Sunday, 2 June 2013
"...that it was empirically meaningless to speak of a number above factorial N, where N was the total of distinguishable particles in the universe. What could a large number count?" (Poul Anderson, Ensign Flandry, London, 1976, p. 85)
Should that read "...a larger number..."?
What can numbers above N count?
Why not call N rather than factorial N the highest meaningful number?
If N+1 and N! (factorial N) are meaningful, then why not N!+1 etc?
The philosopher says that, if you count beyond N!, you get decreasing quantities. Why? Surely N!+1 does not equal N!-1? He also says that:
"The number axis was not linear but circular." (p.85)
A Maths Teacher at my secondary school said, but never explained, that plus infinity and minus infinity are really the same point although I question whether either is a point. We reach a point when we stop counting but with infinity we do not stop counting. His statement, if true, would make the number axis circular, I think, but its highest quantity would be infinity, not N!
As water-dwellers, this Starkadian race experiences space as relation, not extension, finite but unbounded, and confirms this by circumnavigating their globe!
I am a philosopher, not a mathematician, so I would welcome any better informed discussion of these issues.