## Sunday, July 3, 2011

### New Foundational Discoveries

New Foundational Discoveries

July 2 Complex Arq-i-ology

July 2-3 Beyond Vectors

July 3 Limits of Calculus and Geometry as Vectors

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These will most likely be posted after the July 4th Holiday.

Interesting the congress of string theorist concluding- these new insights will certainly apply to the whole discipline.

Summary-

Complex Arq-i-ology is about taking the n-cube puzzles as a literal metaphor (after all it is the equivalent of taking the positive square root if we exclude the origin and negative axis in the complex plane.) Puzzle: 2 x 4 x 4 = 32 tetracubes +i32tetracubes = 64. Arrange these in different patterns to discover the I tetracube can cross both real and imaginary spaces. Compute the patterns.

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Beyond Vectors "In that vectors are intelligibly grounded by our idea of Cartesian dimensions, abstract algebraic properties including applications to infinite dimensional matrices, makes the concept, R^n and Rn+1, of vectors not the most general of space and number ideas to encompass all of physics."

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Limits of Calculus and Geometry as Vectors

"The limitations of our concept of dimensions and vectors carry over to our methods of the calculus. Beyond the supposedly clear intelligibility of vectors, numbers as linear (a primitive form of compaction really) and a general principle of centering at some unstable origin - an ill defined singularity or singularity complex- we extend the concept as a diffuse plane, a disc over which we integrate and so intelligibly mirror the complex functions.

While the Riemann surface is greater than the complex plane, so too the quasic plane is a greater concept wherein the Brane like regions do not preserve magnitude as well as the loss of directionality involved in the higher dimensions. We understand Riemann's is a logarithmic space greater than the complex plane."

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Stray thoughts today:

Of course if the idea of a natural vector basis or dimension is not good enough we have to question the idea that each dimension has one unique associahedron- not to say this view is wrong "as the method does probe into the more general quasic realm of space structures. But it is as incomplete as the vast body of analysis and the string theories itself despite the brilliant minds and elaborate formulas and language.

I find it amazing, to the outside enquiring mind for such considerations, that i to the i power and i factorial have real and computable values. Or that in a physics so based on symmetry there has to be a grounding that is not fractal like as a foundation in itself FX, of the idea of symmetries within symmetries never the less, the 8 in particular of the infinite ones as far as the complex quaterions go and of course the extensions to 240 and the like of the group hypernumbers. But a lot of this is a matter of not yet developed notations of algebra in itself.

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