The Atlantic Monthly | Page 5

is assumed, indeed, that
this is the case, and habit confirms the assumption; yet, when reflection
has overcome habit, it will be seen that its adoption was due to accident
alone,--that it took place before any attention was paid to a general
system, in short, without reflection,--and that its supposed perfection is
a mere delusion; for, as a member of such a system, it presents
disagreements on every hand; as has been said, it has no agreement
with anything, unless it be allowable to say that it agrees with the
Arabic mode of notation. This kind of agreement it has, in common
with every other base. It is this that gives it character. On this account
alone it is believed by many to be the perfection of harmony. They get
the base of numeration and the mode of notation so mingled together,
that they cannot separate them sufficiently to obtain a distinct idea of
either; and some are not conscious that they are distinct, but see in the
Arabic mode nothing save decimal notation, and attribute to it all those
high qualities that belong to the mode only. The Arabic mode is an
invention of the highest merit, not surpassed by any other; but the
admiration that belongs to it is thus bestowed upon a quite
commonplace idea, a misapplication, which, in this as in many other
cases, arises from the fact, that it is much easier to admire than to
investigate. This result of carelessness, if isolated, might be excused;
but all errors are productive, and it should be remembered that this one
has produced that extraordinary perversion of truth to be found in the
reply to the question, How is all this confusion to be brought into
harmony? It has produced it not only in words, but in deed. Was it not
this reply that led the French commission to extend the use of the
present base from numeration to gradation also, under the delusive
hope of producing a perfectly homogeneous system, that would be
practical also? Was it not under its influence, that, adhering to the base
to which the world had been so long accustomed, instead of attempting
to regulate ideal division by real, which might have led to the adoption
of the true base and a practical system, they committed the one great
error of endeavoring to reverse true order, by forcing real division into
conformity with a preconceived ideal? This attempt was made at a time
supposed by many to be peculiarly suited to the purpose, a time of
changes. It was a time of changes, truly; but these were the result of

high excitement, not of quiet thought, such as the subject requires,--a
time for rushing forward, not for retracing misguided steps.
Accordingly, a system was produced which from its magnitude and
importance was truly imposing, and which, to the present day, is highly
applauded by all those who, under the influence of the error alluded to,
conceive decimal numeration to be a sacred truth: applauded, not
because of its adaptation to commerce, but simply because of its
beautiful proportions, its elegant symmetry, to say nothing of the array
of learning and power engaged in its production and inauguration:
imposing, truly, and alike on its authors and admirers; for the qualities
they so much admire are not peculiar to the decimal base, but to the use
of one and the same base for numeration, notation, and gradation. But
if the base ten agrees with nothing, over, on, or under the earth, can it
be the best for scientific use? can it be at all suited to commercial
purposes? If true order is the object to be attained, and that for the sake
of its utility, then agreement between real and ideal division is the one
thing needful, the one essential change without which all other changes
are vain, the only change that will yield the greatest good to the greatest
number,--a change, which, as volition is with the ideal, and inertia with
the real, can be attained only by adaptation of the ideal to the real.
A full investigation of the existing heterogeneous or fragmentary
system will lead to the discovery that it contains two elements which
are at variance with natural division and with each other, and that the
unsuccessful issue of every attempt at regulation hitherto made has
been the proper result of the mistake of supposing agreement between
those elements to be a possible thing.
The first element of discord to be considered is the division of things
by personal proportion, as by fathom, yard, cubit, foot, etc. It is obvious
at a glance, that these do not agree with binary division, nor with
decimal, nor yet with each other. It is this element that has suggested
the duodecimal base, to