M Theory Lesson 61
The purpose of this post is mainly to invite Doug, one of our oldest companions, to comment here on the general direction of the Lesson series. Doug expressed an interest in doing so back in Lesson 59. So just this once, Doug can post a series of long comments here. I hope this will encourage him to set up his own blog. After all, anyone is free to do so!
In Lesson 59 we were looking at theta series for lattices. For the Leech lattice this involved the Ramanujan function, which is a Fourier series for the modular discriminant. Fourier coefficients for cusp forms were part of Conrey's motivation in looking at even moments for the Riemann zeta function.
In Lesson 59 we were looking at theta series for lattices. For the Leech lattice this involved the Ramanujan function, which is a Fourier series for the modular discriminant. Fourier coefficients for cusp forms were part of Conrey's motivation in looking at even moments for the Riemann zeta function.
posted by Kea | 12:48 PM
10 Comments:
Hi Kea,
I will make a different comment in this thread for about 5 of the previous M Theory Lesson ##?
Hi Doug. Comment on any of the posts that you want to. Cheers.
Also how does one comment to the Carl_B blog when his last post was:
Wednesday, February 21, 2007
http://carlbrannen.blogspot.com/
I want to ask him if the following three articles might be different pespectives of the same phenomena if considered as helical trajectories?:
a - David Hestenes, 'The Kinematic Origin of Complex Wave Functions'
Physics and Probability: Essays in Honor of Edwin T Jaynes,1993, 153-160, WT Grandy, PW Miloni, Cambridge U. Press, Cambridge
http://modelingnts.la.asu.edu/pdf/Kinematic.pdf
b - Lisa Randall and R Sundrum, 'A Large Mass Hierarchy from a Small Extra Dimension'
Phys.Rev.Lett. 83 3370-3373 (1999) http://arxiv.org/abs/hep-ph/9905221
c - Nima Arkani-Hamed, S Dimopoulos, and G Dvali, 'Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity'
Phys. Rev D 59, 086004 (1999)
hep-ph9807344
RE: M Theory Lesson 59
I reaaly respect this work 'Sphere Packings, Lattices and Groups' by JH Conway and NJA Sloane.
My only concrn is that perfect sphroid packing seem to be most consistent with bacground independence,
I tend to favor perturbation so would prefer nearly spheroidal ellipses.
Consider Elliptical Packing:
Science 13 February 2004:
Vol. 303. no. 5660, pp. 990 - 993
DOI: 10.1126/science.1093010
Reports
'Improving the Density of Jammed Disordered Packings Using Ellipsoids'
Aleksandar Donev,1,4 Ibrahim Cisse,2,5 David Sachs,2 Evan A. Variano,2,6 Frank H. Stillinger,3 Robert Connelly,7 Salvatore Torquato,1,3,4* P. M. Chaikin2,4
Abstract:
Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction . It is also well known that certain random (amorphous) jammed packings have 0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely — up to = 0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M's Candies — and even approach 0.74 for ellipsoids with other aspect ratios. We suggest that the higher density is directly related to the higher number of degrees of freedom per particle and thus the larger number of particle contacts required to mechanically stabilize the packing. We measured the number of contacts per particle Z 10 for our spheroids, as compared to Z 6 for spheres. Our results have implications for a broad range of scientific disciplines, including the properties of granular media and ceramics, glass formation, and discrete geometry.
RE: M Theory Lesson 58
I have been reading the June 2007 issue of Scientific American.
FEATURE ARTICLES
1 - BIOLOGY
'A Simpler Origin for Life'
By Robert Shapiro
The sudden appearance of a large self-copying molecule such as RNA was exceedingly improbable. Energy-driven networks of small molecules afford better odds as the initiators of life
Considers the possibility that Boron may have been necessary for stable pentose rings [or tilings in nature].
2 - PARTICLE COSMOLOGY
'When Fields Collide'
By David Kaiser
The history of particle cosmology shows that science can benefit from wrenching changes
Includes comments attributed to Lee Smolin.
3 - INFORMATION TECHNOLOGY
'Breaking Network Logjams'
By MICHELLE EFFROS, RALF KOETTER and MURIEL MÉDARD
An approach called network coding could dramatically enhance the efficiency and reliability of communications networks. At its core is the strange notion that transmitting evidence about messages can be more useful than conveying the messages themselves
Could this relate to error-correcting codes?
4 - INNOVATIONS
'Seeing Triple'
By Stuart F. Brown
Anticipated for decades, machines are finally displaying real objects in three true dimensions
Better Imaging for all types of physics?
5 - GAME THEORY
'The Traveler's Dilemma'
By Kaushik Basu
When playing this simple game, people consistently reject the rational choice. In fact, by acting illogically, they end up reaping a larger reward - an outcome that demands a new kind of formal reasoning
Can particles play games with one another?
