Back to AtD Zeta functions

[bandwraith at aol.com]

I think you're making too much of a demon out of math- maybe setting up 
too much of a dichotomy. Numbers don't kill... I think that such a 
dichotomy is a natural reaction to the power of mathematics as it has 
helped create the world we inhabit, for better or worse. But 
"imaginary" or complex numbers weren't discovered (or created by us- 
take your pick) until the early 16th century- plenty of killing, 
empire, slavery, etc., before that. Making the argument that sectarian 
differences or economics, or that our Darwinian nature are the roots of 
our social problems, I think, would be comprable over-simplifications. 
In fact, it would not be impossible to make the opposite argument, that 
logic, mathematics and science have done more than anything to 
ameliorate whatever inherent vices we carry that lead us to atrocity. 
An argument I am not making, but which could be made. The exponential 
aspect of mathematical and scientific knowledge and its multiplicative 
effect on killing efficiency, however, can't be denied.

The question might be better framed by asking: are mathematics and 
science neutral? Is anything we do neutral?  Plato would probabIy say 
that the truth lies somewhere beyond our ability to corrupt it. I think 
what Pynchon might be getting at is how supposedly neutral "truth" is 
inevitably subverted. The process is supposed to prevent that, but the 
unvarnished truth doesn't quite make it to the light of day, or not for 
long. But beyond all the bogosity in ATD there are some hints of 
mathematical beauty, real or imagined.

  ,


-----Original Message-----
From: Mark Kohut <markekohut at yahoo.com>
To: Prashant Kumar <siva.prashant.kumar at gmail.com>
Cc: pynchon -l <pynchon-l at waste.org>.
Sent: Sun, Jul 15, 2012 11:47 am
Subject: Re: Back to AtD Zeta functions



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.




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> 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?