ist 4 information and logic - paradise 0315 p.pdf · not covered in ist4.... re us l8 22 day....
TRANSCRIPT
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IST 4Information and Logic
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Lectures are at:paradise caltech edu/ist4/lectures htmlparadise.caltech.edu/ist4/lectures.html
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Homeworks are at:paradise caltech edu/ist4/homeworks htmlparadise.caltech.edu/ist4/homeworks.html
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mon tue wed thr fri30 M1 1= todayT
6 M1
13 1 2M2x= hw#x out
oh oh
oh oh
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20 227 M2
x= hw#x due
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4 311 3 4Mx= MQx out
midtermsoh
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11 3 418 4 525
Mx= MQx out
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MQ1E h ift!Everyone has a gift!
Due Thursday 4/9/2015 by 10pmDue Thursday 4/9/2015 by 10pm
Please email PDFlastname-firstname.pdfpto [email protected]
Have your name inside the file as well...
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languagelanguagepropertiesp p
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Building Blocks
finite number of building blocks ‘infinitely’ many descriptionsy y p
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Separation
Separation Apbetween syntax and semantics
S ti BSeparation Bbetween what is represented
d lit f ibilit ti Separation Cand reality, feasibility, time, space, ...
pbetween algorithms and implementation
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Languages help in reasoning beyond our natural sensesbeyond our natural senses
Our number sense
Need a language for quantities!g g q
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Why care about quantities Why care about quantities 40,000 years ago?
How will we remember quantities?
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150 000 d h H i~150,000 years ago: modern humans - Homo sapiens
~60,000 years ago: verbal languages60,000 years ago verbal languages
~40,000 years ago: artificial memory for quantities
~5,000 years ago: written symbolic languages
~500 years ago: printing~500 years ago: printing
~50 years ago: electronic forms
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What is this item?
Lebombo bone ~40 000 years agoLebombo bone 40,000 years ago
hint?
A very early device for di titi b m ki recording quantities by making
marks on a bone of a monkey
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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 fibula of a baboon was found marked with 29 clearly defined notches ??????
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Lunar cycle (month): ~29.5 days Lu y (m ) 9. y
Source: Wikipedia
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5 5
Day and night: 210 10
Moon – Earth (month): ~29 days
Earth – Sun (year): ~365 days
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12 is a 12 is a ‘special’ numberspecial number..E l ?Examples?
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B d Beyond natural numbers?
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What was invented first?a. Written text
1. Numbers
a and 1 togethera and 1 together
Why do we need numbers?Why do we need numbers?
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Tokens 8,000 ya, yPhysical Symbols:
shape = meaningshape = meaning
Source: DSB 2009 paper
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one jar of oil one garment Idea: Represent goods with tokens
one sheep one jar of oil one garment
one ingot of metal
Token are physical symbols of real items – a language!
h b
Source: DSB 2009 paper
one honeycomb one garment
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C th t k ith t k ?Can the system work with tokens?
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Secure Transactions:E l (B ll ) Envelopes (Bulla) and Seals, 3,700BCand Seals, 3,700BC
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cylinder seals
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Does it work???Does it work???
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New Idea: Mark on the outside to represent what is inside...
Writing: h i l b l t i i t d b l physical symbols to imprinted symbols
Envelope showing the imprint of three ovoid tokens with an incised line
3,300 BC
tokens with an incised line representing jars of oilSource: DSB 2009 paper
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A crazy idea: No need for an envelope! A crazy idea: p
The tablet is born!
Tablet showing the impression of spheres and cones representing measures of grain3 100BC3,100BC
Source: DSB 2009 paper
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One more crazy idea:Separate between the quantity and the item....
Too many jars of oils m y j ffor markings on the envelope / tablet
Source: DSB 2009 paper
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Separate between the quantity and the itemSeparate between the quantity and the item...
The NUMBER is born!!!
10 1
The NUMBER is born!!!
110
Twelve jars
LLanguage for quantities!!!
Source: DSB 2009 paper
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tablet featuring an account of 33 f il 3 100 BC il
oneten
33 measures of oil, 3,100 BC oil
Source: DSB 2009 paper
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Language for quantities!!!
The item (jar of oil) is ‘left alone’It d t b lItems correspond to symbols
Symbols for oil, and other items – have a sound!
Sounds correspond to symbols
Collection of symbols correspond to words / meaning
b
General writing is born!!! Not covered in IST4....
rebus 22 dayL8
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Denise Schmandt-Besserat1933 - Source: Her 2009 paper
(DSB 2009)
“Tokens and Writing: the C iti D l t ”Cognitive Development,”Will be posted on the class web page
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Where did it start?Where did it start?
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Babylonians and Egyptians5000 ~5000 years ago
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The Egyptians Preferred 10 The Egyptians Preferred 0
How will you representHow will you representa trillion1,000,000,000,000?
2x100 + 7x10 + 6x1 = 276separation 2x100 + 7x10 + 6x1 = 276separat on
However, not a finite number of building blocks!
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Babylonians
The first Positional number system
11
10
Separation: ‘meaningless’ symbols’ - modulationSeparat on mean ngless symbols modulat onThe smallest number (two) of building blocks!!
