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propensive's profile
Jon Pretty
Jon Pretty
Jon Pretty
@propensive

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Jon Pretty

@propensive

Supporting Scala through professional training and open-source software. Responsible for Magnolia, Fury, Scala World and Functional Africa.

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propensive.com
Joined July 2010

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    1. Spritz Imbiber‏ @thattommyhall Mar 20
      Replying to @propensive

      How were negative numbers eliminated?

      1 reply 0 retweets 1 like
    2. Jon Pretty‏ @propensive Mar 20
      Replying to @thattommyhall

      The idea is that at some point in the distant past, there was a system of counting that didn't involve negative numbers. But it didn't give us a way to deal with concepts like "owing", so negative numbers were introduced. We still don't really have an *understading* of a...

      2 replies 0 retweets 1 like
    3. Jon Pretty‏ @propensive Mar 20
      Replying to @propensive @thattommyhall

      ...negative quantity of any material thing, but we can eliminate negative numbers by combining them with other numbers (positive or negative) to get back to a positive number which we can understand. Complex numbers are similar.

      1 reply 0 retweets 0 likes
    4. Spritz Imbiber‏ @thattommyhall Mar 20
      Replying to @propensive

      Not sure eliminated is a good word here, or that these concepts are only introduced to be it

      1 reply 0 retweets 1 like
    5. Jon Pretty‏ @propensive Mar 20
      Replying to @thattommyhall

      How do you mean "introduced to be it"?

      1 reply 0 retweets 0 likes
    6. Spritz Imbiber‏ @thattommyhall Mar 20
      Replying to @propensive

      You said it, "only ever introduced into a preexisting "system" so that they can be eliminated" I dont think thats true (if I understand your non-standard use of the word "eliminated")

      1 reply 0 retweets 0 likes
    7. Spritz Imbiber‏ @thattommyhall Mar 20
      Replying to @thattommyhall @propensive

      I dont think eliminated is a good word I dont think the things you mention are just introduced to be "eliminated"

      2 replies 0 retweets 0 likes
    8. Spritz Imbiber‏ @thattommyhall Mar 20
      Replying to @thattommyhall @propensive

      are you thinking of something like https://www2.clarku.edu/faculty/djoyce/complex/cubic.html … where in solving cubics you need complex numbers but you have real solutions? counterpoint is lots of equations have complex solutions and complex numbers do more for us besides

      1 reply 0 retweets 1 like
    9. Jon Pretty‏ @propensive Mar 20
      Replying to @thattommyhall

      Yes, this is the idea. Complex numbers were introduced as a means of solving cubic equations which could not be evaluated without them, but the solutions eliminate all the complex terms from the answer. The idea is that if they were not eliminated, the answer wouldn't be useful.

      1 reply 0 retweets 0 likes
    10. Spritz Imbiber‏ @thattommyhall Mar 20
      Replying to @propensive

      I think this fact is interesting, I think it shows the utility of complex numbers (you can solve things you could not do before, interesting special case is when you go via complex to get real solutions) But this is not all they do

      1 reply 0 retweets 0 likes
      Jon Pretty‏ @propensive Mar 20
      Replying to @thattommyhall

      It might be that over time, the new concept proves itself so useful for this purpose that it's established as something so fundamental that the original system (the natural numbers without negative numbers, or the reals without complex numbers) seems less useful.

      4:16 AM - 20 Mar 2021
      1 reply 0 retweets 0 likes
        1. New conversation
        2. Spritz Imbiber‏ @thattommyhall Mar 20
          Replying to @propensive

          Do you still assert they only exist to be "eliminated"?

          2 replies 0 retweets 0 likes
        3. Spritz Imbiber‏ @thattommyhall Mar 20
          Replying to @thattommyhall @propensive

          I agree with @berenguel, more like they subsume the existing thing than are later eliminated (though I am really struggling to understand if "eliminated" means removed from mathematics or means it has this property you seem to like to see expressions have sometimes )

          1 reply 0 retweets 1 like
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