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Class 6 SummaryRetracing our steps

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

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Ch. 1: Complexity•Insect colonies•The brain•The immune system•Economies•The World-wide Web

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Agent-based Modeling

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Properties of Complex Systems

•Complex collective behavior• Information processing•Adaptation

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Ch. 2Dynamics, Chaos, and Prediction

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𝑥𝑛+1=𝑅𝑥𝑛 (1−𝑥𝑛)

Logistic population model

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Simple and non-linear

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Show us pictures!

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Feigenbaum’s Constant

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4.6692016

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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 9review

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Ch. 3 Information

Entropy:

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A big picture

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reductionistmechanics

thermodynamics

statisticalmechanics

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Maxwell’s Demon

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Appears to defy the Second Law of thermodynamicsby decreasing entropy

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

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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

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Suppose the message is a single symbol with two possible values

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New Horizons

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12 watts

1000 bits/second

18 months

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Ch. 4 Computation

•The Universe is a computer that computes its own future in real time•We’ll look at a middle ground.

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Computation•Hilbert’s Program: Is mathematics• complete,• consistent and• decidable? (Entscheidungsproblem)

• Answers•Goedel’s theorem• Turing’s machine 18

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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

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The Go-To Book

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A Turing machine

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tapereader

rules andstate

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

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Chapter 5Evolution

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“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 25

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Jean-Baptiste Lamarck, 1744-1829•Advocated inheritance of acquired characteristics•example: wading birds•Evolution had a “tendency to progression”• Initially impressed Charles Darwin

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Charles Darwin, 1809-1882

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1854?

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

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Gregor Mendel, 1822-1884

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Gregor Mendel, 1822-1884• Founder of modern genetics•Disproved Lamarckian inheritance•Discovered discrete “factors” in inheritance• genes occur in pairs• alleles are dominant and recessive

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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 31

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

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Stephen Jay Gould, 1941-2002

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punctuated equilibriascien

ce po

pular

izer

“living legend”

deve

lopmen

tal bi

ology

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Active debatePoints of general agreement• life has a single ancestor•evolution continuing•natural selection an important force•no intelligent directing force

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Ch. 6 Genetics, Simplified

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HC SVNT DRACONES

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Defining and Measuring Complexity

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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

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Some measures of ComplexityMeasures based on•shortest encoding program: Kolmogrov•effective complexity: Gell-Mann• fractal dimensions: D•hierarchy and near-decomposability•Herbert Simon 39

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No satisfactory,universal,

computablemeasure of complexity

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A chronic issue

Connecting reasonable concepts to quantitative measures

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Chapter 8Self-reproducing computer programs

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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

43Where are they?

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John von Neumann, 1903-1957…• interested in self-replicating machines•von Neumann Universal Constructor

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von Neumann probes…current state of the art: 3D printing

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Artificial life

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Jewish folklore

Most famously,16th century Prague

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Artificial life…

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Artificial life (A-Life)

Very contentious topic

Two general forms•Strong A-Life•Weak A-Life

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A-Life…

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an adult hermaphrodite C. elegans worm

www.openworm.org

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Computer replication,evolution and

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TheSingularity

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