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David Evans cs.virginia/evans

David Evans http://www.cs.virginia.edu/evans. Class 15: Golden Ages and Astrophysics. CS200: Computer Science University of Virginia Computer Science. Science’s Endless Golden Age. Astrophysics.

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David Evans cs.virginia/evans

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  1. David Evans http://www.cs.virginia.edu/evans Class 15: Golden Ages and Astrophysics CS200: Computer Science University of Virginia Computer Science

  2. Science’s Endless Golden Age CS 200 Spring 2003

  3. Astrophysics • “If you’re going to use your computer to simulate some phenomenon in the universe, then it only becomes interesting if you change the scale of that phenomenon by at least a factor of 10. … For a 3D simulation, an increase by a factor of 10 in each of the three dimensions increases your volume by a factor of 1000.” • How much work is astrophysics simulation (in  notation)? When we double the size of the simulation, the work octuples! (Just like oceanography octopi simulations) (n3) CS 200 Spring 2003

  4. Orders of Growth simulating universe bubblesort insertsort-tree CS 200 Spring 2003

  5. Astrophysics and Moore’s Law • Simulating universe is(n3) • Moore’s law: computing power doubles every 18 months • Tyson: to understand something new about the universe, need to scale by 10x • How long does it take to know twice as much about the universe? CS 200 Spring 2003

  6. Knowledge of the Universe ;;; doubling every 18 months = ~1.587 * every 12 months (define (computing-power nyears) (if (= nyears 0) 1 (* 1.587 (computing-power (- nyears 1))))) ;;; Simulation is  (n3) work (define (simulation-work scale) (* scale scale scale)) (define (log10 x) (/ (log x) (log 10))) ;;; log is base e ;;; knowledge of the universe is log 10 the scale of universe ;;; we can simulate (define (knowledge-of-universe scale) (log10 scale)) CS 200 Spring 2003

  7. Knowledge of the Universe (define (computing-power nyears) (if (= nyears 0) 1 (* 1.587 (computing-power (- nyears 1))))) ;;; doubling every 18 months = ~1.587 * every 12 months (define (simulation-work scale) (* scale scale scale)) ;;; Simulation is O(n^3) work (define (log10 x) (/ (log x) (log 10))) ;;; primitive log is natural (base e) (define (knowledge-of-universe scale) (log10 scale)) ;;; knowledge of the universe is log 10 the scale of universe we can simulate (define (find-knowledge-of-universe nyears) (define (find-biggest-scale scale) ;;; today, can simulate size 10 universe = 1000 work (if (> (/ (simulation-work scale) 1000) (computing-power nyears)) (- scale 1) (find-biggest-scale (+ scale 1)))) (knowledge-of-universe (find-biggest-scale 1))) CS 200 Spring 2003

  8. > (find-knowledge-of-universe 0) 1.0 > (find-knowledge-of-universe 1) 1.041392685158225 > (find-knowledge-of-universe 2) 1.1139433523068367 > (find-knowledge-of-universe 5) 1.322219294733919 > (find-knowledge-of-universe 10) 1.6627578316815739 > (find-knowledge-of-universe 15) 2.0 > (find-knowledge-of-universe 30) 3.00560944536028 > (find-knowledge-of-universe 60) 5.0115366121349325 > (find-knowledge-of-universe 80) 6.348717927935257 Only two things are infinite, the universe and human stupidity, and I'm not sure about the former. Albert Einstein Will there be any mystery left in the Universe when you die? CS 200 Spring 2003

  9. Any Harder Problems? • Understanding the universe is (n3) • Are there any harder problems? CS 200 Spring 2003

  10. Who’s the real genius? CS 200 Spring 2003

  11. Solving the Peg Board Game • Try all possible moves • Try all possible moves from the positions you get after each possible first move • Try all possible moves from the positions you get after trying each possible move from the positions you get after each possible first move • … CS 200 Spring 2003

  12. Possible Moves Peg board game n = number of holes Initially, there are n-1 pegs. Cracker Barrel’s game has n = 15 Start Assume there are always exactly 2 possible moves, how many possible games are there? CS 200 Spring 2003

  13. Cracker Barrel Game • Each move removes one peg, so if you start with n-1 pegs, there are up to n-2 moves • Assume (conservatively) there are just two possible choices for every move. 2 * 2 * 2 * 2 * … * 2 = 2n-2 • For n = 15, there are 213 = 8192 CS 200 Spring 2003

  14. All Cracker Barrel Games(starting with peg 2 1 missing) CS 200 Spring 2003

  15. How much work is our straightforward peg board solving procedure? Note: I don’t know if this is the best possible procedure for solving the peg board puzzle. So the peg board puzzle problem might not be harder than understanding the Universe (but it probably is.)  (2n) CS 200 Spring 2003

