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Topic: quotation
Replies: 21   Last Post: Aug 27, 1996 12:42 PM

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Kevin Brown

Posts: 360
Registered: 12/6/04
Re: quotation
Posted: Aug 15, 1996 6:53 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply (Paul J. Bell) wrote:
> A friend and I have a different opinion regarding the author of the
> following quotation:
> "Also the astronomers surely will not have to continue to
> exercise the patience which is required for computation.
> It is this that deters them from computing or correcting
> tables, from the construction of Ephemerides, from working
> on hypotheses, anf form discussions of observations with
> each other. For it is unworthy of excellent men to lose
> hours like slaves in the labour of calculation which could
> safely be relegated to anyone else if machines were used."
> Said friend thinks that the author was Leibniz and I think that
> it was Gauss. Opinions, please, with a reference, if possible.

Said friend is correct. The passage is the 2nd to last paragraph
in a manuscript of Leibniz, dated 1685 (several years after he
actually built his first mechanical computer), with the
characteristically Leibnizian title

"Machina arithmetica in qua non additio tantum et subtractio
sed et multiplicatio nullo, divisio vero paene nullo animi
labore peragantur"

This article, translated from the Latin into English, is reproduced
in D. E. Smith's "A Source Book in Mathematics" (Dover, p. 173). The
article begins with Leibniz's account of his moment of inspiration:

When, several years ago, I saw for the first time an
instrument which, when carried, automatically records
the number of steps taken by a pedestrian, it occurred
to me at once that the entire arithmetic could be
subjected to a similar kind of machinery so that not
only counting, but also addition and subtraction,
multiplication and division could be accomplished by
a suitably arranged machine easily, promptly, and with
sure results.

The calculating box of Pascal was not known to me
at that time... When I noticed, however, the mere name
of a calculating machine in the preface of his "posthumous
thoughts"...I immediately inquired about it in a letter
to a Parisian friend. When I learned from him that such
a machine exists I requested the most distinguished
Carcavius by letter to give me an explanation of the
work which it is capable of performing.

I find this interesting because (like the above title) it's so
characteristic of Leibniz. He was a sponge for knowledge and
information, and tireless in ferreting it out of friends,
acquaintences, and strangers alike. Once he had gotten all
the information he could about Pascal's machine, he set
himself the task of making an even better machine.

There are obvious parallels with his development of the calculus.
He learned via Oldenberg in the early 1670s that a secretive man
at Cambridge was evidently in possession of a wonderful method for
solving problems related to tangents, series, sums, etc, but he
would only give hints about the general method. As with the
appearance of "the MERE NAME of a calculating machine" in Pascal's
papers, the mere mention of a wonderful general method for
handling problems of this kind was enough to perk up Leibniz's
ears and set him working on the task. Before long he had a method
that was, for practical purposes, at least the equal of Newton's
fluxions (although his philosophical justification for it was
less sophisticated than Newton's).
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