# 2400 BCE—1820 CE

## Computing devices

## The book of science

Tom Sharp

Tom Sharp

- Sumerian abacus
- invented in Babylonia around 2400 BCE
- a positional sexagesimal table
- for placing pebbles as counters
- Chinese abacus or suanpan
- around 200 BCE
- a frame with beads sliding on rods
- five below the beam and two above
- capable of bi-quinary and hexadecimal calculations
- Roman reckoning board
- a ten-by-ten grid of holes
- holding a single count using a peg
- Roman abacus
- a bi-quinary coded-decimal place-value tray
- with upper and lower grooved columns
- for placing counters known as
*calculi* - *
- Apollonius of Perga’s astrolabe
- around 220 BCE and later astrolabes
- in the Byzantine and medieval Islamic world
- could calculate the time of day
- based on the stars and planets
- or help you find the stars and planets
- based on the time of day.
- The Antikythera mechanism
- around 205 BCE
- with at least thirty gears
- was based on the Egyptian calendar
- and could calculate eclipses
- positions of the sun and moon
- and phases of the moon
- A water-powered celestial globe
- by Liang Lingzan and Yi Xing in the 720s
- computed dawn, dusk,
- and phases of the moon
- A geared mechanical astrolabe
- by Abū Rayhān al-Bīrūnī in 996
- had eight gears, and his planisphere,
- a star-chart, could show the stars
- for any date and time,
- had two adjustable disks
- The Equatorium
- by Abū Ishāq Ibrāhīm al-Zarqālī in 1015
- computed the positions of the planets
- The Torquetum
- by Jabir ibn Aflah (Geber) in 1100
- converted horizonal, equatorial, and ecliptic
- measurements
- Ismail al-Jazari, who wrote
*The Book of Knowledge of Ingenious Mechanical Devices,*- built a large waterpowered castle clock in 1206
- that displayed the zodiac,
- orbits of the sun and moon,
- mannequins popping out of doors on the hours,
- automaton musicians that played music,
- and it was programmable in that
- seasonal length of days could be adjusted
- The Plate of Conjunctions
- by Jamshīd al-Kāshī in 1400
- calculated the times of planetary conjunctions
- *
- Napier’s bones
- made by John Napier in 1617
- to help him calculate tables of logarithms
- a set of multiplication tables
- on square-ended sticks
- that can be arranged on a board
- to multiply, divide, or find square roots
- William Oughtred
- put together two circular logarithmic rules in 1622
- to create the first slide rule
- capable of direct multiplication and division
- *
- The
*machine arithmétique*or*Pascaline* - by Blaise Pascal in 1642
- could add and subtract
- and multiply or divide
- by repeated addition or subtraction
- A non-decimal “Multiplying Instrument”
- by Samuel Morland in 1666
- added English pounds, shillings, and pence
- The Stepped Reckoner
- by Gottfried Wilhelm Leibniz in 1672
- added, subtracted, multiplied, and divided
- eight- to sixteen-digit decimal numbers
- and featured a stepped drum
- now called a “Leibniz wheel”
- The first pinwheel calculator
- by Giovanni Poleni in 1709
- inspired successful adding machines
- such as the Odhner Arithmometer in 1873
- The Arithmometer
- by Charles Xavier Thomas in 1820
- used a Leibniz wheel and was the first
- commercially successful mechanical calculator,
- as though commercial success
- were the goal of history

- Beads above the beam are heaven beads;
- beads below the beam are earth beads.
- Use four earth beads and one heaven bead
- on each rod to count in tens.
- Use five earth beads and two heaven beads
- to count in sixteens for units of weight.
- Cultivate thoughtlessness
- to perform calculations with minimal thought.

- It used the Sothic Egyptian calendar
- and predicted the Olympic-game cycles,
- the positions of sun and moon,
- twenty-seven eclipses of the sun,
- and thirty-eight eclipses of the moon,
- various calendar cycles,
- and possibly positions
- of the five known planets.
- Egyptian names for thirteen months
- are transcribed in the Greek alphabet.
- Corinthian names for twelve lunar months
- are on the perimeter of the Metonic dial.
- It shows the path of the ecliptic
- through the twelve houses of the zodiac
- labeled by their Greek names
- and keyed to specific stars.
- It computes the Metonic cycle,
- the Saros cycle,
- the Olympiad cycle,
- the Callippic cycle,
- and the Exeligmos cycle.
- It tracked the precession of the elliptic.
- It used epicyclic gearing to track
- the eliptical orbit of the moon.
- It used a differential gear
- to track the phases of the moon.
- Nevertheless, its conception
- was finer than its manufacture,
- so that the subtleties it was designed to show
- would have been swamped
- by the crudeness of its gearing.

- Here we have a set
- of multiplication tables
- arrangeable on a board
- to calculate products
- and quotients of large numbers.
- They are like toys
- but without a childish stigma,
- reducing multiplication to addition
- and division to subtraction.

- The modern Acu-Math No. 500
- has nine linear logarithmic scales,
- three scales on each part,
- and three parts, the center free to slide.
- The alignment of scales is assisted
- by a sliding transparent hairline cursor.
- It multiplies and divides,
- finds logarithms and exponentials,
- finds squares and square roots,
- cubes and cube roots,
- finds sines and cosines,
- tangents and cotangents,
- does unit conversions
- and conversion to natural logarithms.
- The modern Acu-Math No. 500
- introduced in 1960, is obsolete.

- It’s useless to claim special abilities:
- “A machine could never do what I do.”
- Let’s just say that a person may take pleasure
- in some tasks, such as peeling garlic, chopping
- onions, and cooking a piece of fish.

Leibniz said, “it is beneath the dignity of excellent men to waste their time in calculation when any peasant could do the work just as accurately with the aid of a machine,” but, of course, as well as being a genius, he was a royal prig. It is beneath the dignity of any person to be forced to perform any kind of work that a machine may perform just as well or better. Fortunately, ingenious people, whether ranked high or low on the social scale, have worked hard to provide better and better machines for the betterment of humankind.

See also in

The book of science:Logarithm—John NapierDifference engine—Charles BabbageComputer—Charles Babbage, Alan Turing, John von NeumannReadings on wikipedia: