The name abacus comes to us by way of the Greek abax, meaning “dust.” Scholars infer that early sums were done schoolboy fashion in Greece with a stylus on a dusty slate, and that the word was carried over to the mechanical counter. The design has changed but little over the years and all abacuses bear a resemblance. The major difference is the number of beads on each row, determined by the mathematical base used in the particular country. Some in India, for example, were set up to handle pounds and shillings for use in shops. Others have a base of twelve. The majority, however, use the decimal system. Each row has seven beads, with a runner separating one or two beads from the others. Some systems use two beads on the narrow side, some only one; this is a mathematical consideration with political implications, incidentally: The Japanese soroban has the single-bead design; Korea’s son pan uses two. When Japan took over Korea the two-bead models were tabu, and went out of use until the Koreans were later able to win their independence again.
About the only thing added to the ancient abacus in recent years is a movable arrow for marking the decimal point. W. D. Loy patented such a gadget in the United States. Today the abacus remains a useful device, not only for business, but also for the teaching of mathematics to youngsters, who can literally “grasp their numbers.” For that reason it ought also to be helpful to the blind, and as a therapeutic aid for manual dexterity. Apparently caught up in the trend toward smaller computers, the abacus has been miniaturized to the extent that it can be worn as earrings or on a key chain.
Even with mechanical counters, early mathematicians needed written numbers. The caveman’s straight-line scratches gave way to hieroglyphics, to the Sumerian cuneiform “wedges,” to Roman numerals, and finally to Hindu and Arabic. Until the numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, and that most wonderful of all, 0 or zero, computations of any but the simplest type were apt to be laborious and time-consuming. Even though the Romans and Greeks had evolved a decimal system, their numbering was complex. To count to 999 in Greek required not ten numbers but twenty-seven. The Roman number for 888 was DCCCLXXXVIII. Multiplying CCXVII times XXIX yielded an answer of MMMMMMCCXCIII, to be sure, but not without some difficulty. It required an abacus to do any kind of multiplication or division.
Indeed, it was perhaps from the abacus that the clue to Arabic simplicity came. The Babylonians, antedating the Greeks, had nevertheless gone them one better in arithmetic by using a “place” system. In other words, the position of a number denoted its value. The Babylonians simply left an empty space between cuneiform number symbols to show an empty space in this positional system. Sometime prior to 300 B.C. a clever mathematician tired of losing track and punched a dot in his clay tablet to fill the empty space and avoid possible error.
The abacus shows these empty spaces on its rows of beads, too, and finally the Hindus combined their nine numerals with a “dot with a hole in it” and gave the mathematical world the zero. In Hindu it was sifr, corrupted to zephirium in Latin, and gives us today both cipher and zero. This enigma of nothingness would one day be used by Leibnitz to prove that God made the world; it would later become half the input of the electronic computer! Meantime, it was developed independently in various other parts of the world; the ancient Mayans being one example.
Impressed as we may be by an electronic computer, it may take some charity to recognize its forebears in the scratchings on a rock. To call the calendar a computer, we must in honesty add a qualifying term like “passive.” The same applies to the abacus despite its movable counters. But time, which produced the simple calendar, also furnished the incentive for the first “active” computers too. The hourglass is a primitive example, as is the sundial. Both had an input, a power source, and a readout. The clock interestingly ended up with not a decimal scheme, but one with a base of twelve. Early astronomers began conventionally bunching days into groups of ten, and located different stars on the horizon to mark the passage of the ten days. It was but a step from here to use these “decans,” as they were called, to further divide each night itself into segments. It turned out that 12 decans did the trick, and since symmetry was a virtue the daylight was similarly divided by twelve, giving us a day of 24 hours rather than 10 or 20.
From the simple hourglass and the more complex water clocks, the Greeks progressed to some truly remarkable celestial motion computers. One of these, built almost a hundred years before the birth of Christ, was recently found on the sea bottom off the Greek island of Antikythera. It had been aboard a ship which sank, and its discovery came as a surprise to scholars since history recorded no such complex devices for that era. The salvaged Greek computer was designed for astronomical work, showing locations of stars, predicting eclipses, and describing various cycles of heavenly bodies. Composed of dozens of gears, shafts, slip rings, and accurately inscribed plates, it was a computer in the best sense of the word and was not exceeded technically for many centuries.
The Greek engineer Vitruvius made an interesting observation when he said, “All machinery is generated by Nature and the revolution of the universe guides and controls. Our fathers took precedents from Nature—developed the comforts of life by their inventions. They rendered some things more convenient by machines and their revolutions.” Hindsight and language being what they are, today we can make a nice play on the word “revolution” as applied to the machine. The Antikythera computer was a prime example of what Vitruvius was talking about. Astronomy was such a complicated business that it was far simpler to make a model of the many motions rather than diagram them or try to retain them in his mind.
There were, of course, some die-hard classicists who decried the use of machines to do the work of pure reasoning. Archytas, who probably invented the screw—or at least discovered its mechanical principle—attempted to apply such mechanical devices to the solving of geometrical problems. For this he was taken to task by purist Plato who sought to preserve the distinct division between “mind” and “machine.”
Yet the syllogistic philosophers themselves, with their major premise, minor premise, and conclusion, were unwittingly setting the stage for a different kind of computer—the logic machine. Plato would be horrified today to see crude decks of cards, or simple electromechanical contrivances, solving problems of “reason” far faster than he could; in fact, as fast as the conditions could be set into them!