multidimensional situs

[AntonioLao]

In 1905, the English translation of the French mathematician Henri Poincaré’s book Science and Hypothesis was published. Chapter 2 was titled “Mathematical Magnitude and Experiment.” In this chapter Poincaré reintroduced a new branch of mathematics called algebraic topology. Following the section on the mathematical continuum of several dimensions, Poincaré wrote: The magnitudes need not always be measurable; there is, for instance, one branch of geometry independent of the measure of magnitude, in which we are only concerned with knowing, for example, if, on a curve ABC, the point B is between the points A and C, and in which it is immaterial whether the arc AB is equal to or twice the arc BC. This branch is called Analysis Situs. Its continued developments by Poincaré and others led to his earlier conjecture of 1904, which is now known as the Poincaré Conjecture for 3-manifold. It is one of the 7 Millennium Problems, which is now presumed solved by the somewhat elusive and reclusive Russian mathematician Grigory Perelman. In 2006, he declined the Fields Medal, the Nobel Prize equivalence for mathematics. He also will not accept the $1 Million reward offered by Clay Institute, sponsor of the Millennium Prize.

Poincaré (1854-1912) was the first to look for topological invariants applicable to higher dimensional manifolds. He invented the 3rd result of the classification theorem in addition to Euler characteristic and orientability. Although the Poincaré Conjecture was proved true for 5 and higher dimensions by Stephen Smale in 1960 and for 4-manifold by Michael Freedman in 1981, the 3-manifold eluded most mathematicians but not until Perelman began posting papers in the Internet indicating his proofs and solutions for the 100-year plus old problem.

[SB_UK]

Sections linked sequentially in red, blue, green and then purple.

http://en.wikipedia.org/wiki/Poincaré conjecture

The claim concerns a space that locally looks like ordinary three dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold). The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is just a three-dimensional sphere.

... ... continuously tightened to a point ... ..

http://en.wikipedia.org/wiki/Fractal

Roots of mathematical interest in fractals can be traced back to the late 19th Century; however, the term "fractal" was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured.

... ... 3-space Poincaré spheres budding 3-space Poincaré spheres orthogonally budding ... ...

http://en.wikipedia.org/wiki/Virus

Most animal viruses are icosahedral or near-spherical with icosahedral symmetry.

http://en.wikipedia.org/wiki/Homology_sphere

The Poincaré homology sphere (also known as Poincaré dodecahedral space) is a particular example of a homology sphere. Being a spherical 3-manifold, it is the only homology 3-sphere (besides the 3-sphere itself) with a finite fundamental group. Its fundamental group is known as the binary icosahedral group and has order 120.

The claim concerns a space that locally looks like ordinary three dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold). The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is just a three-dimensional sphere.

~*~

A defined simple geometry which gives rise to outer concentric orthogonally arrayed similarly defined geometries
- each of which giving the false impression that they're spherical spheres (and not homology spheres)

- each of which (each falsely masquerading spherical sphere) (each emergent structure (each concentric ring)) reducible down to a simple standing wave (2 spatial / 1 temporal dimension).

An exceptionally excellent Theory of Everything dude

[SB_UK]

An exceptionally excellent Theory of Everything



http://www.youtube.com/watch?v=YLlYQQrHmh8



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