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In Mysterious Pattern, Math and Nature Converge
- tw1010 9y agoIs 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?
- adrianratnapala 9y agoMatrices 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.
- chillingeffect 9y agoIs this less-dramatically stated as a particular non-Gaussian PDF (prob dist func)?
- selimthegrim 9y agoIf 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.
- gregfjohnson 9y agoThis 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.)
- mhalle 9y agoHere is an approachable article that puts the subject in more perspective: https://terrytao.wordpress.com/2010/09/14/a-second-draft-of-a-non-technical-article-on-universality/ https://terrytao.wordpress.com/2010/09/14/a-second-draft-of-... And here's journal paper that gives some examples outside of physics: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0004791 http://journals.plos.org/plosone/article?id=10.1371/journal....
- mhalle 9y agoThis 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-universal-law-20141015/ https://www.quantamagazine.org/beyond-the-bell-curve-a-new-u...
- 7373737373 9y agoRelated: 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.