## Computing devices

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 water-powered 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

## Suanpan

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.

## Antikythera mechanism

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.

## Napier’s bones

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.

## Slide rule

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.

## Some tasks

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 in wikipedia: