Part 43 (2/2)
Historians tell us that man was able to count long before he was able to write. Of course, he could not count very far, but it was enough for his needs at that time. He had no money and very few possessions of any kind, so that he did not have much occasion to use arithmetic.
It was fairly simple for prehistoric men to distinguish one from two, and to distinguish a few from a great number, but it was more difficult for him to learn to think of a definite number of objects between these extremes. Those who have studied the evolution of figures say that man found it hard to think of a number of objects without using a mark or a finger or something to stand for each object. That is how the first method of counting came into use.
Because man had ten fingers and thumbs, he learned to count in tens.
When he had counted ten, he could make a mark to remind him of the fact, and then count them over again. Some of the early races learned to designate units from tens and tens from hundreds by working their fingers in various ways. Other peoples also made use of their toes in counting, so that they could count up to twenty without getting bothered.
Cantor, the historian, tells of a South African tribe which employed an unusual system of finger counting. Three men sat together facing a fourth who did the counting. Each of the three held up his fingers for the fourth man to count. The first man's ten fingers and thumbs represented units; the second man represented tens, and the third hundreds. By this means, it was possible to count up to 999.
Who Invented the First Adding Machine?
Early cuneiform inscriptions, made about 2200 B. C., show that the Babylonians had developed a fairly extensive system of figuring. This was in the days of the patriarch Abraham. When men's minds were overtaxed with the strain of counting into the hundreds and thousands, the Babylonians invented the first adding machine, a ”pebble board,” a ruled surface on which pebbles were s.h.i.+fted about to represent different values.
The next adding and calculating machine was an evolution from the digits of the human hand and is known as the abacus in China, and the soroban in j.a.pan.
The abacus may be defined as an arrangement of movable beads which slip along fixed rods, indicating by their arrangement some definite numerical quant.i.ty. Its most familiar form is in a boxlike arrangement, divided longitudinally by a narrow ridge of two compartments, one of which is roughly some three times larger than the other. Cylindrical rods placed at equal intervals apart pa.s.s through the framework and are fixed firmly into the sides. On these rods the counters are beaded. Each counter slides along the rod easily and on each rod there are six tamas or beads. Five of these slide on the longest segment of the rod and the remaining one on the shorter. Addition, subtraction, multiplication, division, and even square and cube root can be performed on the abacus, and in the hands of a skilled operator considerable speed can be obtained.
[Ill.u.s.tration: FINGER COUNTING WAS COMMON AMONG EARLIER PEOPLES, AND WAS BROUGHT TO A FAIR DEGREE OF EFFICIENCY BY SOUTH AFRICANS
_Courtesy of the Burroughs Adding Machine Company._]
[Ill.u.s.tration: THE ”ABACUS” WAS ONE OF THE EARLIEST AIDS TO CALCULATION
It is still used extensively in China, and occasionally will be found in Chinese laundries in the United States.
_Courtesy of the Burroughs Adding Machine Company._]
The Oriental tradesman does not deign to perplex himself by a process of mental arithmetic; he seizes his abacus, prepares it by a tilt, makes a few rapid, clicking movements and his calculations are completed. We always look with some slight contempt upon this method of calculation, but a little experience and investigation would tend to transform this contempt into admiration, for it may be safely a.s.serted that even the simplest of all arithmetical operations, the abacus, possesses distinctive advantages over the mental or figuring process. In compet.i.tion in simple addition between a ”lightning calculator” and an ordinary j.a.panese small tradesman, the j.a.panese would easily win the contest.
Blaise Pascal, the wonderful Frenchman, who discovered the theorem in conic sections, or Pascal's hexogram, was not only one of the foremost mathematicians of his day but also excelled in mechanics; when he was nineteen years old he produced the first machine for the carrying of tens and the first arithmetical machine, as we know it, was invented by him about 1641. This was the first calculating machine made with dials.
The same principle, that of using discs with figures on their peripheries, is employed in present-day calculating machines. Among these are numbering machines of all kinds, speedometers, cyclometers and counters used on printing presses.
[Ill.u.s.tration: A MODERN BOOKKEEPING MACHINE, USED FOR LEDGER POSTING AND STATEMENT MAKING
It has seventeen ”banks” or rows of keys, is electrically operated, and automatically adds, subtracts, and computes balances.
_Courtesy of the Burroughs Adding Machine Company._]
Who Discovered the Slide Rule Principle?
It was early in the seventeenth century that Napier, a native of Naples, invented the first actual mechanical means of calculating. He arranged strips of bone, on which were figures, so that they could be brought into various fixed combinations. The instrument was called ”Napier's rod” or ”Napier's bones.” It was the beginning of the slide rule, which has been found of invaluable aid to accountants and engineers.
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