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Why Complexify? Universality Principles of Complex Systems - - PowerPoint PPT Presentation

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Why Complexify? Why Complexify? Universality Principles of Complex Systems Symmetry CSYS/MATH 300, Spring, 2013 | #SpringPoCS2013 Breaking The Big Theory Final words Prof. Peter Dodds For your consideration @peterdodds References

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 1 of 28

Why Complexify?

Principles of Complex Systems CSYS/MATH 300, Spring, 2013 | #SpringPoCS2013

  • Prof. Peter Dodds

@peterdodds

Department of Mathematics & Statistics | Center for Complex Systems | Vermont Advanced Computing Center | University of Vermont

Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 2 of 28

These slides brought to you by:

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 3 of 28

Outline

Universality Symmetry Breaking The Big Theory Final words For your consideration References

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 4 of 28

Limits to what’s possible:

Universality (⊞):

◮ The property that the macroscopic aspects of a

system do not depend sensitively on the system’s details.

◮ Key figure: Leo Kadanoff (⊞).

Examples:

◮ The Central Limit Theorem:

P(x; µ, σ)dx = 1 √ 2πσ e−(x−µ)2/2σ2dx .

◮ Navier Stokes equation for fluids. ◮ Nature of phase transitions in statistical mechanics.

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SLIDE 5

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 4 of 28

Limits to what’s possible:

Universality (⊞):

◮ The property that the macroscopic aspects of a

system do not depend sensitively on the system’s details.

◮ Key figure: Leo Kadanoff (⊞).

Examples:

◮ The Central Limit Theorem:

P(x; µ, σ)dx = 1 √ 2πσ e−(x−µ)2/2σ2dx .

◮ Navier Stokes equation for fluids. ◮ Nature of phase transitions in statistical mechanics.

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SLIDE 6

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 4 of 28

Limits to what’s possible:

Universality (⊞):

◮ The property that the macroscopic aspects of a

system do not depend sensitively on the system’s details.

◮ Key figure: Leo Kadanoff (⊞).

Examples:

◮ The Central Limit Theorem:

P(x; µ, σ)dx = 1 √ 2πσ e−(x−µ)2/2σ2dx .

◮ Navier Stokes equation for fluids. ◮ Nature of phase transitions in statistical mechanics.

slide-7
SLIDE 7

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 4 of 28

Limits to what’s possible:

Universality (⊞):

◮ The property that the macroscopic aspects of a

system do not depend sensitively on the system’s details.

◮ Key figure: Leo Kadanoff (⊞).

Examples:

◮ The Central Limit Theorem:

P(x; µ, σ)dx = 1 √ 2πσ e−(x−µ)2/2σ2dx .

◮ Navier Stokes equation for fluids. ◮ Nature of phase transitions in statistical mechanics.

slide-8
SLIDE 8

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 4 of 28

Limits to what’s possible:

Universality (⊞):

◮ The property that the macroscopic aspects of a

system do not depend sensitively on the system’s details.

◮ Key figure: Leo Kadanoff (⊞).

Examples:

◮ The Central Limit Theorem:

P(x; µ, σ)dx = 1 √ 2πσ e−(x−µ)2/2σ2dx .

◮ Navier Stokes equation for fluids. ◮ Nature of phase transitions in statistical mechanics.

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SLIDE 9

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 5 of 28

Universality

◮ Sometimes details don’t matter too much. ◮ Many-to-one mapping from micro to macro ◮ Suggests not all possible behaviors are available

at higher levels of complexity.

Large questions:

◮ How universal is universality? ◮ What are the possible long-time states (attractors) for

a universe?

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 5 of 28

Universality

◮ Sometimes details don’t matter too much. ◮ Many-to-one mapping from micro to macro ◮ Suggests not all possible behaviors are available

at higher levels of complexity.

Large questions:

◮ How universal is universality? ◮ What are the possible long-time states (attractors) for

a universe?

