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From: O5O on 11 Mar 2010 18:30
On Mar 11, 1:32 am, "Androcles" <Headmas...(a)Hogwarts.physics_v> wrote:
> "O5O" <christoffur...(a)gmail.com> wrote in message
>
> news:a1c7faeb-5550-496f-b632-d42decdca799(a)k6g2000prg.googlegroups.com...
> On Mar 10, 6:51 pm, "Androcles" <Headmas...(a)Hogwarts.physics_v> wrote:
>
>
>
> > "O5O" <christoffur...(a)gmail.com> wrote in message
>
> >news:28d74bc2-0ab9-4e18-ace0-8104924a8dad(a)w9g2000prb.googlegroups.com...
>
> > >I have waited a week or so for the math groups to comment, but no
> > > takers yet. So now I'm trolling on sci.physics. Maybe some of you
> > > physic's guys (or gal's) might have something to say?
>
> > > I saw part of a program on Japanese T.V. NHK channel 18.2 here in Los
> > > Angeles. It was named "NHK Special: The cosmic code breakers - The
> > > struggle to prove the Riemann hypothesis." Roughly it was about how
> > > different physical characteristics are observed in nature that have
> > > some kind of a bearing on the Riemann zeta-function or visa-versa.
> > > There is also some interest in the Mathematics world, I think, for
> > > using it to determine prime numbers somehow. With my primary interest
> > > in Engineering, I am not all that well versed in the zeta-function,
> > > particle physics, or higher order conceptual theories of anything.
>
> > > So to keep my blabbering to a minimum, I'll let any interested parties
> > > check out the web site.
>
> > > What I am basically interested in, is this connection between the zeta-
> > > function and physics, and if there is any real connection to the
> > > patterns that I see in this series of number factor pattern pictures.
>
> > > I see images on the left side of the pictures that I liken to
> > > interference patterns, but they don't seem to be related to the prime
> > > numbers in any particular way that I am aware of. They repeat
> > > regularly at (I suppose) prime intervals such as 2x3, 2x3x5, 2x3x5x7,
> > > 2x3x5x7x11, ..., etc, but that is the only connection I see so far.
>
> > > I also see some kind of wavy looking things around the square root
> > > function that become more pronounced and more spread out the deeper
> > > into the number line we go. I think that there are some continuous
> > > functions that can be teased out, but haven't really spent the time to
> > > evaluate them yet.
>
> > > As far as atomic structure, particle physics, and interference
> > > patterns are concerned I suppose that we are dealing with a small and
> > > limited number of integers, so my question then becomes what part of
> > > the zeta-function is actually pertinent to physics problems, and how
> > > so?
>
> > > These images are large and my web site is slow so your patience will
> > > vary, as well as the capabilities of your browsers to handle the
> > > complete 15 page series.
>
> > > "http://www.christopherthompson.me/Primes/" is the main web location
> > > right now.
>
> > > "http://www.christopherthompson.me/Primes/index525.shtml" is the
> > > smallest series of images where the patterns are readily apparent.
>
> > > "http://www.christopherthompson.me/Primes/index840.shtml" and "http://
> > >www.christopherthompson.me/Primes/index1050.shtml" are each
> > > progressively larger, and will take exponentially longer to load.
>
> > > Google downloads these things every day or so, but I haven't yet
> > > determined where they are cached. They have cached the text part of
> > > the html pages, but the images still come to my web site for download..
> > > I don't know what they are doing with them, but if they are going to
> > > use my bandwidth to grab them off of my web site they ought to make
> > > them available for viewing off of their servers sometime.
>
> > > The 5250x5250 sized pages are probably the minimum sized pages where
> > > the text is barely legible.
>
> > > For viewing in PDF, I created a file with all fifteen pages and
> > > diagonal lines that I can recommend for download as a compromise
> > > between pattern viewing, legibility, and bandwidth utilization at:
>
> > > "http://www.christopherthompson.me/PrimesFL/
> > > FactorTableWithDiagonals32+65.pdf"
>
> > > It is 5.11 MegaBytes, but just page 1 at 10500x10500 is 98 MegaBytes.
> > > Multiply by fifteen and you see the difference.
>
> > > Chris
>
> > If you have a question, ask it. Otherwise I'm not interested in Google's
> > computer downloading your images and then deciding they were too large
> > to bother with.
> >http://christopherthompson.me/sm08937.jpg
> > Your gutter needs a coat of paint and your junk beside the bike needs
> > cleaning up.
>
> Wonderful observations Adrocles! Next time read the text and look for
> the question marks. Edit->Find->"?"->Enter->Repeat-Find->Enter
>
> ============================================
>
> You see images on the left side of the pictures that you liken to
> interference patterns.
> You also see some kind of wavy looking things around the square root
> function that become more pronounced and more spread out the deeper
> into the number line you go.
>
> Mandelbrot saw this:
>  http://mandelbrot.collettivamente.com/mandel.cgi
>
> Instead of generating 5.11 Megabyte images and then running out
> of space and time, the trick is to zoom in on the portion of the image
> that you are actually interested in.
> Mathematically the Mandelbrot set can be defined as the set of complex
> values of c for which the orbit of 0 under iteration of the complex
> quadratic polynomial  z_(n+1) = (z_n)^2 + c remains bounded.
> Ref:  http://en.wikipedia.org/wiki/Mandelbrot_set
>
>  As far as chocolate eggs are concerned I suppose that we are dealing
> with some kind of wavy looking small and limited intellect better suited
> to painting gutters and cleaning up yards, so my question then becomes
> "what part of the Mandelbrot-function is actually pertinent to the Easter
> Bunny egg-laying problem, and how so?"
> I suppose the answer is "None at all, chocolate eggs are moulded by
> machinery", which may seem strange to small children that have learnt
> birds lay eggs and amateurs that hallucinate "all mathematics is physics"
> rather than "physics uses some mathematics".
>
> I gave a ride to some hitchers in PA, once. In the snow,  a man, a
> woman, a younger girl aged about 12, trudging out of a rest stop on I80.
> They turned out to be weirdoes, when I dropped them at I79 the
> guy offered to sell me some pencilled drawings that look a lot like
> yours, and he reckoned they held all the secrets of the universe.
> Was that you in 1984?
>
> BTW, I did read the text, I even saw the question mark. I omitted
> "sensible" in "If you have a sensible question, ask it."

Sorry if I have offended your "gutter" sensibilities. I guess I was
hoping for a different kind of comment pertaining more to the
relevance of the Riemann hypothesis and the Riemann zeta-function to
different physical phenomenon as discussed in the TV program which due
to my limited intellect, I have not fully comprehended. Indeed may
never fully comprehend. I was not aware that this was fractal. Thanks
for sharing, and no... I've never been to PA. Would you be able to
point me in the right direction of the Mandelbrot set that generates
these? I was thinking about writing a program to do what you suggest
with the zoom in and zoom out on various locations but it seems from
your comments that this would be rather pointless and a waste of time.
From: Androcles on 11 Mar 2010 20:21

"O5O" <christoffur050(a)gmail.com> wrote in message
news:1005ec57-2224-4110-a962-9f9ac46ccd07(a)t17g2000prg.googlegroups.com...
On Mar 11, 1:32 am, "Androcles" <Headmas...(a)Hogwarts.physics_v> wrote:
> "O5O" <christoffur...(a)gmail.com> wrote in message
>
> news:a1c7faeb-5550-496f-b632-d42decdca799(a)k6g2000prg.googlegroups.com...
> On Mar 10, 6:51 pm, "Androcles" <Headmas...(a)Hogwarts.physics_v> wrote:
>
>
>
> > "O5O" <christoffur...(a)gmail.com> wrote in message
>
> >news:28d74bc2-0ab9-4e18-ace0-8104924a8dad(a)w9g2000prb.googlegroups.com...
>
> > >I have waited a week or so for the math groups to comment, but no
> > > takers yet. So now I'm trolling on sci.physics. Maybe some of you
> > > physic's guys (or gal's) might have something to say?
>
> > > I saw part of a program on Japanese T.V. NHK channel 18.2 here in Los
> > > Angeles. It was named "NHK Special: The cosmic code breakers - The
> > > struggle to prove the Riemann hypothesis." Roughly it was about how
> > > different physical characteristics are observed in nature that have
> > > some kind of a bearing on the Riemann zeta-function or visa-versa.
> > > There is also some interest in the Mathematics world, I think, for
> > > using it to determine prime numbers somehow. With my primary interest
> > > in Engineering, I am not all that well versed in the zeta-function,
> > > particle physics, or higher order conceptual theories of anything.
>
> > > So to keep my blabbering to a minimum, I'll let any interested parties
> > > check out the web site.
>
> > > What I am basically interested in, is this connection between the
> > > zeta-
> > > function and physics, and if there is any real connection to the
> > > patterns that I see in this series of number factor pattern pictures.
>
> > > I see images on the left side of the pictures that I liken to
> > > interference patterns, but they don't seem to be related to the prime
> > > numbers in any particular way that I am aware of. They repeat
> > > regularly at (I suppose) prime intervals such as 2x3, 2x3x5, 2x3x5x7,
> > > 2x3x5x7x11, ..., etc, but that is the only connection I see so far.
>
> > > I also see some kind of wavy looking things around the square root
> > > function that become more pronounced and more spread out the deeper
> > > into the number line we go. I think that there are some continuous
> > > functions that can be teased out, but haven't really spent the time to
> > > evaluate them yet.
>
> > > As far as atomic structure, particle physics, and interference
> > > patterns are concerned I suppose that we are dealing with a small and
> > > limited number of integers, so my question then becomes what part of
> > > the zeta-function is actually pertinent to physics problems, and how
> > > so?
>
> > > These images are large and my web site is slow so your patience will
> > > vary, as well as the capabilities of your browsers to handle the
> > > complete 15 page series.
>
> > > "http://www.christopherthompson.me/Primes/" is the main web location
> > > right now.
>
> > > "http://www.christopherthompson.me/Primes/index525.shtml" is the
> > > smallest series of images where the patterns are readily apparent.
>
> > > "http://www.christopherthompson.me/Primes/index840.shtml" and "http://
> > >www.christopherthompson.me/Primes/index1050.shtml" are each
> > > progressively larger, and will take exponentially longer to load.
>
> > > Google downloads these things every day or so, but I haven't yet
> > > determined where they are cached. They have cached the text part of
> > > the html pages, but the images still come to my web site for download.
> > > I don't know what they are doing with them, but if they are going to
> > > use my bandwidth to grab them off of my web site they ought to make
> > > them available for viewing off of their servers sometime.
>
> > > The 5250x5250 sized pages are probably the minimum sized pages where
> > > the text is barely legible.
>
> > > For viewing in PDF, I created a file with all fifteen pages and
> > > diagonal lines that I can recommend for download as a compromise
> > > between pattern viewing, legibility, and bandwidth utilization at:
>
> > > "http://www.christopherthompson.me/PrimesFL/
> > > FactorTableWithDiagonals32+65.pdf"
>
> > > It is 5.11 MegaBytes, but just page 1 at 10500x10500 is 98 MegaBytes.
> > > Multiply by fifteen and you see the difference.
>
> > > Chris
>
> > If you have a question, ask it. Otherwise I'm not interested in Google's
> > computer downloading your images and then deciding they were too large
> > to bother with.
> >http://christopherthompson.me/sm08937.jpg
> > Your gutter needs a coat of paint and your junk beside the bike needs
> > cleaning up.
>
> Wonderful observations Adrocles! Next time read the text and look for
> the question marks. Edit->Find->"?"->Enter->Repeat-Find->Enter
>
> ============================================
>
> You see images on the left side of the pictures that you liken to
> interference patterns.
> You also see some kind of wavy looking things around the square root
> function that become more pronounced and more spread out the deeper
> into the number line you go.
>
> Mandelbrot saw this:
> http://mandelbrot.collettivamente.com/mandel.cgi
>
> Instead of generating 5.11 Megabyte images and then running out
> of space and time, the trick is to zoom in on the portion of the image
> that you are actually interested in.
> Mathematically the Mandelbrot set can be defined as the set of complex
> values of c for which the orbit of 0 under iteration of the complex
> quadratic polynomial z_(n+1) = (z_n)^2 + c remains bounded.
> Ref: http://en.wikipedia.org/wiki/Mandelbrot_set
>
> As far as chocolate eggs are concerned I suppose that we are dealing
> with some kind of wavy looking small and limited intellect better suited
> to painting gutters and cleaning up yards, so my question then becomes
> "what part of the Mandelbrot-function is actually pertinent to the Easter
> Bunny egg-laying problem, and how so?"
> I suppose the answer is "None at all, chocolate eggs are moulded by
> machinery", which may seem strange to small children that have learnt
> birds lay eggs and amateurs that hallucinate "all mathematics is physics"
> rather than "physics uses some mathematics".
>
> I gave a ride to some hitchers in PA, once. In the snow, a man, a
> woman, a younger girl aged about 12, trudging out of a rest stop on I80.
> They turned out to be weirdoes, when I dropped them at I79 the
> guy offered to sell me some pencilled drawings that look a lot like
> yours, and he reckoned they held all the secrets of the universe.
> Was that you in 1984?
>
> BTW, I did read the text, I even saw the question mark. I omitted
> "sensible" in "If you have a sensible question, ask it."

Sorry if I have offended your "gutter" sensibilities. I guess I was
hoping for a different kind of comment pertaining more to the
relevance of the Riemann hypothesis and the Riemann zeta-function to
different physical phenomenon as discussed in the TV program which due
to my limited intellect, I have not fully comprehended. Indeed may
never fully comprehend. I was not aware that this was fractal. Thanks
for sharing, and no... I've never been to PA. Would you be able to
point me in the right direction of the Mandelbrot set that generates
these? I was thinking about writing a program to do what you suggest
with the zoom in and zoom out on various locations but it seems from
your comments that this would be rather pointless and a waste of time.
=================================================
The Riemann hypothesis would have been the Riemann theorem
if Riemann had been able to prove it. The simple fact that he couldn't
is indicative of it being difficult to prove, and he was a mathematician.
However, you are more interested in seeing patterns, in particular
you've mentioned sqrt, so let's discuss roots.
In the complex plane construct a circle of unit radius centred on the
origin.
Notice that (-1 + i0) is a rotation of 180 degrees (from 1), and
(-1 + i0)^2 = 1.
Further notice that (0, i1)^2 = -1 by definition of i and i is a rotation of
90 degrees from 1, -i is a rotation of 270 degrees from 1.
So (0+ i1)^4 = 1.
Now look at the cube roots of 1. They are 1 (of course), (cos(120),
i.sin(120)),
(cos(240), i.sin(240)) (angles in degrees)

