Set Theory in Javascript

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Vortex Solution to Navier Stokes Equations

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This is a solution I found to the Navier Stokes equations . It uses the flow lines of the Hopf Fibration (which is basically just a way of covering the entire 3D space in circles). The flow lines can be seen in this image below: You can see my paper here. Solution to Navier-Stokes equation . Unfortunately I won't get a million pounds for winning the Clay Millennium prize because this is a compressible not incompressible solution. :( Oh, well. Nice try! I think it's pretty nice anyway. :) Also it uses the nice identity: which paramaterizes the Pythagorean quadruples!
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Conjugate of Lie Algebra

Conjugate of Lie Algebra A little article noting the similarities between momentum conservation (continuous) and charge conservation (discrete). We all know that the conjugate coordinate to position is momentum . Thus a term such as  ∫O(-k)O(-q)O(k+q)dk 4 dq 4 = ∫O'(x)O'(x)O'(x)dx 4 But a lie group given by it's root vectors (charges) also has a similar form which looks a lot like momentum: O {-A} O {-B} O {A+B} + (A n )O {A} O {-A} O n So we should be able to find conjugate variables to the root vectors. So we can write the above as: O' C O' C O' C The O' C  being linear combinations of the Os. In the case of E 8 , the {A} are 8 dimensional unit vectors. One difficulty are the neutral particles, O n  , which seemingly have no equivalent in the momentum picture. Such a term would look like:  ∫O(k)O(-k)kμAμ(0)dk 4 =  ∫O(x)Bμ∂μO(x)dx 4   which is not Lorenz invariant.... [ unless O(x) were spinors and Bμ were Dirac matrices?? B...
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M-Theory equals Loop Quantum Gravity?

A string world sheet can be decomposed into a sum of Feynman diagrams (graphs). Likewise a membrane should be decomposed into a sum of graphs also (or spin-networks). Hence Loop Quantum Gravity should be considered as a membrane theory. The differences are that Loop Quantum Gravity is a gravity only theory with no supersymmetry. It only exists in 4 dimensions whereas M-Theory exists in 11 dimensions.
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