Back to AtD Zeta functions

[Prashant Kumar]

Wrong in thinking that certain types of mathematics cannot describe the
natural world, that is.

The analogy I use when describing imaginary numbers to people is this
(don't remember the source, sorry, but it's not mine). A person walking on
the beach counting sand has no use for decimals, or even fractions. The
Ancient Greeks had no idea about anything beyond fractions; irrational
numbers (those which can't be represented as a fraction) didn't exist for
them. Imaginary numbers are a generalisation of real numbers (btw the
quaternions in AtD are a further generalisation of imaginary numbers [!]).
The "reality" of certain classes of mathematical objects is difficult,
nebulous. On the one hand, you can just check to see whether that
mathematical object turns up in physics (in a way that one can't simply
reformulate out. This last is important; usually one uses measurement.),
but this is an ostensive definition, and not a way to build a philosophy of
maths.

So what do you do? Well, I think its bound up in this question: is
metaphysics supervenient on epistemology, or the converse? More concretely,
do you think that the reason we see maths everywhere is because the brain
is a product of the universe, and the universe is governed by laws which
are mathematical because if they weren't, brains which are capable of
asking such a question wouldn't arise (invocation of the weak anthropic
principle optional)? If you say yes to this last, then to what extent are
we really decoupled from the universe; how far away from "reality" do our
perceptions move us, and is it possible to compensate for this?

I don't think it matters. Math is abstraction, but it happens in our
brains; it is encoded as information. It "exists" in the universe.
Therefore it is real.

On 16 July 2012 22:36, Mark Kohut <markekohut at yahoo.com <javascript:_e({},
'cvml', 'markekohut at yahoo.com');>> wrote:

> The Annie Liebowitz reminder was wonderfully ironic about a solid woman
> thinker/writer who was NOT as ironic as TRP, imho.
>
> And, short Wittgenstein answer is we need a longer answer and time but
> that TRP might use the ideas creatively, metaphorically, as
> he does the concepts of entropy and other concepts is still possible.
>
>   *From:* Paul Mackin <mackin.paul at verizon.net <javascript:_e({}, 'cvml',
> 'mackin.paul at verizon.net');>>
> *To:* pynchon-l at waste.org <javascript:_e({}, 'cvml',
> 'pynchon-l at waste.org');>
> *Sent:* Monday, July 16, 2012 6:57 AM
>
> *Subject:* Re: Back to AtD Zeta functions
>
>  On 7/16/2012 12:08 AM, Prashant Kumar wrote:
>
> So actually the imaginary numbers used in representing voltage don't
> represent real or *measurable* quantities. It's just a mathematical
> convenience. The salient point is this: we can't directly measure anything
> with an *i*.
>
> Strangely, physical entities with imaginary components do exist, such as
> the wavefunction of a quantum mechanical system. There was a result in
> Nature recently that proved that the wavefunction is not just a statement
> of knowledge, it represents more than just probabilities. If anyone is
> interested I can go into this, but the short answer is Witt was wrong
>
>
> Thanks, Prashant.  I withdraw my voltage example.
>
> Luddy wrong too.  I'm in such good company.
>
> P
>
>
> On 16 July 2012 11:01, Lemuel Underwing <luunderwing at gmail.com<javascript:_e({}, 'cvml', 'luunderwing at gmail.com');>
> > wrote:
>
> As someone who suffers from an inability to properly understand maths I
> thank you, 'twas certainly helpful.
>
> It is hard for me to imagine who any of this has to do with Annie
> Leibovitz... I take it some folks have a hard time figuring out what is
> just *White Noise* in Pynchon...?
>
>
> On Sun, Jul 15, 2012 at 8:25 AM, Prashant Kumar <
> siva.prashant.kumar at gmail.com <javascript:_e({}, 'cvml',
> 'siva.prashant.kumar at gmail.com');>> wrote:
>
> First we're gonna need complex numbers, made of a real part (normal
> numbers) plus an imaginary part. Imaginary numbers are defined by multiples
> of *i*=squareroot(-1). Imagine a 2D graph, the vertical axis marked with
> multiples of *i* and the horizontal axis with real numbers. So on this 2D
> graph we can define a complex number as a point. Call such a point s =
> \sigma + \rho, \sigma and \rho being real and imaginary numbers resp.
>
> Since it takes real and imaginary inputs, and we plot the output in the
> third dimension, the Riemann Zeta function can be visualised as a surface
> sitting above the complex number graph; that's what you saw, Mark (see here
> http://en.wikipedia.org/wiki/Riemann_zeta_function for the same thing
> with magnitude represented as colour).  If I have a RZ function, writing R
> as a function of s as R(s), the zeroes are the values of s for which
> R(s)=0.  The Riemann Hypothesis (unproven) states that the zeroes of the RZ
> function have real part 1/2. Formally, R(1/2 + \rho) = 0. This gives you a
> line on the surface of the RZ function (known as the critical line) along
> which the zeroes are hypothesised to lie. That wasn't too bad, right?
>
> Verifying this hypothesis is notoriously hard.
>
> On 15 July 2012 21:27, Mark Kohut <markekohut at yahoo.com<javascript:_e({}, 'cvml', 'markekohut at yahoo.com');>
> > wrote:
>
> "Except that this one's horizontal and drawn on a grid of latitude and
> longitude,
> instead of rel vs imaginary values---where Riemann said that all the
> zeroes of the
> Beta function will be found."
>
> p. 937 Don't know enough math to have a feel for Zeta functions but
> Wolfram's
> maths guide online shows Beta functions kinda graphed in three dimensions,
> with raised sections, waves, folds etc....
>
> And all I can associate at the moment are the raised maps, showing land
> formations,
> and the phrase
>
> History is a step-function.
>
> Anyone, anyone? Bueller?
>
>
>
>
>
>
>
>
>
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