Mathematical Mathematical TablesTables

ScientistsScientists NavigatorsNavigators EngineersEngineers SurveyorsSurveyors Actuaries Actuaries

A random selection of 40 volumes of numerical tables contained A random selection of 40 volumes of numerical tables contained 3,700 acknowledged errata and ?!?!?!? unacknowledged ones 3,700 acknowledged errata and ?!?!?!? unacknowledged ones

Dionysius Lardner (1834) Dionysius Lardner (1834)

1800’s1800’sFurther development of Further development of mechanical calculating mechanical calculating machinesmachines

Thomas de ColmarThomas de Colmar

stepped drum gears stepped drum gears reverse the operating function reverse the operating function

in the result registers (up to 16 in the result registers (up to 16 digits), allowing reliable, stable digits), allowing reliable, stable calculation over extended calculation over extended periods of time without gear re-periods of time without gear re-alignment alignment

1785-1870

arithmometerarithmometer 1820 -18301820 -1830 1500 models sold1500 models sold banksbanks insurance companiesinsurance companies similar businesses similar businesses

Thomas promotes Thomas promotes arithmometerarithmometer

Piano Arithmometer Gift for Tsar Nicolas I

Maurel & JayetMaurel & Jayet 1840’s1840’s Took basic design of Thomas and greatly Took basic design of Thomas and greatly

improved itimproved it

Results as high as 8 digitsResults as high as 8 digits

Transmission tooTransmission too delicate delicate

The ArithmaurelThe Arithmaurel

Odhmer Odhmer Baldwin Baldwin

Swedish engineerSwedish engineer American engineerAmerican engineer

fluted drums replaced by a "variable-toothed fluted drums replaced by a "variable-toothed gear" design: a disk with radial pegs that can be gear" design: a disk with radial pegs that can be made to protrude or retract from it. made to protrude or retract from it.

1845-1903 1838 to 1925

Pin-wheel mechanical calculators

The The typewritertypewriter

Introduction of the keyboard

The first adding machine The first adding machine with keyboardwith keyboard

It was feasible because of It was feasible because of a carry mechanism fast a carry mechanism fast enough to act while the enough to act while the keys return from being keys return from being pressedpressed

Dorr E. Felt (1862-1930)Dorr E. Felt (1862-1930)

ComptometerComptometerChicago 1884Chicago 1884

Worldwide successWorldwide success

The disadvantages of The disadvantages of these machinesthese machines

Operation required direct manipulation by Operation required direct manipulation by the operatorthe operator

Multiplication performed as successive Multiplication performed as successive additionsadditions

Keyboard improved speed but…Keyboard improved speed but…

Well trained operator still necessaryWell trained operator still necessary

Charles BabbageCharles Babbage 1791 - 1871 1791 - 1871

English mathematicianEnglish mathematicianBorn in Teignmoth, Devonshire, UKBorn in Teignmoth, Devonshire, UK

analytical philosopheranalytical philosopher

proto-computerproto-computer scientistscientist

The Difference Engine NThe Difference Engine Noo 1 1Designed to produce mathematical tablesDesigned to produce mathematical tables

Construction funded by British government Construction funded by British government and Babbage himselfand Babbage himself

Never completedNever completed

Babbage lost interest in this deviceBabbage lost interest in this devicewhen he realized that its design waswhen he realized that its design wasflawedflawed

He started working onHe started working onDifference Engine No 2Difference Engine No 2

The Difference Engine NThe Difference Engine No o

22 design completed 1830design completed 1830 built 1991 built 1991

The The Analytical Analytical EngineEngine

Babbage formulated ideas for it between 1834-1837

The The Analytical EngineAnalytical EngineStoreStore - 1000 50-digits numbers - 1000 50-digits numbers

MillMill – (CPU) added, subtracted, – (CPU) added, subtracted, multiplied or divided, and multiplied or divided, and returned a result to the store returned a result to the store

Punched cards Punched cards – several – several readers for programs and datareaders for programs and data

PrinterPrinter for output for output making making hardcopy data available to the hardcopy data available to the useruser

Why did Babbage not Why did Babbage not invent the computer?invent the computer?

Machine tools not adequate in his dayMachine tools not adequate in his day

Mathematics and logic not sufficiently Mathematics and logic not sufficiently developeddeveloped

Mechanical memory store just too Mechanical memory store just too slow and too limited to hold a useful slow and too limited to hold a useful programprogram

Augusta Ada ByronAugusta Ada ByronCountess of LovelaceCountess of Lovelace

Daughter of Lord ByronDaughter of Lord Byron famous romantic poet famous romantic poet

Her mother did not want her Her mother did not want her to grow up to be a poet….to grow up to be a poet….

Competent mathematicianCompetent mathematician

Member of London’s high Member of London’s high societysociety

Ada 1815 - 1852Ada 1815 - 1852 Met Babbage when she was 17Met Babbage when she was 17

Public relations for BabbagePublic relations for Babbage

Translated an article by Luigi Menebrea Translated an article by Luigi Menebrea on the A.E. and added extensive noteson the A.E. and added extensive notes

Some give her credit for writing the first Some give her credit for writing the first computer programcomputer program

New Yorker of German originNew Yorker of German origin

Trained as a mining engineerTrained as a mining engineer

Ph.D at MITPh.D at MIT

Developed a mechanism for reading holes in the Developed a mechanism for reading holes in the cards using spring-mounted needlescards using spring-mounted needles

Needles passed through the holes to make Needles passed through the holes to make electrical connections to trigger a counter to record electrical connections to trigger a counter to record one more of each value one more of each value

Herman Herman HollerithHollerithElectronic tabulation of statistical dataElectronic tabulation of statistical data

1860-1929

1890 census completed 1890 census completed in record timein record time

• Built tabulators on a contract for the US governmentBuilt tabulators on a contract for the US government• Many other governments wanted tabulators tooMany other governments wanted tabulators too• Started Tabulating Machine Company in 1986Started Tabulating Machine Company in 1986• Merged with 2 others in 1911Merged with 2 others in 1911• Changed name to IBM in 1924Changed name to IBM in 1924