Eureka! A simple underlying
form generates our universe:
An IO-Sphere which turns inside out [evert],
outside in [invert],
at the cubed speed of light.
The sphere which shapes our world
Extended animation of Bill
Thurston's "Outside In"
If humanity is indeed the measure of the cosmos,
whatever primal structure which creates the universe should
echo the key attributes of cosmos nature and our bodies.
We are powered by vital functions such as the human lungs,
heart and sex organs. Scroll at right to see: The contraction
of the heart. Ribs over a membrane which expands and contracts.
A phallic penetration --the reverse of which is the drawing
apart which powers cell division. And much more.
human-centered approach regards the human view of the universe
as the defining perspective on the creation. Therefore, as humanity
lives on a sphere, a sphere must be the key structure.
I became convinced that because a mirror plane runs down our bodies;
and as mirrors turn things inside-out; then an inside out sphere
must be the answer.
Yet, such a primal universal structure must surely underlie the
form of our vital human organs; must drive key aspects of the
cosmos, integrate with nuclear physics; and explain the mechanisms
Could I really find all these features in one all-encompassing
fundamental structure? I went looking. What I eventually found
took my breath away.
A number of mathematical solutions have been developed to evert
a sphere(see Footnote). I found Bill Thurston's 1970's topological
technique to turn a sphere inside-out, while also minimizing it's
surface bending energy. Thurston's solution was completely unrelated
to our topic. Just an exercise in topology. Yet it fit the criteria
The true IO-Sphere incorporates a "cubing" of the sphere
not seen in the above animation. (See Part
1). And, of course, the real eversion runs way beyond
our scientific and human perception --at the cubed speed of light.
By the way, the above is not the only way in which the
universal sphere turns inside out. There is more to this story
(touching on the wave nature of reality). To be detailed in an
article available online soon.
END PART 2: Sphere
Eversion: Oscillating the Whole Universe
SEE PART 1:
A Cubed IO-Sphere Creates the World
& SEE ALSO: The
Mirror Mind of the Cyclic Universe
Fintan Dunne, 9th October, 2003
Copyright © TreeIncarnation.com
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EXTRACT from A
brief history of sphere eversions by Silvio Levy
There are a number of topological methods for turning a sphere
inside out, while avoiding a crease and minimizing surface bending
energy. The above animation is an extended version of Bill
In" sphere eversion. This in turn arose out of Steve
Smale's 1957 discovery that a sphere can be turned inside out
--using smooth motions and self-intersections.
The history of sphere eversions starts in 1957, when Stephen
Smale proved a very general fact about immersions of spheres [Smale
1958]. One consequence of his proof is that there should be
a way to turn the sphere inside out by a regular homotopy.
For a little while, this claim met with skepticism. The mathematician
Raoul Bott, who had been Smale's graduate adviser and who is one
of the founders of differential topology, flatly told Smale that
he was wrong, and explained why he thought so. Later he became
persuaded that Smale's reasoning was correct, but he, like many
other mathematicians, was still frustrated by the inscrutability
of Smale's proof, and wished to see a more direct sphere eversion.
In 1961, Arnold Shapiro invented the first explicit eversion,
but did not publish or divulge it widely. He did explain it to
the French mathematician Bernard Morin, who passed it on to his
compatriot René Thom, and eventually this eversion became
more widely known thanks to Morin and George Francis, and especially
to the article [Francis
and Morin 1987].
The first time that most mathematicians and the public at large
became aware of an explicit eversion was when Tony Phillips ...published
a beautifully written article in Scientific American [Phillips
People began searching for simpler and more symmetrical solutions.
Morin, in particular, devised in 1967 a new eversion that was
simpler than all the preceding ones in terms of the number of
crossings. Charles Pugh made wire-mesh models of various stages
of it, and Nelson Max digitized these models and used them as
the basis for the movie [Max 1977].
The rendering of the evolving sphere was done by Jim Blinn; here
is a frame:
In the mid-seventies, Bill
Thurston developed his idea of corrugations. This gives another
route for the eversion, as explained in Outside
In, and it can also be applied to other more general situations.