That is, the nth roots of 1 correspond to n equal segments of the unit
circle.
http://www.androcles01.pwp.blueyonder.co.uk/ComplexPlane.GIF

So... i is a rotation of 90 degrees,
i^2 is a rotation of 180 degrees,
i^3 is a rotation of 270 degrees,
i^4 = ( i *i)*(i*i) = -1*-1 = 1 is full circle, 360 degrees.

Multiplying a complex number by itself is rotating it.
(-0.5 + i 0.866) * (-0.5 + i 0.866) * (-0.5 + i 0.866) = (1+ i0)
That is what Mandelbrot did, except he added the original
complex number and repeated the operation. Adding a complex
number is translation, squaring is rotation.

Now, any real number will be a multiple of 1, so if we find its
one real nth-root and construct a circle with that as the radius, the
other n-1 roots will all lie on that circle when we divide it into
n segments.
The one real root can be found by the extended Newton-Raphson
iterative method, root_x = [x/{(root_x)^(n-1)} + (n-1)*root_x]/n.

As to you writing a program and it being a waste of time...No. Anything
you do with determination is worthwhile, you can only learn from the
experience. In 1989 I was photographing my own fractals on my
computer screen and my girlfriend was selling the prints for $800 - as art.













From: O5O on 12 Mar 2010 15:23
On Mar 11, 5:21 pm, "Androcles" <Headmas...(a)Hogwarts.physics_v> wrote:
> "O5O" <christoffur...(a)gmail.com> wrote in message
>
> news:1005ec57-2224-4110-a962-9f9ac46ccd07(a)t17g2000prg.googlegroups.com...
> On Mar 11, 1:32 am, "Androcles" <Headmas...(a)Hogwarts.physics_v> wrote:
>
>
>
> > "O5O" <christoffur...(a)gmail.com> wrote in message
>
> >news:a1c7faeb-5550-496f-b632-d42decdca799(a)k6g2000prg.googlegroups.com...
> > On Mar 10, 6:51 pm, "Androcles" <Headmas...(a)Hogwarts.physics_v> wrote:
>
> > > "O5O" <christoffur...(a)gmail.com> wrote in message
>
> > >news:28d74bc2-0ab9-4e18-ace0-8104924a8dad(a)w9g2000prb.googlegroups.com....
>
> > > >I have waited a week or so for the math groups to comment, but no
> > > > takers yet. So now I'm trolling on sci.physics. Maybe some of you
> > > > physic's guys (or gal's) might have something to say?
>
> > > > I saw part of a program on Japanese T.V. NHK channel 18.2 here in Los
> > > > Angeles. It was named "NHK Special: The cosmic code breakers - The
> > > > struggle to prove the Riemann hypothesis." Roughly it was about how
> > > > different physical characteristics are observed in nature that have
> > > > some kind of a bearing on the Riemann zeta-function or visa-versa.
> > > > There is also some interest in the Mathematics world, I think, for
> > > > using it to determine prime numbers somehow. With my primary interest
> > > > in Engineering, I am not all that well versed in the zeta-function,
> > > > particle physics, or higher order conceptual theories of anything.
>
> > > > So to keep my blabbering to a minimum, I'll let any interested parties
> > > > check out the web site.
>
> > > > What I am basically interested in, is this connection between the
> > > > zeta-
> > > > function and physics, and if there is any real connection to the
> > > > patterns that I see in this series of number factor pattern pictures.
>
> > > > I see images on the left side of the pictures that I liken to
> > > > interference patterns, but they don't seem to be related to the prime
> > > > numbers in any particular way that I am aware of. They repeat
> > > > regularly at (I suppose) prime intervals such as 2x3, 2x3x5, 2x3x5x7,
> > > > 2x3x5x7x11, ..., etc, but that is the only connection I see so far.
>
> > > > I also see some kind of wavy looking things around the square root
> > > > function that become more pronounced and more spread out the deeper
> > > > into the number line we go. I think that there are some continuous
> > > > functions that can be teased out, but haven't really spent the time to
> > > > evaluate them yet.
>
> > > > As far as atomic structure, particle physics, and interference
> > > > patterns are concerned I suppose that we are dealing with a small and
> > > > limited number of integers, so my question then becomes what part of
> > > > the zeta-function is actually pertinent to physics problems, and how
> > > > so?
>
> > > > These images are large and my web site is slow so your patience will
> > > > vary, as well as the capabilities of your browsers to handle the
> > > > complete 15 page series.
>
> > > > "http://www.christopherthompson.me/Primes/" is the main web location
> > > > right now.
>
> > > > "http://www.christopherthompson.me/Primes/index525.shtml" is the
> > > > smallest series of images where the patterns are readily apparent.
>
> > > > "http://www.christopherthompson.me/Primes/index840.shtml" and "http://
> > > >www.christopherthompson.me/Primes/index1050.shtml" are each
> > > > progressively larger, and will take exponentially longer to load.
>
> > > > Google downloads these things every day or so, but I haven't yet
> > > > determined where they are cached. They have cached the text part of
> > > > the html pages, but the images still come to my web site for download.
> > > > I don't know what they are doing with them, but if they are going to
> > > > use my bandwidth to grab them off of my web site they ought to make
> > > > them available for viewing off of their servers sometime.
>
> > > > The 5250x5250 sized pages are probably the minimum sized pages where
> > > > the text is barely legible.
>
> > > > For viewing in PDF, I created a file with all fifteen pages and
> > > > diagonal lines that I can recommend for download as a compromise
> > > > between pattern viewing, legibility, and bandwidth utilization at:
>
