IST 4 Information and Logic
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1 IST 4 Information and Logic
2 Lectures are at: paradise.caltech.edu/ist4/lectures.html edu/ist4/lectures html
3 Homeworks are at: paradise.caltech.edu/ist4/homeworks.html edu/ist4/homeworks html
4 T = today x= hw#x out x= hw#x due mon tue wed thr fri 30 M1 1 6 T oh M1 oh 13 oh 1 oh 2M2M 20 oh oh 2 Mx= MQx out 27 oh M2 oh oh = office hours oh 3 4 oh oh midterms oh Mx= MQx due 18 oh oh oh 5 oh oh oh
5 MQ1 Everyone has a gift! Due Thursday 4/9/2015 by 10pm Please PDF lastname-firstname.pdf to ta4@paradise.caltech.edu Have your name inside the file as well...
6 language properties p
7 Building Blocks finite number of building blocks infinitely many descriptions
8 Separation Separation A between syntax and semantics Separation B between what is represented and reality, feasibility, time, space,... Separation C between algorithms and implementation
9 Languages help in reasoning beyond our natural senses Our number sense Need a language g for quantities!
10 Why care about quantities 40,000 years ago? How will we remember quantities?
11 ~150, years ago: modern humans - Homo sapiens ~60,000 years ago: verbal languages ~40,000 years ago: artificial memory for quantities ~5,000 years ago: written symbolic languages ~500 years ago: printing ~50 years ago: electronic forms
12 What is this item? Lebombo bone ~40, years ago hint? A very early device for recording quantities by making marks on a bone of a monkey
13 Early Counting Devices ~40,000 ago lebombo bone 1970's excavations in Lebombo Mountains, a piece of the fibula of a baboon was found marked with 29 clearly defined notches???
14
15 Lunar cycle (month): ~29.5 days Source: Wikipedia
16 Day and night: 2 10 Moon Earth (month): ~29 days Earth Sun (year): ~365 days
17
18 12 is a special number.. Examples?
19 Beyond natural numbers?
20 What was invented first? a. Written text 1. Numbers a and 1 together Why do we need numbers?
21
22
23
24 Tokens 8,000 ya Physical Symbols: shape = meaning Source: DSB 2009 paper
25 Idea: Represent goods with tokens one garment one jar of oil one ingot of metal one sheep Token are physical symbols of real items a language! one honeycomb one garment Source: DSB 2009 paper
26 Can the system work with tokens?
27 Secure Transactions: Envelopes (Bulla) and Seals, 3,700BC
28 cylinder seals
29 Does it work???
30 New Idea: Mark on the outside to represent what is inside... Writing: physical symbols to imprintedi symbols Envelope showing the imprint of three ovoid tokens with an incised line representing jars of oil Source: DSB 2009 paper 3,300 BC
31 A crazy idea: No need for an envelope! The tablet is born! Tablet showing the impression of spheres and cones representing measures of grain 3,100BC Source: DSB 2009 paper
32 One more crazy idea: Separate between the quantity and the item... Too many jars of oils for markings on the envelope / tablet Source: DSB 2009 paper
33 Separate between the quantity and the item... The NUMBER is born!!! Twelve jars Language for quantities!!! Source: DSB 2009 paper
34 ten one tablet featuring an account of 33 measures of oil, 3,100 BC oil Source: DSB 2009 paper
35 Language for quantities!!! The item (jar of oil) is left alone Items correspond to symbols Symbols for oil, and other items have a sound! Sounds correspond to symbols Collection of symbols correspond to words / meaning rebus L8 22 day General writing is born!!! Not covered in IST4...
36 Denise Schmandt-Besserat Source: Her 2009 paper (DSB 2009) Tokens and Writing: the Cognitive Development, Will be posted on the class web page
37 Where did it start?
38 Babylonians and Egyptians ~5000 years ago
39 The Egyptians Preferred 10 How will you represent a trillion 1,000,000,000,000? separation 2x x10 + 6x1 = 276 However, not a finite number of building blocks!
40 Babylonians The first Positional number system 1 10 Separation: meaningless ngless symbols - modulation on The smallest number (two) of building blocks!!
41 Babylonians The first Positional number system 1 10 The Babylonian preferred 60
42 Babylonians The first Positional number system 4x x1 = 276
43 Babylonians were Masters of Abstractions Why 60? Good for computation and representing fractions: 1/2 = 30/60 1/3 = 20/60 1/4 = 15/60 1/5 = 12/60 1/6 = 10/60 60 i th ll t b th t h 60 is the smallest base that has a simple representation of the first five fractions
44 Babylonian Number Systems What is the number? 31 What is the number? 31x = 1891
45
46 The Babylonians knew everything!
47 Deciphering the Babylonians
48 Austria (BS) > Germany (BS) > Denmark (PHD) > US (Brown U) Otto Neugebauer Mathematics > History of Exact Sciences Participated in WWI, was POW Escaped Europe in 1939, WWII 1945 His son: Gerry Neugebauer (PhD 60) Millikan Professor of Physics, Emeritus
49 Mathematics > Teaching Math ->History of Exact Sciences Asger Aaboe Denmark > US (PhD 1957, Brown U) -> 1961,Yale U Otto Neugebauer
50 Asger Aaboe Otto Neugebauer Today, you will get to be Otto and Asger!
51 Multiplication table for ? , , , ,30?? 1,39 1, ,57 2,6 2,15 2,24 2,33 2, ,51 3,0 4,30 6,0 7,30
52 Multiplication instead of division??
53 Geometry
54 The Babylonians knew everything! even Geometry
55 The Babylonians knew everything! hint even Geometry
56 The Babylonians knew everything! even Geometry
57 The Babylonians knew everything! even Geometry
58 The Babylonians knew everything! even Geometry again!! 12?12 2,24
59 Which Number Does not Belong? is a space between two digits
60 Which Number Does not Belong?
61 Take-homes from today: The language of numbers and written languages evolved from the need for secure transactions The Babylonians knew EVERYTHING!
