Class 6 Summary Retracing our steps Class 6 Summary 1 review

Preface: Reductionism good for classical physics relativity quantum mechanics bad for nonlinear, chaotic systems weather prediction population dynamics Class 6 Summary 2 review

Ch. 1: Complexity Insect colonies The brain The immune system Economies The World-wide Web Class 6 Summary 3 review

Agent-based Modeling Class 6 Summary 4 review

Properties of Complex Systems Complex collective behavior Information processing Adaptation Class 6 Summary 5 review

Ch. 2 Dynamics, Chaos, and Prediction Class 6 Summary 6 Logistic population model review Simple and non-linear

Show us pictures! Class 6 Summary 7 review

Feigenbaum’s Constant Class 6 Summary review

Ch. 2 Takeaway Simple, deterministic systems can generate apparent random behavior Long term prediction for such systems may be impossible in principle Such systems may show surprising regularities: period-doubling and Feigenbaum’s Constant Class 6 Summary 9 review

Ch. 3 Information Class 6 Summary 10

A big picture Class 6 Summary 11 reductionist mechanics thermodynamics statistical mechanics

Maxwell’s Demon Class 6 Summary 12 Appears to defy the Second Law of thermodynamics by decreasing entropy

Maxwell’s Demon and Entropy This issue is not completely settled. It appears that entropy increases because the demon acquires and subsequently erases information Class 6 Summary 13

Shannon’s theory Information channel is a stream of symbols Shannon entropy is expressed in terms of the probabilities of the symbols in the channel Class 6 Summary 14

Suppose the message is a single symbol with two possible values Class 6 Summary 15

New Horizons Class 6 Summary watts 1000 bits/second 18 months

Ch. 4 Computation Class 6 Summary 17

Computation Hilbert’s Program: Is mathematics complete, consistent and decidable? (Entscheidungsproblem) Answers Goedel’s theorem Turing’s machine Class 6 Summary 18

Godel’s Theorem If arithmetic is consistent then there are true statements about arithmetic which cannot be proved. Mitchell’s example: This statement is not provable If false, then a false statement can be proved (really bad news). If true, then a true statement cannot be proved. Class 6 Summary 19

The Go-To Book Class 6 Summary 20

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A Turing machine Class 6 Summary 22 tape reader rules and state

Turing showed… There is no definite procedure for proving any mathematical statement true or false in a finite number of steps. Class 6 Summary 23

Class 6 Summary 24 Chapter 5 Evolution

“All great truths begin as blasphemies.” -- GBS “No idea in science has been more threatening to humans’ conceptions about themselves than Darwin’s theory of evolution; it arguably has been the most controversial idea in the history of science.” - MM Class 6 Summary 25

Jean-Baptiste Lamarck, Advocated inheritance of acquired characteristics example: wading birds Evolution had a “tendency to progression” Initially impressed Charles Darwin Class 6 Summary 26

Charles Darwin, Class 6 Summary ?

Evolution by natural selection Offspring influenced by random mutations not acquired characteristics Competition for reproduction tests individuals Improvements passed to offspring Change is gradual Class 6 Summary 28

Gregor Mendel, Class 6 Summary 29

Gregor Mendel, Founder of modern genetics Disproved Lamarckian inheritance Discovered discrete “factors” in inheritance genes occur in pairs alleles are dominant and recessive Class 6 Summary 30

The Modern Synthesis Natural selection is the major mechanism of evolutionary change Evolution is a gradual process, driven by random mutation genetic recombination Speciation is the result of a microscopic process of selection Class 6 Summary 31

Challenges to the Modern Synthesis punctuated equilibria versus gradualism evolution by “jerks” evolution by “creeps” historical contingency including catastrophes biological constraints limitations on evolution Class 6 Summary 32

Stephen Jay Gould, Class 6 Summary 33 punctuated equilibria science popularizer “living legend” developmental biology

Active debate Points of general agreement life has a single ancestor evolution continuing natural selection an important force no intelligent directing force Class 6 Summary 34

Ch. 6 Genetics, Simplified Class 6 Summary 35

Class 6 Summary 36 HC SVNT DRACONES

Chapter 7 Defining and Measuring Complexity Class 6 Summary 37

What is Complexity? no agreed-upon definition of complexity Wikipedia lists eight fields in which complexity is defined in different ways no single science of complexity Class 6 Summary 38

Some measures of Complexity Measures based on shortest encoding program: Kolmogrov effective complexity: Gell-Mann fractal dimensions: D hierarchy and near- decomposability Herbert Simon Class 6 Summary 39

Class 6 Summary 40 No satisfactory, universal, computable measure of complexity

A chronic issue Connecting reasonable concepts to quantitative measures Class 6 Summary 41

Chapter 8 Self-reproducing computer programs Class 6 Summary 42

The Fermi Paradox… Our sun is a typical star Billions of stars are billions of years older than the sun Plenty of time for advanced cultures to explore the Milky Way Class 6 Summary 43 Where are they?

John von Neumann, … interested in self-replicating machines von Neumann Universal Constructor Class 6 Summary 44

von Neumann probes… current state of the art: 3D printing Class 6 Summary 45

Artificial life Class 6 Summary 46 Jewish folklore Most famously, 16 th century Prague

Artificial life… Class 6 Summary 47

Artificial life (A-Life) Very contentious topic Two general forms Strong A-Life Weak A-Life Class 6 Summary 48

A-Life… Class 6 Summary 49 an adult hermaphrodite C. elegans worm

Computer replication, evolution and Class 6 Summary 50 The Singularity

Class 6 Summary 51 Finis review