Back to AtD Zeta functions

[Prashant Kumar]

So actually the imaginary numbers used in representing voltage don't
represent real or *measurable* quantities. It's just a mathematical
convenience. The salient point is this: we can't directly measure anything
with an *i*.

Strangely, physical entities with imaginary components do exist, such as
the wavefunction of a quantum mechanical system. There was a result in
Nature recently that proved that the wavefunction is not just a statement
of knowledge, it represents more than just probabilities. If anyone is
interested I can go into this, but the short answer is Witt was wrong.

On 16 July 2012 11:01, Lemuel Underwing <luunderwing at gmail.com> wrote:

> As someone who suffers from an inability to properly understand maths I
> thank you, 'twas certainly helpful.
>
> It is hard for me to imagine who any of this has to do with Annie
> Leibovitz... I take it some folks have a hard time figuring out what is
> just *White Noise* in Pynchon...?
>
>
> On Sun, Jul 15, 2012 at 8:25 AM, Prashant Kumar <
> siva.prashant.kumar at gmail.com> wrote:
>
>> 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?
>>>
>>
>>
>
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