Looking for a web-source of info on Perelman/Poincare

[Kyriakos]

Some source which is to be trusted as having no mistakes, and present the work of Perelman on the Poincare question about the 2D ants walking in a plane which may be curved or not.

Ideally i would buy a book, but the books on that tend to cost upwards of 30 euros, so for the time being that is not an option

 

[brennan]

What's your interest, out of, um, interest?

 

[Kyriakos]

More general, for the time being.. i read that Perelman solved this famously a few years ago, and it used to be one of the so-called 'millenium prize problems'. Furthermore i was wondering about topology as a math category for some time now (i know it originates officially with Gauss, in the late 18th century, but not much more really, apart from stuff about forms altering or not to other forms in a finite number of steps given a set symmetry system) and i suppose this Poincare question is centered on that.

 

[brennan]

We figured out that space has to be modelled with an extra dimension to take account of gravity. I tend to view that as an object lesson.

 

[Kyriakos]

Not sure how you mean, but would it have to do with the ambiguousness inherent in any axiom-based system if it does not also feature some meta-parameter set to exist outside of the system itself? (cause that would still potentially be '1 more dimension' or something of that variety, and it is part of my current study/presentation of some Eleatic/Platonic stuff)

 

[brennan]

It proves that you don't have to be able to perceive a dimension directly to see evidence that it exists - But that may not be what you mean.

 

[Kyriakos]

It proves that you don't have to be able to perceive a dimension directly to see evidence that it exists - But that may not be what you mean.

It is of interest to me At any rate the Eleatics (eg Parmenides and his student Zeno) argued that 'possibly' one can identify with logic the existence of a next plane of categories/eternal types (so-called archetypes in platonic terms), and that this would back the work on any previous/lower system of thought (ie the human one).

At any rate no final answer is given. Even Zeno -with his paradoxa and so on- does not aim to prove if that next and independent of human thought, plane of stable reality, exists or not. Instead he aims to show that those claiming it cannot exist are 'more evidently in the wrong' than Parmenides who argues it possibly does exist.