1. COMPLEXITY How to celebrate it, leverage it, and NOT avoid it! Are YOU sufficiently complex? Simple = Best FROM OCCAM’S RAZOR

2. COMPLEXITY Are YOU sufficiently complex? Simple = Best Simple but no Simpler FROM OCCAM’S RAZOR How to celebrate it, leverage it, and NOT avoid it!

3. COMPLEXITY Are YOU sufficiently complex? FROM OCCAM’S RAZOR TO MANDELBROT’S REVENGE Simple = Best Simple but no Simpler Keep it Complex, Stupid! How to celebrate it, leverage it, and NOT avoid it!

4. COURTESY: xkcd Blog. The definition of a scientific black box……

5. COURTESY: xkcd Blog. BRAIN STATE X STIMULI i N CORRELATES Y …is usually modeled as an I/O system…. Feedback between brain and stimuli, correlates, and future brain states?

6. COURTESY: xkcd Blog. …..but actually involves recursion…… BRAIN STATE X STIMULI i N CORRELATES Y LESSON: Embracing complexity turns a black box into a gray one.

7. Sometimes, small events…… Small-scale events: a butterfly flaps its wings in Kansas, hello Hurricane Dolly). Small perturbations, magnified….

8. ….have extreme sensitivity to their initial condition…… COURTESY: Wikipedia (http://en.wikipedia.org/wiki/Butterfly_effect)

9. LESSON: complex systems live and “think” outside the box!..…lead to BIG consequences! COURTESY: http://ecosystems.noaa.gov/

10. Poincare is dead. Long live Poincare! Want to see a neat trick? Count to 11……. Q: How many ways can you rearrange the pixels of an image? A: the number of pixels! (that’s factorial).

11. Poincare is dead. Long live Poincare! Poincare Recurrence: Crutchfield, J. et.al Chaos. Scientific American, December (1986). Want to see a neat trick? Count to 11……. NO PEEKING! BUT there’s a surprise in store (stay tuned)!

12. Poincare is dead. Long live Poincare! Ta-da! I’m a self-fulfilling and recurrent phenomenon! NO PEEKING! Poincare Recurrence: Crutchfield, J. et.al Chaos. Scientific American, December (1986). Want to see a neat trick? Count to 11…….

13. “Computational” Complexity Think big data….think parallel!

14. “Computational” Complexity Think big data….think parallel! Think leaderless….think swarms OR

15. “Computational” Complexity Limit for conventional computational approaches? Where do scientific problems fit into this scheme? Think big data….think parallel!

16. HAPPY 50 th Birthday, Chaos Theory! COURTESY: Advanced Tree Generator, OpenProcessing http://www.openprocessing.org/sketch/8941 Is this a tree, or a forest?

17. HAPPY 50 th Birthday, Chaos Theory! COURTESY: Advanced Tree Generator, OpenProcessing http://www.openprocessing.org/sketch/8941 I have infinite subsets!

18. HAPPY 50 th Birthday, Chaos Theory! COURTESY: Advanced Tree Generator, OpenProcessing http://www.openprocessing.org/sketch/8941 I have infinite subsets! LESSON: sometimes the forest is composed of trees (of course!) CORROLARY: sometimes that forest is chaotic!

19. The End (or is it?) Mobius Strip (surface with no beginning and no end)

20. The End (or is it?) Douglas Hofstadter, Godel, Escher, Bach: an eternal golden braid (1979). Mobius Strip (surface with no beginning and no end)