Is there really such thing as an unsolvable paradox?

[CosmosCranium]

So I was reading this article that talks about how just because we are unable to explain something now, doesn't mean its unsolvable. Perhaps we are just taking the wrong approach.

 

Link removed

 

What do you guys think?

[ACG52]

I think you're just promoting your website.

[CosmosCranium]

I'm promoting a conversation. I want to hear what you guys have to say about this article. Its relative content, I'm trying to contribute.

[ACG52]

You're spamming your website. I imagine, with your advertisers, the more hits you get, the more you make.

 

If you want to promote a conversation, post your points here.

[Amaton]

So I was reading this article that talks about how just because we are unable to explain something now, doesn't mean its unsolvable. Perhaps we are just taking the wrong approach.

 

I agree with ACG52. I don't know about the forum's policy on this, but it is preferred that one provides the information here rather than reference his/her own source. The article was rather short and could be summarized, even written out entirely with due formatting, right here. (EDIT: Considering how you phrased the original post, it certainly does seem like self-promotion. Hope mods take quick action)

 

Nonetheless, the question seems sincere, and I find it interesting.

 

There are, in fact, such scenarios if one looks at it a certain way. Abstract statements certainly exist whose validities are impossible to determine with a given set of axioms. The most famous of these may be Cantor's Continuum Hypothesis. It's not a paradox, per say, but it can be neither proven nor falsified within the standard framework of mathematics, which is ZFC+Choice. See this: List of statements undecidable in ZFC.

 

In light of theoretical physics, the mathematics therein is very difficult and complex. Almost everyone suspects that a Theory of Everything will be formulated in the language of mathematics, just as all the major and matured theories of physics have been. (how such a unifying theory can work without being mathematical in nature, I don't know)

 

Before Einstein's renowned work, there were observations that simply could not be explained by previous theory. Then General Relativity emerged with development in differential geometry, and it is very accurate and consistent with what it concerns. Though the subject is miles ahead of me, I highly doubt it can be anything without due application of differential geometry. You can't mow the lawn with a sponge.

 

Likewise, any unifying theory, not necessarily a ToE, may have to be approached differently in regards to mathematics. Noncommutative geometry is a branch of mathematics that concerns the geometry of noncommutative operations. This mathematical formulation will certainly work differently than any mathematics where (for sake of simplicity) multiplication is commutative, and thus it may be possible that such a theory can only be described consistently a certain way. See Noncommutative standard model.

Edited June 2, 2013 by Amaton