The most certain and effectual check upon errors which arise in the
process of computation, is to cause the same computations to be made by
separate and independent computers; and this check is rendered still
more decisive if they make their computations by different methods. It
is, nevertheless, a remarkable fact, that several computers, working
separately and independently, do frequently commit precisely the same
error; so that falsehood in this case assumes that character of
consistency, which is regarded as the exclusive attribute of truth.
Instances of this are familiar to most persons who have had the
management of the computation of tables. We have reason to know, that M.
Prony experienced it on many occasions in the management of the great
French tables, when he found three, and even a greater number of
computers, working separately and independently, to return him the same
numerical result, and _that result wrong_. Mr Stratford, the conductor of
the Nautical Almanac, to whose talents and zeal that work owes the
execution of its recent improvements, has more than once observed a
similar occurrence. But one of the most signal examples of this kind, of
which we are aware, is related by Mr Baily. The catalogue of stars
published by the Astronomical Society was computed by two separate and
independent persons, and was afterwards compared and examined with great
care and attention by Mr Stratford. On examining this catalogue, and
recalculating a portion of it, Mr Baily discovered an error in the case
of the star, χ Cephei. Its right ascension was calculated _wrongly_, and
yet _consistently_, by two computers working separately. Their numerical
results agreed precisely in every figure; and Mr Stratford, on examining
the catalogue, failed to detect the error. Mr Baily having reason, from
some discordancy which he observed, to suspect an error, recomputed the
place of the star with a view to discover it; and he himself, in the
first instance, obtained precisely _the same erroneous numerical result_.
It was only on going over the operation a second time that he
_accidentally_ discovered that he had inadvertently committed the same
error.[10]
[Footnote 10: Memoirs Ast. Soc. vol. iv., p. 290.]
It appears, therefore, that the coincidence of different tables, even
when it is certain that they could not have been copied one from
another, but must have been computed independently, is not a decisive
test of their correctness, neither is it possible to ensure accuracy by
the device of separate and independent computation.
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