Saturday, February 26, 2005

Mersenne Primes and Censorship

Lubos Motl commented at his blog site about the largest known Mersenne prime , which is 2^24,036,583 -1. This inspired me to write a comment copied below (I have added a couple of links and added some detail).

....Not only Mersennes ....

Mersenne primes are in Topological Geometrodynamics framework the most interesting primes since they correspond to most important p-adic length scales. Only Mersennes up to M_127 =2^127-1 are interesting physically since next Mersenne corresponds to a completely super astrophysical length scale. M_127 corresponds to electron whereas M_107 corresponds to the hadronic length scale (QCD length scale). M_89 corresponds to intermediate boson length scale. There is an interesting number theoretic conjecture due to Hilbert that iterated Mersennes M_{n+1}= M_{M_n} form an infinite sequence of primes: 2,3,7,127,;M-_{127},.... etc. Quantum computers would be needed to kill the conjecture. Physically the higher levels of this hierarchy could be also very interesting.

...but also Gaussian Mersennes are important in TGD Universe

Also Gaussian primes associated with complex integers are important in TGD framework. Gaussian Mersennes defined by the formula (1\pm i)^n-1 exist also and correspond to powers p=about 2^k, k prime. k=113 corresponds to the p-adic length scale of muon and atomic nucleus in TGD framework. Neutrinos could correspond to several Gaussian Mersennes populating the biologically important length scales in the range 10 nanometers 5 micrometers. k=151,k=157,k=163, k=167 all correspond to Gaussian Mersennes. There is evidence that neutrinos can appear with masses corresponding to several mass scales. These mass scales do not however correspond to these mass scales but to scale k=13^2=169 about 5 micrometers and k=173. The interpretation is that condensed matter neutrinos are confined by long range classical Z^0 force predicted by TGD inside condensed matter structures at space-time sheets k=151,...,167 and those coming from say Sun are at larger space-time sheets such as k=169 and k=173. p-Adic mass calculations are briefly explained here and here, where also links to the relevant chapters of p-Adic numbers and TGD can be found. That Gaussian Mersennes populate the biologically most interesting length scale range is probably not an accident. The hierarchical multiple coiling structure of DNA could directly correspond to these Gaussian Mersennes. The ideas about the role of Gaussian Mersennes in biology are discussed briefly here can be found. For more details see the chapter Biological realization of self hierarchy of "TGD Inspired Theory of Consciousness...".

...and how Lubos Motl responded...

Here is Lubos Motl's response which reflects his characteristic deep respect of intellectual integrity: "Matti - well, let me admit that I don't believe any of the things about "TGD" you wrote." The response was not surprising in view of what I have learned about Lubos Motl's typical behavioral patterns. I wonder whether the open censoring of ideas and opinions which do not conform with those of hegemony relates to change that has occurred during the regime of Bush. For instance, in a recent poll it was found that about one half of student agreed when it was asked whether the full freedom of speech guaranteed in constitution law should be restricted. Food for a worried thought! My response, which I unfortunately did not store to my computer, was related to the basic trauma suffered by theoretical physicists at the end of the era of hard-boiled reductionism. It could be called Planck length syndrome and manifests itself as desperate attempts to explain all elementary particle masses in terms of Planck mass scale although the first glance at elementary particle mass spectrum demonstrates that there are obviously several mass mass scales involved: electron, mu, and tau or quarks simply cannot belong to same multiplet of symmetry group in any conceivable scenario based on a unifying gauge group. p-Adic length scale hypothesis resolves the paradox and allows to understand among other things the basic mystery number 10^38=about 2^127-1 (largest Mersenne prime of physical signficance in human scales) of physics. Also a far reaching generalization of the scope of what physics can describe emerges: p-adic physics is physics of cognition which must be also a part of theory of everything. The response of Lubos is a school example about how difficult it is to communicate new, radical, and working idea. Other typical and equally brilliant response would have been "You cannot be right because Witten would have discovered it before you!". Matti Pitkanen


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