  16. “Genius is one percent inspiration, and ninety-nine percent perspiration.” Thomas Alva Edison “Genius is one percent sheer luck, but it takes real brilliance to be a true eg-no-ra-moose.” Cracker Barrel True Genius? “80% of life is just showing up.” Woody Allen CS 200 Spring 2003

  17. Orders of Growth simulating universe peg board game bubblesort insertsort-tree CS 200 Spring 2003

  18. Orders of Growth peg board game simulating universe bubblesort insertsort-tree CS 200 Spring 2003

  19. Orders of Growth peg board game “intractable” “tractable” simulating universe I do nothing that a man of unlimited funds, superb physical endurance, and maximum scientific knowledge could not do. – Batman (may be able to solve intractable problems, but computer scientists can only solve tractable ones for large n)

  20. Any other procedures we’ve seen that are more work than simulating the Universe? CS 200 Spring 2003

  21. Break Lorenz Cipher Procedure • Try all possible wheel settings • How many possible wheel settings: 5 choices for first wheel * 5 choices for second wheel * 5 choices for third wheel • What is n? • The number of wheels • There are 5n possible wheel settings CS 200 Spring 2003

  22. Lorenz Deciphering • For PS4: you had 3 wheels, each with 5 possible settings: 53 = 125 possible combinations to try • For WWII: Nazis has 12 wheels, each with more than 5 settings (up to 61 settings) 512 = 244 140 625 possible combinations CS 200 Spring 2003

  23. PS4 • Bletchley Park’s cryptographers had to solve a problem that is 1 953 125 times harder than PS4! • And they also had to figure out the structure of the Lorenz machine themselves! • But…having bombs dropping on you is at least 1 million times more motivating than getting a gold star! CS 200 Spring 2003

  24. The Endless Golden Age • Golden Age – period in which knowledge/quality of something doubles quickly • At any point in history, half of what is known about astrophysics was discovered in the previous 15 years! • Moore’s law today, but other advances previously: telescopes, photocopiers, clocks, etc. CS 200 Spring 2003

  25. The Real Golden Rule? Why do fields like astrophysics, medicine, biology and computer science (?) have “endless golden ages”, but fields like • music (1775-1825) • rock n’ roll (1962-1973, or whatever was popular when you were 16) • philosophy (400BC-350BC?) • art (1875-1925?) • soccer (1950-1974) • baseball (1925-1950) • movies (1930-1940) have short golden ages? CS 200 Spring 2003

  26. Goal-den age Average Goals per Game, FIFA World Cups Changed goalkeeper passback rule

  27. Endless Golden Age and “Grade Inflation” • Average student gets twice as smart and well-prepared every 15 years • You had grade school teachers (maybe even parents) who went to college! • If average GPA in 1970 is 2.00 what should it be today (if grading standards didn’t change)? CS 200 Spring 2003

  28. Grade Inflation or Scale Compression? 2.00 average GPA in 1970 (“gentleman’s C”?) * 2 better students 1970-1985 * 2 better students 1985-2003 * 3 admitting women, non-whites (1971) * 1.54 population increase * 0.58 increase in enrollment Students 1970 11,000 Students 2002 18,848 (12,595 UG) Average GPA today should be: 21.4 CS200 has only the best of the best students, and only the best 35/40 of them stayed in the course after PS1, so the average grade in CS200 should be 21.4*2*2*40/35 = 98.0 CS 200 Spring 2003

  29. From Lecture 1: The Liberal Arts language numbers Quadrivium (4 roads) Trivium (3 roads) Grammar Rhetoric Logic Arithmetic Music Geometry Astronomy CS 200 Spring 2003

  30. From Lecture 1: Liberal Arts BNF replacement rules for describing languages, rules of evaluation for meaning • Grammar: study of meaning in written expression • Rhetoric: comprehension of verbal and written discourse • Logic: argumentative discourse for discovering truth • Arithmetic: understanding numbers • Geometry: quantification of space • Music: number in time • Astronomy Not yet… Interfaces between components, program and user Trivium Rules of evaluation, if, recursive definitions Not much yet… wait until April Curves as procedures, fractals Quadrivium Yes, even if we can’t figure out how to play “Hey Jude!” Yes: Neil deGrasse Tyson says so CS 200 Spring 2003

  31. Charge • Enough with all the liberal arts stuff, every problem on Exam 1 is about money! • No problem in Exam 1 is as hard as simulating the universe • If you want to do something important and be remembered, work in a field that has a short golden age from 2003-2018 • Shakespeare will be known a thousand years from now, but no one will have heard of any 21st century playwright CS 200 Spring 2003

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