The Atlantic Monthly | Page 2

mode bear no resemblance to those proper to a base. The
qualities of the present mode are well known and well accepted. Those
of the present base are accepted with the mode, but those proper to a
base remain to be determined. In attempting to ascertain these, it will
be necessary to consider the uses of numeration and of notation.
These may be arranged in three divisions,--scientific, mechanical, and
commercial. The first is limited, being confined to a few; the second is
general, being common to many; the third is universal, being necessary
to all. Commercial use, therefore, will govern the present inquiry.
Commerce, being the exchange of property, requires real quantity to be
determined, and this in such proportions as are most readily obtained
and most frequently required. This can be done only by the adoption of
a unit of quantity that is both real and constant, and such multiples and
divisions of it as are consistent with the nature of things and the
requirements of use: real, because property, being real, can be
measured by real measures only; constant, because the determination of
quantity requires a standard of comparison that is invariable;
conveniently proportioned, because both time and labor are precious.
These rules being acted on, the result will be a system of real, constant,
and convenient weights, measures, and coins. Consequently, the
numeration and notation best suited to commerce will be those which
agree best with such a system.
From the earliest periods, special attention has been paid to units of
quantity, and, in the ignorance of more constant quantities, the
governors of men have offered their own persons as measures; hence
the fathom, yard, pace, cubit, foot, span, hand, digit, pound, and pint. It
is quite probable that the Egyptians first gave to such measures the
permanent form of government standards, and that copies of them were
carried by commerce, and otherwise, to surrounding nations. In time,
these became vitiated, and should have been verified by their originals;
but for distant nations this was not convenient; moreover, the governors
of those nations had a variety of reasons for preferring to verify them

by their own persons. Thus they became doubly vitiated; yet, as they
were not duly enforced, the people pleased themselves, so that almost
every market-town and fair had its own weights and measures; and as,
in the regulation of coins, governments, like the people, pleased
themselves, so that almost every nation had a peculiar currency, the
general result was, that with the laws and the practices of the governors
and the governed, neither of whom pursued a legitimate course,
confusion reigned supreme. Indeed, a system of weights, measures, and
coins, with a constant and real standard, and corresponding multiples
and divisions, though indulged in as a day-dream by a few, has never
yet been presented to the world in a definite form; and as, in the
absence of such a system, a corresponding system of numeration and
notation can be of no real use, the probability is, that neither the one
nor the other has ever been fully idealized. On the contrary, the present
base is taken to be a fixed fact, of the order of the laws of the Medes
and Persians; so much so, that, when the great question is asked, one of
the leading questions of the age,--How is this mass of confusion to be
brought into harmony?--the reply is,--It is only necessary to adopt one
constant and real standard, with decimal multiples and divisions, and a
corresponding nomenclature, and the work is done: a reply that is still
persisted in, though the proposition has been fairly tried, and clearly
proved to be impracticable.
Ever since commerce began, merchants, and governments for them,
have, from time to time, established multiples and divisions of given
standards; yet, for some reason, they have seldom chosen the number
ten as a base. From the long-continued and intimate connection of
decimal numeration and notation with the quantities commerce requires,
may not the fact, that it has not been so used more frequently, be
considered as sufficient evidence that this use is not proper to it? That it
is not may be shown thus:--A thing may be divided directly into equal
parts only by first dividing it into two, then dividing each of the parts
into two, etc., producing 2, 4, 8, 16, etc., equal parts, but ten never.
This results from the fact, that doubling or folding is the only direct
mode of dividing real quantities into equal parts, and that balancing is
the nearest indirect mode,--two facts that go far to prove binary
division to be proper to weights, measures, and coins. Moreover, use

evidently requires things to be divided by two more frequently than by
any other number,--a fact apparently due to a natural agreement