Computing Hessians in My Sleep

Herbert and I are working on a paper that will be a good portion of my dissertation.  We want to prove that a particular critical value is a maximum.  Sounds easier than it is, since the function I am looking at is an n-dimensional Gaussian Mixture Model (a sum of Gaussians in high-dimensional space).  After my discussion with Herbert about graduating and finding a post-doc, I decided that I need to finish my dissertation first.  So, I’ve been working extra-hard to finish the result.  Seems like an obvious step, I guess.

After working on this one part of the problem for about a week, I was beginning to think that I should put it aside and start thinking about something else for a little while.  But — last night, Dave called me just as I was on the brink of falling asleep.  I right away ask him “when is e^(-x) = x?”  He was confused, but plotted it and told me that it was around 0.55, which was the answer that I was looking for.  Knowing that I wouldn’t be able to reconstruct my almost-sleeping thoughts, I had Dave send me an email to tell me this.  It took me all day to reconstruct the proof that I thought of in my mind in five minutes, but I believe that the proof is complete now!  Moreover, I convinced Herbert that it is plausible.

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3 Responses to “Computing Hessians in My Sleep”

  1. Paul Klingsberg Says:

    Cool!!!

  2. Laura Says:

    I understood so little of this.

  3. bfasy Says:

    The short story is: I solved a problem in my sleep. It was weird because it was a difficult problem to think about without pen and paper because there were lots of equations involved. It was even stranger that it took me all day to reconstruct my proof from my sleep. lol.

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