IJ footnote

[Paul Mackin]

Thanks, Adam, for looking at the math in footnote 123. I guess the "joke" 
I was looking for is simply the imcompetence of Pemulis.

				P. 


On Thu, 21 Mar 1996, Adam Lou Stephanides wrote:
> 
> 
> 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
>