IST 4 Information and Logic
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1 IST 4 Information and Logic
2 MQ1 Everyone has a gift! Due Today by 10pm Please PDF lastname-firstname.pdf to ta4@paradise.caltech.edu HW #1 Due Tuesday, 4/ :30pm in class
3 T = today x= hw#x out x= hw#x due mon tue wed thr fri 30 M1 1 6 oh T 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
4 Perspective Challenges Research
5 facilitate Languages g efficient management of our memory understanding di The knowledge Challenge? Teaching remember, transmit, evolve... English, Chinese, Spanish,... Music, Dance, Painting... Algebra, Calculus, Physics, Chemistry, biology, engineering... History, Anthropology, Law, Medicine...
6 facilitate Languages g efficient management of our memory understanding di The knowledge Challenge? Teaching remember, transmit, evolve... Need to invent of artificial memory devices for storing information captured by the different languages
7 The impact of artificial memory technology Spoken languages 60Kya printing press 500ya Source: Wikipedia Writing 5Kya
8 Artificial memory Evolution
9 MB 1 Ton 256 GB very light $160,000 today $1.3M $200 $250M per GB $1 per GB 10 8 : 1
10 Artificial memory The next challenge? Infinite it capacity... Q: What do we have?
11 Artificial memory Do you know what is the information that you have? On your laptop / / dropbox? Q: What do we have?
12 How do you know your information? Associations What is our associative sense?
13 ice cream cold vanilla
14 phone pay call line Mednick 1962, The associative basis of the creative process
15 Our associative sense is 3 3 is a small number need a number system for associations
16 Associative Artificial Memory Do you know what is the information that you have? On your laptop / / dropbox? Research challenge: Invention of artificial memory devices with associative retrieval??
17 Associative Memories Yue Li Caltech
18 Back to the language g of numbers
19 Bones Tokens What happened after mathematics? Numbers Mathematics
20 our first algorithm The language of numbers Translation between languages
21 Positional number systems
22 Base-10 is embedded in our language and thought Base-b Positional Systems
23 Translation between languages Base-b Conversion n to Base-B B French French to English English Spanish English to Spanish
24 Translation between languages Base-b Conversion n to Base-B 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
25 Base-b: Conversion to Base-B using base-10 arithmetic 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
26 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 id by 2 to expose the next block... Our first algorithm - syntax manipulation
27 Base-b: Conversion from Base 10 Conversion from base-10 to binary: The PPT COMPUTER
28 The PPT COMPUTER Base-b: Conversion from Base 10 Conversion from base-10 to binary:
29 The language of numbers weighted and weighted positional
30 Number Systems weighted positional system weighted system 4x x1 = x x10 + 6x1 = 276 2x x10 + 6x1 = 276 CCLXXVI 2x x50 + 2x10 + 1x5 + 1x1= 276
31 What does a positional number system have that is unique? bounded syntax 0
32 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
33 No 0 Can we represent a number in a positional system without a 0? Assume base 10 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
34 No 0 base 10 base 10 no-0 same weights Different digits Q: How many different quantities can be represented by at most two digits? 100 base base 10 no-0
35 Base-10 No-0 Positional System???
36 Base-10 No-0 Positional System It is all about syntax!!
37 Base-10 No-0 Positional System It is all about syntax!!??????
38 Base-10 No-0 Positional System It is all about syntax!!
39 Base-10 No-0 Positional System It is all about syntax!!??? You will study this algorithm in HW#2
40 The language of numbers Q: Can we represent everything with integers? Approximations
41 The Babylonians knew everything! YBC 7289 ~1700BC
42 (1,24, 51,10) (42,2 5, 35)
43 (1,24,51,10) x (0;30) (42,25,35) x + (42,25,35) (2) (1,10) (50,0) (1,24,0,0) (1,24,51,10) (1,24, 51,10) (42,2 5, 35) (2) x (0;30) = (1)
44 The Babylonians loved reciprocals!!! (1;24,51,10) x (0;30) (0;42,25,35) So what?? (1;24,51,10) x (0;42,25,35) ~(1) Assume an exact value... (1,24, 51,10) (42,2 5, 35)
45 So what?? (1,24, 51,10) (42,2 5, 35) The Babylonians knew Pythagoras Theorem and how to approximate the square root...
46 (1,24, 51,10) (42,2 5, 35) The Babylonians knew Pythagoras Theorem and how to approximate the square root...
47 The Babylonians knew everything... However,... They created a highly advanced civilization: music, literature, law, medicine, science, engineering, mathematics... They had (schools) a formal education system! Schools had both boys and girls!
48 The Babylonians knew everything... However,... For 1,000 years they made very little progress in mathematics... My Conjecture: They taught only the how and did not teach the why... NO (documented...) proofs... Why are proofs important?
49 The Babylonians knew everything... However,... For 1,000 years they made very little progress in mathematics... To make progress: We need to impart the sensation of ideas as they are conceived and not only as they are known NO (documented...) proofs... Why are proofs important?
50 The Babylonians NO proofs... knew everything... They taught the how and not the why The solution came with the Greeks
51 Alexander the Great, BC Captured Egypt, Babylonia 331BC Died in June, 323 BC, age 32 in Babylonia Recorded in the Babylonian astronomical diaries 800 years of records!! source: wikipedia
52 The language of proofs rational numbers
53 Pythagoras Proofs Euclid,300BC BC The solution came with the Greeks
54 Pythagoras Proof: Euclid,300BC BC Our first proof - contradiction, parity... Assume that p and q are relatively prime (simplified) Reach a contradiction!! p odd? p even? p odd, q even: NO p even, q even: NO p odd, q odd: NO p even, q odd: NO which had to be demonstrated Quod Erat Demonstrandum QED
55 The Babylonians knew Pythagoras Theorem and how to approximate the square root... The Babylonians knew everything...
56 The Babylonians knew Pythagoras Theorem and how to approximate the square root...
57 A tablet called: Plimpton 322, from 1800 BC, at Columbia U 9x13 cm
58 The Babylonians knew Pythagoras Theorem and how to approximate the square root... and compute Pythagorean triples??
59 The Babylonians knew Pythagoras Theorem and how to approximate the square root... and compute Pythagorean triples??
60 The language of proofs Babylonian / Pythagoras Theorem
61 Proof?? Pythagoras BC Euclid,300BC Thm: Given a right triangle with sides a, b and c, where a and b are the legs, then:
62 China ~400BC Book named 'Chou pei Suan Ching'
63 Idea: Compute the area QED
64 Babylonian Clay Tablets Greek Proofs... DNA of mathematical knowledge
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 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 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 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 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 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 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 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 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 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 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 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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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
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