archived as
(also …Pitkanen_66.pdf) =>doc pdf URL-doc URL-pdf
more TGD physics-related articles on the /Pitkanen.htm page at doc pdf URL
note: because important websites are frequently "here today but gone tomorrow", the following was archived from on 06/28/2011. This is NOT an attempt to divert readers from the aforementioned website. Indeed, the reader should only read this back-up copy if the updated original cannot be found at the original author's site.
comments about the beautiful mathematics in Brane theory
Dr. Matti Pitkänen
June, 2011
Postal address:
Köydenpunojankatu 2 D 11
10940, Hanko, Finland
E-mail:
URL-address:
(former address:)
"Blog" forum:
(the following was in the 'Comments' section of the blog post "K-theory, Branes, and TGD")
1. At 10:54 AM, hamed said...
Hello Matti,
What's your idea about Musean hypernumbers? Dr. Charles A. Mus`es (1919–2000) discovered a series of higher-dimensional types of unity which he termed hypernumbers. He wrote about these numbers from the 1960s to the 1990s in many articles. He discovered a relation between Consciousness and hypernumbers and wrote about them in some articles.
You can find about this numbers at .
2. At 7:47 PM, said...
I encounterd hypernumbers a couple of years ago as I asked whether the Mandelbrot fractal has a higher-dimensional generalization. Hypernumbers is one manner to produce the analogs of these fractals. But the result is effectively 2-dimensional in most cases.
Hyper-numbers have no special role in TGD where Classical number fields and their complexifications are natural. The field character guaranteeing the existence of inverse is lacking. The mathematician might consider manifolds with hypernumber structure in tangent space.
3. At 9:11 AM, ThePeSla said...
So Matti …
I understand why hypernumbers have no special role in the TGD framework. But I am not sure what your excellent post and links like on the D 9 brane string-like ideas have to do with it either.
Other than the 3D extension, I think your question on the Mandelbrot fractal a good one (branes in a sense seem to answer it, at least suggest a vision of it). But such compactions of space for me is too limited in the first place. A dead end if the only view.
I am also amazed at the analogy that Branes can be considered charged or is that a higher metaphor- do they radiate.
In numbers, the square and cubed things together do raise the question of something like 6 space and so on... But that deeper than branes that always are n-dimensional in fact in the first place.
I think hamed asked this question because there are 9 such hypernumbers which are based on the idea of a root of unity which is not necessarily positive one.
And quite simply, space does seem to be filled cube-wise and sphere-wise at whatever they think happens at 9 dimensions.
But with all leftover interpretations of just a Q-M theory as a method- such hypernumbers were (in the 70s) thought intimate in the description of Consciousness.
The PeSla
4. At 9:46 PM, said...
Dear Pesla,
My view is that branes define an extremely powerfulmathematical tool for a mathematician although the basic step leading to the idea about generalized gauge potentials coupling to branes suggests interpretation of the theory as semi-Classical idealization of supergravity theory using various lower-dimensional objects as idealized configurations rather than something generalizing supergravity as QFT.
The irony is that just the completely lacking connection to real world physics has forced to concentrate on the general aspects of the theory with fantastic mathematical outcome.
Sad that I have not been motivated to learn the mathematical side of M-theory. I have allowed the idiotic hype by the rock stars of theoretical physics and equally idiotic concentration of too many bloggers to the ridicule of this hype (easy manner to get readers!!) to blind me so that I have not really grasped how incredibly powerful mathematics (bound to also be very useful to TGD framework)that the mathematicians like Witten have discovered during the years. Big fishes swim in silent waters and the media is interested only on the simplest possible music played with maximal volume.
In TGD framework, the counterparts of branes have different interpretation. But the comparison with M-theory and superstrings might provide for string theorists valuable insights about TGD.
For instance, 4-D general coordinate invariance in strong form implies holography in strong form and for the analogs of 2-branes both electric-magnetic duality and T-duality exchanging von Neumann and Dirichlet boundary conditions. See the post.
This morning I read about Witten's work with knot classification 4-D SUSY gauge theory. I proposed analogous approach based on TGD and 4-D space-time surfaces for some time ago =>
.
I added a couple of comments about this to this posting.
Everything is ready for the breakthrough of TGD. Whether it can happen depends only on political will. Let us hope that data from LHC will settle the situation soon. I believe that a correct prediction of a new hadronic physics, prediction of several other new branches of physics, and the understanding of dark matter (among other things) must eventually turn the heads of theoreticians.
5. At 11:52 AM, ThePeSla said...
Matti, Indeed!
BTW, Fractals from a complex number viewpoint into higher dimensions… Well, that could show some interesting results after all. Yes, our views do not need this.
Seems to me that they will also see the depth of your generalizations too. It seems to be a steep learning curve for them I would say if you asked me today :-)
The PeSla
if on the Internet, Press <BACK> on your browser to return to the previous page (or go to
else if accessing these files from the CD in a MS-Word session, simply <CLOSE> this file's window-session; the previous window-session should still remain 'active'
1