Back to AtD Zeta functions

[Paul Mackin]

On 7/15/2012 11:47 AM, Mark Kohut wrote:
> Very helpful, Prashant and it leads me to my textual speculation based on
> TRP using it here, as he does almost everything, as a metaphor.....
> One level (specualtive): the imaginary is the future that is being 
> more than hinted at here.
> More speculative second level: imaginary numbers are, by definition, 
> not real.....it is
> unreality---unnatural nation-states, nations BEYOND natural 
> formations, math beyond
> what we need to get the world---that will kill.
>
It reminds me of that old jokey saying, learned in childhood, that goes 
something like this:

Austria got Hungary and ate Turkey fried in Greece.

P
>
> *From:* Prashant Kumar <siva.prashant.kumar at gmail.com>
> *To:* Mark Kohut <markekohut at yahoo.com>
> *Cc:* pynchon -l <pynchon-l at waste.org>
> *Sent:* Sunday, July 15, 2012 9:25 AM
> *Subject:* Re: Back to AtD Zeta functions
>
> 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 
> <mailto: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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