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

2. 21 February 2003CS 200 Spring 20032 Science’s Endless Golden Age

3. 21 February 2003CS 200 Spring 20033 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)? (n3)(n3) When we double the size of the simulation, the work octuples! (Just like oceanography octopi simulations)

4. 21 February 2003CS 200 Spring 20034 Orders of Growth bubblesort simulating universe insertsort-tree

5. 21 February 2003CS 200 Spring 20035 Astrophysics and Moore’s Law Simulating universe is  ( n 3 ) 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?

6. 21 February 2003CS 200 Spring 20036 ;;; 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  (n 3 ) 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)) Knowledge of the Universe

7. 21 February 2003CS 200 Spring 20037 (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))) Knowledge of the Universe

8. 21 February 2003CS 200 Spring 20038 > (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 Will there be any mystery left in the Universe when you die? Only two things are infinite, the universe and human stupidity, and I'm not sure about the former. Albert Einstein

9. 21 February 2003CS 200 Spring 20039 Any Harder Problems? Understanding the universe is  ( n 3 ) Are there any harder problems?

10. 21 February 2003CS 200 Spring 200310 Who’s the real genius?

11. 21 February 2003CS 200 Spring 200311 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 …

12. 21 February 2003CS 200 Spring 200312 Possible Moves Start Peg board game n = number of holes Initially, there are n-1 pegs. Cracker Barrel’s game has n = 15 Assume there are always exactly 2 possible moves, how many possible games are there?

13. 21 February 2003CS 200 Spring 200313 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 = 2 n-2 For n = 15, there are 2 13 = 8192

14. 21 February 2003CS 200 Spring 200314 All Cracker Barrel Games (starting with peg 2 1 missing) Pegs Left Number of Ways Fraction of Games IQ Rating 115500.01 “You’re Genius” 2206860.15 “You’re Purty Smart” 3627360.46 “Just Plain Dumb” 4467280.33 “Just Plain Eg-no-ra-moose” 556880.04 63740.0027 7820.00058 1020.00001

15. 21 February 2003CS 200 Spring 200315 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) (2n)

16. 21 February 2003CS 200 Spring 200316 True Genius? “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 “80% of life is just showing up.” Woody Allen

17. 21 February 2003CS 200 Spring 200317 Orders of Growth bubblesort simulating universe insertsort-tree peg board game

18. 21 February 2003CS 200 Spring 200318 Orders of Growth bubblesort simulating universe insertsort-tree peg board game

19. Orders of Growth simulating universe peg board game “tractable” “intractable” 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. 21 February 2003CS 200 Spring 200320 Any other procedures we’ve seen that are more work than simulating the Universe?

21. 21 February 2003CS 200 Spring 200321 Break Lorenz Cipher Procedure Try all possible wheel settings How many possible wheel settings: 5choices for first wheel * 5choices for second wheel * 5 choices for third wheel What is n ? –The number of wheels There are 5 n possible wheel settings

22. 21 February 2003CS 200 Spring 200322 Lorenz Deciphering For PS4: you had 3 wheels, each with 5 possible settings: 5 3 = 125 possible combinations to try For WWII: Nazis has 12 wheels, each with more than 5 settings (up to 61 settings) 5 12 = 244 140 625 possible combinations

23. 21 February 2003CS 200 Spring 200323 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!

24. 21 February 2003CS 200 Spring 200324 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.

25. 21 February 2003CS 200 Spring 200325 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?

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

27. 21 February 2003CS 200 Spring 200327 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)?

28. 21 February 2003CS 200 Spring 200328 Grade Inflation or Scale Compression? 2.00average GPA in 1970 (“gentleman’s C”?) * 2better students 1970-1985 * 2better students 1985-2003 * 3admitting women, non-whites (1971) * 1.54 population increase * 0.58increase in enrollment Virginia 19704,648,494 Virginia 20007,078,515 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 Students 1970 11,000 Students 2002 18,848 (12,595 UG)

29. 21 February 2003CS 200 Spring 200329 The Liberal Arts Trivium (3 roads) language Quadrivium (4 roads) numbers GrammarRhetoricLogicArithmetic Geometry Music Astronomy From Lecture 1:

30. 21 February 2003CS 200 Spring 200330 Liberal Arts 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 BNF replacement rules for describing languages, rules of evaluation for meaning Not yet… Interfaces between components, program and user Rules of evaluation, if, recursive definitions Not much yet… wait until April Curves as procedures, fractals Yes, even if we can’t figure out how to play “Hey Jude!” Yes: Neil deGrasse Tyson says so Trivium Quadrivium From Lecture 1:

31. 21 February 2003CS 200 Spring 200331 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 21 st century playwright