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by Mr_Natural Abstractor of the Quintessence on March 31st, 2009

Mr_Natural Abstractor of the Quintessence

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Can someone explain the origin and purpose of e [~2.718...], the base of 'natural' logarithms? Why is it 'natural'? Why not base 2 or 3 instead of this irrational number? What is its proper name? Thanks.

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  • by Peetee on April 7th, 2009

    Peetee

    Unfortunately, I have no simple answer, because I've forgotten all the fun stuff. You need to do advanced calculus and eventually you'll learn the answer. The closest I can tell you is that the integral of (1/x) is the natural log of x, the integral of e^x is e^x, and the derivative of e^x is e^x, e being the natural number 2.7182818... etc.

    So, as crazy as it sounds, e is as natural as 1.

    If you go on to learn about imaginary numbers (i = square root of -1), then eventually you'll also discover that e^(iπ)+1=0, so there you go, all the freaky numbers neatly tied up with the numbers we do understand - one and zero.

    Comments

    • so is i "natural" as all this "cool" stuff can be done with it?

      Darth 5349U11

      by Darth 5349U11 on April 7th, 2009

    • No. i is imaginary. They had to call it an imaginary number because all the other numbers were already called "real", and i definitely wasn't one of them other numbers, so it couldn't be called "real", so it was only natural that it be called "imaginary".

      Peetee

      by Peetee on April 7th, 2009

    • >>it was only natural that it be called "imaginary".

      Very good! :)

      Mr_Natural Abstractor of the Quintessence

      by Mr_Natural Abstractor of the Quintessence on April 15th, 2009

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