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Various links

September 4th, 2009

A few things where I’ve had a direct or indirect interest

* This study of media bias by econobloggers Andrew Leigh and Joshua Gans has unsurprisingly attracted interest from the media and econobloggers (Andrew gives some links). The striking (if not particularly surprising) finding is that the ABC as a whole is to the right of most newspapers. One aspect of it was how much the media cited public intellectuals identified as partisan by the fact that they were commonly mentioned in favorable terms in Parliament by one side, but not by the other. Interestingly, I didn’t pass this test. I had about 30 favorable mentions, of which about 30 per cent were from the Coalition.

* My Senate submission on deposit guarantees got a good run in this SMH piece, which opens with a look at the incidence of John Dillinger’s bankrobbing exploits, as described by Johnny Depp. Since been romantically linked with Angelina Jolie, I’m keen for more brushes with fame.

* Back when I was doing my Pure Maths degree, I studied fixed point theorems. One implication of the standard Brouwer fixed point theorem is the hairy ball theorem which implies, among other things, that there must always be a place on earth where the wind isn’t blowing. I said at the time that I aimed to get a research grant to test this theoretical result in practice, by travelling round the world and moving on whenever the wind blew. Today, my fellow-student and major source of technical advice for this blog, Martin Ellison, advises me that I’ve missed my chance. These guys have found the spot, in remotest Antarctica.

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  1. September 4th, 2009 at 18:56 | #1

    “One implication of the standard Brouwer fixed point theorem is the hairy ball theorem…”

    Is that actually true, or is it just that Brouwer proved the latter as well? The reason I ask is that the wikipedia article provides a link to a proof of the Hairy Ball Theorem that uses a stronger variant of Sperner’s Lemma rather than Sperner’s Lemma itself. That suggests that the straight Sperner’s Lemma can’t do it – but the Brouwer Fixed Point Theorem is equivalent to Sperner’s Lemma (each implies the other). Also, this uses the Hairy Ball Theorem to prove the Brouwer Fixed Point Theorem rather than the other way round, which is also suggestive.

    Aside: as I’m sure many people know, John Nash used Sperner’s Lemma in his work on the Nash Equilibrium.

  2. jquiggin
    September 4th, 2009 at 19:30 | #2

    PML, you’re right. Hairy Ball is (equivalent to) a generalization of Brouwer, not an implication of it. You can also go via the Lefschetz FPT. And economic equilibrium results are standardly derived from fixed point theorems, the reason for my original interest.

  3. Alice
    September 4th, 2009 at 20:54 | #3

    I am astonished…I wouldnt have thought the results of Andrew Leigh and Joshua Gans fell within the expected outcome, particularly with regard their finding that the age is biased towards Labor….? Could it have possibly been a perverse result?

  4. Alice
    September 4th, 2009 at 21:00 | #4

    You cant possibly have been upstaged by Johnny Depp in the Angelina stakes JQ?

  5. Uncle Milton
    September 7th, 2009 at 08:28 | #5

    The Kakutani fixed point theorem is also a generalisation of Brouwer. Does that makes Kakutani equivalent to Hairy Ball, or are they different generalisations?

  6. jquiggin
    September 7th, 2009 at 08:49 | #6

    Different – Kakutani extends from functions to correspondences.

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