Measurement E8
Carl Brannen's E8 applet now has a sidebar link. Also check out his new preon E8 blog post and don't forget the oodles of E8 facts at Tony Smith's site. For the best kindergarten introduction to this kind of symmetry see the Neighbourhood of Infinity.
posted by Kea | 9:29 AM
7 Comments:
Hi Kea,
Although the 2D images of E8 are magnificent, I suspect that 3D images would be even better.
Thanks to the mathematics of chemistry, EE and physics, 3D medical imaging appears to be more powerful than 2D mathematical representations.
NMR Imaging:
Felix Bloch [engineer and physics] and Edward Mills Purcell [electrical engineering and physics] shared the physics Nobel Prize in 1952 "for their development of new methods for nuclear magnetic precision measurements and discoveries in connection therewith".
http://nobelprize.org/nobel_prizes/physics/laureates/1952/
Richard Ernst ["Diplomierter Ingenieur Chemiker"] was awarded the chemistry Nobel Prize in 1991 "for his contributions to the development of the methodology of high resolution nuclear magnetic resonance (NMR) spectroscopy”.
http://nobelprize.org/nobel_prizes/chemistry/laureates/1991/ernst-autobio.html
For imaging “biological macromolecules” with NMR, the chemistry Nobel Prize in 2002 was shared by Kurt Wüthrich [mathematics and physics], Koichi Tanaka [electrical engineering] and John B Fenn [physical chemistry].
http://nobelprize.org/nobel_prizes/chemistry/laureates/2002/
Nuclear magnetic resonance (NMR) uses “quantum mechanical magnetic properties” ... “intrinsic magnetic moment and angular momentum” ... “in accordance with the equation for the Larmor precession frequency.”
http://en.wikipedia.org/wiki/Nuclear_magnetic_resonance
Reinhard Wimmer has a PDF on NMR imaging,
http://www.agnmr.at/handouts2001/Wimmer/Imaging-Niederoeblarn2001.pdf
The blog Biocurious has a post ‘Protein calms the waters’. I again think ‘liquid [water] may have solenoid-like activity from the 3D image.
http://biocurious.com/protein-calms-the-waters#c001822
Biomechanics:
The blog Loom has a post ‘Rules of the Swarm’ which refers to the webpage of Iain Couzin [Princeton, Oxford, Bath Collective Animal Behaviour PhD]. There is a listing of recent publications on “swarm mechanics” [my term] which I think can be modified to study the rings of Saturn and the asteroid belt. The first paper deals with a multi-discipline approach. The second paper ’From disorder to order in marching locusts’ refers to theoretical physics in the abstract.
http://scienceblogs.com/loom/2007/11/13/rules_of_the_swarm.php#comments
doug said "... Although the 2D images of E8 are magnificent, I suspect that 3D images would be even better. ...".
How about 4D ?
A friend of mine, Michael Gibbs, wrote a java applet that lets you see a stero image (for 3D) with color coding for the 4th dimension (red to green to blue).
You can play with it at
http://members.aol.com/jmtsgibbs/draw4d.htm
Select stereo color and the 600 cell, and then choose either cross-eyed or wall-eyed for the way you prefer to see stereograms.
The 600 cell is a 4-dim polytope with 120 vertices, which make up half of the 8-dim 240 E8 vertices.
By moving the slide-bars on the sides of the window, you can rotate the image in various ways.
Tony Smith
PS - I have some related material on my web site, including the page at
http://www.valdostamuseum.org/hamsmith/24anime.html
PPS - I have a pdf file abour E8 and Cl(8) on dot Mac at
http://web.mac.com/t0ny5m17h/Site/E8Cl8phys.pdf
It has some pictures about how E8 includes E7, E6, etc.
Hi,
I wrote critical comments about Lisi's theory at my blog.
To me the only reasonable option is replacement of gauge group with Kac-Moody algebra of noncompact E_8. It seems that E_8 Kac Moody representations might be obtained in stringy picture (M^8 coordinates as conformal fields at partonic 2-surface) in the dual formulation of TGD with M^8 as imbedding space.
Also the standard model symmetry group has rank 8 (Poincarexstandard model symmetry group has translations of M^4 plus SU(3)xU(2)_ew as Cartan alegbra) so that it results more naturally as Kac-Moody type algebra and there is no problem with statistics.
Since partonic 2-surfaces are 2-dimensional, E_8 is at least formally obtained using the standard construction of tachyonig ground state using ordered exponents of quantized M^8 coordinates. Bosons with effective spin 1/2 could correspond to anyonic statistics based on braiding rather than permutation as exchange operation.
Family replication gives in TGD rise to dynamical SU(3) permuting fermionic genera g=0,1,2 for which partonic 2-surface has always Z_2 conformal symmetry. SU(3)triality replaces Lisi's triality.
Lisi's identification of genera is not consistent with that in TGD since family SU(3) cannot define conformal symmetry (would require that genus of partonic 2-surface depends on its point!).
In TGD E_8 and many other rank 8 algebras could be realized by standard construction and my interpretation would be that TGD Universe is able to emulate various gauge and Kac-Moody symmetries as a kind of Turing machine. The conjecture is that almost any ADE gauge Lie algebra or ADE Kac-Moody algebra allows this kind of emulation.
Hi Tony,
1 - Thanks for the link to the 4D polytope viewer.
From MathWorld:
Polychoron: A polytope in four dimensions. Polychora are bounded by polyhedra.
http://mathworld.wolfram.com/Polychoron.html
Regular Polychoron:
“the 600- and 120-cells are dual to each other”
http://mathworld.wolfram.com/RegularPolychoron.html
2 - I am particularly interested in the E8 and Monster relation, especially since Edward Witten has apparently embraced the Monster.
3 - For “E8 and Cl(8) on dot Mac“, I can view only Blank [underlined] E8 and Cl(8).
I will be getting a new computer next quarter in 2008 which hopefully will be able to employ the graphics from this site.
4 - Some sites for viewing 3D proteins from NMR:
The Protein Data Bank [PDB] has 47403 Structures.
http://www.rcsb.org/pdb/home/home.do
There are several different viewers.
http://www.pdb.org/robohelp/molecular_viewers/introduction_to_molecular_viewers.htm
I like Jmol best, most often using First Glance in Jmol with NMR.
http://molvis.sdsc.edu/fgij/index.htm
For Molecule of the Month [NOV 07]: Multidrug Resistance Transporters, Enter a PDB identification code here as 2onj found in more ... p2.
Rotating cartoon with option for other styles of view.
http://molvis.sdsc.edu/fgij/fg.htm?mol=2onj
Doug, if you insist on posting so many links (sigh), could you please linkify them with < a href = etc. Please keep posts on topic and brief.
Hi Kea,
Sorry for the excessive links.
I am unsure how to use < a href = etc.
I will probably have to upgrade to a computer with better graphics capabilities sometime next quarter 2008.
Presently I am a commenter not a blogger.
I may begin a blog on multidiscipline mathematics with a focus on my understanding of biomathematics.
I am leaning towards wordpress rather than blogger.
Thanks for your patience.
Hi Kea,
I finally found instructions for using HTML tags
Still an old dog learning new tricks.
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