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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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Complexity

COMPLEXITY

Are YOU sufficiently complex?

How to celebrate it, leverage it, and NOT avoid it!

FROM OCCAM’S

RAZOR

Simple = Best


Complexity

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


Complexity

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


Complexity

The definition of a scientific black box……

COURTESY:xkcd Blog.


Complexity

…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?


Complexity

…..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.


Complexity

  • Sometimes, small events……

Small-scale events: a butterfly flaps its wings in Kansas, hello Hurricane Dolly).

Small perturbations, magnified….


Complexity

  • ….have extreme sensitivity to their initial condition……

COURTESY: Wikipedia

(http://en.wikipedia.org/wiki/Butterfly_effect)


Complexity

  • ..…lead to BIG consequences!

COURTESY:

http://ecosystems.noaa.gov/

  • LESSON: complex systems live and “think” outside the box!


Poincare is dead long live poincare

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…….


Poincare is dead long live poincare1

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).


Poincare is dead long live poincare2

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).


Computational complexity

“Computational” Complexity

Think big data….think parallel!


Computational complexity1

“Computational” Complexity

Think big data….think parallel!

Think leaderless….think swarms

OR


Computational complexity2

“Computational” Complexity

Limit for conventional

computational approaches?

Think big data….think parallel!

Where do scientific problems fit into this scheme?


Happy 50 th birthday chaos theory

HAPPY 50th Birthday, Chaos Theory!

Is this a tree, or a forest?

COURTESY: Advanced Tree Generator,

OpenProcessing

http://www.openprocessing.org/sketch/8941


Happy 50 th birthday chaos theory1

HAPPY 50th Birthday, Chaos Theory!

I have infinite subsets!

COURTESY: Advanced Tree Generator,

OpenProcessing

http://www.openprocessing.org/sketch/8941


Happy 50 th birthday chaos theory2

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


The end or is it

The End (or is it?)

Mobius Strip (surface with

no beginning and no end)


The end or is it1

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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