Back to AtD Zeta functions

[Paul Mackin]

On 7/16/2012 12:08 AM, Prashant Kumar wrote:
> 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

Thanks, Prashant.  I withdraw my voltage example.

Luddy wrong too.  I'm in such good company.

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