Fw: Back to AtD Zeta functions

[Paul Mackin]

On 7/15/2012 3:42 PM, Mark Kohut wrote:
> point being lost by me here is that LW din't much believe that 
> functions drawn from the square
> root of a negative numbercaptured the real world.....

but mathematically they do capture real things. Like voltage. When 
voltage is partly imaginary it just means that its peaks are ahead of 
the current peaks in the cycle.

I just wanted to emphasize that imaginary doesn't mean non-existent, and 
probably you never said it did.


P

>
> ----- Forwarded Message -----
> *From:* Mark Kohut <markekohut at yahoo.com>
> *To:* Paul Mackin <mackin.paul at verizon.net>; "pynchon-l at waste.org" 
> <pynchon-l at waste.org>
> *Sent:* Sunday, July 15, 2012 3:32 PM
> *Subject:* Re: Back to AtD Zeta functions
>
> in my abortive 'career' as a philospher-in-training, I did learn me 
> some Wittgenstein including
> sumpin' about his Philosophy of.........
> This is from the Stanford Ency article about LW. Much more there , if 
> time and interest:
> "Similarly, in saying that “[t]he logic of the world” is shown by 
> tautologies and true mathematical equations (i.e., #2), Wittgenstein 
> may be saying that since mathematics was invented to help us count and 
> measure, insofar as it enables us to infer contingent proposition(s) 
> from contingent proposition(s) (see 6.211 below), it thereby 
> /reflects/ contingent facts and “[t]he logic of the world.”  Though 
> logic—which is inherent in natural (‘everyday’) language (4.002, 
> 4.003, 6.124) and which has evolved to meet our communicative, 
> exploratory, and survival needs—is not /invented/ in the same way, a 
> valid logical inference captures the relationship between possible 
> facts and a /sound/ logical inference captures the relationship 
> between existent facts."
> We do know that TRP knew some Witt. How much and his take, we don't 
> much about, but I'd present a case for much of Witt's philosophy of 
> math not only being known to TRP (easy one) but deeply influential in 
> Against the Day.
>
> *From:* Paul Mackin <mackin.paul at verizon.net>
> *To:* pynchon-l at waste.org
> *Sent:* Sunday, July 15, 2012 2:50 PM
> *Subject:* Re: Back to AtD Zeta functions
>
> 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 mailto:siva.prashant.kumar at gmail.com
>> *To:* Mark Kohut mailto:markekohut at yahoo.com
>> *Cc:* pynchon -l mailto: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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