> > > > "http://www.christopherthompson.me/PrimesFL/
> > > > FactorTableWithDiagonals32+65.pdf"
>
> > > > It is 5.11 MegaBytes, but just page 1 at 10500x10500 is 98 MegaBytes.
> > > > Multiply by fifteen and you see the difference.
>
> > > > Chris
>
> > > If you have a question, ask it. Otherwise I'm not interested in Google's
> > > computer downloading your images and then deciding they were too large
> > > to bother with.
> > >http://christopherthompson.me/sm08937.jpg
> > > Your gutter needs a coat of paint and your junk beside the bike needs
> > > cleaning up.
>
> > Wonderful observations Adrocles! Next time read the text and look for
> > the question marks. Edit->Find->"?"->Enter->Repeat-Find->Enter
>
> > ============================================
>
> > You see images on the left side of the pictures that you liken to
> > interference patterns.
> > You also see some kind of wavy looking things around the square root
> > function that become more pronounced and more spread out the deeper
> > into the number line you go.
>
> > Mandelbrot saw this:
> >http://mandelbrot.collettivamente.com/mandel.cgi
>
> > Instead of generating 5.11 Megabyte images and then running out
> > of space and time, the trick is to zoom in on the portion of the image
> > that you are actually interested in.
> > Mathematically the Mandelbrot set can be defined as the set of complex
> > values of c for which the orbit of 0 under iteration of the complex
> > quadratic polynomial z_(n+1) = (z_n)^2 + c remains bounded.
> > Ref:http://en.wikipedia.org/wiki/Mandelbrot_set
>
> > As far as chocolate eggs are concerned I suppose that we are dealing
> > with some kind of wavy looking small and limited intellect better suited
> > to painting gutters and cleaning up yards, so my question then becomes
> > "what part of the Mandelbrot-function is actually pertinent to the Easter
> > Bunny egg-laying problem, and how so?"
> > I suppose the answer is "None at all, chocolate eggs are moulded by
> > machinery", which may seem strange to small children that have learnt
> > birds lay eggs and amateurs that hallucinate "all mathematics is physics"
> > rather than "physics uses some mathematics".
>
> > I gave a ride to some hitchers in PA, once. In the snow, a man, a
> > woman, a younger girl aged about 12, trudging out of a rest stop on I80..
> > They turned out to be weirdoes, when I dropped them at I79 the
> > guy offered to sell me some pencilled drawings that look a lot like
> > yours, and he reckoned they held all the secrets of the universe.
> > Was that you in 1984?
>
> > BTW, I did read the text, I even saw the question mark. I omitted
> > "sensible" in "If you have a sensible question, ask it."
>
> Sorry if I have offended your "gutter" sensibilities. I guess I was
> hoping for a different kind of comment pertaining more to the
> relevance of the Riemann hypothesis and the Riemann zeta-function to
> different physical phenomenon as discussed in the TV program which due
> to my limited intellect, I have not fully comprehended. Indeed may
> never fully comprehend. I was not aware that this was fractal. Thanks
> for sharing, and no... I've never been to PA. Would you be able to
> point me in the right direction of the Mandelbrot set that generates
> these? I was thinking about writing a program to do what you suggest
> with the zoom in and zoom out on various locations but it seems from
> your comments that this would be rather pointless and a waste of time.
> =================================================
> The Riemann hypothesis would have been the Riemann theorem
> if Riemann had been able to prove it. The simple fact that he couldn't
> is indicative of it being difficult to prove, and he was a mathematician.
> However, you are more interested in seeing patterns, in particular
> you've mentioned sqrt, so let's discuss roots.
> In the complex plane construct a circle of unit radius centred on the
> origin.
> Notice that (-1 + i0) is a rotation of 180 degrees (from 1), and
> (-1 + i0)^2 = 1.
> Further notice that (0, i1)^2 = -1 by definition of i and i is a rotation of
>  90 degrees from 1, -i is a rotation of 270 degrees from 1.
> So (0+ i1)^4 = 1.
> Now look at the cube roots of 1. They are 1 (of course), (cos(120),
> i.sin(120)),
> (cos(240), i.sin(240))  (angles in degrees)
>
> That is, the nth roots of 1 correspond to n equal segments of the unit
> circle.
>  http://www.androcles01.pwp.blueyonder.co.uk/ComplexPlane.GIF
>
> So... i is a rotation of 90 degrees,
>         i^2 is a rotation of 180 degrees,
>         i^3 is a rotation of 270 degrees,
>         i^4  = ( i *i)*(i*i) = -1*-1 = 1 is full circle, 360 degrees.
>
> Multiplying a complex number by itself is rotating it.
>  (-0.5 + i 0.866) *  (-0.5 + i 0.866) * (-0.5 + i 0.866) = (1+ i0)
> That is what Mandelbrot did, except he added the original
> complex number and repeated the operation. Adding a complex
> number is translation, squaring is rotation.
>
> Now, any real number will be a multiple of 1, so if we find its
> one real nth-root and construct a circle with that as the radius, the
> other n-1 roots will all lie on that circle when we divide it into
> n segments.
>  The one real root can be found by the extended Newton-Raphson
> iterative method,   root_x = [x/{(root_x)^(n-1)} + (n-1)*root_x]/n.
>
> As to you writing a program and it being a waste of time...No. Anything
> you do with determination is worthwhile, you can only learn from the
> experience. In 1989 I was photographing my own fractals on my
> computer screen and my girlfriend was selling the prints for $800 - as art.

