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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. Jon Pretty‏ @propensive Mar 20
      Replying to @thattommyhall

      No, elimination is the correct word. It's like eliminating terms in an expression, that is, removing completely.

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

      your statement is "complex numbers were only ever introduced into a preexisting 'system'* so that they can be eliminated later" * presumably the reals?

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

      I dont think this is true

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

      If we introduce them, but can't eliminate them, then we end up with a solution defined in terms of something we just invented, and we haven't made progress towards a solution.

      4:09 AM - 20 Mar 2021
      1 reply 0 retweets 0 likes
        1. New conversation
        1. Spritz Imbiber‏ @thattommyhall Mar 20
          Replying to @propensive

          Sorry, if the solution to a cubic is complex, its complex. You have a solution. You just seem to think its neater not to be in extended system somehow

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

          But those two (of the three) complex roots aren't useful to you unless you can eliminate them at some point. If you've introduced complex numbers as a means of describing those two roots, when you couldn't represent them before, that wasn't helpful if you can't get answers in...

          1 reply 0 retweets 0 likes
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