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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. Steven Strogatz‏Verified account @stevenstrogatz 5 Apr 2017
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      Having fun rereading Rota's "Indiscrete Thoughts". These aphorisms give its flavor. cc @nntalebpic.twitter.com/clgsYRD7yq

      1 reply 6 retweets 35 likes
    2. Ole Peters‏ @ole_b_peters 23 Apr 2017
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      Replying to @stevenstrogatz @nntaleb

      Surprisingly common objection when doing something new: but I can already solve the problems I can already solve. Excellent response by Rotapic.twitter.com/5P7fPMWFFK

      3 replies 28 retweets 61 likes
    3. Jordan Ellenberg‏ @JSEllenberg 23 Apr 2017
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      Replying to @ole_b_peters @stevenstrogatz @nntaleb

      Rota is right about disclosing new worlds but dismisses the objection too easily.

      1 reply 1 retweet 4 likes
    4. Jordan Ellenberg‏ @JSEllenberg 23 Apr 2017
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      Replying to @JSEllenberg @ole_b_peters and

      Objector is actually asking: "How do I know I'm looking at a new world and not old ideas in new clothes?" Fair question.

      2 replies 1 retweet 7 likes
    5. Steven Strogatz‏Verified account @stevenstrogatz 23 Apr 2017
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      Replying to @JSEllenberg @ole_b_peters @nntaleb

      Shameful confession: I have felt inclined to this kind of objection when classical mechanics is redone with cotangent bundles.

      2 replies 0 retweets 3 likes
    6. DynamicalSystemsSIAM‏ @DynamicsSIAM 23 Apr 2017
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      Replying to @stevenstrogatz @JSEllenberg and

      Re: cotangent bundles: Another question is whether the new mathematical clothing makes ideas easier to understand or harder to understand.

      1 reply 1 retweet 2 likes
    7. DynamicalSystemsSIAM‏ @DynamicsSIAM 23 Apr 2017
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      Replying to @DynamicsSIAM @stevenstrogatz and

      These ideas did eventually lead to nice advances in topics like symplectic integration that benefited from the increased formalism.

      1 reply 0 retweets 1 like
    8. Steven Strogatz‏Verified account @stevenstrogatz 23 Apr 2017
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      Replying to @DynamicsSIAM @JSEllenberg and

      That's interesting. Thanks!

      1 reply 0 retweets 0 likes
      Laurens Gunnarsen‏ @MathPrinceps 23 Apr 2017
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      Replying to @stevenstrogatz @DynamicsSIAM and

      But the question remains: why cotangent bundles (and not tangent bundles, on which certain natural tangent vector fields are 2nd-ord. ODEs)?

      8:22 PM - 23 Apr 2017
      1 reply 0 retweets 0 likes
        1. New conversation
        2. Laurens Gunnarsen‏ @MathPrinceps 23 Apr 2017
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          Replying to @MathPrinceps @stevenstrogatz and

          The answer is profoundly interesting, but very seldom given. First appeared in the work of Lie, but traces all the way back to Jacobi.

          1 reply 0 retweets 0 likes
        3. Laurens Gunnarsen‏ @MathPrinceps 23 Apr 2017
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          Replying to @MathPrinceps @stevenstrogatz and

          Not even remotely enough to say that cotangent bundles alone have contact 1-forms with symplectic exterior derivatives. True, but so what?

          1 reply 0 retweets 0 likes
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