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Babylonians
The first Positional number system
11
10
The Babylonian preferred 60 The Babylonian preferred 60
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Babylonians
The first Positional number system
4x60 + 36x1 = 276
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Babylonians were Masters of Abstractions
Why 60?
y
Why 60?Good for computation and representing fractions:
1/2 = 30/601/2 30/601/3 = 20/601/4 = 15/60 1/5 = 12/601/5 = 12/601/6 = 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
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Babylonian Number Systemsy y
What is the number?
31
What is the number?
31 60 31 189131x60 31+ = 1891
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The Babyloniansknew everything!knew everything!
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Deciphering the Deciphering the BabyloniansBabylonians
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Otto NeugebauerAustria (BS) –> Germany (BS) –> Denmark (PHD) –> US (Brown U) Otto Neugebauer
1899-1990
Mathematics –> History of Exact Sciences
Participated in WWI, was POWEscaped Europe in 1939 WWIIEscaped Europe in 1939, WWII
His son:His son:Gerry Neugebauer1932-2014 (PhD ‘60)( )Millikan Professor of Physics, Emeritus
1945
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Asger AaboeMathematics –> Teaching Math ->History of Exact Sciences
Denmark –> US (PhD 1957, Brown U) -> 1961,Yale U 1922–2007
Otto Neugebauer1899 19901899-1990
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Otto Neugebauer1899-1990
Asger Aaboe1922–2007
Today you will get to be Otto and Asger!Today, you will get to be Otto and Asger!
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1 159 2,15
Multiplication table for 9123
5161718
91827
, 52,242,332,422 514
567
1819?20
40
364554
63 1 3
2,513,04,306,0
27030789
10
4050??
631,121,211 30
1,3 6,07,3072 450
811011121
1,301,391,481 5713
14
1,572,6
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Multiplication instead of division
????
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GeometryGeometry
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The Babyloniansknew everything!knew everything!
even Geometryeven Geometry...
3
945
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The Babyloniansknew everything!knew everything!
even Geometryhint even Geometry...4
hint
161
![Page 56: IST 4 Information and Logic - Paradise 0315 p.pdf · Not covered in IST4.... re us L8 22 day. Denise Schmandt-Besserat 1933 - Source:Her 2009 paper (DSB 2009) “Tokens and Writing:](https://reader033.vdocuments.mx/reader033/viewer/2022060219/5f06d5467e708231d419f699/html5/thumbnails/56.jpg)
The Babyloniansknew everything!knew everything!
even Geometryeven Geometry...
3
945
![Page 57: IST 4 Information and Logic - Paradise 0315 p.pdf · Not covered in IST4.... re us L8 22 day. Denise Schmandt-Besserat 1933 - Source:Her 2009 paper (DSB 2009) “Tokens and Writing:](https://reader033.vdocuments.mx/reader033/viewer/2022060219/5f06d5467e708231d419f699/html5/thumbnails/57.jpg)
The Babyloniansknew everything!knew everything!
even Geometryeven Geometry...
3
945
![Page 58: IST 4 Information and Logic - Paradise 0315 p.pdf · Not covered in IST4.... re us L8 22 day. Denise Schmandt-Besserat 1933 - Source:Her 2009 paper (DSB 2009) “Tokens and Writing:](https://reader033.vdocuments.mx/reader033/viewer/2022060219/5f06d5467e708231d419f699/html5/thumbnails/58.jpg)
The Babyloniansknew everything!knew everything!
even Geometryeven Geometry...
12 again!!12
12 again!!
2,24?12
![Page 59: IST 4 Information and Logic - Paradise 0315 p.pdf · Not covered in IST4.... re us L8 22 day. Denise Schmandt-Besserat 1933 - Source:Her 2009 paper (DSB 2009) “Tokens and Writing:](https://reader033.vdocuments.mx/reader033/viewer/2022060219/5f06d5467e708231d419f699/html5/thumbnails/59.jpg)
Which Number Does not Belong?g
is a space between two digits
![Page 60: IST 4 Information and Logic - Paradise 0315 p.pdf · Not covered in IST4.... re us L8 22 day. Denise Schmandt-Besserat 1933 - Source:Her 2009 paper (DSB 2009) “Tokens and Writing:](https://reader033.vdocuments.mx/reader033/viewer/2022060219/5f06d5467e708231d419f699/html5/thumbnails/60.jpg)
Which Number Does not Belong?g
139 25512763139 25512763
64-1 128-1 256-1
![Page 61: IST 4 Information and Logic - Paradise 0315 p.pdf · Not covered in IST4.... re us L8 22 day. Denise Schmandt-Besserat 1933 - Source:Her 2009 paper (DSB 2009) “Tokens and Writing:](https://reader033.vdocuments.mx/reader033/viewer/2022060219/5f06d5467e708231d419f699/html5/thumbnails/61.jpg)
Take-homes from today:
The language of numbers andwritten languages evolved from the need for secure from the need for secure transactions
The Babylonians knew EVERYTHING!The Babylonians knew EVERYTHING!