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By Aaron Bakst

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If we start out with single weights of 1, 2, 4, 8, 16, and 32 pounds, we may obtain weights up to and including 63 pounds. For example, the combination of 1-, 4-, 8-, and 32pound weights provides 45 pounds. In the "two-system" of numeration 45 is represented by 101101. In terms of the weights to be used, 101101 simply means, reading from right to left, one weight each marked L-pound, 4-pound (22 ) , 8-pound (2"i), and 32-pound (25). If we wish to obtain weights up to and including 127 pounds a 64 pound weight will have to be added.

We do not know whether the ROIIlan schoolboy was ever taught to perform arithmetic operations by writing numbers, but it is generally believed that all arithmetic operations were performed on a computing device called an abacus. The word calculate is derived from the Latin word calculus which means pebble or small stone. The abacus was a small board with grooves in which the pebbles (or calculi) were placed. The value of each groove was determined In advance. Thus, a Roman schoolboy, instead of carrying with him some pencils and paper, or a slate and chalk, lugged to school a grooved table and a lot of small stones.

But each theory is just as good as the next. Actually, the development of any system of numeration is evidence that men are inclined to systematize their actions. To be systematic is to conserve time and energy. 25 THE NOTCH ARITHMETIC In any system of numeration we count, by steps of one (1) until we reach some definite quantity. As soon as this quantity is reached, the process of counting reverts to the original few numbers. However, the first counted collection of numbers is set aside, and it is assigned a number "one" (1) thus indicating that a collection of a definite size was reached.

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