Question: I'm always intrigued by the lack of numerical evidence from experimental mathematics for or against the P vs NP question. While the Riemann Hypothesis has some supporting evidence from numerical verification, I'm not aware of similar evidence for the P vs NP question. 

Additionally, I'm not aware of any direct physical world consequences of the existence of undecidable problems (or existence of uncomputable functions). Protein folding is NP-complete problem but it appears to be taking place very efficiently in biological systems. Scott Aaronson proposed using the NP Hardness Assumption as a principle of physics. He states the assumption informally as "*NP-complete problems are intractable in the physical world*". 

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> Assuming NP Hardness Assumption, Why is it hard to design a scientific experiment that decides whether our universe respects the NP Hardness Assumption or not?
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Also, Is there any known numerical evidence from experimental mathematics for or against $P\ne NP$?

**EDIT:** Here is a nice presentation by Scott Aaronson titled [Computational Intractability As A Law of Physics](http://www.scottaaronson.com/talks/colloq2.ppt)

Answer: 
The definitions of "polynomial time" and "exponential time" describe the limiting behavior of the running time as the input size grows to infinity. On the other hand, any physical experiment necessarily considers only inputs of bounded size. Thus, there is absolutely no way to determine experimentally whether a given algorithm runs in polynomial time, exponential time, or something else.

Or in other words: what Robin said.
I still vote for the n-body problem as an example of NP intractability. The gentlemen who refer to numeric solutions forget that the numeric solution is a recursive model, and not a solution in principle in the same way that an analytic solution is. Qui Dong Wang's analytic solution is intractable. Proteins which can fold, and planets which can orbit in systems of more than two bodies are physical systems, not algorithmic solutions of the kind which the P-NP problem addresses. 

I must also appreciate chazisop's difficulties with solutions in continuous time. If either time or space is continuous, potential state spaces become uncountable (aleph one).