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Date: Mon, 31 Jul 2000 01:32:45 -0500 (EST)
From: Alfred M Kriman <akriman@darwin.helios.nd.edu>
Message-Id: <200007310632.e6V6WjU29932@darwin.helios.nd.edu>
To: classics@u.washington.edu
Subject: Roman computation (was: query on a quote)

Kathryn Fiscelli asked Thursday
> I was asked this question by the father of one of my students which I
> could not answer and I hope someone on the list might know off the top of
> his or her head.  He asked whether the Romans used their written numeric
> system to make the calculations for their engineering projects which
> seemed cumbersome (but it may seem that way only from out point of view).

As Adalbert Goertz noted, Roman engineering did not require any very
sophisticated mathematics.  Any quantity that would in principle require
more sophisticated computation than +,-,x,/ could have been extrapolated
from experience.

> Do we know how they made their calculations for their structures?

The abacus has been mentioned, but I don't think it has been emphasized
how much more convenient abacus calculation is than written calculation.
As recently as about 1946, there was a race between a calculator with an
electronic calculating machine and a calculator using a Japanese abacus,
and I think the Japanese abacus won most heats.  The long reign of the
abacus is evident in the language of government: an exchequer is a
checkerboard -- a board ruled for placing the calculi.

I agree that use of the abacus was not a universal skill at any time,
but it is too much to call it
AG> ... kind of a secret art where only a few magic masters of the
AG> self-taught would operate with no assistance from schools or universities.

It was certainly taught by tutors and in schools, but most people
didn't go to school.  Some calculators were slaves.

> Where might he look to learn more?  ...

A recent popular book (with a dusting of PC-ness) is Georges Ifrah:
_The Universal History of Numbers_ (Wiley, 2000).  Chapter 16 is
"Greek and Roman Numerals" (pp. 182-211).

Some journal references were posted to the list by John Durham [[1]]
in 1997, who also mentioned
> Menninger (tr. Broneer) Number Words and Number Symbols:  A Cultural
> History of Numbers, MIT Press 1969, is still a pretty good summary of
> things like the fractions.  The fraction system seems to have originated
> somewhat separately (fractions would originate primarily in a measurement
> context, especially weights, while number tend to originate in a counting
> context).

[[1]] John Durham: Re: Roman numerals and decimals (fwd)
gopher://140.142.56.13/0R96841-100151-/public/classics/classics.log9703d
.