Fw: Back to AtD Zeta functions

[Paul Mackin]

and speaking of real and imagined . . .

http://opinionator.blogs.nytimes.com/2012/07/14/what-is-real-is-imagined/?hp


On 7/15/2012 5:16 PM, Paul Mackin wrote:
> 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?
>>>
>>>
>>>
>>>
>>
>>
>>
>>
>>
>>
>
>


-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://waste.org/pipermail/pynchon-l/attachments/20120715/bfb4ed7f/attachment.html>