Back to AtD Zeta functions

[Mark Kohut]

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>
To: 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> 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> 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> 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? 
>>>>
>>>
>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://waste.org/pipermail/pynchon-l/attachments/20120716/a692fcd6/attachment.html>