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Computation

Computation

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Computation

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  1. Computation

  2. Binary Numbers • Decimal numbers • Binary numbers http://faculty.mc3.edu/pvetere/Applets/APPLETS/NUMSYS/applet_frame.htm

  3. Text Computers have revolutionized our world. They have changed the course of our daily lives, the way we do science, the way we entertain ourselves, the way that business is conducted, and the way we protect our security.

  4. Text Computers have revolutionized our world. They have changed the course of our daily lives, the way we do science, the way we entertain ourselves, the way that business is conducted, and the way we protect our security. Les ordinateurs ont révolutionné notre monde. Ils ont changé le cours de notre vie quotidienne, notre façon de faire la science, la façon dont nous nous divertissons, la façon dont les affaires sont menées, et la façon dont nous protégeons notre sécurité.

  5. Text Computers have revolutionized our world. They have changed the course of our daily lives, the way we do science, the way we entertain ourselves, the way that business is conducted, and the way we protect our security. Les ordinateurs ont révolutionné notre monde. Ils ont changé le cours de notre vie quotidienne, notre façon de faire la science, la façon dont nous nous divertissons, la façon dont les affaires sont menées, et la façon dont nous protégeons notre sécurité. 計算機已經徹底改變我們的世界。當然,他們已經改變了我們的日常生活中,我們這樣做科研,我們自娛自樂的方式,經營的方式進行的方式,以及我們保護我們的安全。

  6. Representing Text • Decide how many characters we need to represent. • Determine the required number of bits. • Ascii: 7 bits. Can encode 27 = 128 different symbols.

  7. Ascii http://www.krisl.net/cgi-bin/ascbin.pl

  8. Representing Text F o u r 01000110 01101111 01110101 01110010

  9. Representing Text T h e n u m b e r i s 1 7 . 54 68 65 20 6E 75 6D 62 65 72 20 69 73 20 31 37 2E

  10. When We Need More Characters What about things like: 简体字

  11. When We Need More Characters What about things like: 简体字 Answer: Unicode: 32 bits. Over 4 million characters. http://www.unicode.org/charts/ A conversion applet: http://www.pinyin.info/tools/converter/chars2uninumbers.html

  12. But What Do Symbols Look Like? Computers have revolutionized our world. Computers have revolutionized our world. Computers have revolutionized our world. Computers have revolutionized our world. Computers have revolutionized our world.

  13. The Basic Idea results = google(text, query)

  14. The Basic Idea results = google(text, query) if word_count(text) > 5000: return(“Done!!”) else: return(“No sleep yet.”)

  15. The Basic Idea results = google(text, query) if word_count(text) > 5000: return(“Done!!”) else: return(“No sleep yet.” display = render(text, font)

  16. The Basic Idea Computers have revolutionized our world.

  17. Digital Images

  18. Pixels

  19. Pixels Now we must turn this 2-dimensional bit matrix into a string of bits.

  20. Pixels 0000110000 0001111000 0011111100 0111111110 0111111110 0111111110 0111001110 0111001110 0111001110 0111001110

  21. Digital Images

  22. Two Color Models

  23. RGB The red channel

  24. RGB The green channel

  25. RGB Red Green Blue

  26. Experimenting with RGB http://www.jgiesen.de/ColorTheory/RGBColorApplet/rgbcolorapplet.html

  27. Representing Sounds

  28. Digitizing Sound

  29. Representing Programs public static TreeMap<String, Integer> create() throws IOException public static TreeMap<String, Integer> create() throws IOException { Integer freq; String word; TreeMap<String, Integer> result = new TreeMap<String, Integer>(); JFileChooser c = new JFileChooser(); int retval = c.showOpenDialog(null); if (retval == JFileChooser.APPROVE_OPTION) { Scanner s = new Scanner( c.getSelectedFile()); while( s.hasNext() ) { word = s.next().toLowerCase(); freq = result.get(word); result.put(word, (freq == null ? 1 : freq + 1)); } } return result; } }

  30. Chess Boards Forsythe-Edwards Notation rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1 http://en.wikipedia.org/wiki/Forsyth-Edwards_Notation

  31. Molecules It’s just a string: AUGACGGAGCUUCGGAGCUAG

  32. The Roots of Modern Technology 1834 Charles Babbage’s Analytical Engine Ada writes of the engine, “The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform.” The picture is of a model built in the late 1800s by Babbage’s son from Babbage’s drawings.

  33. Using Logic • TaiShanHasTail • SmokyHasTail • PuffyHasTail • ChumpyHasTail • SnowflakeHasTail

  34. Using Logic • Panda(TaiShan). • Bear(Smoky). • x (Panda(x) Bear(x). • x (Bear(x) HasPart(x, Tail)). • x (Bear(x) Animal(x)). • x (Animal(x) Bear(x)). • x (Animal(x) y (Mother-of(y, x))). • x ((Animal(x) Dead(x)) Alive(x)). Does TaiShan have a tail?

  35. Search Start state Goal state http://www.javaonthebrain.com/java/puzz15/

  36. What is a Heuristic?

  37. What is a Heuristic? The word heuristic comes from the Greek word  (heuriskein), meaning “to discover”, which is also the origin of eureka, derived from Archimedes’ reputed exclamation, heurika (“I have found”), uttered when he had discovered that the volume of water displaced in the bath equals the volume of whatever (him) got put in the water. This could be used as a method for determining the purity of gold.

  38. What is a Heuristic? The word heuristic comes from the Greek word  (heuriskein), meaning “to discover”, which is also the origin of eureka, derived from Archimedes’ reputed exclamation, heurika (“I have found”), uttered when he had discovered that the volume of water displaced in the bath equals the volume of whatever (him) got put in the water. This could be used as a method for determining the purity of gold. A heuristic is a rule that helps us find something.

  39. An Aside on Checking Facts on the Web Who invented the 15-puzzle? Sam Loyd did: (http://www.jimloy.com/puzz/15.htm) Did he or didn’t he: (http://www.archimedes-lab.org/game_slide15/slide15_puzzle.html) No he didn’t: (http://www.cut-the-knot.org/pythagoras/fifteen.shtml)

  40. Breadth-First Search Is this a good idea?

  41. Depth-First Search

  42. More Interesting Problems The 20 legal initial moves

  43. Scalability Solving hard problems requires search in a large space. To play master-level chess requires searching about 8 ply deep. So about 358 or 21012 nodes must be examined.

  44. Growth Rates of Functions

  45. Scalability

  46. Yet This Exists How?

  47. A Heuristic Function for Chess c1 * material + c2 * mobility + c3 * king safety + c4 * center control + ... Computing material: Pawn     100    Knight    320    Bishop   325    Rook     500    Queen    975    King      32767

  48. The Advent of the Computer 1945 ENIAC The first electronic digital computer 1948 Modified to be a stored program machine

  49. 1949 EDVAC Possibly the first stored program computer

  50. Moore’s Law http://www.intel.com/technology/mooreslaw/