Vviewpoints
DOI: 10.1145/1721654.1721666
historical Reflections
Be Careful what
You wish For

Part of the collection of books of mathematical tables assembled by Charles Babbage.

FOR SOMe PeOPLe it’s type- writers. For other people it’s mechanical calculating ma- chines that bring a nostalgic tear to the eye. For me it’s mathematical tables. The sight—even the smell—of a set of four-figure tables transports me to my distant school and college days. You can still find mathematical tables—their yellowed pages filled with decimal digits and not much else—in secondhand book stores and occasionally on eBay. I once thought I might like to collect mathematical tables, but then I discovered from the Index to Mathematical Tables1 that many hundreds of tables have been published. Even a selective collection would prove burdensome, if not grounds for divorce. Ironically, the Index to Mathematical Tables, a monumental bibliographical endeavor, was published in 1962, just as tables were going out of business.

PhotograPh CoUrtesy oF sCIenCe MUseUM/ssPL

Mathematical tables were excruci-
atingly tedious to calculate. Take for
example logarithmic tables, which
ruled the calculating roost for about
300 years. Logarithms were invented
by the great Scottish philosopher John
Napier around 1614, and a practical
table of logarithms to base 10, the Ar-
ithmetica Logarithmica, was calculated
by the English mathematician Henry
Briggs and published in 1624. While
the logarithm was an invention of ge-
nius, computing them to 14 decimal
places was assuredly a labor of Her-
cules. It is said that when Napier and
Briggs first met “almost one quarter
of an hour was spent, each beholding
the other with admiration, before one
word was spoken.”
Logarithms were so laborious to cal-
culate that subsequent tables were not
recomputed but were compiled from
the existing canons. The raw logarithms
would be reduced to four, five, six, or
seven decimal places and conveniently
arranged and printed using the best ty-
pography of the day. It is said that the
most accurate table of logarithms ever
produced was Charles Babbage’s seven-
figure tables. Babbage was somewhat
a connoisseur of tables and owned ap-
proximately 300 volumes. Like his pre-
decessors, he did not recompute the
logarithms but copied them from exist-
ing tables. Where there was a discrep-
ancy in his sources he would recom-