Class 30: Sex, Religion, and Politics

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Problems and ProceduresP=NP RecapEndless Golden AgesGolden CatastrophesOptimism

Transcript of Class 30: Sex, Religion, and Politics

  • 1. Class 30:Sex, Religion, andPoliticscs1120 Fall 2011David Evans2 November 2011

2. PlanRecap big ideas from Monday (withoutHalloweenization)Tysons Sciences Endless Golden Age 2 3. What is a problem? 3 4. Procedures vs. ProblemsProcedure: Problem:a well-defined description of ansequence of stepsinput and desiredthat can be executed outputmechanically (i.e., bya Turing Machine) 4 5. Example: FactoringFactoring Procedure Factoring Problemdef factors(n): Input: a number, n, that is res = [] a product of two primes for d in range(2, n):numbers if n % d == 0: Output: two primeres.append(d) numbers, p and q, such return res that pq = nWhat is the running time ofWhat is the time complexitythis factoring procedure?of the factoring problem? 5 6. P=NP ?P = set of all problems that can be solved byalgorithms with running times in O(Nk)where N is the input size and k is anyconstant.NP = set of all problems whose answer can bechecked by algorithms with running timesin O(Nk) where N is the input size and k isany constant. 7. What about factoring?How hard is the factoring problem? Input: a number, n Output: two integers > 1, p and q, such that pq = nHow hard is the CHECK-FACTORS problem?Input: p, q, n (three integers, all greater than 1)Output: true if n = pq, false otherwise 8. ACM1: Beyond Cyberspace (2001) Neil de Grasse Tyson: "Awash in Data, Awash in Discoveries: Defining the Golden Age of ScienceRice Hall Dedication Speaker!Alan Kay: "The Computer Revolution Hasnt Happened Yet"Friday,President and Disney Fellow, Walt Disney(Vice Nov 18, 3pm: The FutureBelongs to the InnovatorsImagineering) Dean Kamen: "Engineering the Future Depends on Future Engineers" (President and Owner, DEKA Research & Development Corporation and Founder of FIRST) 9. Sciences Endless Golden Age 10. If youre going to use your computer tosimulate some phenomenon in theuniverse, then it only becomes interestingif you change the scale of thatphenomenon by at least a factor of 10. For a 3D simulation, an increase by a factorof 10 in each of the three dimensionsincreases your volume by a factor of 1000.What is the asymptotic running timefor simulating the universe? 11. If youre going to use yourcomputer to simulate somephenomenon in theuniverse, then it only becomesinteresting if you change thescale of that phenomenon by atleast a factor of 10. For a 3Dsimulation, an increase by afactor of 10 in each of the threedimensions increases yourvolume by a factor of 1000. 12. Simulating the UniverseWork scales linearly with volume ofsimulation: scales cubically with scale(n3) When we double the scale of the simulation, the work octuples! (Just like oceanography octopi simulations) 13. Orders of Growth140 n3 simulating120 universe100 80 60 40 n2 20 n 0123 45 14. Orders of Growth1400000 simulating1200000 universe1000000 800000 600000 400000 200000 01 11 21 31 41 51 61 71 81 91 101 15. Orders of Growth7E+32factors 2n6E+325E+324E+323E+322E+321E+320 simulating1 11 21 31 41 51 61 71 81 91 101universe 16. Astrophysics and Moores LawSimulating universe is (n 3)Moores law: computing powerdoubles every 18 monthsDr. Tyson: to understand somethingnew about the universe, need toscale by 10x How long does it take to know twice as much about the universe? 17. Knowledge of the Universeimport math# 18 months * 2 = 12 months * 3yearlyrate = math.pow(4, 1.0/3.0) # cube rootdef simulation_work(scale):return scale ** 3def knowledge_of_universe(scale):return math.log(scale, 10) # log base 10def computing_power(nyears): 18. Knowledge of the Universeimport math# 18 months * 2 = 12 months * 3yearlyrate = math.pow(4, 1.0/3.0) # cube rootdef simulation_work(scale):return scale ** 3def knowledge_of_universe(scale):return math.log(scale, 10) # log base 10def computing_power(nyears):def computing_power(nyears):return yearlyrate ** nyearsif nyears == 0: return 1else: return yearlyrate * computing_power(nyears - 1) 19. Knowledge of the Universedef computing_power(nyears):return yearlyrate ** nyearsdef simulation_work(scale):return scale ** 3def knowledge_of_universe(scale):return math.log(scale, 10) # log base 10def relative_knowledge_of_universe(nyears):scale = 1while simulation_work(scale + 1) >> relative_knowledge_of_universe(0)1.0>>> relative_knowledge_of_universe(1)1.0413926851582249>>> relative_knowledge_of_universe(2)1.1139433523068367>>> relative_knowledge_of_universe(10)1.6627578316815739>>> relative_knowledge_of_universe(15)2.0>>> relative_knowledge_of_universe(30)3.0064660422492313>>> relative_knowledge_of_universe(60)5.0137301937137719>>> relative_knowledge_of_universe(80)6.351644238569782Will there be any mystery left in the Universe when you die? 23. Only two things areinfinite, the universeand humanstupidity, and Imnot sure about theformer. Albert Einstein 24. The Endless Golden AgeGolden Age period in which knowledge/qualityof something improves exponentiallyAt any point in history, half of what is knownabout astrophysics was discovered in theprevious 15 years!Moores law today, but other advances previously:telescopes, photocopiers, clocks, agriculture, etc. Accumulating 4% per year => doubling every 15 years! 