
Hegelian contradiction and the prime numbers (part 2) - h0p3
https://ianwrightsite.wordpress.com/2019/02/09/hegelian-contradiction-and-the-prime-numbers-part-2/
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challenger22
[https://ianwrightsite.wordpress.com/2018/11/24/hegelian-
cont...](https://ianwrightsite.wordpress.com/2018/11/24/hegelian-
contradiction-and-the-prime-numbers-part-1/)

Both TFA and the linked article referenced by TFA seem to me to be the
ramblings of somebody trying really, really, hard to pull a rabbit out of a
hat. By linking together abstract concepts you can prove that philosophy and
mathematics are one and the same!

>So it’s very remarkable that Hegel’s mystical starting point, which is purely
conceptual and abstract – and makes no reference to physical reality or
empirical knowledge whatsoever – nonetheless implies a structure of ‘becoming’
that is equivalent to the fundamental structure found everywhere in physical
science.

Well, you can read Hegel this way... I guess. Figure it makes for some really
warm and fuzzy insightful feelings, regardless of whether they are meaningful.

~~~
mannykannot
"Hegel aims to merely observe what is there – once we drop all our knowledge,
all our presuppositions, all our theories, and even the sense of our own
existence.

...

"I think it’s worth emphasising that when Hegel talks about pure being he
isn’t talking about an abstract concept. He’s actually talking about a real
phenomenon, an actually existing thing, which he claims we all have immediate
access to, if we’re prepared to perform the mental exercise."

I cannot help but read the claim of the second paragraph as being a
presupposition of the sort disavowed in the first.

~~~
Avshalom
well, hegel did-apparently-love his contradictions.

~~~
cryptonector
Doublethink is a powerful thing!

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gjm11
This is pretty silly.

The only real connection to Hegel is that Hegel talks about "being" and
"nothing" kinda-sorta turning into one another, which the author riffs on in
terms of differential equations and takes as corresponding to the differential
equation for a harmonic oscillator.

The rest -- the idea that you can see the Riemann zeta function as something a
bit like a Fourier transform of the integers -- is old hat. (As Terry Tao put
it at one point: "the Riemann zeta function is essentially the Mellin
transform of the Dirac comb on the natural numbers". See also du Sautoy's
popular book about RH, "The music of the primes".)

The idea that sometimes you have two things turning into one another is not
exactly startling, nor is it original to Hegel. The idea that this yields
harmonic-oscillator-like dynamics is also not exactly startling, and in any
case it's not something Hegel had any idea about. The thing that's distinctly
Hegelian here, so far as I can tell (note: I am very far indeed from being a
Hegel expert) is the idea that it's _being and nothing_ that are in this
relationship, and that specific aspect has nothing to do with the author's
calculations. (He just writes them as _x_ and _y_. They could equally have
been "ham" and "eggs" or "Vishnu" and "Shiva" or "Linux" and "Windows" instead
of "being" and "nothing".)

~~~
hermeticist99
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
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.

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thanatropism
I actually recommend reading Lacan to everyone interested in Hegel.

It takes some suspension of disbelief (but then, the scientific psychologies
that took over clinical practices are skating on thin ice and only successful
in certain serious mental illnesses ) but it's well worth reading at least
Malcolm Bowie's intellectual biography of him and maybe Zizek's "Less than
nothing" to have some access to Lacan. (Lacan, of course, is a long self-
winding reiteration of Hegelian theory on a pseudoclinical domain)

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jwgarber
> The success of Riemann’s project is strong evidence that the whole numbers –
> which we think of as static, unchanging quantities – are really some kind of
> shadow or projection of the Hegelian integers. The Zeta function reveals
> more because it represents whole numbers as what they actually are, that is
> dynamic contradictions of being and nothing.

> But, in addition, the Zeta function represents the whole numbers as a
> sublated unity, where the entities internally relate via the exchange of a
> conserved substance. And this whole moves and changes with time. This is
> quite unlike the vision offered by set theory.

The way modelling normally works is you have a certain phenomenon (falling
rocks, fish populations, market booms-and-busts) that you attempt to describe
numerically, and then create a mathematical model to make conclusions about
the phenomenon. Here we have the opposite: the author takes the phenomenon
(the Hegelian contradiction) and uses the model to make conclusions about
mathematics!

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Causality1
>Hegel aims to discover the fundamental structure of everything from pure
reflection alone.

Ok, so after his navel-gazing was tested against observation, how accurate was
it at describing life, the universe, and everything?

The problem with linking small pieces of science to large works of metaphysics
is like finding shapes in the clouds or "Five ways TV shows predicted the
future!" If you have enough material to sift through you can draw a circle in
it and decide this particular piece of the morass is significant while
ignoring the rest of the meaningless unfalsifiable piffle.

~~~
beat
If you read Hegel (or read someone interpreting him, I don't recommend reading
Hegel unless you're a masochist), you'll find a key part of his approach was
the limitations of observation. And Hegel wasn't even first to the gate on
that one - philosophers have been questioning the value of observation
relative to a comprehensive understanding of reality since the ancient Greeks
(and the ancient Chinese, if you bring Taoism into it).

There's a lot more to it than "meaningless unfalsifiable piffle".

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not_a_moth
This claim will be hard for anyone to assess without having read and
understood Hegel, particularly the incredibly long and dense "Science of
Logic." While I haven't read the latter, his interpretation on the surface
seems like a gross simplification of something that few scholars agree on,
regarding a book that few have read. If Hegel's ontology were as simple as the
author described, it would be standard knowledge in how to interpret Hegel,
something I would have learned in my college modern philosophy class.

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tim333
The prime numbers of course would have been just fine and irreducible as ever
if Hegel had never existed. He did however manage to influence a lot of other
iffy stuff:

> Maurice Merleau-Ponty wrote that "all the great philosophical ideas of the
> past century—the philosophies of Marx and Nietzsche, phenomenology, German
> existentialism, and psychoanalysis—had their beginnings in
> Hegel."(wikipedia)

~~~
beat
I don't think of any of those things as "iffy", myself.

But if you wanna take a shot at dismissing anything that Nietzsche or
Heidegger wrote, without resorting to cultural bias points, be my guest.
There's a PhD in it for you.

~~~
theoh
They might be seen as iffy because of the damage that has been done in the
name of each of their theories. Marx obviously has a lot to answer for if you
consider him responsible for everything that went wrong in the USSR; Freud's
influence is probably as much bad as good, if you consider it as having
brought a compelling but pseudoscientific method to bear on psychology. And so
on.

It does sound anti-intellectual to dismiss all those thinkers as iffy, but I'd
much rather retain the option of treating their views with skepticism than
enrol in a PhD programme where it's implicit that all one can do is write
footnotes on the work of these great men. (You seem to imply that — unless,
that is, the student is a rare and impertinent genius who has the temerity to
take them on.)

~~~
Avshalom
to steal a line from Stroustrup:

"there are to kinds of philosophies: the ones people kill each other over and
the ones nobody uses"

~~~
tim333
Though some like humanism tend to lead to less killing than might have gone on
otherwise.

~~~
xamuel
Let it run its full course, and humanism will lead to an unimaginably horrific
dystopia. Think "Brave New World", by Aldous Huxley. The surest way to make a
man stumble and fall is to puff him up with flattery and tell him how wise and
sure-footed he is.

~~~
tim333
Maybe though I rather doubt it. Time will tell.

~~~
Avshalom
The problem is that humanism is more of a flavor found in philosophies rather
than a specific lineage or school.

Marx was humanist, so time already told I guess.

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ptah
I wonder what zizek has to say about this

