Enter the matrix: the deep law that shapes our reality

[n2doc]

07 April 2010 by Mark Buchanan

SUPPOSE we had a theory that could explain everything. Not just atoms and quarks but aspects of our everyday lives too. Sound impossible? Perhaps not.

It's all part of the recent explosion of work in an area of physics known as random matrix theory. Originally developed more than 50 years ago to describe the energy levels of atomic nuclei, the theory is turning up in everything from inflation rates to the behaviour of solids. So much so that many researchers believe that it points to some kind of deep pattern in nature that we don't yet understand. "It really does feel like the ideas of random matrix theory are somehow buried deep in the heart of nature," says electrical engineer Raj Nadakuditi of the University of Michigan, Ann Arbor.

All of this, oddly enough, emerged from an effort to turn physicists' ignorance into an advantage. In 1956, when we knew very little about the internal workings of large, complex atomic nuclei, such as uranium, the German physicist Eugene Wigner suggested simply guessing.

Quantum theory tells us that atomic nuclei have many discrete energy levels, like unevenly spaced rungs on a ladder. To calculate the spacing between each of the rungs, you would need to know the myriad possible ways the nucleus can hop from one to another, and the probabilities for those events to happen. Wigner didn't know, so instead he picked numbers at random for the probabilities and arranged them in a square array called a matrix.

The matrix was a neat way to express the many connections between the different rungs. It also allowed Wigner to exploit the powerful mathematics of matrices in order to make predictions about the energy levels.

more

http://www.newscientist.com/article/mg20627550.200-enter-the-matrix-the-deep-law-that-shapes-our-reality.html

[bananas]

1. No, it is impossible. nt

[On the Road]

2. This is Pretty Amazing

I love this kind of thing, and I had never heard of random matrix theory before.

The article was very coy. Do you understand anything about what this matrix theory is like or how it operates? It sounds like a universal function like the Bell curve or the Mandelbrot set that shows up everywhere.

I wasted a whole semester once learning how to solve matrices by hand. This is something very different, but that New Scientist site treats us like we're all tourists and doesn't give much of a clue.

[On the Road]

3. OK, So It's Not Exactly a Function Like the Bell Curve

Apparently what you do is populate a matrix with random values -- not completely random, but random numbers from some specified distribution. You evaluate a whole bunch of these matrices, then look at the variation in the results. Then, from the posted article:

Their result allows you to calculate how much correlation between data sets you should expect to find simply by chance. This makes it possible to distinguish truly special cases from chance accidents.

It sounds interesting, but it does not seem to be a particular function or distribution -- more like a general mathematical tool, like taking a derivative, that can be applied to all kinds of things.

[WheelWalker]

4. Now you've given me a headache. I need

a mushroom.