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Home , Arithmometer, Difference Engine, Z1 (computer)

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Analytical Engine Turing Harvard The : 1834 Mark I Relay Difference 1936 1944 The Early Days Engine 1 1835 1821 Difference Harvard Engine 2 1941 Mark II Napier’s Arithmometer 1849 1949 Bones 1820 Sector 1617 Stepped 1892 1598 Slide Rule Drum Differential 1622 1694 Analyzer Abacus Millionaire Avi Yadgar 1921 Curta 1300 Pascaline 1899 1947 Gala Yadgar 1642

Memory Mechanical Electro- General aids magnetic purpose

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1300 Abacus 1300 Chinese Abacus

1445 The printing 9+7=1699+7 press Invented (10-3) 5 1+1+1+110+1 • First record: 14th Century, China • “The first ” • Still used in Asian countries (-3) • Uses: add, subtract, multiply, divide – Fractions and square roots • 1946 Contest: – Japanese abacus vs. electric http://www.tux.org/~bagleyd/java/AbacusApp.html 3 4

O 1598 Sector 1598 Sector α

100 OA O' A' = • Principle: AB A' B'

• Thomas Hood, London 1598 100 = ? 27 (Galileo, Padua 1592) • Problem: 3 AB • Problems of the time: O’ • Solution: 100 X – Cannon elevation = – Amount of gun powder 27 9 α X – Drawing, architecture, surveying AB A' B' = ⇒ X = 100 • Proportions 3 3 9 5 6 A’ B’

1 1598 Sector 1617 Napier’s Bones/Rods • The lines: • John Napier, – Arithmetic Scotland 1617 – Geometric • Multiplication – Stereometric table disassembled – Polygraphic – Tetragonic – Metallic

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1617 Napier’s Bones/Rods 1614

• John Napier, Scotland 1614 • Uses: (Jobst Burgi, Switzerland) – Multiplication • Principle: – Division log(a×b) = log(a) + log(b) – Square roots a log( ) = log(a) − log(b) b 46,785,399 x 7 = a×b =10log(a)+log(b) ⇒ a =10log(a)−log(b) b • Logarithmic tables

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1622 Slide Rule 1622 Slide Rule - Operations

• Replaces logarithmic tables • Unary functions: • Gunter's Line of Numbers – Edmund Gunter, England – Reciprocals • Slide rule – Square/Square Root – William Oughtred, England, 1622 – Cube/Cube Root • Precision depends on length – Common Logarithms – and Cosines – Tangents and Cotangents • Binary operations: – Multiplication – Division

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2 1642 Pascaline 1642 Pascaline - disadvantages

• Blaise Pascal France, 1642 • Wheels turned Manually • Numbers • Too complex entered in – Only Pascal could repair sequence • Expensive • Cumulative sum – Cost more than replaced people • Technophobia – Mathematicians feared for jobs • Decimal – French currency system was not 13 http://perso.orange.fr/therese.eveilleau/pages/truc_mat/textes/pascaline.htm 14

1694 Stepped Drum 1820 Arithmometer

1829 • Design: Gottfried Leibniz, Germany 1694 First mainline • Produced: Phillip Hann, Germany 1774 locomotive • Commercial: Charles Xavier Thomas, Philippines 1820

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1820 Arithmometer 1947 Stepped Drum - Curta

• Add by one turn of the handle • Developed: Curt Herzstark, Buchenwald, 1940’s • Multiply by multiple turns of the handle • Produced: Liechtenstein, 1947 • Subtract and divide by reversing a switch • Sold at ~ $120 until 1973 • Disadvantage: “dialing in the digits”

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3 7 7 Stepped Drum - Curta 194 Stepped Drum - Curta 194

• Simulator: http://www.vcalc.net/curta_simulator_en.htm 19 20

1887 Felt & Tarrant Comptometer 1887 Comptometer

1876: First long distance phone call

1879: First cash register

1888: Production of automobiles

• Dorr E. Felt, 1887 • Produced: 1892-1930 • Key driven • Fully automatic carries 21 22

1887 Comptometer 1887 Comptometer • Improved user interface • “Software”: instructions for figuring – multiplication – Fail-safe keys – subtractions • Locked the machine if the operator failed to press – division them completely – square root – Allow multiple keys to be pressed at once – cube root • One per column – interest • Faster adding – exchange • Multiplication of some numbers – discount * English currency

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4 1899 Millionaire Calculator 1899 Millionaire Multiplication Table

• Invented: Otto Steiger, 1892 • Manufactured: Hans W. Egli, Switzerland 1899 • Direct multiplication • Also slower – – Subtraction – Division

1897 First radio station

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1899 Inside The Millionaire 1834 Back to Tables

• Dionysius Lardner’s Cabinet Cyclopaedia – 40 volumes in 1834, grew up to 134 – 3,700 acknowledged errata – How many unacknowledged?

