Unifying Lie Algebras with Mathematical Game Theory to assist in GUT / TOE

[Dcase]

This speculative effort may be only wishful thinking, but if mathematical [geometrical] objects can be represented by Lie [and other] Algebras and Groups as well as by Mathematical Games, then this may aid in the search for a GUT / TOE.

This effort is not rigorous, but a tenuous association of analogous ideas.

1 - John Nash is probably best known for
a - Nash Equilibrium [Nobel Economics 1994]
http://nobelprize.org/nobel_prizes/economics/laureates/1994/presentation-speech.html
b - Nash “embedding theorems (or imbedding theorems) ... state that every Riemannian manifold can be isometrically embedded in a Euclidean space”
http://en.wikipedia.org/wiki/Nash_embedding_theorem

That the same mind conceived of two diverse mathematical representations suggests the possibility of a relationship between these representations.

2 - Game Theory in the History of Mathematics of 20-th Century from the Department of Mathematics, University of Rhode Island discusses the relationship to John von Neumann's Minimax Theorem and to the saddle point as ‘... an equilibrium decision point ...” for “... in which the maximum of the row minimax equals the minimum of the column maxima ...”
http://www.math.uri.edu/~kulenm/mth381pr/GAMETH/gametheory.html

This appears to suggest that any representation with saddle points may be a Nash Equilibria.

3 - Christopher J. Marzec in MATHEMATICAL MORPHOGENESIS from Institute for Biomolecular Stereodynamics, University at Albany, State University of New York discusses various symmetries [Spherical, Helices, Icosahedral, Octahedral] and accretions [Sphere and Cylinder] related to nucleic acid life and proto-life.
http://www.albany.edu/~cmarzec/

This appears to suggest that the helix is some type of attractor.

4 - Ivars Peterson in Science News ‘Surface Story: Inspired by spiral soap films, mathematicians zero in on a novel, economical, and infinite helix’ states “... At every point, a minimal surface is either flat, like a disk, or has a saddle shape ...”
http://www.sciencenews.org/articles/20051217/bob9.asp

This appears to suggest that a helix may have saddle points equivalent to Nash Equilibria.

5 - The helix is known to be a generalized geodesic.
http://mathworld.wolfram.com/GeneralizedHelix.html

6 - Richard S. Palais, Professor Emeritus at Brandeis, Department of Mathematics in
"The Visualization of Mathematics: Towards a Mathematical Exploratorium" [June/July 1999 issue of the Notices of the American Mathematical Society] aids in the visualization of helicoids and psuedospheres.
http://vmm.math.uci.edu/3D-XplorMath/DocumentationPages/VisOfMath.pdf

There may be a relationship to helicoid trajectories and psuedospheres.

7 - One form of the ‘Double Bubble’ minimal surface resembles a psuedosphere with “... one bubble torus-shaped and the other is shaped like a dumbbell ...”
http://mathworld.wolfram.com/DoubleBubble.html

One might conceive of this [our] solar system or a spiral galaxy as a double bubble psuedosphere with the sun or galactic core producing both a magnetic field and a disk that evolves into planets or stars respectively. Could this also occur at Planck gauges?

8 - From a science fictional perspective various life forms may be to nucleic acids as ‘MechWarriors’ are to humans in computer game play.

9 - The last speculation is that over 500 million years of biophysical evolution may have used various trial and error mathematical games and energy interactions [manifested as differential geometries] to provide clues about dealing with both QM and GR. Perhaps various neurosensory organs and the mechanisms of response to these inputs may assist with GUT / TOE as the study of birds did for flight and bats for sonar.

10 - Both games and groups [algebras] tend to have graph theory and bifurcation theory relationships.

 

[arivero]

'

\r\n1 - John Nash is probably best known for\r\na - Nash Equilibrium [Nobel Economics 1994]\r\nhttp://nobelprize.org/nobel_prizes/economics/laureates/1994/presentation-speech.html\r\nb - Nash “embedding theorems (or imbedding theorems) ... state that every Riemannian manifold can be isometrically embedded in a Euclidean space”\r\nhttp://en.wikipedia.org/wiki/Nash_embedding_theorem\r\n\r\nThat the same mind conceived of two diverse mathematical representations suggests the possibility of a relationship between these representations.\r\n .

\r\n\r\nSorry the bad joke, but it is disgusting to start an argument based on the asumption that John Nash had a single mind. Of course, being a living person, we have no access to the medical information, but I\'d bet he had at least two or three.'

 

[Dcase]

Evolutionary topology

'This comment attempts to demonstrate how over 500 million years of evolution [natural selection?] may use string theory topologies.\r\n\r\nThis comment addresses cellular cooperation within an organism with respect to competition between organisms using \'Auditory Space\' topological mapping for neurosensory input [with eventual output algorithms for action via cerebrum and cerebellum]. \r\n\r\nConsider an article from a special edition of Scientific American ‘Secrets of the Senses’ 12 DEC 2006 by Masakazu Konishi [CIT] “Listening with two ears” with page 30 ‘Coordinates of Sound’ diagrams [p28-35].\r\n\r\nFrom my perspective this ‘Auditory Space’ may be a stereoscopic dual [spherical] coordinate topology possibly employing a vector operator algebra similar to that of Borcherds for a 3D-space with string and time dimensions. In this example, the string dimension may be the sound energy dimension referred to as intensity by the author. Intensity may be equivalent to the amplitude of the energy string vibration or frequency. The author does discuss possible neural algorithms.\r\n\r\nA CIT press release discusses [without diagrams] this work of Konishi and Eric Knudsen awarded the Peter Gruber Foundation Neuroscience Prize in JUL 2005.\r\nhttp://pr.caltech.edu/media/Press_Releases/PR12719.html\r\n\r\nSome aspects of this material are discussed in \'Auditory Cues and Ecolocation\' from Psychology 403, Section Q1\r\n\'Animal Navigation and Wayfinding\' [Michael Snyder, U-Alberta CA]. \r\nhttp://www.psych.uAlberta.ca/~msnyder/Academic/psych403/week8/w8oh.html'