How to celebrate it leverage it and NOT avoid it Are YOU sufficiently complex Simple Best FROM OCCAMS RAZOR COMPLEXITY Are YOU sufficiently complex Simple Best Simple but no Simpler ID: 153390
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Slide1
COMPLEXITY
How to celebrate it, leverage it, and NOT avoid it!
Are YOU sufficiently complex?
Simple = Best
FROM OCCAM’S
RAZORSlide2
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!Slide3
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!Slide4
COURTESY:
xkcd
Blog.
The definition of a scientific black box……Slide5
COURTESY:
xkcd Blog.
BRAIN STATE
X
STIMULI
i
ϵ
N
CORRELATES
Y
…is usually modeled as an I/O system….
Feedback between brain and stimuli, correlates, and future brain states?Slide6
COURTESY:
xkcd Blog.
…..but actually involves recursion……
BRAIN STATE
X
STIMULI
i
ϵ
N
CORRELATES
Y
LESSON:
Embracing complexity turns a black box into a gray one.Slide7
Sometimes,
small events……
Small-scale events: a butterfly flaps its wings in Kansas, hello Hurricane Dolly).
Small perturbations, magnified….Slide8
….have extreme sensitivity to their initial condition……
COURTESY: Wikipedia
(http://en.wikipedia.org/wiki/Butterfly_effect)Slide9
LESSON: complex systems
live and “think”
outside the box!
..…lead to BIG
consequences!
COURTESY:
http://ecosystems.noaa.gov/Slide10
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). Slide11
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)!Slide12
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…….Slide13
“Computational” Complexity
Think big data….think parallel!Slide14
“Computational” Complexity
Think big data….think parallel!
Think leaderless….think swarms
ORSlide15
“Computational” Complexity
Limit for conventional
computational approaches?
Where do scientific problems fit into this scheme?
Think big data….think parallel!Slide16
HAPPY 50th Birthday, Chaos Theory!
COURTESY:
Advanced Tree Generator,
OpenProcessing
http://www.openprocessing.org/sketch/8941
Is this a tree, or a forest?Slide17
HAPPY 50th Birthday, Chaos Theory!
COURTESY:
Advanced Tree Generator,
OpenProcessing
http://www.openprocessing.org/sketch/8941
I have infinite subsets!Slide18
HAPPY 50th 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!Slide19
The End (or is it?)
Mobius
Strip (surface with no beginning and no end)Slide20
The End (or is it?)
Douglas Hofstadter,
Godel
, Escher, Bach: an eternal golden braid (1979).
Mobius Strip (surface with
no beginning and no end)