Yeah... Ok. I looked at the zeta-function on Wikipedia, and did some
reading on particle physics. The only reference to the zeta function
there was in the field equations, and I don't see any particular
reference to prime numbers, proton / neutron packing functions,
interference patterns or electron energy levels. I assume they can be
derived somehow from the field equations, but I am not up to the task
right now. After looking more closely at the zeta-function itself, I
don't see any particular correspondence with prime numbers, or with
the patterns generated on the spreadsheet jpg's. It seems my
observation of "interference patterns" is purely coincidence, a
mathematical aberration, and has no real bearing on any physical
construct or process, or the zeta-function either for that matter.

However I am still interested in finding someone who could discuss the
TV program. I guess I'm going to have to wait till I can find it on
the air again. There is supposed to be some connection with the prime
numbers, and that is what I am really interested in. This physics
thing is just an aside for me.

I did find it interesting that the zeta-function is found in fractals.
I know that there is work being done by other people in chaos-theory
using fractal techniques to model real physical processes like
erosion, coastlines, biological constructs, and I have seen where cell
phone antennas are now designed using fractals. Haven't completely got
the connection to the zeta-function, but someday...

Thanks for the input,
Chris
From: Androcles on 12 Mar 2010 16:37

"O5O" <christoffur050(a)gmail.com> wrote in message
news:26daa933-287f-4030-bb87-c3fc403eb7f3(a)s36g2000prh.googlegroups.com...
On Mar 11, 5:21 pm, "Androcles" <Headmas...(a)Hogwarts.physics_v> wrote:
> "O5O" <christoffur...(a)gmail.com> wrote in message
>
> news:1005ec57-2224-4110-a962-9f9ac46ccd07(a)t17g2000prg.googlegroups.com...
> On Mar 11, 1:32 am, "Androcles" <Headmas...(a)Hogwarts.physics_v> wrote:
>
>
>
> > "O5O" <christoffur...(a)gmail.com> wrote in message
>
> >news:a1c7faeb-5550-496f-b632-d42decdca799(a)k6g2000prg.googlegroups.com...
> > On Mar 10, 6:51 pm, "Androcles" <Headmas...(a)Hogwarts.physics_v> wrote:
>
> > > "O5O" <christoffur...(a)gmail.com> wrote in message
>
> > >news:28d74bc2-0ab9-4e18-ace0-8104924a8dad(a)w9g2000prb.googlegroups.com...
>
> > > >I have waited a week or so for the math groups to comment, but no
> > > > takers yet. So now I'm trolling on sci.physics. Maybe some of you
> > > > physic's guys (or gal's) might have something to say?
>
> > > > I saw part of a program on Japanese T.V. NHK channel 18.2 here in
> > > > Los
> > > > Angeles. It was named "NHK Special: The cosmic code breakers - The
> > > > struggle to prove the Riemann hypothesis." Roughly it was about how
> > > > different physical characteristics are observed in nature that have
> > > > some kind of a bearing on the Riemann zeta-function or visa-versa.
> > > > There is also some interest in the Mathematics world, I think, for
> > > > using it to determine prime numbers somehow. With my primary
> > > > interest
> > > > in Engineering, I am not all that well versed in the zeta-function,
> > > > particle physics, or higher order conceptual theories of anything.
>
> > > > So to keep my blabbering to a minimum, I'll let any interested
> > > > parties
> > > > check out the web site.
>
> > > > What I am basically interested in, is this connection between the
> > > > zeta-
> > > > function and physics, and if there is any real connection to the
> > > > patterns that I see in this series of number factor pattern
> > > > pictures.
>
> > > > I see images on the left side of the pictures that I liken to
> > > > interference patterns, but they don't seem to be related to the
> > > > prime
> > > > numbers in any particular way that I am aware of. They repeat
> > > > regularly at (I suppose) prime intervals such as 2x3, 2x3x5,
> > > > 2x3x5x7,
> > > > 2x3x5x7x11, ..., etc, but that is the only connection I see so far.
>
> > > > I also see some kind of wavy looking things around the square root
> > > > function that become more pronounced and more spread out the deeper
> > > > into the number line we go. I think that there are some continuous
> > > > functions that can be teased out, but haven't really spent the time
> > > > to
> > > > evaluate them yet.
>
> > > > As far as atomic structure, particle physics, and interference
> > > > patterns are concerned I suppose that we are dealing with a small
> > > > and
> > > > limited number of integers, so my question then becomes what part of
> > > > the zeta-function is actually pertinent to physics problems, and how
> > > > so?
>
> > > > These images are large and my web site is slow so your patience will
> > > > vary, as well as the capabilities of your browsers to handle the
> > > > complete 15 page series.
>
> > > > "http://www.christopherthompson.me/Primes/" is the main web location
> > > > right now.
>
> > > > "http://www.christopherthompson.me/Primes/index525.shtml" is the
> > > > smallest series of images where the patterns are readily apparent.
>
> > > > "http://www.christopherthompson.me/Primes/index840.shtml" and
> > > > "http://
> > > >www.christopherthompson.me/Primes/index1050.shtml" are each
> > > > progressively larger, and will take exponentially longer to load.
>
> > > > Google downloads these things every day or so, but I haven't yet
> > > > determined where they are cached. They have cached the text part of
> > > > the html pages, but the images still come to my web site for
> > > > download.
> > > > I don't know what they are doing with them, but if they are going to
> > > > use my bandwidth to grab them off of my web site they ought to make
> > > > them available for viewing off of their servers sometime.
>
> > > > The 5250x5250 sized pages are probably the minimum sized pages where
