On Thu, 14 Apr 2005, Dick wrote:

> What is the difference between heuristic data or values and asymptotic

> data or values. Are these terms interchangeable? If not, how does

> one distinguish which is proper to use? Curious to any thoughts on

> this.

Heuristics are educated guesses--whenever possible based on solid

mathematics, "established conjectures" and massive computing; but educated

*guesses* none the less.

Asymptote on the other hand are values (functions) that another function

approaches. For example the ration pi(x) / (x/ln(x)) is asymptotic to

1. This is proven. Or more simply, x^2/(x^2+1) is also asymptotic to

1 as x -> infinity.

SO if by asymptotic data you mean data obtained by using asymptotic

approximations (like x/ln(x) for pi(x)) then there is a world of

difference. One can be proven, the other lives in the netherworld of

speculation.

Hope that is of some use...

Chris.