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.

I don't think, Mark, imaginary numbers would make a very good analogy 
for something that is "unnatural,"  unreal, or happening in the future.

When we're first presented with imaginary numbers, in high school 
algebra II, they do seem kind of weird, but a short time latter, after a 
smattering of Cartesian geometry, they seem as normal and usual as anything.

Whoever decided to call them "imaginary" because they don't fall on the 
one dimensional number line has some explaining to do.

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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