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SLIDE 11

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 5 of 28

Universality

◮ Sometimes details don’t matter too much. ◮ Many-to-one mapping from micro to macro ◮ Suggests not all possible behaviors are available

at higher levels of complexity.

Large questions:

◮ How universal is universality? ◮ What are the possible long-time states (attractors) for

a universe?

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SLIDE 12

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 5 of 28

Universality

◮ Sometimes details don’t matter too much. ◮ Many-to-one mapping from micro to macro ◮ Suggests not all possible behaviors are available

at higher levels of complexity.

Large questions:

◮ How universal is universality? ◮ What are the possible long-time states (attractors) for

a universe?

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SLIDE 13

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 5 of 28

Universality

◮ Sometimes details don’t matter too much. ◮ Many-to-one mapping from micro to macro ◮ Suggests not all possible behaviors are available

at higher levels of complexity.

Large questions:

◮ How universal is universality? ◮ What are the possible long-time states (attractors) for

a universe?

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SLIDE 14

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 5 of 28

Universality

◮ Sometimes details don’t matter too much. ◮ Many-to-one mapping from micro to macro ◮ Suggests not all possible behaviors are available

at higher levels of complexity.

Large questions:

◮ How universal is universality? ◮ What are the possible long-time states (attractors) for

a universe?

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SLIDE 15

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 6 of 28

Fluid mechanics

◮ Fluid mechanics = One of the great successes of

understanding complex systems.

◮ Navier-Stokes equations: micro-macro system

evolution.

◮ The big three: Experiment + Theory + Simulations. ◮ Works for many very different ‘fluids’:

◮ the atmosphere, ◮ oceans, ◮ blood, ◮ galaxies, ◮ the earth’s mantle... ◮ and ball bearings on lattices...?

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 6 of 28

Fluid mechanics

◮ Fluid mechanics = One of the great successes of

understanding complex systems.

◮ Navier-Stokes equations: micro-macro system

evolution.

◮ The big three: Experiment + Theory + Simulations. ◮ Works for many very different ‘fluids’:

◮ the atmosphere, ◮ oceans, ◮ blood, ◮ galaxies, ◮ the earth’s mantle... ◮ and ball bearings on lattices...?

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 6 of 28

Fluid mechanics

◮ Fluid mechanics = One of the great successes of

understanding complex systems.

◮ Navier-Stokes equations: micro-macro system

evolution.

◮ The big three: Experiment + Theory + Simulations. ◮ Works for many very different ‘fluids’:

◮ the atmosphere, ◮ oceans, ◮ blood, ◮ galaxies, ◮ the earth’s mantle... ◮ and ball bearings on lattices...?

slide-18
SLIDE 18

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 6 of 28

Fluid mechanics

◮ Fluid mechanics = One of the great successes of

understanding complex systems.

◮ Navier-Stokes equations: micro-macro system

evolution.

◮ The big three: Experiment + Theory + Simulations. ◮ Works for many very different ‘fluids’:

◮ the atmosphere, ◮ oceans, ◮ blood, ◮ galaxies, ◮ the earth’s mantle... ◮ and ball bearings on lattices...?

slide-19
SLIDE 19

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 6 of 28

Fluid mechanics

◮ Fluid mechanics = One of the great successes of

understanding complex systems.

◮ Navier-Stokes equations: micro-macro system

evolution.

◮ The big three: Experiment + Theory + Simulations. ◮ Works for many very different ‘fluids’:

◮ the atmosphere, ◮ oceans, ◮ blood, ◮ galaxies, ◮ the earth’s mantle... ◮ and ball bearings on lattices...?

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 7 of 28

Lattice gas models

Collision rules in 2-d on a hexagonal lattice:

◮ Lattice matters... ◮ No ‘good’ lattice in 3-d. ◮ Upshot: play with ‘particles’ of a system to obtain

new or specific macro behaviours.

