The History of Computation

Dr. Sidney Marshall

Associate professor

Rochester Institute of Technology

Why Do We Calculate? Ancient History

• Ancient History–Measurement and Surveying - Nile River– Astronomy - Predicting Spring– Business Records

The Abacus

• Originally stones on counting board

• Chinese "swan pan" in China since 1300 A.D.

• Imported as Japanese soroban

• In 1946 the best abacus user beat the best electrically driven mechanical calculator in a contest

Chinese Swan Pan

Japanese Soroban

Russian Peasant Multiplication

• Only requires doubling and halving– (duplation and mediation)

Multiplication - continued

• How to do it–Write the two numbers at top– On successive rows halve the first

number and double the second number– Stop when you get to 1– Cross off every row with an even number

in the first column– Add up the remaining numbers in the

second column

Multiplication Example:

• 21 27

• 10 54

• 5 108

• 2 216

• 1 432

• 567 = 21 x 27

Finger Reckoning

• Educated people knew up to 5 x 5

• To multiply two numbers greater than 5:– Extend fingers for amount over 5– Answer is sum of extended fingers

followed by product of "closed" fingers

• 7 x 8 = (2+3) and (3 times 2) = 5 6

Tally Sticks

• Notched sticks used throughout history for record keeping

• Used by English Government for accounts– Sticks were notched and split length-

wise into two pieces for each party– Accounts "tallied" by matching sticks

Tally Sticks

Tally for £11 18s 8d from the reign of Henry III to the Reeve of Ledicumbe

A tally for 6s 8d issued by the Treasurer of Edward I to the Sheriff of Lincolnshire

Tally Stick Fire of 1834• The order went out that the tally

sticks should be burned in a stove in the House of Lords. The stove, overgorged with these preposterous sticks, set fire to the panelling; the panelling set fire to the House of Commons; the two houses of government were reduced to ashes.

Fire caused by burning tally sticks

The Quadrant

• A portable analog computer for trigonometrical and astronomical calculations– Calculations were performed using

dividers to measure and transfer distances

The Sector

• A hinged version of the quadrant

• Used for artillery calculations

• Calculations could be performed by measuring distances with a divider

Napier's Bones (1550-1617)

• Tiles containing a column of the multiplication table

Napier's invention of Logarithms 1614

• Method of prosthaphaeresis– sin a sin b = [cos(a-b) - cos(a+b)]/2

• Using Napier's Logarithms– log ab = log a + log b

Slide Rules

• Based on logarithms

• Could do multiplication, division, powers, roots, and trigonometric computations

• Nearly 3 decimal digits of accuracy– All engineers used to have one

Slide Rule Operation

• Adding lengths on a logarithm scale is equivalent to multiplying

Slide Rules

Slide Rules

• More accuracy required a longer scale or more accurate mechanism

• Many types of slide rules were invented– spiral, cylindrical, long steel tapes,

magnifying devices

Cylindrical Slide Rule

Spiral Slide Rule

Graphical computing

• planimeters

• integrators

The Planimeter

Wilhelm Schickard (1592-1635)

• First workable mechanical adding machine

Blaise Pascal (1623-1662)

• Several dials like telephone for entering numbers

• 9's complement used for subtraction

Mathematical Tables - 1780's

• Big effort to produce accurate tables– Powers and roots– Logarithms (addition/subtraction

logarithms, quarter squares)– Trigonometric and Exponential tables

for geometry

• Most scientific calculations carried out with the help of tables

Jacquard's Loom (1752-1834)

• Punched cards controlled weaving

Charles Babbage (1791-1871)

• Designed many mechanical calculating machines– His "Difference Engine" was designed

to calculate tables

• Designed the "Analytical Engine" with many of the properties of our modern computers

Method of Differences0.7242758696 0.00081865150.7250945211 -0.0000015403 0.0008171112 0.00000000580.7259116323 -0.0000015345 0.0008155767 0.00000000580.7267272090 -0.0000015287 0.0008140480 0.00000000570.7275412570 -0.0000015230 0.0008125250 0.00000000570.7283537820 -0.0000015173 0.0008110077 0.00000000570.7291647897 -0.0000015117 0.00080949600.7299742857

