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from the BASIC:-But-Any-String-Is-Complicated! dept.
Carlos Shahbazi has presented the first two articles of a series that introduce the layman to the basics of String Theory.
link: http://mappingignorance.org/2015/05/06/the-geometry-of-string-theory-compactifications-i-the-basics/
"The sphere is also a simple example of a compact manifold, which is a particular class of manifolds of utmost importance in String Theory compactifications, as we will see in a moment. The compactness condition can be intuitively understood using Euclidean space. A manifold embedded in Euclidean space, as the sphere in figure 3, is compact if and only if it is bounded, namely it is contained in a finite size region of E and it is closed, namely it contains all its limiting points."
[The second article is "The geometry of String Theory compactifications (II): finding the Calabi-Yau manifold" -Ed.]
If that's too easy for you; the same author also has "Black hole solutions of N=2, d=4 super-gravity with a quantum correction, in the H-FGK formalism"
link: http://www.mathpubs.com/author/Carlos+S.+Shahbazi
Original Submission
(Score: 2) by c0lo on Sunday July 26 2015, @09:00PM
Inconsequential.
The mathematicians (and physics theoreticians) don't deal with the trivial matter of map navigation, for them the existence of an isomorphism* between the two maps is more than enough (remember? a topologist is a mathematician who can't tell the difference between a coffee mug and a donut).
And you know what? They are usually demonstrable right quite a long time before somebody find a domain of applicability for their distorted view of the mundane reality.
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* supplementary, to be useful, the isomorphism need to preserve intact some properties of the model, all the other properties be damn'd (as inconsequential).
You know? Pretty much like car analogies, except that they need to be rigorous analogues in the... ummm... matters that matter.
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 2) by hendrikboom on Monday July 27 2015, @06:13PM
The isomorphisms are topological; in particular, stretching and shrinking is allowed. But even with stretching and shrinking, you can only map local pieces of the surface of a sphere 1-1 onto a Euclidean plane. Mapping a whole sphere 1-1 onto a plane is not possible. You have to leave out at least one point.
That's why the mathematicians invented this whole local patches thing. They stitch complicated manifolds together out of patches, much as a seamstress might sew a pair of pants out of many ordinary pieces of cloth.