IST 4 Information and Logic
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1 IST 4 Information and Logic
2 MQ1 Computers outperform the human brain? Due Today by 10pm Have your name inside the file as well... Please PDF lastname-firstname.pdf to 2d is extra credit HW #1 Due Tuesday, 4/18 2:30pm in class
3 mon tue wed thr fri sun T = today 3 M1 oh 1 x= hw#x out 10 oh T M1 17 oh oh 1 2 M2 oh oh x= hw#x due 24 oh oh 2 oh = office hours oh 1 oh M2 8 3 oh midterms oh oh Mx= MQx out 15 oh 3 4 oh Mx= MQx due 22 oh oh oh oh oh 5 oh 5 oh
4 So Far - Lecture 1: Life evolution - Lecture 2: The human brain languages - Lecture 3: Artificial languages - numbers and writing
5 3.7 Bya The appearance of life is the first Information Megamorphosis I I 75 Kya The appearance of the human brain is the second Information Megamorphosis We are memory machines However, our memory sense is limited... We are doing well because we found a way to
6 building blocks sepa ration languages We are doing well because we found a way to
7 Our number sense is limited... We are doing well because we found a way to
8 Our number sense is limited... language for quantities
9 Our number sense is limited... managing time
10 Our number sense is limited... managing trade
11 Our memory sense is limited... rebus an idea: recording our speech Writing is the recording of the sounds of our verbal language
12 tokens = items symbols = items items = meaning = sounds symbols = sounds collection of symbols = words words = recordings of spoken languages writing is born!!!
13 The Babylonians knew everything! Babylonian Building Blocks
14 2x x1 = 139 1x60 + 3x1 = 63 1x x x1 = 3751
15 Deciphering the Babylonians
16 Austria (EE) > Germany (Math) > Denmark (History) > US (Brown U) Otto Neugebauer Mathematics > History of Exact Sciences Born in Austria Participated in WWI, was POW Germany 1933, lost his job Escaped Germany to Denmark in 1934 Escaped Europe to the US in 1939, WWII 1945 His son: Gerry Neugebauer (PhD 60) Millikan Professor of Physics, Emeritus
17 Mathematics > Teaching Math ->History of Exact Sciences Asger Aaboe Denmark > US (PhD 1957, Brown U) -> 1961, Yale U Otto Neugebauer
18 Asger Aaboe Otto Neugebauer Today, you will get to be Otto and Asger!
19
20 ? ?? ,12 1,21 1,30 1,39 1,48 1,57 2,6 1,3 2,15 2,24 2,33 2,42 2,51 3,0 4,30 6,0 7,
21 ? ?? ,12 1,21 1,30 1,39 1,48 1,57 2,6 1,3 2,15 2,24 2,33 2,42 2,51 3,0 4,30 6,0 7, Multiplication table for 9 30
22 ?? Multiplication instead of division
23
24
25 fraction No fractional point
26 7 and 11 and other numbers are missing? Why? fraction No fractional point
27 Q: What are the possible values for a? a, b are integers, must divide A number that its prime factors are at most 5 is called a regular number a must be a regular number Is 24 a regular number? Is 896 a regular number? Is 900 a regular number? 2x2x2x3 2x2x2x2x2x2x2x7 2x2x3x3x5x5
28 Our number sense is limited... language for quantities time trade geometry
29 The Babylonians knew everything! even Geometry
30 The Babylonians knew everything! A square hint A = Area C = Circumference even Geometry... 4 A = (C/4) x (C/4) 1 16 A = (C x C)/16
31 The Babylonians knew everything! A square hint A = Area C = Circumference even Geometry... C = 4 A = (C/4) x (C/4) A=1 CxC = 16 A = (C x C)/16 A= (16)/16 = 1
32 The Babylonians knew everything! even Geometry...?? 3? 45 9
33 The Babylonians knew everything! even Geometry
34 The Babylonians knew everything! even Geometry
35 The Babylonians knew everything! even Geometry again!! 12 12? 2,24
36 Algorithms
37 building Blocks separation compute using the rules of the syntax independent of the semantics using building blocks algorithms
38 Our first algorithm The language of numbers Translation between languages
39 Positional number systems
40 Base-10 is embedded in our language and thought Base-b Positional Systems
41 Translation between languages Base-b Conversion to Base-B French French to English English Spanish English to Spanish
42 Translation between languages Base-b Conversion to Base-B b Base b to base Base 10 to base B B Sum the corresponding weights using base-10 arithmetic Successive division by B using base-10 arithmetic
43 Translation between languages Base-b Conversion to Base-B b Base b to base Base 10 to base B B Sum the corresponding weights using base-10 arithmetic Successive division by B using base-10 arithmetic
44 Idea: discover the blue blocks! Base-b: Conversion from Base 10 Conversion from base-10 to binary: Even number the right most block is yellow Odd number the right most block is blue If odd subtract 1 Divide by 2 to expose the next block... Our first algorithm - syntax manipulation
45 Base-b: Conversion from Base 10 Conversion from base-10 to binary: The PPT COMPUTER
46 The PPT COMPUTER Base-b: Conversion from Base 10 Conversion from base-10 to binary:
47 A faster PPT COMPUTER Base-b: Conversion from Base 10 Conversion from base-10 to binary:
48 The language of numbers weighted and weighted positional
49 Babylonians and Egyptians ~5000 years ago positional weighted
50 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!
51 Number Systems weighted positional system weighted system 4x x1 = x x10 + 6x1 = 276 2x x10 + 6x1 = 276 CCLXXVI 2x x50 + 2x10 + 1x5 + 1x1= 276
52 What does a positional number system have that is unique? bounded syntax 0
53 Number Systems finite alphabet unbounded alphabet weighted positional system weighted system 4x x1 = x x10 + 6x1 = 276 2x x10 + 6x1 = 276 CCLXXVI 2x x50 + 2x10 + 1x5 + 1x1= 276
54 No 0 Assume base 10 Can we represent a number in a positional system without a 0? Answer: Yes?? How will you represent 10 without a 0? idea - represent 10 with a new digit: A How will you represent 100 without a 0? 100 = 9A 100 =
55 No 0 base 10 base 10 no-0 same weights Different digits
56 base 10 base 10 no-0 Q: How many different quantities can be represented by at most two digits? base base 10 no-0 1-AA
57 Base-10 No-0 Positional System Conversion from decimal do no-zero? Start from the right, translate X0 to (X-1)A Repeat until there are no zeros
58 Conversion from base-10 to base-10 no zero Start from the right, translate X0 to (X-1)A Repeat until there are no zeros You will explore this number system in HW#2 and now in quiz #2
59 Quiz #2
60 Quiz #2 10min Translate the following numbers base-10 to the representation base-10 no zero using the algorithm presented in class. 1. Show your work!! Conversion from base-10 to base-10 no zero Start from the right, translate X0 to (X-1)A Repeat until there are no zeros
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 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 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, 4/14 230 2:30pm in class T = today x= hw#x
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 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 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 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 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 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 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 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 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 T Mx= MQx out 27 oh M2 oh oh = office hours 4 3 11 oh 3 4 oh oh midterms
CS 340: Discrete Structures for Engineers
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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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