Babbage's Difference Engine

Babbage's Analytical Engine

Dorr Felt - Comptometer (1886)

Designed (out of a macaroni box!) a reliable carrying mechanism

Mechanical Calculating Machines

• The 1900's development of many calculators and cash registers– Some were hand powered and some

were driven with an electrical motor

• Calculators were the workhorse for scientific computation in the 1950’s– A “computer” was a person operating a

mechanical calculator

Monroe calculator

Mechanical Differential Analyzers

• Vannevar Bush developed the Differential Analyzer - 1930's– All mechanical machine for solving

differential equations• Solved the equation dz = y dx

– Electrical versions were made later• OP amps and analog computers• Digital differential analyzers

Bush Differential Analyzer

Card Punch equipment

• 1880 census results available in 1888

• For the 1890 census Hollerith developed a punched card system

• The 1900 census done 1 year 7 months after the results were in

Uses of "Tabulating" Cards

• Business records

• Subscription cards

• Billing

• Code Breaking

• Atom Bomb Calculations

IBM Card

IBM Punched Card machines

Punch Card Control Panel

The telephone company

• Largest distributed relay computer

• Specification for telephone office was 1/2 hour outage in 40 years

• George Stibitz built a relay computer in 1939 with telephone relays

The "modern" computer era

• World War II– Code Breaking– Artillery firing tables– Atom Bomb Calculations

The ENIAC - 1944

The IBM 704• First "modern" mass produced

computer

Storage Technology

• Mercury Delay Lines

• Williams Storage Tube

• Magnetic Core Memory

• Semiconductor Memory– The Rule of 4

Core Memory

Off-line Storage

• Punched Cards– Paper tape

• Magnetic Tape

• Magnetic Drum

• Magnetic Disk

FORTRAN 1954-1957

• Written for the IBM 704– 4096 words of 36-bit memory

• Written by a team of programmers lead by John W. Backus

• Still in use today

Fortran Program

• C THIS PROGRAM CALCULATES BINOMIAL COEFFICIENTS• C• DIMENSION NBINOM(20)• 1 FORMAT(20I4)• DO 10 K=1,20• 10 NBINOM(K) = 0• NBINOM(1) = 1• DO 30 K=1,20• DO 20 J=K,2,-1• 20 NBINOM(J) = NBINOM(J) + NBINOM(J-1)• 30 PRINT 1, (NBINOM(I),I=1,K)• END

The SAGE System

• The AN/FSQ-7 computer built by IBM for the Air Force in the late 1950’s

• It consumed 1,000,000 watts of power

• Designed as a computer aid for intercepting enemy bombers

Sage - cont

• Required a building to house it

• About 30 were built– 113 ton computer

• When deployed in 1958 this was the first large-scale, real-time digital computer supporting a major military mission

Sage AN/FSQ-7 Computer

Sage operator console

LGP-30

• Serial Design

• Magnetic drum

• 101 vacuum tubes

• optimizing by placing data and instructions around the drum

• 60 – 200 instructions / second

Dartmouth Timesharing

• 1961-2– LGP-30 DOPE

• 1964– Basic - Tom Kurtz, John Kemeny– Dartmouth Timesharing

• 1965-1967 DTSS II

Computation Power Increase

• Circuit simulation takes a kiloflop

• Optics design takes a megaflop

• Weather prediction takes 8 teraflops

• The change in computation power changes the possibilities for calculation

ARPANET

• Totally new concept for connecting computers together

Valuable vs Free

• Memory

• Bandwidth

• Cycles

• Computers

Conclusion

• There has been an amazing growth of computer power in less than 50 years

• Control of individual vs control of industry– Intellectual property rights

• Probably the last free decade• Governments will probably side with industry

• Rise of Databases– Who will control information and databases?

References

• Prof. Tim Bergin at American University

• A History of Computing Technology by Michael Williams

• IBM Historical Archives

• Computer History Museum

• Google!!