RE: M Theory Lesson 57
"... Bilson-Thompson diagrams for left and right handed electrons are formed with three strands, each with a full negative twist representing a one third charge ..."
Right and left isomers would still have an annihilation transformation as matter and anti-matter.
Ignoring mass, considering only charge:
I am going to use
d and ddd for 1/3 negative charge and the -1 charge
u and uuu for 2/3 positive charge and the +2 charge
These homogeneous tri-quarks are allowed in QCD, but not in the standard model.
With recognized heterogeneous tri-quarks
ddu for the neutron
duu for the proton
total charge is zero in equilibrium
with
ddu duu ddd
[neutron proton electron]
and
ddd uuu ddd
[electron di_proton[+2]? electon]
which might be able to transform with a reciprocal exchange of d for u into
ddu duu ddd
[neutron proton electron]
Thus charge may be a zero-sum-game with conservation, perhaps with symmetry folded rather than broken?
I do not yet know how to incorporate mass unless there exists something like a Higgs particle(s) or
unless inductance [electricity] is used rather than mass [mechanics]
Yet matter v anti-matter may be a non-zero-sum-game?
'Why Is The Universe More Partial To Matter Than Antimatter?'
June 24, 2006, Sciemce Daily
http://www.sciencedaily.com/releases/2006/06/060624115839.htm
RE: M Theory Lesson 60
The Hodges papers
1 - Twistor diagram recursion
I prefer the round or elliptical diagrams.
Section 7 Twistor quilts.
I am going to play with the wording.
Quilts should have a weave.
The 'fabric of the cosmos' should have a weave.
If one loks at this 'weave' from "Clint Sprott's web server in the Physics Department at the University of Wisconsin - Madison":
there is a curved quality which might be a helix or a spiral.
http://sprott.physics.wisc.edu/fractals/collect/1999/White%20Weave.jpg
2 - Helicity-independent formalism
I have difficulty understanding the independence of helicity from twistor theory.
I really suspect that helicity is natural to particles in the cosmos or HEP because of the David Hestenes, 'The Kinematic Origin of Complex Wave Functions' paper and other papers on 'unseen dimensions' which may be helical trajectories.
http://modelingnts.la.asu.edu/pdf/Kinematic.pdf
RE: M Theory Lesson 42
Demonstration of strategic v space dimensions.
I will be mixing some different terminologies:
For the [3D_space] cube diagram, let:
O be the origin of edge vector X
I be the end of edge vector Y
E be the end of edge vector Z
O is then antipodal E
or O->E is a;
volume vector, 3-vector, 3-blade.
O->I is a:
surface vector, 2-vector, 2-blade.
X, Y, Z are examples of:
Edge vector, 1-vector, 1-blade.
There are six permutations of how three_edge_vetors [strategic-D] may go from vertex [or Node(s)] O to E, as if using the edges as rails or roads. Only one is the X->Y->Z as diagrammed.
There are three permutations of how "one_edge_one_surface_vectors" [strategic_D] may go from O to E as if using sea or air travel.
Likewise there are three permutations of how "one_surface_one_edge_vectors" [strategic_D] may go from O to E as if using sea or air travel.
There is one "volume_vector" from O to E as if in space travel.
Thus there are 13 possible strategic-D between two antipooidal nodes in 3D cubic space, but not all may be usable.
Kea,
Thank you for allowing me to comment on a few thoughts about some of your past M Theory Lesson(s) after their initial publication.
Have you seen these blog topics?:
1 - Cosmic Variance 'Hunt for the Higgs!.
The image appears to be composed of ribbons and braids [strings] with at least one of the latter a helix.
http://cosmicvariance.com/2007/05/30/hunt-for-the-higgs/
2 - Asymptotia ‘Taking the Time to Work it out’
Itzhak Bars and his website discussing 'Two-Time Physics' are featured.
http://asymptotia.com/2007/05/15/taking-the-time-to-work-it-out/#more-1206
Could these be strategic time-D?
a - There has been an arxiv paper discussing the idea of two time scales from a strategic perspective [of mathematical game theory] in robotics.
H Iizuka and T Ikegami [U_Tokyo], ‘Adaptability and Diversity in Simulated Turn-taking Behaviour’, section 3.2, p 5, 2003, used the “vehicle navigation time scale” and “neural computation time scale” in presuming “... navigation ... is faster than ... neural ...”
http://arxiv.org/PS_cache/nlin/pdf/0310/0310041v1.pdf
b - There may be evidence that animals such as humans may strategically use two time scales. The autonomic nervous system [ANS] and somatic or central nervous system [CNS] behave differently within the same standard measure of time. The ANS is nearly immediate while the CNS allows for a calculated response which may have varying times of action.
U_Arizona contrasts this in ‘Autonomic versus Somatic NS’ [or CNS].
http://microvet.arizona.edu/Courses/VSC401/autonomicNervous.html
Thanks, Doug. The 'two time' links look interesting.
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