IST 4 Information and Logic
IST 4 Information and Logic Lectures are at: paradise.caltech.edu/ist4/lectures.html edu/ist4/lectures html Homeworks are at: paradise.caltech.edu/ist4/homeworks.html edu/ist4/homeworks html T = today
IST 4 Information and Logic
IST 4 Information and Logic MQ1 Everyone has a gift! Due Today by 10pm Please email PDF lastname-firstname.pdf to ta4@paradise.caltech.edu HW #1 Due Tuesday, 4/12 2:30pm in class T = today x= hw#x out
IST 4 Information and Logic
IST 4 Information and Logic MQ1 Computers outperform the human brain? Due Today by 10pm Have your name inside the file as well... Please email PDF lastname-firstname.pdf to istta4@paradise.caltech.edu
IST 4 Information and Logic
IST 4 Information and Logic MQ1 Everyone has a gift! Due Today by 10pm Please email PDF lastname-firstname.pdf to ta4@paradise.caltech.edu HW #1 Due Tuesday, 4/14 230 2:30pm in class T = today x= hw#x
IST 4 Information and Logic
IST 4 Information and Logic mon tue wed thr fri sun T = today 3 M oh x= hw#x out oh M 7 oh oh 2 M2 oh oh x= hw#x due 24 oh oh 2 oh = office hours oh oh T M2 8 3 oh midterms oh oh Mx= MQx out 5 oh 3 4 oh
IST 4 Information and Logic
IST 4 Information and Logic Quizzes grade (6): average of top n-2 T = today x= hw#x out x= hw#x due mon tue wed thr fri 1 M1 oh 1 8 oh M1 15 oh 1 T 2 oh M2 22 oh PCP oh 2 oh sun oh 29 oh M2 oh = office
IST 4 Information and Logic
IST 4 Information and Logic HW2 will be returned today Average is 53/6~=88% T = today x= hw#x out x= hw#x due mon tue wed thr fri 3 M 6 oh M oh 3 oh oh 2M2M 2 oh oh 2 Mx= MQx out 27 oh M2 oh oh = office
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 3 M 7 oh M 4 oh oh 2M2 2 oh oh 2 oh T Mx= MQx out 28 oh M2 oh oh = office hours 5 3 2 oh 3 4 oh oh midterms oh Mx= MQx
IST 4 Information and Logic
IST 4 Information and Logic mon tue wed thr fri sun T = today 3 M oh x= hw#x out oh M 7 oh oh 2 M2 oh oh x= hw#x due 24 oh oh 2 oh = office hours oh oh M2 8 3 oh midterms oh oh Mx= MQx out 5 oh 3 4 oh
IST 4 Information and Logic
IST 4 Information and Logic mon tue wed thr fri sun T = today 3 M oh x= hw#x out 0 oh M 7 oh oh 2 M2 oh oh x= hw#x due 24 oh oh 2 oh = office hours oh oh M2 8 3 oh midterms oh oh Mx= MQx out 5 oh 3 4 oh
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 31 M1 1 7 oh M1 14 oh 1 oh 2M2 21 oh oh 2 oh Mx= MQx out 28 oh M2 oh oh = office hours 5 3 12 oh 3 4 oh oh T midterms oh
IST 4 Information and Logic
IST 4 Information and Logic T = today mon tue wed thr 3 M1 oh 1 fri sun x= hw#x out 10 oh M1 17 oh oh 1 2 M2 oh oh x= hw#x due 24 oh oh 2 Mx= MQx out 1 oh M2 oh = office hours oh T 8 3 15 oh 3 4 oh oh
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 30 M 6 oh M oh 3 oh oh 2M2M 20 oh oh 2 27 oh M2 oh midterms Students MQ oh = office hours Mx= MQx out 4 3 oh 3 4 oh oh
IST 4 Information and Logic
IST 4 Information and Logi T = today x= hw#x out x= hw#x due mon tue wed thr fri 3 M 7 oh M 4 oh oh 2M2 2 oh oh 2 oh 28 oh M2 oh oh = offie hours 5 3 Mx= MQx out 2 oh 3 4 oh oh midterms oh Mx= MQx due
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 30 M1 1 6 oh M1 oh 13 oh 1 oh 2M2M 20 oh oh 2 Mx= MQx out 27 oh M2 h T oh = office hours oh T 4 3 11 oh 3 4 oh oh midterms
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 30 M1 1 6 oh M1 oh 13 oh 1 oh 2M2M 20 oh oh 2 T Mx= MQx out 27 oh M2 oh oh = office hours 4 3 11 oh 3 4 oh oh midterms
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out mon tue wed thr fri 31 M1 1 7 oh M1 14 oh 1 oh 2M2 oh x= hw#x due 21 oh oh 2 T Mx= MQx out 28 oh M2 oh oh = office hours 5 3 12 oh 3 4 oh oh midterms oh
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