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 7 of 28

Lattice gas models

Collision rules in 2-d on a hexagonal lattice:

◮ Lattice matters... ◮ No ‘good’ lattice in 3-d. ◮ Upshot: play with ‘particles’ of a system to obtain

new or specific macro behaviours.

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 7 of 28

Lattice gas models

Collision rules in 2-d on a hexagonal lattice:

◮ Lattice matters... ◮ No ‘good’ lattice in 3-d. ◮ Upshot: play with ‘particles’ of a system to obtain

new or specific macro behaviours.

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SLIDE 23

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 7 of 28

Lattice gas models

Collision rules in 2-d on a hexagonal lattice:

◮ Lattice matters... ◮ No ‘good’ lattice in 3-d. ◮ Upshot: play with ‘particles’ of a system to obtain

new or specific macro behaviours.

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 8 of 28

Hexagons—Honeycomb: (⊞)

◮ Orchestrated? Or an accident of bees working hard? ◮ See “On Growth and Form” by D’Arcy Wentworth

Thompson (⊞). [4, 5]

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 8 of 28

Hexagons—Honeycomb: (⊞)

◮ Orchestrated? Or an accident of bees working hard? ◮ See “On Growth and Form” by D’Arcy Wentworth

Thompson (⊞). [4, 5]

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 9 of 28

Hexagons—Giant’s Causeway: (⊞)

http://newdesktopwallpapers.info

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 10 of 28

Hexagons—Giant’s Causeway: (⊞)

http://www.physics.utoronto.ca/

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 11 of 28

Hexagons run amok:

◮ Graphene (⊞): single layer of

carbon molecules in a perfect hexagonal lattice (super strong).

◮ Chicken wire (⊞) . . .

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 12 of 28

Whimsical but great example of real science:

“How Cats Lap: Water Uptake by Felis catus” (⊞) Reis et al., Science, 2010. Amusing interview here (⊞)

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 13 of 28

Symmetry Breaking

Philip Anderson (⊞)—“More is Different,” Science, 1972 [1]

◮ Argues against idea that

the only real scientists are those working on the fundamental laws.

◮ Symmetry breaking →

different laws/rules at different scales...

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SLIDE 31

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 13 of 28

Symmetry Breaking

Philip Anderson (⊞)—“More is Different,” Science, 1972 [1]

◮ Argues against idea that

the only real scientists are those working on the fundamental laws.

◮ Symmetry breaking →

different laws/rules at different scales...

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 13 of 28

Symmetry Breaking

Philip Anderson (⊞)—“More is Different,” Science, 1972 [1]

◮ Argues against idea that

the only real scientists are those working on the fundamental laws.

◮ Symmetry breaking →

different laws/rules at different scales...

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SLIDE 33

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 13 of 28

Symmetry Breaking

Philip Anderson (⊞)—“More is Different,” Science, 1972 [1]

◮ Argues against idea that

the only real scientists are those working on the fundamental laws.

◮ Symmetry breaking →

different laws/rules at different scales... 2006 study → “most creative physicist in the world” (⊞)

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 14 of 28

Symmetry Breaking

“Elementary entities of science X obey the laws of science Y”

◮ X ◮ solid state or

many-body physics

◮ chemistry ◮ molecular biology ◮ cell biology

. . .

◮ psychology ◮ social sciences ◮ Y ◮ elementary particle

physics

◮ solid state

many-body physics

◮ chemistry ◮ molecular biology

. . .

◮ physiology ◮ psychology

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 15 of 28

Symmetry Breaking

Anderson:

◮ [the more we know about] “fundamental laws, the

less relevance they seem to have to the very real problems of the rest of science.”

◮ Scale and complexity thwart the constructionist

hypothesis.

◮ Accidents of history and path dependence (⊞)

matter.

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 15 of 28

Symmetry Breaking

Anderson:

◮ [the more we know about] “fundamental laws, the

less relevance they seem to have to the very real problems of the rest of science.”

◮ Scale and complexity thwart the constructionist

hypothesis.

◮ Accidents of history and path dependence (⊞)

matter.

