Monday, October 05, 2015

Is Kim Davis also against Nonconstrutive proofs?

Recall that Kim Davis is the Kentucky clerk who refused to issue marriage licenses for same-sex couples and was cheered on by Mike Huckabee and other Republican candidates for Prez. Had she refused to issue marriage license for couples that had been previously divorced than  Mike Huckabee would not be supporting her, and the Pope wouldn't have a private 15 minute meeting with her telling her to stay strong (NOTE- I wrote this post in that tiny window of time when it was believed she did have such a meeting with the Pope, which is not true. The Pope DID meet with a former student of his who is gay, and that studen'ts partner.) Had she refused to issue marriage licenses to inter-racial couples (this did happen in the years after the Supreme court said that states could not ban interracial marriage, Loving vs Virginia, 1967 ) then ... hmm, I'm curious what would happen. Suffie to say that Mike H and the others would prob not be supporting her.

David Hilbert solved Gordon's problem using methods that were nonconstructive in (I think) the 1890's. This was considered controversial and Gordon famously said this is not math, this is theology. Had someone else solved this problem in 1990 then the fact that the proof is non-constructive might be noted, and the desire for a constructive proof might have been stated, but nobody would think the proof was merely theology.

I don't think the Prob Method was ever controversial; however, it was originally not used much and a paper might highlight its use in the title or abstract. Now its used so often that it would be unusual to point to it as a novel part of a paper. If I maintained a website of Uses of the Prob Method in Computer Science then it would be very hard to maintain since papers use it without commentary.

The same is becoming true of Ramsey Theory. I DO maintain a website of apps of Ramsey Theory to CS (see here) and its geting harder to maintain since using Ramsey Theory is not quite so novel as to be worth a mention.

SO- when does a math technique (e.g., prob method) or a social attuitude (e.g., acceptance of same-sex marriage) cross a threshold where its no longer controversial? Or no longer novel? How can you tell? Is it sudden or gradual? Comment on other examples from Math! CS!


  1. Herman Chernoff used to use the example of Taylor series. You wouldn't cite Taylor (1715) or whatever.

  2. GASARCH wonders "When does a math technique or a social attitude cross a threshold where it's no longer controversial? Or no longer novel? How can you tell? Is it sudden or gradual?"
    That's one of Computational Complexity's easiest questions: transformational mathematical, social, and moral thresholds are always crossed suddenly, and this crossing is always heralded by a trusted authority figure, such as Captain Jean-Luc Picard, or Gandalf the Grey, or Boromir of Gondor.

    Picards's embrace  "It [Waiting for Godot] was especially ahead of its time in its humor … we've since learned not to be afraid of something that seems a little paradoxical and abstract."

    Gandalf's vision  "Is there a plot? No! It's life … that's what you're looking at."

    Boromir's choice  "Choose the lesser risk of losing six people, over the greater risk of losing one."

    Commonplace ideas now, but revolutionary in their time!

  3. A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather its opponents eventually die, and a new generation grows up that is familiar with it.
    — Max Planck
    Scientific Autobiography and Other Papers, trans. F. Gaynor (1950), 33.