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heuristics vs asymptotics

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  • Dick
    Hello, What is the difference between heuristic data or values and asymptotic data or values. Are these terms interchangeable? If not, how does one
    Message 1 of 2 , Apr 14 5:45 AM
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      Hello,

      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.

      Thanks

      -Dick
    • Chris Caldwell
      ... Heuristics are educated guesses--whenever possible based on solid mathematics, established conjectures and massive computing; but educated *guesses* none
      Message 2 of 2 , Apr 14 6:39 AM
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        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.
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