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Yes, it's well known that Riemann's zeta is the Mellin transform of the Dirac comb of the natural numbers. The philosophical, rather than the mathematical, ques

Yes, it's well known that Riemann's zeta is the Mellin transform of the Dirac comb of the natural numbers. The philosophical, rather than the mathematical, question the author addresses is: Why is the Zeta representation uniquely informative of the order in the primes? Why must we move to the complex plane? Why analytic number theory? What is the possible meaning of this mathematical move? etc. The central claim is the efficacy of the Zeta representation is strong evidence that the natural numbers are, contrary to appearances, not static and independent quantities, but fundamentally dynamic and interdependent structures of being and nothing (literally Hegelian contradictions). So this is a philosophical or metaphysical interpretation of existing results in number theory.

gjm11 7y ago
I'm afraid this seems all wrong to me. First of all: If that's your idea of "strong evidence" then there are a bunch of other things that seem preposterous to me but have "strong evidence" for them. For instance: Mathematicians have found it very useful to build mathematics on top of set theory; that is, to think of numbers (and everything else) in terms of structures of things belonging to other things. This is "strong evidence" that the notion of belonging-to is fundamental, and therefore that capitalism is the One True Economic System. (This absolutely honestly seems to me no more far-fetched than your argument here.) Second: so far as I can see, even if we take the argument of the OP seriously, there is absolutely no reason to say that the things in these "dynamic and independent structures" are being and nothing. As I said above, they could just as well be any two things. Horizontal and vertical. Penn and Teller. Red and blue. But taking them to be "being and nothing" is the only thing that really connects this to Hegel at all. Of course anyone's welcome to see parallels to anything anywhere. If the Riemann zeta function makes you think of Hegel, fair enough. It might make someone else think of Beethoven, or civil engineering. The only thing I take any exception to here is the idea that this somehow indicates that there's something specially insightful in Hegel rather than that human brains are good at spotting patterns, including patterns that aren't really there.

gjm11 7y ago

I'm afraid this seems all wrong to me. First of all: If that's your idea of "strong evidence" then there are a bunch of other things that seem preposterous to me but have "strong evidence" for them. For instance: Mathematicians have found it very useful to build mathematics on top of set theory; that is, to think of numbers (and everything else) in terms of structures of things belonging to other things. This is "strong evidence" that the notion of belonging-to is fundamental, and therefore that capitalism is the One True Economic System. (This absolutely honestly seems to me no more far-fetched than your argument here.) Second: so far as I can see, even if we take the argument of the OP seriously, there is absolutely no reason to say that the things in these "dynamic and independent structures" are being and nothing. As I said above, they could just as well be any two things. Horizontal and vertical. Penn and Teller. Red and blue. But taking them to be "being and nothing" is the only thing that really connects this to Hegel at all. Of course anyone's welcome to see parallels to anything anywhere. If the Riemann zeta function makes you think of Hegel, fair enough. It might make someone else think of Beethoven, or civil engineering. The only thing I take any exception to here is the idea that this somehow indicates that there's something specially insightful in Hegel rather than that human brains are good at spotting patterns, including patterns that aren't really there.