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COMPLEXITY

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

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COMPLEXITY

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

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

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

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

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

  6. …..but actually involves recursion…… STIMULI iϵN CORRELATES Y BRAIN STATE X COURTESY:xkcd Blog. 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. ..…lead to BIG consequences! COURTESY: http://ecosystems.noaa.gov/ • LESSON: complex systems live and “think” outside the box!

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

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

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

  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? Think big data….think parallel! Where do scientific problems fit into this scheme?

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

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

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

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

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

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