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I What did Newton mean by "Ghosts of Departed Quantities"

  1. Jun 11, 2017 #1
    "Ghosts of Departed Quantities"

    And a host of ones own deity?
     
  2. jcsd
  3. Jun 11, 2017 #2

    jedishrfu

    Staff: Mentor

    Best answer is here:

    https://plus.maths.org/content/news-world-maths-attacks-foundations-calculus

    And here

    http://notebookeleven.razorsmile.org/the-ghosts-of-departed-quantities/

    The ghosts were the infinitesimals used in Calculus which disappear in the limit.

    This is why Calculus was recast using limits as the basis of understanding derivatives until Robinson in 1966 showed that infinitesimals could be added to the real numbers to create the hyperreals which had all the same algebraic properties as reals and thus could be added, subtracted, multiplied by and divided in expressions just like reals.

    This was the way Calculus was taught early on. Conceptually it's easy to construct derivatives with infinitesimals and then algebraically evaluate expressions treating them like regular numbers.

    There's a Calculus book by Keisler that follows this style of teaching:

    https://www.math.wisc.edu/~keisler/calc.html
     
    Last edited: Jun 11, 2017
  4. Jun 12, 2017 #3

    WWGD

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  5. Jun 24, 2017 #4

    Ssnow

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    Yes it was Berkeley.
    At the time of Newton there wasn't the concept of limit and He did calculation using '' vanishing quantities ''.
    Berkeley criticizes these methods considered not rigorous but the calculus of Newton works very well and it is the analogue of our modern calculus ...

    I suggest to read History and Philosophy of Infinitesimal Calculus, of L.Geymonat (1947).
    Ssnow
     
  6. Jun 24, 2017 #5

    mathwonk

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    I suggest to read newton. the masters offer more than the (is it safe yet to say misguided in this case) critics.
     
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