Jude Gomila

Hi Jude, First off I should say that I think you...

2012-04-20T14:34:31.810+01:00

Hi Jude,
First off I should say that I think your ideas do hit quite close to the mark. Equally I think one needs to be careful when discussing these concepts using English, since it is possible to draw analogies and assert potential equivalences when none actually exist at the level of the mathematics. Saying that I think you'd probably be interested to know that a lot of what you say has been thought about before.

As you already alluded to, the proof of the Riemann hypothesis would allow one to express the prime counting function (i.e. the function that returns the number of primes less than N) as a Fourier series in which the frequencies are precisely the imaginary parts of the Riemann zeros. Now part of what it appears you want to do, is interpret this Fourier series as a wavefunction for some quantum system. Each particular frequency in the Fourier series would the correspond to the eigenstate of some operator, perhaps energy. Whether this interpretation can be made or not, I am not sure. However, this is very close in spirit to certain approaches to proving the Riemann hypothesis.

Basically, in the 60s it was noted that the zeros of the zeta function are distributed in the same manner as the eigenvalues of matrices with random entries drawn from a Gaussian probability distribution. (Incidentally such random matrices are actually something I do work on, if you want to talk about that more :). Now, it turns out that quantum systems that exhibit chaos have Hamiltonians which are well approximated by such random matrices. The upshot of this, is that it appears the zeros of the zeta function should correspond to the energy states of some quantum chaotic system. Furthermore, the RH would be proved simply by the requirement that such energy eigenstate possessed real energies. This is a topic that is under active investigation, just have a look at the search results for "random matrix riemann zeta function chaos" :)

Regarding your other thoughts concerning the uncertainty principle; this is where I feel your analogies break down. Quantum mechanics has two different forms of dynamics. The first kind of dynamic is that governed by the Schrodinger equation and allows the wave function to be determined at all times from initial condition. The second form of dynamics is inherently stochastic (non-deterministic) and is referred to as the wave-function collapse. The latter form of dynamics describes the moment of measurement, and to some extent the jury is still out about the best way to interpret it. The Heisenberg uncertainty principle basically tells you something about the second kind of dynamics. However, the analogy of the zeta function to a quantum system only involves the first kind of dynamics. I can not see how once could introduce the wave-function collapse into the quantum interpretation of the zeta function. Although perhaps we just need to read more :)

Best,
Max

Nice graph but switch off the spellchecker next ti...

2009-11-29T17:23:07.136Z

Nice graph but switch off the spellchecker next time ;-)

Check it out, still living the life of Riley in Sa...

2009-11-11T16:39:00.303Z

Check it out, still living the life of Riley in San Fran then I see hahah. When u back in London ? Like the mapping...

thanks for this post web design India

Hello! I translated this article and map into Japa...

2009-06-22T10:05:48.667+01:00

Hello!
I translated this article and map into Japanese.
http://www.kotono8.com/2009/06/22webbusinessmapping.html
Your insights are very suggestive and useful!

2009-06-22T10:03:25.700+01:00

This comment has been removed by the author.

Great advice, thanks for posting.

2009-06-09T22:45:59.163+01:00

Great advice, thanks for posting.

"Support", should that be part of the retention en...

2009-06-02T20:20:50.514+01:00

"Support", should that be part of the retention engine?

Great map! I would personally also add a support e...

2009-06-02T15:14:09.123+01:00

Great map! I would personally also add a support engine.

Just finishing off my site, thanks for that, big h...

2009-06-01T12:43:32.605+01:00

Just finishing off my site, thanks for that, big help.

Thanks guys. Made in powerpoint

2009-05-31T23:55:16.509+01:00

Thanks guys. Made in powerpoint

Very Nice. Did you create it using Powerpoint?

2009-05-31T21:49:57.541+01:00

Very Nice. Did you create it using Powerpoint?

Great analysis Jude! Glad to see someone build on ...

2009-05-31T20:40:10.093+01:00

Great analysis Jude! Glad to see someone build on Dave's models.

I'd be interested to hear specific areas in which new opportunities and optimizations arose from mapping out any of your startups.

Thats something similar I've started on my blog . But , here I found some new stuff. Cheers!

very nice article

2009-05-31T18:12:43.436+01:00

very nice article

nice map! You should send it in to harvard busines...

2009-05-31T12:05:35.579+01:00

nice map! You should send it in to harvard business review..

I hijacked your original color scheme as well.

2009-05-31T10:17:46.532+01:00

I hijacked your original color scheme as well.

awesome stuff jude :)

2009-05-31T08:15:22.083+01:00

awesome stuff jude :)

A presentation by Andrew Chen with further ideas:<...

2008-10-03T22:44:00.000+01:00

A presentation by Andrew Chen with further ideas:

http://www.slideshare.net/Startonomics/revenue-the-internet-wants-to-be-free-but-you-need-to-get-paid-presentation?type=powerpoint

Yeah - got to get round to mapping some other stuf...

2008-07-19T01:09:00.000+01:00

Yeah - got to get round to mapping some other stuff out!

Nice. I hope this is the first of a series of post...

2008-07-18T11:47:00.000+01:00

Nice. I hope this is the first of a series of posts on processes.

How about the this-is-what-I-just-had-for-lunch tw...

2008-06-17T14:51:00.000+01:00

How about the this-is-what-I-just-had-for-lunch twitterer?

Forgot the spammer, and also the bot...

2008-05-24T22:29:00.000+01:00

Forgot the spammer, and also the bot...

the "omigod i don't understand how twitter works!"...

2008-05-24T14:23:00.000+01:00

the "omigod i don't understand how twitter works!" first post, and never posts again ... 1 reciprocal follower - your friend who made you join twitter in the first place.

Any others I have missed?

2008-05-24T12:46:00.000+01:00

Any others I have missed?