Complexity and the Role of Math (...and Toddlers)

"Physicists can predict what atoms will do.  But gather enough atoms, and the calculations grow unwieldy. We need new, emergent laws -- chemical laws. Then, gather enough chemicals, and complexity overwhelms us again. We need biology to step in with new theories and rules. And so on down the line. At each tipping point, the role of math evolves: from certain to tentative, from deterministic to statistical, from consensus to controversy. Simple phenomena (like quarks) follow mathematical rules with slavish fidelity. Complex phenomena (like toddlers) less so."
                                                    -- Ben Orlin from "Change Is the Only Constant"

 (incredibly here, Ben almost succeeds in stringing together 9 sentences without a joke being involved... but, then he had to throw in "toddlers" at the end  ;)

More On Complexity...

A great introduction (with several links) today to complexity theory and chaos, from RJ Lipton here:

http://rjlipton.wordpress.com/2011/02/21/butterflies-and-complexity-theories/

...and I learned that the "Butterfly Effect" actually goes all the way back to a Ray Bradbury novel... (since I don't read science fiction, or any fiction for that matter, I never knew that... or, did the notion come to Bradbury from yet someone or something else... who got it from.....?!)

Biology, Complexity, Dynamics... and Math

"Biology is not yet a predictive science, there are essentially no fundamental laws [as with physics]... biology, in terms of maturity, is at the stage that physics was 300 years ago..."

Interesting post over at plus.maths.org on the work of Thomas Fink et.al., essentially trying to mathematically model biological systems.

a bit more therefrom:

"Everyone says the standard model for evolution is mutation, selection and inheritance. Put those ingredients together in a box and you get evolution. But the reality is, when we put those things into models of evolution, or set up appropriate systems of artificial life, we just don't get life-like evolution — we don't find the evolution of complex, surprising things. Some fundamental is missing. What gives a system the capacity to evolve? What makes a system evolvable?"

...and later:

"The problem is, to be able to know what is interesting, one needs to know what is boring."