> > > > the text is barely legible.
>
> > > > For viewing in PDF, I created a file with all fifteen pages and
> > > > diagonal lines that I can recommend for download as a compromise
> > > > between pattern viewing, legibility, and bandwidth utilization at:
>
> > > > "http://www.christopherthompson.me/PrimesFL/
> > > > FactorTableWithDiagonals32+65.pdf"
>
> > > > It is 5.11 MegaBytes, but just page 1 at 10500x10500 is 98
> > > > MegaBytes.
> > > > Multiply by fifteen and you see the difference.
>
> > > > Chris
>
> > > If you have a question, ask it. Otherwise I'm not interested in
> > > Google's
> > > computer downloading your images and then deciding they were too large
> > > to bother with.
> > >http://christopherthompson.me/sm08937.jpg
> > > Your gutter needs a coat of paint and your junk beside the bike needs
> > > cleaning up.
>
> > Wonderful observations Adrocles! Next time read the text and look for
> > the question marks. Edit->Find->"?"->Enter->Repeat-Find->Enter
>
> > ============================================
>
> > You see images on the left side of the pictures that you liken to
> > interference patterns.
> > You also see some kind of wavy looking things around the square root
> > function that become more pronounced and more spread out the deeper
> > into the number line you go.
>
> > Mandelbrot saw this:
> >http://mandelbrot.collettivamente.com/mandel.cgi
>
> > Instead of generating 5.11 Megabyte images and then running out
> > of space and time, the trick is to zoom in on the portion of the image
> > that you are actually interested in.
> > Mathematically the Mandelbrot set can be defined as the set of complex
> > values of c for which the orbit of 0 under iteration of the complex
> > quadratic polynomial z_(n+1) = (z_n)^2 + c remains bounded.
> > Ref:http://en.wikipedia.org/wiki/Mandelbrot_set
>
> > As far as chocolate eggs are concerned I suppose that we are dealing
> > with some kind of wavy looking small and limited intellect better suited
> > to painting gutters and cleaning up yards, so my question then becomes
> > "what part of the Mandelbrot-function is actually pertinent to the
> > Easter
> > Bunny egg-laying problem, and how so?"
> > I suppose the answer is "None at all, chocolate eggs are moulded by
> > machinery", which may seem strange to small children that have learnt
> > birds lay eggs and amateurs that hallucinate "all mathematics is
> > physics"
> > rather than "physics uses some mathematics".
>
> > I gave a ride to some hitchers in PA, once. In the snow, a man, a
> > woman, a younger girl aged about 12, trudging out of a rest stop on I80.
> > They turned out to be weirdoes, when I dropped them at I79 the
> > guy offered to sell me some pencilled drawings that look a lot like
> > yours, and he reckoned they held all the secrets of the universe.
> > Was that you in 1984?
>
> > BTW, I did read the text, I even saw the question mark. I omitted
> > "sensible" in "If you have a sensible question, ask it."
>
> Sorry if I have offended your "gutter" sensibilities. I guess I was
> hoping for a different kind of comment pertaining more to the
> relevance of the Riemann hypothesis and the Riemann zeta-function to
> different physical phenomenon as discussed in the TV program which due
> to my limited intellect, I have not fully comprehended. Indeed may
> never fully comprehend. I was not aware that this was fractal. Thanks
> for sharing, and no... I've never been to PA. Would you be able to
> point me in the right direction of the Mandelbrot set that generates
> these? I was thinking about writing a program to do what you suggest
> with the zoom in and zoom out on various locations but it seems from
> your comments that this would be rather pointless and a waste of time.
> =================================================
> The Riemann hypothesis would have been the Riemann theorem
> if Riemann had been able to prove it. The simple fact that he couldn't
> is indicative of it being difficult to prove, and he was a mathematician.
> However, you are more interested in seeing patterns, in particular
> you've mentioned sqrt, so let's discuss roots.
> In the complex plane construct a circle of unit radius centred on the
> origin.
> Notice that (-1 + i0) is a rotation of 180 degrees (from 1), and
> (-1 + i0)^2 = 1.
> Further notice that (0, i1)^2 = -1 by definition of i and i is a rotation
> of
> 90 degrees from 1, -i is a rotation of 270 degrees from 1.
> So (0+ i1)^4 = 1.
> Now look at the cube roots of 1. They are 1 (of course), (cos(120),
> i.sin(120)),
> (cos(240), i.sin(240)) (angles in degrees)
>
> That is, the nth roots of 1 correspond to n equal segments of the unit
> circle.
> http://www.androcles01.pwp.blueyonder.co.uk/ComplexPlane.GIF
>
> So... i is a rotation of 90 degrees,
> i^2 is a rotation of 180 degrees,
> i^3 is a rotation of 270 degrees,
> i^4 = ( i *i)*(i*i) = -1*-1 = 1 is full circle, 360 degrees.
>
> Multiplying a complex number by itself is rotating it.
> (-0.5 + i 0.866) * (-0.5 + i 0.866) * (-0.5 + i 0.866) = (1+ i0)
> That is what Mandelbrot did, except he added the original
> complex number and repeated the operation. Adding a complex
> number is translation, squaring is rotation.
>
> Now, any real number will be a multiple of 1, so if we find its
> one real nth-root and construct a circle with that as the radius, the
> other n-1 roots will all lie on that circle when we divide it into
> n segments.
> The one real root can be found by the extended Newton-Raphson
> iterative method, root_x = [x/{(root_x)^(n-1)} + (n-1)*root_x]/n.
>
> As to you writing a program and it being a waste of time...No. Anything
> you do with determination is worthwhile, you can only learn from the
> experience. In 1989 I was photographing my own fractals on my
> computer screen and my girlfriend was selling the prints for $800 - as
> art.

