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MathPrinceps's profile
Laurens Gunnarsen
Laurens Gunnarsen
Laurens Gunnarsen
@MathPrinceps

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Laurens Gunnarsen

@MathPrinceps

Mathematical physicist and mentor to mathematically talented youth. Talent is that which bridges the gap between what can be taught and what must be learned.

Joined June 2012

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    1. John Carlos Baez‏ @johncarlosbaez 1 Dec 2018
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      @Cshearer41 posed a nice puzzle. These 3 rectangles are congruent, each with area 4. The dots mark the midpoints of the short sides, and 3 long sides intersect at a point as shown. What's the total area covered by these rectangles? You can solve it with one sentence, no trig!pic.twitter.com/VTXvJ6Kqif

      9 replies 5 retweets 16 likes
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    2. Laurens Gunnarsen‏ @MathPrinceps 1 Dec 2018
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      Replying to @johncarlosbaez @Cshearer41

      Each of the overlap pieces is composed of two corners of the base rectangle, and each such corner has one-eighth the area of the base rectangle.

      1 reply 0 retweets 1 like
    3. Laurens Gunnarsen‏ @MathPrinceps 1 Dec 2018
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      Replying to @MathPrinceps @johncarlosbaez @Cshearer41

      But the really interesting question concerns the aesthetic value of puzzles. Does this consist essentially (exclusively?) in their susceptibility to neat, self-evident resolution? I, for one, certainly hope not.

      1 reply 0 retweets 1 like
    4. John Carlos Baez‏ @johncarlosbaez 1 Dec 2018
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      Replying to @MathPrinceps @Cshearer41

      So what do you hope *is* the aesthetic value of puzzles? I have my own thoughts on this, but I'd rather hear yours. (I say "aesthetic" value because that's what you said. They also have lots of other virtues.)

      1 reply 0 retweets 0 likes
    5. Laurens Gunnarsen‏ @MathPrinceps 2 Dec 2018
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      Replying to @johncarlosbaez @Cshearer41

      Well, if we are to benefit each other by discussing this matter, we must first agree on the meanings to be attached to the terms we use. I have tended to think of a puzzle as a question devised by one human being to divert another -- that is, as something essentially artificial.

      1 reply 0 retweets 0 likes
    6. Laurens Gunnarsen‏ @MathPrinceps 2 Dec 2018
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      Replying to @MathPrinceps @johncarlosbaez @Cshearer41

      If we use the word "puzzle" here in this way, then we must recognize that many tantalizing mysteries are not puzzles. It's absurd, for example, to label the question, "Why does the fine structure constant have its observed value?" a puzzle. There's nothing artificial about it.

      1 reply 0 retweets 0 likes
    7. Laurens Gunnarsen‏ @MathPrinceps 2 Dec 2018
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      Replying to @MathPrinceps @johncarlosbaez @Cshearer41

      I would likewise argue that we cannot label with the word "puzzle" such questions as, for example, "Which prime numbers arise as divisors of the values taken on by x^3 - x - 1, as x ranges over the positive integers?"

      2 replies 0 retweets 0 likes
      Laurens Gunnarsen‏ @MathPrinceps 2 Dec 2018
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      Replying to @MathPrinceps @johncarlosbaez @Cshearer41

      As Poincare says, "There are questions that one poses, and questions that pose themselves." Certain problems have a species of inevitability that contrasts rather markedly with the contingency and artificiality that seem to me characteristic of puzzles, properly so called.

      2:14 PM - 2 Dec 2018
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      • John Carlos Baez
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        2. Laurens Gunnarsen‏ @MathPrinceps 2 Dec 2018
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          Replying to @MathPrinceps @johncarlosbaez @Cshearer41

          If we can agree that a puzzle is essentially an artificial entertainment, like a play or a joke or a musical composition, then I presume we can also agree that the aesthetic value of a puzzle lies in its power to affect us emotionally. Art matters only because it moves us.

          1 reply 0 retweets 1 like
        3. Laurens Gunnarsen‏ @MathPrinceps 2 Dec 2018
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          Replying to @MathPrinceps @johncarlosbaez @Cshearer41

          I would argue that most of the aesthetic value of a mathematical puzzle lies in its power to surprise and delight us. Penrose makes this point eloquently; he notes that we're deeply affected when we discover at a glance an answer we feared we could get only by tedious struggling.

          1 reply 0 retweets 1 like
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