COMPLEXITY
Download
1 / 20

COMPLEXITY - PowerPoint PPT Presentation


  • 101 Views
  • Uploaded on
  • Presentation posted in: General

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha

Download Presentation

COMPLEXITY

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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

…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

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

Small perturbations, magnified….


Complexity

COURTESY: Wikipedia

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


Complexity

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! condition……

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! condition……

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! condition……

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 condition……

Think big data….think parallel!


Computational complexity1
“Computational” Complexity condition……

Think big data….think parallel!

Think leaderless….think swarms

OR


Computational complexity2
“Computational” Complexity condition……

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 50 condition……th 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 50 condition……th 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 50 condition……th 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?) condition……

Mobius Strip (surface with

no beginning and no end)


The end or is it1
The End (or is it?) condition……

Mobius Strip (surface with

no beginning and no end)

Douglas Hofstadter, Godel, Escher,

Bach: an eternal golden braid (1979).


ad
  • Login