25. Endless/Short Golden AgesEndless golden age: at any point in history, theamount known is twice what was known 15years agoContinuous exponential growth: (kn) k is some constant (e.g., 1.04), n is number of yearsShort golden age: knowledge doubles during ashort, golden period, but only improveslinearly most of the timeMostly linear growth: (n) n is number of years 26. Average Goals per Game, FIFA World Cups3456 21930193419381950195419581962 Goal-den age1966197019741978198219861990passback rule1994 Changed goalkeeper1998200220062010 27. 27 28. Computing Power 1969-2011(in Apollo Control Computer Units)300,000,000250,000,000200,000,000150,000,000100,000,000 50,000,000 0 29. Computing Power 1969-1990 (in Apollo Control Computer Units)18,00016,00014,00012,00010,000 8,000 6,000 4,000 2,0000 .5.5.5 .5.5 .5.5 69 727578 8184 8790707376 7982 85881919 19 1919 1919 1919 19 1919 1919 19 30. Computing Power 2008-2050?450,000400,000 Theres an unwritten rule in350,000 astrophysics: your computer 30 years from now?!300,000 simulation must end before you die.250,000Neil deGrasse Tyson200,000150,000 Human brain:Brain simulator today (IBM Blue Brain):~100 Billion 100,00010,000 neurons neurons30 Million connections50,000 100 Trillion connections 02008 2011 2014 2017 2020 2023 2026 2029 2032 2035 2038 2041 2044 2047 20502011 = 1 computing unit 31. More Moores Law?Any physical quantity thats growing Current technologies are alreadyexponentially predicts a disaster, you simply slowing down...cant go beyond certain major limits.Gordon Moore (2007) An analysis of the history of technology shows that technological change is exponential, contrary to the common-sense intuitive linear view. So we wont experience 100 years of progress in the 21st century-it will be more like 20,000 years of progress (at todays rate). The returns, such as chip speed and cost- effectiveness, also increase exponentially. Theres even exponential growth in the rate of exponential growth. Within a few decades, machine intelligence will surpass human intelligence, leading to the Singularity technological change so rapid and profound it represents a rupture in the fabric of human history. The implications include the merger of biological and non-biological intelligence, immortal software-based humans, and ultra-high levels of intelligence that expand outward in the universe at the speed of light.but advances wont come from more transistors withRay Kurzweilcurrent technologies...newtechnologies, algorithms, parallelization, architectures, 32. Log scale: straight line = exponential curve!32 33. The Real Golden Rule?Why do fields like astrophysics, medicine, biology andcomputer science have endless golden ages, butfields likemusic (1775-1825)rock n roll (1962-1973)*philosophy (400BC-350BC?)art (1875-1925?)soccer (1950-1966)baseball (1925-1950?)movies (1920-1940?)have short golden ages?* or whatever was popular when you were 16. 34. Golden Ages orGolden Catastrophes? 35. PS5, Question 1eQuestion 1: For each f and g pair below, argueconvincingly whether or not g is (1) O(f), (2)(f), and (3) (g) (e) g: the federal debt n years from today,f: the US population n years from today 36. Malthusian CatastropheReverend ThomasRobertMalthus, Essay onthe Principle ofPopulation, 1798 37. 37 38. Malthusian CatastropheThe great and unlooked for discoveries that have takenplace of late years in natural philosophy, the increasingdiffusion of general knowledge from the extension ofthe art of printing, the ardent and unshackled spirit ofinquiry that prevails throughout the lettered and evenunlettered world, have all concurred to lead manyable men into the opinion that we were touching on aperiod big with the most important changes, changesthat would in some measure be decisive of the futurefate of mankind. 39. Malthus PostulatesI think I may fairly make two postulata.First, that food is necessary to the existence ofman.Secondly, that the passion between the sexesis necessary and will remain nearly in itspresent state. These two laws, ever since we have had any knowledge of mankind, appear to have been fixed laws of our nature, and, as we have not hitherto seen any alteration in them, we have no right to conclude that they will ever cease to be what they now are 40. Malthus ConclusionAssuming then my postulata as granted, Isay, that the power of population is indefinitelygreater than the power in the earth to producesubsistence for man. Population, when unchecked, increases in ageometrical ratio. Subsistence increases only inan arithmetical ratio. A slight acquaintancewith numbers will show the immensity of thefirst power in comparison of the second. 41. Malthusian Cata