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SLIDE 37

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 15 of 28

Symmetry Breaking

Anderson:

◮ [the more we know about] “fundamental laws, the

less relevance they seem to have to the very real problems of the rest of science.”

◮ Scale and complexity thwart the constructionist

hypothesis.

◮ Accidents of history and path dependence (⊞)

matter.

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 16 of 28

Symmetry Breaking

◮ Page 291–292 of Sornette [3]:

Renormalization ≡ Anderson’s hierarchy.

◮ But Anderson’s hierarchy is not a simple one: the

rules change.

◮ Crucial dichotomy between evolving systems

following stochastic paths that lead to (a) inevitable or (b) particular destinations (states).

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SLIDE 39

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 16 of 28

Symmetry Breaking

◮ Page 291–292 of Sornette [3]:

Renormalization ≡ Anderson’s hierarchy.

◮ But Anderson’s hierarchy is not a simple one: the

rules change.

◮ Crucial dichotomy between evolving systems

following stochastic paths that lead to (a) inevitable or (b) particular destinations (states).

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SLIDE 40

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 16 of 28

Symmetry Breaking

◮ Page 291–292 of Sornette [3]:

Renormalization ≡ Anderson’s hierarchy.

◮ But Anderson’s hierarchy is not a simple one: the

rules change.

◮ Crucial dichotomy between evolving systems

following stochastic paths that lead to (a) inevitable or (b) particular destinations (states).

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SLIDE 41

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 17 of 28

More is different:

http://xkcd.com/435/ (⊞)

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 18 of 28

A real science of complexity:

A real theory of everything anything:

  • 1. Is not just about the ridiculously small stuff...
  • 2. It’s about the increase of complexity

Symmetry breaking/ Accidents of history vs. Universality

◮ Second law of thermodynamics: we’re toast in the

long run.

◮ So how likely is the local complexification of structure

we enjoy?

◮ How likely are the Big Transitions?

slide-43
SLIDE 43

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 18 of 28

A real science of complexity:

A real theory of everything anything:

  • 1. Is not just about the ridiculously small stuff...
  • 2. It’s about the increase of complexity

Symmetry breaking/ Accidents of history vs. Universality

◮ Second law of thermodynamics: we’re toast in the

long run.

◮ So how likely is the local complexification of structure

we enjoy?

◮ How likely are the Big Transitions?

slide-44
SLIDE 44

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 18 of 28

A real science of complexity:

A real theory of everything anything:

  • 1. Is not just about the ridiculously small stuff...
  • 2. It’s about the increase of complexity

Symmetry breaking/ Accidents of history vs. Universality

◮ Second law of thermodynamics: we’re toast in the

long run.

◮ So how likely is the local complexification of structure

we enjoy?

◮ How likely are the Big Transitions?

slide-45
SLIDE 45

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 18 of 28

A real science of complexity:

A real theory of everything anything:

  • 1. Is not just about the ridiculously small stuff...
  • 2. It’s about the increase of complexity

Symmetry breaking/ Accidents of history vs. Universality

◮ Second law of thermodynamics: we’re toast in the

long run.

◮ So how likely is the local complexification of structure

we enjoy?

◮ How likely are the Big Transitions?

slide-46
SLIDE 46

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 18 of 28

A real science of complexity:

A real theory of everything anything:

  • 1. Is not just about the ridiculously small stuff...
  • 2. It’s about the increase of complexity

Symmetry breaking/ Accidents of history vs. Universality

◮ Second law of thermodynamics: we’re toast in the

long run.

◮ So how likely is the local complexification of structure

we enjoy?

◮ How likely are the Big Transitions?

slide-47
SLIDE 47

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 18 of 28

A real science of complexity:

A real theory of everything anything:

  • 1. Is not just about the ridiculously small stuff...
  • 2. It’s about the increase of complexity

Symmetry breaking/ Accidents of history vs. Universality

◮ Second law of thermodynamics: we’re toast in the

long run.

