Dear Georgina,
You said "I wish to congratulate you for making, what is to me something very complex, a little more comprehensible than many of the "conversations" we have had on FQXi blogs, and that you have had with other mathematically competent contributors."
Thank you for your comments. I apologize that I have been busy lately and have not read as many essays (including yours) as I would like to read. At least I have another month to read these essays...
These essays gave us an opportunity to explain our ideas better - whether "better" means more diagrams, more references, more analogies, more explainations, or more mathematics than we would ordinarily use on these blog sites.
You also said "It does not seem foundational to me but I understand that you and others such as Lawrence Crowell do think that these kinds of ideas and mathematics really are promising avenues of investigation, potentially leading to more complete predictive models of the universe. I do not feel qualified to argue with that."
The recent results by Coldea et al (attached) have convinced me that a 5-fold "pentality" symmetry, and the related Golden Ratio, are relevant to the origin of mass.
You also said "Sometimes it seems that this modeling is a puzzle like "Eternity 2". Some pieces fit easily together but it is never so easy to complete.A board full of linked pieces looks good but so does the empty board that is full with potential.I agree that reality is most probably both digital and analogue and that the wave- particle duality is an important consideration."
I agree. I kept this essay more basic, and did not include all of my radical ideas, because I am constantly reconsidering those ideas. For example, I think that Fibonacci's sequence is relevant: 1,1,2,3,5,8,... partially because 1*1*2*3*5*8=240 roots of the largest classical exceptional group, E8, and partially because of its relationship with the Golden Ratio and Coldea et al's paper. However, at vixra log:
http://blog.vixra.org/2011/02/12/string-theory-and-partitions-numbers/
Philip Gibbs has presented Ken Ono's ideas about partition numbers: 1,1,2,3,5,7,... which differs from Fibonacci's sequence beginning with the sixth entry (and includes more small prime numbers than Fibonacci). Partition functions occur in Statistical Mechanics and are relevant to concepts such as Information and Entropy which are proportional to N*ln(N). But should partitions be additive, or multiplicative, or a hybrid function of both? To further confuse the picture, I have a 14-fold (G2 or Klein's Chi(7)) symmetry in my TOE models, but I don't think it is a 7-fold symmetry, and I don't think that it exactly supports Ono's ideas.
Questions such as these have caused me to focus more on specific components of a TOE - such as my Quantum Statistcal Grand Unified Theory (new developments in Prespacetime Journal volume 1, issue 9), on the pentality symmetry and Golden Ratio (new developments with Lawrence Crowell in Prespacetime Journal volume 1, issue 7), and on the possible application of Laurent Nottale's Scales.
Have Fun!
Dr. Cosmic RayAttachment #1: Coldea_Golden_Ratio_Mass.pdf