Presentation Main Seminar „Didactics of Computer Science“

1. PresentationMain Seminar „Didactics of Computer Science“ Version: 2003-02-27 Binary Coding: Alex Wagenknecht Abacus: Christian Simon Leibniz (general): Katrin Radloff Leibniz (calculating machine): Torsten Brandes Babbage: Anja Jentzsch Hollerith: Jörg Dieckmann

2. The binary code The old chinese tri- and hexagrams of the historical „I Ging“. Gottfried Wilhelm Leibniz and his Dyadic. And, at the end, the modern ASCII-code.

3. The I-Ging (#1) • The emergence of the Chinese I-Ging, that is known as „The book of transformations“, is approximately dated on the 8th century B.C. and is to have been written by several mythical,Chinese kings or emperors.

4. The I-Ging (#2) • The book represents a system of 64 hexagrams, to which certain characteristics were awarded. • Furthermore it gives late continuously extended appendix, in which these characteristics are interpreted.

5. The I-Ging (#3) • The pointingnesses and explanations were applied to political decisions and questions of social living together and moral behavior. Even scientific phenomena should be described and explained with the help of these book.

6. The I-Ging (#4) • A hexagram consists of a combination of two trigrams. • Such a tri gram consists of three horizontal lines, which are drawn either broken in the center or drawn constantly.

7. The I-Ging (#5) • These linesare to be seen as a binary character. The oppositeness expressed thereby was interpreted laterin the sense of Yin Yang dualism.

8. The I-Ging (#6) • The 64 possible combinations of the trigrams were brought now with further meanings in connection and arranged according to different criteria. One of the most dominant orders is those of the Fu-Hsi, a mythicalgod-emperor of old China.

9. The I-Ging (#7) the order of Fu-Hsi

10. Leibniz and the Dyadic (#1) • That the completely outweighing number of the computers works binary, is today school book wisdom. • But, that the mathematicalybasiswere put exactly 300 years ago, knows perhaps still a few historian and interested mathematicians and/or computer scientists.

11. Leibniz and the Dyadic (#2) • On 15 March l679 Gottfried Willhelm Leibniz wrote his work with the title „The dyadic system of numbers". • Behind theDyadic of Leibniz hides itselfs nothing less than binary arithmetics, thus the replacement of the common decimal number system by the representation of all numbers only with the numbers 0 and 1.

12. Leibniz and the Dyadic (#3) the binaries from 0 to16

13. Leibniz and the Dyadic (#4) • Out of its handwritten manuscript you can take the following description: "I turn into now for multiplication. Here it is again clear that you can`t imagine anything easier. Because you don`t need a pythagoreical board (note: a table with squarearrangement of the multiplication table) and this multiplication is the only one, which admits no different multiplication than the already known. You write only the number or, at their place, 0.

14. Leibniz and the Dyadic (#5) • Approximately half a century Leibniz stated in letters and writings its strong and continuous interest in China. • If this concentrated at first on questions to the language, primarily the special writing language of China, then and deepened it extended lastingly 1689 by the discussions led in Rome with the pater of the Jesuit Order Grimaldi.

15. Leibniz and the Dyadic (#6) • Thus did developLeibniz‘vision of an up to then unknown culture and knowledge exchange with China: Not the trade with spices and silk against precious metals should shape the relationship with Europe, but a realization exchange in all areas, in theory such as in practice.

16. The ASCII-code (#1) • The “AmericanStandard Code for Information Interchange“ ASCII was suggested in 1968 on a small letter as standard X3.4-1963 of the ASP and extended version X3.4-1967. • The code specifies a dispatching, in which each sign of latin alphabet and each arabic number corresponds to a clear value.

17. The ASCII-code (#2) • This standardisation made now information exchange possible between different computer systems. • 128 characters were specified, from which an code length of 7 bits results. • The ASCII-code was taken over of the ISO as an ISO 7-Bit code and registered later in Germany as DIN 66003.

18. The ASCII-code (#3) • The modern ASCII-code is a modification of the ISO 7-Bit code (in Germany DIN 66003 and/or German Referenzversion/DRV). • It has the word length 7 and codes decimal digits, the characters of the latin alphabet as well as special character. From the 128 possible binary words are 32 pseudo-words and/or control characters.

19. The ASCII-code (#4) The 7-bit ASCII-code

20. The ASCII-code (#5) • Later developed extended 8-bit versions of ASCII have 256 characters, in order to code further, partial country dependent special characters. • Unfortunately there are however very different versions, which differ from one to another, what a uniform decoding prevented. • Later developments like the unicode try to include the different alphabets by a larger word length (16 bits, 32 bits).

21. History of abacus The abacus' history started ca. 2600 years ago in Madagaskar. There to count the amount of soldiers, every soldier had to pass a narrow passage. For each passing soldier a little stone was put into a groove. When ten stones were in that groove they were removed and one stone was put into the next groove.

