compactification vs. fractal

[AntonioLao]

The biggest mathematical or physical argument to ever come out of superstring theory is dimension compactification. How and why does nature choose to present herself in 3-space and 1-time dimension and curled the rest into infinitesimal insignificance? Compounding this quandary perplexity is the fact the source of mass generation lies within a significant infinitesimal and the mother of all infinitesimals is the big bang singularity herself, some proposed there was none. On the other hand, a non-Abelian Yang-Mills gauge theory asserts the existence of continuous differentiable compactified rotation Lie groups.

These infinitesimal rotation groups can be represented by the unitary operator exp(iq) on the unit circle of a complex plane centered at the origin (0,0) whose Hermitian conjugate is exp(-iq) where the angular measure q is expressed in rational multiples of p radians. The products of all conjugate pairs are gauge invariance of value unity. For the quantum extension, exp(±iq) become known as the phase factors and q is replaced by the dimensionless ratio of a quantum of action or quantized angular momentum over its uncertainty constant (ħ), which can be expressed in 3 different equivalent differential paths: Dx×Dp³ ħ, Df×DJ³ ħ, and Dt×DE³ ħ. For a succinct presentation see Quantum Mechanics, pages 7 and 8, a classic textbook by world famous L.I. Schiff (1915-71).

However, if these quantum infinitesimal rotation groups are replaced by squares symmetric singular Hadamard matrices and using yin-yang algebra then it is easier and also more logical to introduce fractal dimensions as reciprocals of matrix dimensions. For examples: a 2x2 matrix has fractal dimension ½, 3x3 is 1/3, 4x4 is ¼ 5x5 is 1/5, and 6x6 is 1/6. Furthermore, a 4x4 can be built up using 4 of 2x2 submatrices, likewise, 6x6 by 4 of 3x3 or 9 of 2x2 submatrices. All 11 dimensions matrices have fractal dimensions of 1/11. Now, sensibly, these can be the results of compactification. It is notable in their historical developments that Pauli’s spin matrices are 2x2 complex imaginary nonsingular, Gell-Mann’s 3x3 complex imaginary nonsingular, and Dirac’s 4x4 complex imaginary nonsingular. Nonetheless, all Hadamard matrices are real symmetric, serving as their own Hermitian conjugates.

[mkirkpatrick]

Folding in, life preparing for expression known as involution,a principle folded within a
principle,prehaps also expressed as Ying prior to the birth of Yang?Could also be seen
as compactification!

Unfolding,life becoming expressed,consciousness dawning,known as evolution,momentary
pause,unfolding sequence commences,birth of fractalcality,Yang comes online,dual spin
now fully "releases life essence into relative universal consciousness"


Just a few thoughts Antonio on your excellent thread starter.



regards michael.

[AntonioLao]

Then is there such a thing as separated fractal consciousness? If mine is 1/3 and yours is 1/2 you are at a higher level of consciousness than me. To equalize our combined consciousness is to find the common denominator which is 6 then yours becomes the equivalent fractal consciousness of 3/6 and mine becomes 2/6 added up to 5/6 which is higher than our individual separate consciousness.

[mkirkpatrick]

Then is there such a thing as separated fractal consciousness? If mine is 1/3 and yours is 1/2 you are at a higher level of consciousness than me. To equalize our combined consciousness is to find the common denominator which is 6 then yours becomes the equivalent fractal consciousness of 3/6 and mine becomes 2/6 added up to 5/6 which is higher than our individual separate consciousness.

I can understand that question Antonio,seperated fractal consciousness?Prehaps,as a flower unfolds,several of them on the "same stem" will all be slightly more open,or closed
as its immediate neighbour;therfore if that were the case,we as "mankind enmass" are
all at differing (fractal)levels of unfoldment,but all firmly held by the one branch!



regards michael.