123 (p. 1023). It's some kind of 
> derivation of the stats for the Eschaton game. I didn't attempt to go 
> through the arithmetic but I have the feeling there is probably a pretty 
> good joke hidden there. Maybe someone on the list who finds reading math 
> relatively easy could go though it and enlighten us?

Well, for one thing, the footnote is wrong.  It's true that if you have
a continuous function, say f(x), over an interval, say between 0 and 1,
then the mean value theorem implies that there is a number y between
0 and 1 such that f(y) equals the average value of f(x) between 0 and 1.
But it doesn't follow from this that you can calculate the average
value knowing only the highest and lowest values of f(x).  It's easy
to come up with functions which have the same highest and lowest values
between 0 and 1, but different average values--e. g. f(x) = x and
f(x) = x squared.  I don't know if this is a deliberate error on DFW's
part, or if it's just a mistake.

There is at least one other math error in the footnotes: Cantor's
Diagonal Proof doesn't mean that between any two objects you can put
an infinity of other objects.  And I have no idea what that guy meant
by saying that if you graph two asynchronously blinking pulses you
get an ellipse.

I think that the math in GR, on the other hand, is always correct.
Does anybody have any ideas more generally about the role of math
in IJ as compared to GR?  My first thoughts off the top of my head
would be that math is something Pemulis and that guy watching the
pulses use to distract themselves, no more significant than any
other form of entertainment.

--Adam