- 1 7 - 2 14 - 4 28 - 8 56

A line before the first, second, and fourth of these numbers indicated that it is necessary to multiply 7 by 1 plus 2 plus 8 - that is, by 11, in order to obtain 77; that is to say, 7 goes 11 times in 77. All this seems very cumbersome indeed, yet we must not overlook the fact that the process which goes on in our own minds in performing such a problem as this is precisely similar, except that we have learned to slur over certain of the intermediate steps with the aid of a memorized multiplication table. In the last analysis, division is only the obverse side of multiplication, and any one who has not learned his multiplication table is reduced to some such expedient as that of the Egyptian. Indeed, whenever we pass beyond the range of our memorized multiplication table-which for most of us ends with the twelves - the experimental character of the trial multiplication through which division is finally effected does not so greatly differ from the experimental efforts which the Egyptian was obliged to apply to smaller numbers.

Despite his defective comprehension of fractions, the Egyptian was able to work out problems of relative complexity; for example, he could determine the answer of such a problem as this: a number together with its fifth part makes 21; what is the number? The process by which the Egyptian solved this problem seems very cumbersome to any one for whom a rudimentary knowledge of algebra makes it simple, yet the method which we employ differs only in that we are enabled, thanks to our hypothetical x, to make a short cut, and the essential fact must not be overlooked that the Egyptian reached a correct solution of the problem. With all due desire to give credit, however, the fact remains that the Egyptian was but a crude mathematician. Here, as elsewhere, it is impossible to admire him for any high development of theoretical science. First, last, and all the time, he was practical, and there is nothing to show that the thought of science for its own sake, for the mere love of knowing, ever entered his head.

In general, then, we must admit that the Egyptian had not progressed far in the hard way of abstract thinking. He worshipped everything about him because he feared the result of failing to do so. He embalmed the dead lest the spirit of the neglected one might come to torment him. Eye-minded as he was, he came to have an artistic sense, to love decorative effects. But he let these always take precedence over his sense of truth; as, for example, when he modified his lists of kings at Abydos to fit the space which the architect had left to be filled; he had no historical sense to show to him that truth should take precedence over mere decoration. And everywhere he lived in the same happy-go-lucky way. He loved personal ease, the pleasures of the table, the luxuries of life, games, recreations, festivals. He took no heed for the morrow, except as the morrow might minister to his personal needs. Essentially a sensual being, he scarcely conceived the meaning of the intellectual life in the modern sense of the term. He had perforce learned some things about astronomy, because these were necessary to his worship of the gods; about practical medicine, because this ministered to his material needs; about practical arithmetic, because this aided him in every-day affairs. The bare rudiments of an historical science may be said to be crudely outlined in his defective lists of kings. But beyond this he did not go. Science as science, and for its own sake, was unknown to him. He had gods for all material functions, and festivals in honor of every god; but there was no goddess of mere wisdom in his pantheon. The conception of Minerva was reserved for the creative genius of another people.