ABSTRACT SCIENCE
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 hand-book 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 every-day 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 stand-point 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.
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.