It matters little whether we progress with understanding the diophantine approximation

Jared Diamond on the Lang-Huntington affair, 1987:

As to the relative importance of soft and hard science for humanity’s future, there can be no comparison.  It matters little whether we progress with understanding the diophantine approximation.  Our survival depends on whether we progress with understanding how people behave, why some societies become frustrated, whether their governments tend to become unstable, and how political leaders make decisions like whether to press a red button.

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8 thoughts on “It matters little whether we progress with understanding the diophantine approximation

  1. Rob H. says:

    While I agree that answering the tough questions in the “soft” sciences is indeed quite hard, I have to disagree with most of what Jared Diamond has said. For one, arguing against ignorance while engaging in it kinda weakens his writing (I mean, he could’ve at least learned how to grammatically use the term “Diophantine approximation” in a sentence). He doesn’t seem to realize that “operationalizing” can be a difficult task in mathematics, as well. For example, defining the term “many” in any given situation can be quite an endeavour indeed. We aren’t just counting bananas (to several decimal places!). He also seems to use the Lang–Huntington affair as an abstract jump off point; he treats Lang as your average snotty hard scientist (who’s work is useless!) and presents Huntington as an undeservedly attacked brilliant scientist (who seemingly has never made a mistake). Anyway…

    This was in 1987, has anything transpired from this since then?

  2. Frank says:

    ” ‘Let A be an abelian variety defined over a number field K. We suppose that A is embedded in projective space. Let A_K be the group of points on A rational over K.’ How many people feel entitled to ridicule these statements while touting their own opinions on abelian varieties?”

    Obviously he should have been working with an arbitrary group scheme. And he excludes the characteristic p case from the very beginning? Clearly actually reading the book would be a vacuous waste of time.

  3. Kevin Lin says:

    You can find a response by Lang in his book ‘Challenges’:

    I googled ‘serge lang jared diamond’ and found this:
    I took the “Huntington Test” from Lang in 2005; like everyone else, I also failed.

  4. Yemon Choi says:

    I am reminded of what is probably now an overquoted passage from Solzhenitsyn’s The First Circle:

    Topology belonged to the stratosphere of human thought. It might conceivably turn out to be of some use in the twenty-fourth century, but for the time being…

    (and yes, I know this doesn’t address the point Diamond was presumably making)

  5. If and when the National Academy of Sciences changes its name to the National Academy of Things of Importance for Humanity’s Future, I think Jared Diamond will have an excellent point. Until then, pesky things like methodology and rigor are going to be held very highly, and it seems inevitable that sound, technically difficult work on Diophantine approximation is going to more greatly esteeemed than potentially very important, but methodologically questionable, work on human politics and society.

    Maybe someone should found that second academy after all — it sounds, well, important.

    And may I ask: who is the go-to guy for mercilessly ripping people to shreds based on their perceived methodological weaknesses and lack of acceptable rigor now that Lang is gone? This seems like an awfully important job. People who know me may see that I have a moderate streak of that in me, but nowhere nearly enough: I would get tired and feel like a mean bastard after about seven hours of work. Lang was an unmatchable titan in this field: it’s going to take a lot of people to replace him. Maybe we have a good idea for yet a third academy here?

  6. “going to be more greatly esteemed”, I meant to say.

  7. JSE says:

    Do you read Andrew Gelman’s blog? He does some of this and certainly has the methodological chops for the job. But there’s some level of interior ferocity and not-caring-what-impression-you-make that one encounters in Lang, and otherwise very seldom.

  8. No, I hadn’t heard of him. But perhaps now I will look him up…

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