Williams 
But, indeed, practical
knowledge was, as has been said over and over, the essential characteristic
of Egyptian science. Yet another illustration of this is furnished us if
we turn to the more abstract departments of thought and inquire what were
the Egyptian attempts in such a field as mathematics. The answer does not
tend greatly to increase our admiration for the Egyptian mind. We are led
to see, indeed, that the Egyptian merchant was able to perform all the
computations necessary to his craft, but we are forced to conclude that
the knowledge of numbers scarcely extended beyond this, and that even here
the methods of reckoning were tedious and cumbersome. Our knowledge of
the subject rests largely upon the so called papyrus Rhind,[10] which
is a sort of mythological handbook of the ancient Egyptians. Analyzing
this document, Professor Erman concludes that the knowledge of the Egyptians
was adequate to all practical requirements. Their mathematics taught them
"how in the exchange of bread for beer the respective value was to be determined
when converted into a quantity of corn; how to reckon the size of a field;
how to determine how a given quantity of corn would go into a granary of
a certain size," and like everyday problems. Yet they were obliged to
make some of their simple computations in a very roundabout way. It would
appear, for example, that their mental arithmetic did not enable them to
multiply by a number larger than two, and that they did not reach a clear
conception of complex fractional numbers. They did, indeed, recognize that
each part of an object divided into 10 pieces became 1/10 of that object;
they even grasped the idea of 2/3 this being a conception easily visualized;
but they apparently did not visualize such a conception as 3/10 except
in the crude form of 1/10 plus 1/10 plus 1/10. Their entire idea of division
seems defective. They viewed the subject from the more elementary standpoint
of multiplication. Thus, in order to find out how many times 7 is contained
in 77, an existing example shows that the numbers representing 1 times
7, 2 times 7, 4 times 7, 8 times 7 were set down successively and various
experimental additions made to find out which sets of these numbers aggregated
77.
 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 tablewhich
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. Eyeminded 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 happygolucky
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 everyday 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. 
