Wikipedia:Mathematical_models_in_physics. I deleted material on the Banach-Tarski paradox

[gustavolacerda]

A couple weeks ago I made a big edit on the Wikipedia article titled "Mathematical_models_in_physics", deleting some stuff that seemed to imply that "mathematics is not always faithful to physics" because of the Banach-Tarski Paradox.

I posted my justification for this here

Also here:

Comments

[jbouwens]

Quoth the server: "404"

[gustavolacerda]

Thanks. fixed.

[jbouwens]

Luckily the correct URL is embedded in there somewhere, so I checked it. Please note that it is considered good form to not post anonymously. The Wiki software has several handy tags that allow you to sign a message with your name and time etc.

[gustavolacerda]

I thought I was logged in, and assumed all that would happen automatically.

[grant_w_pollard]

If it's of interest, here is a take on this issue from a pro-category theory POV:

"The axiom of choice seems quite plausible since we are allowing "arbitrary" mappings s. In categories in which only geometrically "reasonable" mappings are allowed, the axiom of choice is usually not true; but this only points out that such categories are distinct from the category of constant sets and arbitrary maps, which itself exists as an especially simple extreme case with which to contrast the others (Cantor's abstraction). Some of the opposition to the axiom of choice stems from its consequence, the Banach-Tarski Paradox... The abstractness of the sets, correlated with the arbitrary nature of the mappings, makes such paradoxes possible, but of course such paradoxes are not possible in the real world where things have variation and cohesion and mappings are not arbitrary. Nonetheless, since Cantor mathematicians have found the constant noncohesive sets useful as an extreme case with which continuously variable sets can be contrasted