The folks Emergent Chaos think they've spotted a scientific revolution:

This paper, “More Really is Different,” may be one of the most important papers of the last half-millenium. It argues that P.W. Anderson's concept of “emergence” is provable. It may have even proved it.

The idea of emergence, from whence this blog gets its name is the opposite of reductionism. It is the idea that a complex system acquires properties that the underlying parts cannot predict. It's nothing more and nothing less than a formalization of the adage, “The whole is more than the sum of its parts.”

The authors, Mile Gu, Christian Weedbrook, Alvaro Perales, and Michael A. Nielsen, argue directly that this may mean that a “Theory of Everything” may therefore be impossible.

This is big, big news. Read the paper. Read the commentary in The New Scientist, “Why nature can't be reduced to mathematical laws.”

If they are right, this goes to the core of the philosophical underpinnings of the way we understand the world. It may help explain everything from weather prediction to the origins of life to whether souls exist. I might even be engaging in understatement rather than hyperbole on that last bit. You may think it's a long way down to the chemist's, but this is big.

While you're at it, expect some highly entertaining debate, and pseudo-scientific whackos of every stripe to start quoting this. Maybe the next Kuhnian revolution has begun.

I am not a (series of) numbers, I am a free man.

[PS. New Scientist seems to be behind a paywall, alas.]

This is an unimportant paper. They encode a Turing machine in the Hamiltonian of a set of spins on a lattice. Thus, the lowest-energy state of the lattice has properties that depend on the results of the TM’s computation. But since that problem is undecidable in the general case, so too is the general problem of deciding whether the the lowest-energy state has property X. True enough, but so? If it’s undecidable, then not only is there no reliable way of answering the question by looking at the rules of the lower-level systems, there no reliable way of answering the question AT ALL. That’s what undecidability is.

And no, we can’t just let the system settle into its lowest-energy state and see what results; their proof only works if the lattice is infinitely large. Good luck making one of those.

Computational universality is a profound idea. Undecidability is a profound idea. Emergence is a significant idea that may also be profound. This paper is technically clever, but it is not profound — because it doesn’t tell us anything interesting about emergence.

Just to be clear, the paper that Mordaxus links to is on Arxiv.org, and is freely available. The paywall’d article on New Scientist is their commentary.