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Reductio ad Trivium*, a commentary on the nature of science

At first,
(1) The problem appears impossible to solve.
After an enormous amount of effort, you discover with great elation that after all
(2) You can solve the problem, although no one understands your solution.
Then someone down the corridor makes an off the cuff comment which clarifies everything wonderfully, as a result of which you realise that
(3) The problem can be solved in a beautiful and elegant fashion.
You should publish your solution now, if you didn't already do so at point (2), because as you continue to think about the problem, it gradually dawns on you that
(4) The problem is actually completely trivial and obvious.
In fact it's so simple you are embarrassed you ever had anything to do with it.

*I have no idea if this is a bona fide Latin phrase. The word trivia is the plural of the Latin noun trivium, meaning a place where three ways meet, hence a public meeting place. The associated adjective trivius means pertaining to such a place, hence pertaining to the common crowd, hence common or vulgar.


Apply Reductio ad Trivium to the following problem:

  • Solve for the structure and evolution of an isolated spherical black hole including vacuum fluctuations, with particular attention to the region inside the horizon, but outside the central singularity (cf. N D Birrel & P C W Davies 1982, Quantum Fields in Curved Spacetime, CUP; R Brout, S Massar, Parentani R & Spindel Ph 1995, A Primer for Black Hole Quantum Physics, Physics Reports 260, 329-454).

    For some solutions, try:

  • here,
  • or here.

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    Updated 24 Mar 1998