(10-28-2013, 06:46 PM)Jester Wrote: But ... nonlinear dynamical systems are deterministic, no? They may be messy in all sorts of fun ways involving topology, sensitivity to initial conditions, periodicity and so on, but in the end they yield fixed outputs per input just the same as 2+2=4.First, I believe we have thousands of years of understanding of linear systems, and linear equations. Only a slim number of mathematicians work in non-linear systems. It's really hard. Real work in non-linear mathematics only started in the past hundred years or so, namely work by Euler, Lagrange, and Poincaré. Then only recently with work on chaos, by people like Lorenz.
If all the variables are deterministic, the topology is predictable. Life, being comprised of self organized nonlinear dynamical systems, is non-deterministic due to the inherent chaos of the universe. Like the butterfly effect (which is negligible), but I think of the asteroid event 55 million years ago, or the comet explosion over Canada 12,900 years ago. We've survived and adapted to deal with this unpredictability, and in so doing we've become unpredictable ourselves. I'd like to think that because life is short, and dangerous, we've evolved to rise to a level at least where we can comprehend the bigger challenges for life, like rogue asteroids, dying suns, colliding galaxies and super novas.