◮ So how likely is the local complexification of structure

we enjoy?

◮ How likely are the Big Transitions?

slide-48
SLIDE 48

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 18 of 28

A real science of complexity:

A real theory of everything anything:

  • 1. Is not just about the ridiculously small stuff...
  • 2. It’s about the increase of complexity

Symmetry breaking/ Accidents of history vs. Universality

◮ Second law of thermodynamics: we’re toast in the

long run.

◮ So how likely is the local complexification of structure

we enjoy?

◮ How likely are the Big Transitions?

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SLIDE 49

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 19 of 28

Complexification—the Big Transitions:

◮ Big Bang. ◮ Big Random-

ness.

◮ Big Replicate. ◮ Big Life. ◮ Big Evolve. ◮ Big Word. ◮ Big Story. ◮ Big

Number.

◮ Big God. ◮ Big Make. ◮ Big Science. ◮ Big Data. ◮ Big Information. ◮ Big Algorithm. ◮ Big Connection. ◮ Big Social. ◮ Big Awareness.

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SLIDE 50

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 20 of 28

Why complexify?

◮ “Why do things become more complex?” [2]

Brian Arthur Scientific American, 268, 92, 1993.

◮ Complexification ≡ evolution of algorithms? ◮ Differential equations and stories ⊂ Algorithms. ◮ Life is a loaded word: The Search for Extraterrestrial

Algorithms (SETA)?

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 21 of 28

Why complexify?

Driving complexity’s trajectory:

◮ Big Bang ◮ Randomness leads to replicating structures; ◮ Biological evolution; ◮ Sociocultural evolution; ◮ Technological evolution; ◮ Sociotechnological evolution.

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 22 of 28

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 23 of 28

Homo narrativus—What’s the Story?:

http://xkcd.com/904/ (⊞)

◮ Mechanisms =

Evolution equations, algorithms, stories, ...

◮ Rollover zing: “Also, all

financial analysis. And, more directly, D&D.”

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SLIDE 54

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 23 of 28

Homo narrativus—What’s the Story?:

http://xkcd.com/904/ (⊞)

◮ Mechanisms =

Evolution equations, algorithms, stories, ...

◮ Rollover zing: “Also, all

financial analysis. And, more directly, D&D.”

slide-55
SLIDE 55

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 24 of 28

(Sir Terry) Pratchett’s (⊞) Narrativium (⊞):

◮ “The most common element on the

disc, although not included in the list of the standard five: earth, fire, air, water and surprise. It ensures that everything runs properly as a story.”

◮ “A little narrativium goes a long

way: the simpler the story, the better you understand it. Storytelling is the opposite of reductionism: 26 letters and some rules of grammar are no story at all.”

◮ “Heroes only win when outnumbered, and things

which have a one-in-a-million chance of succeeding

  • ften do so.”
slide-56
SLIDE 56

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 24 of 28

(Sir Terry) Pratchett’s (⊞) Narrativium (⊞):

◮ “The most common element on the

disc, although not included in the list of the standard five: earth, fire, air, water and surprise. It ensures that everything runs properly as a story.”

◮ “A little narrativium goes a long

way: the simpler the story, the better you understand it. Storytelling is the opposite of reductionism: 26 letters and some rules of grammar are no story at all.”

◮ “Heroes only win when outnumbered, and things

which have a one-in-a-million chance of succeeding

  • ften do so.”
slide-57
SLIDE 57

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 24 of 28

(Sir Terry) Pratchett’s (⊞) Narrativium (⊞):

◮ “The most common element on the

disc, although not included in the list of the standard five: earth, fire, air, water and surprise. It ensures that everything runs properly as a story.”

◮ “A little narrativium goes a long

way: the simpler the story, the better you understand it. Storytelling is the opposite of reductionism: 26 letters and some rules of grammar are no story at all.”