• Sources of error: – Calculation – Transcription – Typesetting and printing

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1821 Difference engine 1849 Difference Engine

x F(x) 1st diff 2nd diff 1878 • (1791 –1871) First 1 5 phonograph 3 – English mathematician, philosopher, mechanical engineer and 2 (proto-) computer scientist 2 8 • Calculating with 5 • Calculating polynomials with “repeated differences” “repeated differences” 3 13 2 – “Complete complex computation” •nth degree polynomials 7 • Conceived in 1821 th 4 20 2 – Starting with the n difference 9 • Difference Engine No.2 1847-1849 2 – Require n registers 5 29 – Simpler mechanical design • No multiplication 11 2 •Example: fx()= x+ 4 6 40 2 – Require 2 differences 13 aXnn++ aX−−12 aX n +++... a X a 01 2nn− 1 7 53 2

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5 1849 Building the engine 1853 Building the engine

• Never built by Babbage • 1853 - First full-scale difference engine – Lack of funding • Scheutz (Sweden) – Insufficient manufacturing technology • “Tabulating Machine” – 15-digit numbers – 4th-order differences – Printed output

Casting: cheap but inaccurate

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1991 Building the engine 1991

• 1985 – 1991: Difference Engine No. 2 • The Science Museum in London – ~4,000 moving parts – 2.6 tons – Built to original designs – Original materials – Accurate repeat parts – 31 figures (103 bits)

– 7 differences 3m x 0.7m x 2.5m 33 34

1995 1834

• First General Purpose Machine (1834) – A ‘store’ for holding intermediate results – A ‘mill’ for arithmetic computations – Loops – Conditional branching – Programmable using punched cards • Borrowed from weaving looms • Would have required a steam engine – But never been built 35 36

6 1834 1834 Analytical Engine Analytical Engine • created nzdz! I/O Memory programs for the Bn = zn+1 Device 21πiev∫ − PunchedProgram StoreData Analytical Engine TapeMemory Memory I/O – Bernoulli numbers Device

I/O Device

µ Controller I/O ALUMill Device CPU 37 38 The mill - 1871

1876 Analog 1876 Differential Analyzer

1903 • Physical representation of data • The differential analyzer Wright brother’s first flight – Voltages – Invented: 1876, James Thomson – Currents – Constructed: 1927, MIT – Speed of shafts – Solves differential equations by integration – Wheel-and-disc mechanisms perform the integration

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1927 Differential Analyzer 1927 Differential Analyzer

1906 1929 Electric washing First residential machine elevator

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7 1949 Analog Computers - Moniac 1920 The Enigma

• London, 1949 • 1920 to the end of WWII • Electromechanical ciphering machine • Water represent money • Applies polyalphabetic encryption • Tanks represent means of – State dependant encoding spending money • Mechanical and electrical state • Flow represents flow… – Modeled after financial models

• Surprisingly accurate…

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1920 The Enigma 1890 Punched cards

1920’s Household • Used in the textile industry refrigerators • First adaptation by Babbage – input and data storage • A competition was held for the US 1890 census – 1880 US census had taken 7 years to complete • Winner: Herman Hollerith – Later founded the Tabulating Machine Company – Became IBM • Used mechanical relays to increment mechanical counters. • The 1890 census was completed in 6 weeks

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1928 Punched cards Punched Tape

• Specifically-designed layouts • Based on punched cards • “General purpose“ at 1928 • Each IBM-style card had 80 – Paper or polyester characters – Still being sold (1.5m/KB) – Followed by early terminals – Last two digits for a year • 30% of the profit of IBM in 1931 • Use in : –Sorter – Duplicating Punch – Collator

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8 1835 Relays 1835 Electromagnetic Relay

• Joseph Henry 1835 •A latching relay • Electronically controlled electrical switch – Two relaxed states – Controlled by an electromagnet (bistable) – Controls a set of contacts – a.k.a 'keep' relays

• With no current the armature and contacts are released • The coil requires low power • The contacts can switch high powers 49 50

8 1 184 Logical Gates by Relays 194 's Z3

1935 1936: Turing First regular 1848: Boolean machine TV broadcast algebra +V • 1941 - First programmable fully automatic machine 10 • 2500 relays b b 01 c b or c b or c • Program on punched tape •5 Hz • 64 22bits words b c OUT +V 0 0 0 • Floating point 0 1 1 • Based on the mechanical Z1 0 1 0 1 c 1 1 1

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1 4 194 Konrad Zuse's Z3 194 Harvard Mark I and Mark II

• Built for Harvard by IBM • Mark I - 1944 – Fully automatic – Electromagnetic control – Mechanical counters – 765K components – Hundreds KM of wires – 12m x 2.5m x 0.7m – 4,500kg – Mechanical clock – 72 words – 23 decimal digits words Z1 – 30,000 moving parts 53 54

9 1835 Harvard Mark I 1835 Harvard Mark I - Front-end

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7 7 194 Harvard Mark II 194 Harvard Mark II

• Mark II - 1947 – Electromagnetic components – Complicated programming – Binary representation • 8 instructions µs – Floating point – 125,000 addition µs – Operation specific hardware – 750,000 multiplication

Harvard Mark II storage 57 58

???? Bugs References • Wikipedia, the free encyclopedia http://www.wikipedia.org/ • What is the origin of the • S.O.S. MATHematics term “bug”? http://www.sosmath.com/ • Online lecture by Michelle Hoyle http://lecture.eingang.org/index.html • September 1947 – A moth trapped in a relay • Online Museum Exhibits: – The ENIAC Museum online of Mark II http://www.seas.upenn.edu/~museum/index.html – Computer History Museum, Mountain View, CA http://www.computerhistory.org/ “First actual case of bug being found” – The Science Museum, London http://www.sciencemuseum.org.uk/on-line/babbage/index.asp – The Computer Museum, System Source • “Bugs” came before computers and computer software http://www.syssrc.com/html/museum/ – The Museum of HP Calculators – Thomas Edison,1878 http://www.hpmuseum.org/ – John Wolff's Web Museum “… and it is then that “bugs” – as such little faults and http://home.vicnet.net.au/~wolff/calculators/ – Stephen Johnston’s web pages difficulties are called – show themselves…” http://www.mhs.ox.ac.uk/staff/saj/arithmometer/ 59 60

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