Yeah... Ok. I looked at the zeta-function on Wikipedia, and did some
reading on particle physics. The only reference to the zeta function
there was in the field equations, and I don't see any particular
reference to prime numbers, proton / neutron packing functions,
interference patterns or electron energy levels. I assume they can be
derived somehow from the field equations, but I am not up to the task
right now. After looking more closely at the zeta-function itself, I
don't see any particular correspondence with prime numbers, or with
the patterns generated on the spreadsheet jpg's. It seems my
observation of "interference patterns" is purely coincidence, a
mathematical aberration, and has no real bearing on any physical
construct or process, or the zeta-function either for that matter.

However I am still interested in finding someone who could discuss the
TV program. I guess I'm going to have to wait till I can find it on
the air again. There is supposed to be some connection with the prime
numbers, and that is what I am really interested in. This physics
thing is just an aside for me.

I did find it interesting that the zeta-function is found in fractals.
I know that there is work being done by other people in chaos-theory
using fractal techniques to model real physical processes like
erosion, coastlines, biological constructs, and I have seen where cell
phone antennas are now designed using fractals. Haven't completely got
the connection to the zeta-function, but someday...

Thanks for the input,
Chris
==============================================
The mathematical fractal nature of a coastline is unlimited in its depth.
The physical fractal nature of a coastline ends when you arrive at the
atomic level, you just can't go any deeper. But then something that
doesn't apply to fractals takes place... motion. Fractals are static,
atoms are not.
In exploring Nature we use mathematical models, but those models
cease to apply in the extreme. I often quote the case for the volume
of a gas as a function of temperature. At zero kelvin the volume is
zero -- but the gas is no longer a gas.



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