◮ “Heroes only win when outnumbered, and things

which have a one-in-a-million chance of succeeding

  • ften do so.”
slide-58
SLIDE 58

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 24 of 28

(Sir Terry) Pratchett’s (⊞) Narrativium (⊞):

◮ “The most common element on the

disc, although not included in the list of the standard five: earth, fire, air, water and surprise. It ensures that everything runs properly as a story.”

◮ “A little narrativium goes a long

way: the simpler the story, the better you understand it. Storytelling is the opposite of reductionism: 26 letters and some rules of grammar are no story at all.”

◮ “Heroes only win when outnumbered, and things

which have a one-in-a-million chance of succeeding

  • ften do so.”
slide-59
SLIDE 59

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 25 of 28

The absolute basics:

Modern basic science in three steps:

  • 1. Find interesting/meaningful/important phenomena

involving spectacular amounts of data.

  • 2. Describe what you see.
  • 3. Explain it.

Beware your assumptions:

Don’t use tools/models because they’re there, or because everyone else does...

slide-60
SLIDE 60

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 25 of 28

The absolute basics:

Modern basic science in three steps:

  • 1. Find interesting/meaningful/important phenomena

involving spectacular amounts of data.

  • 2. Describe what you see.
  • 3. Explain it.

Beware your assumptions:

Don’t use tools/models because they’re there, or because everyone else does...

slide-61
SLIDE 61

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 25 of 28

The absolute basics:

Modern basic science in three steps:

  • 1. Find interesting/meaningful/important phenomena

involving spectacular amounts of data.

  • 2. Describe what you see.
  • 3. Explain it.

Beware your assumptions:

Don’t use tools/models because they’re there, or because everyone else does...

slide-62
SLIDE 62

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 25 of 28

The absolute basics:

Modern basic science in three steps:

  • 1. Find interesting/meaningful/important phenomena

involving spectacular amounts of data.

  • 2. Describe what you see.
  • 3. Explain it.

Beware your assumptions:

Don’t use tools/models because they’re there, or because everyone else does...

slide-63
SLIDE 63

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 26 of 28

Next:

Spring 2014: Complex Networks (CSYS/MATH 303)

◮ Branching networks (rivers, cardiovascular systems) ◮ Redistribution networks (airlines, post) ◮ Structure detection for complex systems ◮ Contagion ◮ Random networks-arama ◮ Distributed Search ◮ Organizational networks ◮ Deeper investigations of scale-free networks ◮ and more...

slide-64
SLIDE 64

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 26 of 28

Next:

Spring 2014: Complex Networks (CSYS/MATH 303)

◮ Branching networks (rivers, cardiovascular systems) ◮ Redistribution networks (airlines, post) ◮ Structure detection for complex systems ◮ Contagion ◮ Random networks-arama ◮ Distributed Search ◮ Organizational networks ◮ Deeper investigations of scale-free networks ◮ and more...

slide-65
SLIDE 65

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 26 of 28

Next:

Spring 2014: Complex Networks (CSYS/MATH 303)

◮ Branching networks (rivers, cardiovascular systems) ◮ Redistribution networks (airlines, post) ◮ Structure detection for complex systems ◮ Contagion ◮ Random networks-arama ◮ Distributed Search ◮ Organizational networks ◮ Deeper investigations of scale-free networks ◮ and more...

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SLIDE 66

Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 27 of 28

References I

[1] P . W. Anderson. More is different. Science, 177(4047):393–396, 1972. pdf (⊞) [2] W. B. Arthur. Why do things become more complex? Scientific American, 268:92, 1993. pdf (⊞) [3] D. Sornette. Critical Phenomena in Natural Sciences. Springer-Verlag, Berlin, 1st edition, 2003. [4] D. W. Thompson. On Growth and From. Cambridge University Pres, Great Britain, 2nd edition, 1952.

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Why Complexify? Universality Symmetry Breaking The Big Theory Final words For your consideration References 28 of 28

References II

[5] D. W. Thompson. On Growth and Form — Abridged Edition. Cambridge University Press, Great Britain, 1961.