
In Mysterious Pattern, Math and Nature Converge - nature24
https://www.quantamagazine.org/in-mysterious-pattern-math-and-nature-converge-20130205/
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tw1010
Is it really _that_ strange that random matrix theory models so many things
though? Matrices without stochasticity can already model so many things in
nature. And the reason for that is much more because they are a really well
studied area of math, rather than because of some deep mysterious thing about
nature. (It's much more about that being the conventional tool that physicists
learn in school.) Take some really well used technique (matrix theory) and add
another property (randomness) and is it really that strange that the result
(random matrix theory) explains a larger set of phenomenon than what was
explained by each piece individually?

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adrianratnapala
Matrices don't have to be "some deep mysterious thing about nature" to be
important in themselves and not just beause they are well-studied. They merely
need to be deep.

"Matrices" is just a word for "Linear operators over finite-dimensioned
spaces". Linear stuff is important. Finite dimensional systems are imporant.
And even infinite dimensional linear systems tend to have the same properties
as finite dimensional ones. All of this makes matricies important in their own
right.

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mhalle
Here is an approachable article that puts the subject in more perspective:
[https://terrytao.wordpress.com/2010/09/14/a-second-draft-
of-...](https://terrytao.wordpress.com/2010/09/14/a-second-draft-of-a-non-
technical-article-on-universality/)

And here's journal paper that gives some examples outside of physics:

[http://journals.plos.org/plosone/article?id=10.1371/journal....](http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0004791)

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gregfjohnson
This made me think of the Central Limit Theorem. (If 'non-contrived'
independent observations with random variability are summed and normalized,
they end up exhibiting the standard Gaussian "bell curve".) All kinds of
natural "real world" phenomena end up neatly obeying a function that seems
odd:

f(x) = K / sqrt(exp(x*x))

(The above characterization assumes N(0,1), and re-arranges terms a slight
amount to highlight the interesting nature of the function.)

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mhalle
This article is (2013). Same magazine posted another article in 2014 that
provided a different look at the same broad topic:

[https://www.quantamagazine.org/beyond-the-bell-curve-a-
new-u...](https://www.quantamagazine.org/beyond-the-bell-curve-a-new-
universal-law-20141015/)

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7373737373
Related: Computation at the edge of Chaos (Langton):
[http://www.romanpoet.org/223/langton.edgeofchaos.pdf](http://www.romanpoet.org/223/langton.edgeofchaos.pdf)

The fine balance between chaos and order in computational terms.

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chillingeffect
Is this less-dramatically stated as a particular non-Gaussian PDF (prob dist
func)?

~~~
selimthegrim
If you study the so-called level spacing of a Hamiltonian with disorder drawn
from a uniform random distribution, you will recover a Poisson distribution.
As you turn down the disorder, you will reproduce the statistics the Czechs
discovered in the bus system.