22. Counting soldiers

23. Mutation of grooves and stones

24. Development of soroban In 607 the japanese regent Shotoku Taishi made a cultural approach to China. The chinese suan-pan comes to Japan and became optimized by Taishi by removing one of the upper balls. Since 1940 the new soroban with only four lower balls is used.

25. Roman abacus

26. Calculating on tables This structure was found on tables, boards and on kerchiefs.

27. 1 2 3 0 0 1 4 8 2 4 0 1 1 5 0 5 5 0 1 1 6 2 8 6 Gelosia procedure of writing calculation 0 5 6 0 8 8 123 · 456 = 56008

28. 2 3 1 9 2 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 7 8 0 0 0 3 1 2 2 0 0 0 0 1 4 5 6 2 4 4 6 8 2 5 6 1 0 4 7 4 3 2 6 8 6 8 3 2 4 5 1 5 8 9 9 2 9 8 7 7 6 3 2 1 Napier Bones

29. 3 9 2 1 1 0 1 0 0 1 1 3 0 1 8 7 0 5 6 1 2 2 2 2 0 1 0 1 4 0 6 4 3 6 6 8 1 8 5 7 9 4 2 9 5 2 4 2 4 2 1 3 0 6 8 8 7 Calculating with Napier Bones 239 · 8 = 1 9 1 2

30. Gottfried Wilhelm Leibniz(1646-1716) http://www.ualberta.co/~nfriesen/582/enlight.htm A presentation by Kati Radloff 27.02.2003 radloff@inf.fu-berlin.de

31. Leibniz‘ Fields of Interest Mathematics Physics Philosophy

32. Leibniz‘ Father • died, when Leibniz was six years of age. • Leibniz‘ mother followed him a couple of years later

33. Nikolai-School Leibniz taught himself Latin at the age of 8. He graduated from this high school at 14 years of age as one of the best students. He then attended the philosophical and juridical faculty of the University of Altdorf. http://www.genetalogie.de/gallery/leib/leibhtml/leib1a.html

34. The University of Altdorf Here, Leibniz graduated after 6 years of intense studying with a doctor‘s degree and a habilitation at the age of 20. http://www.genetalogie.de/gallery/leib/leibhtml/leib2.html Leibniz was offered a place to work as professor, but refused to become politically active.

35. Leibniz‘ mathematical discoveries http://www.awf.musin.de/comenius/4_3_tangent.html Infinitesimal calculus Determinant calculus Binary System

36. Leibniz‘ mathematical discoveries Mathematics Physics Infinitesimal calculus Determinant calculus Binary arithmetics Philosophy

37. Leibniz‘ Correspondences Among his 60000 pieces of writing are extensive correspondences, e.g. with mathematicians from China and Vietnam. http://www.awg.musin.de/comenius/4_4_correspondence_e.html

38. Leibniz‘ Intersubjectivity(1) Mathematics Physics Infinitesimal calculus Binary machine Determinant calculus Binary arithmetics theodizee Philosophy

39. „One created everything out of nothing“ Just as the whole of mathematics was constructed from 0 and 1, so the whole universe was generated of the pure being of God and nothingness. http;//pauillac.inria.fr/cidigbet/web.html

40. Leibniz‘ Achievements Mathematics Physics Infinitesimal calculus Relativity theory Binary machine Determinant calculus Sentence of energy maintenance Calculator Binary arithmetics Continuity principle The term of „function“ theodizee monadology Philosophy

41. Binary Machine and Calculator Binary machine Calculator

42. Gottfried Wilhelm Leibniz and his calculatingmachine report by Torsten Brandes

43. Chapter 1 • Construction of mechanical calculating machines

44. Structure of a mechanical calculating machine • counting mechanism two counting wheels

45. counting mechanism • Every counting wheel represents a digit. • By rotating in positive direction it is able to add, by rotating in negative direction it is able to subtract. • If the capacity of a digit is exceeded, a carry occurs. • The carry has to be handed over the next digit.

46. counting mechanism S – lever Zi – toothed wheel dealing with the carry between two digits

47. Chapter 2: calculating machines bevore and after Leibniz • 1623 Wilhelm Schickard developes a calculating machine for all the four basic arithmetic operations. It helped Johann Kepler to calculate planet‘s orbits. • 1641 Blaise Pascal developes an adding- and subtracting machine to maintain his father, who worked as a taxman. • 1670 - 1700 Leibniz is working on his calculator.  • 1774 Philipp Matthäus Hahn (1739-1790) contructed the first solid machine.

48. Leibniz‘ calculating machine. • Leibniz began in the 1670 to deal with the topic. • He intended to construct a machine which could perform the four basic arithmetic operations automatically. • There where four machines at all. One (the last one) is preserved.

49. stepped drum A configuration of staggered teeth. The toothed wheel can be turned 0 to 9 teeth, depending of the position of this wheel.

50. four basic operations performing machine by Leibniz