Gravity's Rainbow

botany, shoes, books, and justice

Mathematicians’ glasses

| 4 Comments

Many of the papers I’m reading leap between equations with phrases like

  • “The equation may readily be solved to give [next equation which looks totally unlike previous equation],”
  • “The reader may easily supply the details [of the derivation I read this paper to learn],” and
  •  “[the next step I really need to make my model work] is obvious, and hence left as an exercise for the reader.”

Clearly I need to get a pair of the special glasses mathematicians must be wearing to make three pages of torturous algebraic manipulation and tricky rearrangements and substitutions “obvious.” Or perhaps “clear,” “obvious,” “trivial,” and “easy” are defined differently in math?

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4 Comments

  1. At least you are getting past the equations to the sentences that follow. I think plenty of people probably stop at the sight of those weird long S shapes and go straight to the discussion!

    A thing that bugs me about those phrases is that the authors likely spent AT LEAST a few months working through the ideas. For a reader to follow them through the steps would require being either a close colleague who saw the development of the ideas or similar large amounts of time. 

    Then again, if it is not in a mathematics-focused journal, there might not be a need to go through all of the details. And if the author skips the details, they need to make it seem like they are confident that it is correct (by taunting readers into challenging the theory, haha).

    • Some of the papers I’ve read lately are hardly anything _but_ equations, like this Kimura paper. One of the things that’s helped me keep plugging away at these papers (and kept me from feeling like there’s no hope for me as a scientist) is talking about these sorts of papers in discussion groups. Last week I asked a question I thought was probably stupid about how to get from equation c to equation d in some paper. But my question sent someone I really admire running to her office for an entire book chapter describing how to do it and the hidden assumptions in the paper.

  2. Mathematician’s glasses, I’ve found (inasmuch as they resemble theoretical physicists’ glasses), just instantly show everything as few degrees’ worth of polynomial approximation around a point of interest.
    At least, they did in my field of physics.

  3. R. A. Fisher was infamous for this kind of thing. It’s why it took decades for people to figure out what he was talking about with the Fundamental Theorem of Natural Selection.

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