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4 March 2009 / April

Yes.

I just finished reading a book that deals with non-Euclidean geometry, Gödel, knots, the strange deaths of mathematicians, string theory, and hypothetical solitary intelligent jellyfish.  Clearly, I am now going to present a very negative view of Mario Livio’s Is God a Mathematician?

Obligatory caution: Livio doesn’t answer the question of the title until the final chapter, and even then it may not be the answer you expect.

Obligatory digression: This is what pisses me off about philosophy, particularly compared to, oh I don’t know, mathematics.  Philosophers are such teases.  They pose these great, important questions, so deep the profoundity practically bursts out of them—then they dance away from the anticipated conclusion, insisting coyly that the question was the wrong one.  Mathematicians just give you the damn proof and take you to bed.  QED.

(Of course, once they’re there, all they often do is show you the existence of certain things…  But I think this digression has digressed long enough.)

What Livio does do more thoroughly is tell you how other smart people in history have considered the question of what Eugene Wigner dubbed, catchily, “the unreasonable effectiveness of mathematics.”

He is careful to focus on the issue at hand rather than providing in-depth biographical information about these individuals, lest his neat 450-page book become a bloated history of absolutely everything.  But we still get a good taste of Pythagoras’ bizarre sexist numerology, Descartes’ New York City geometry, and more obscure people like poor Quetelet, whose normal curve was unfairly named after Gauss (as if he didn’t already have enough mathematics named after him).

And of course, while we’re on the topic of mathematicians, I cannot resist quoting a snippet of Kurt Gödel’s examination for US citizenship in 1946, which the mathematician and economist Oskar Morgenstern witnessed and later recalled, with rather poor spelling.  It was an event for which Gödel prepared as a perfectionist does for a Regents exam: much more meticulously than necessary.  When the day came…

[The Examiner:] Now, Mr. Gödel, where do you come from?
Gödel: Where I come from?  Austria.
The Examinor [sic]: What kind of government did you have in Austria?
Gödel: It was a republic, but the constitution was such that it finally was changed into a dictatorship.
The Examinor: Oh!  This is very bad.  This could not happen in this country.
Gödel: Oh, yes, I can prove it.
[… The Examiner:] Oh God, let’s not go into this.

In the very next, very brief paragraph, Livio states, succinctly and matter-of-factly, that Gödel starved himself to death.  And all this, in a nutshell, is why mathematicians are weird.

By the final chapter then, Livio has developed enough historical context to address two separate but related questions: “Does mathematics have an existence independent of the human mind?” (the issue of whether math is discovered or invented) and “Why do mathematical concepts have applicability far beyond the context in which they have originally been developed?” (the issue of math’s unreasonable effectiveness).

Incidentally, I posed to my mother the question of whether math is an invention or a discovery (yes, my family discusses these matters), and she, without hesitation, replied, “Oh, it’s the second one.”  Plenty of those smart people I mentioned before would agree with her, notably Plato, but once I got her to actually think about it (as Livio did for me), she realized it’s a bit more complex than that.

We can look to the Fibonacci numbers and the golden ratio to see how mathematics could in fact be both invention and discovery.  The concepts themselves were arguably invented simply by being given a name, but the relation between them—that the ratio between two consecutive Fibonacci numbers approaches phi—was certainly discovered.

But surely at least some things must be so fundamental that studying them was inevitable, as sailing around the world and bumping into a continent is inevitable?

This is where jellyfish become involved.  Because even something as natural as the natural numbers seems more dependent on the physical world when you consider an intelligent and completely isolated jellyfish deep underwater, where there is nothing to count.

Perhaps this seems not only improbable but fairly insane to you.  It’s food for thought, and I encourage you to feed upon it.  However, as you may have suspected from the very beginning, I personally am not entirely convinced.  After all, the universe does have quantum mechanics agreeing with experiment to an astounding degree of precision.  The universe does not have isolated intelligent jellyfish.

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3 Comments

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  1. Rafael Lizarralde / Mar 4 2009 11:45 pm

    Yeah, my initial reaction to “is mathematics an invention or a discovery” was that they both seem like different ways of saying the same thing. Sure, the “system” we call mathematics may be an invented network of arbitrary symbols, but the patterns that mathematics attempts (and usually succeeds) in analyzing are patterns that exist in the universe. It could also be said that mathematics is simply a description for how reality can operate.

  2. Jenny Kenkel / Mar 5 2009 11:22 pm

    So this is my favorite blog post of yours ever. It even tops that one where you told that story about me in APUSH and made it sound like I was kind of funny (it was the one about pants, and not wearing them). I am so intrigued. If I were to go into this book knowing that he was going to be a philosopher about it, would I enjoy it? Secondly, can you be an unintellectual Seminar-skipper like myself and enjoy it?
    Mathematicians just give you the damn proof and take you to bed. QED.
    Teehee.

    • April / Mar 6 2009 9:03 am

      Even if Livio’s being a philosopher, he still talks about mathematicians… so it’s kind of like mathematical porn, I guess? Or perhaps the analogy has gone too far.

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