Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!mnetor!seismo!rutgers!clyde!watmath!watnot!watcgl!awpaeth
From: awpaeth@watcgl.UUCP (Alan W. Paeth)
Newsgroups: comp.arch
Subject: Re: Byte Order: On Holy Wars and a Plea for Peace
Message-ID: <228@watcgl.UUCP>
Date: Tue, 2-Dec-86 13:45:22 EST
Article-I.D.: watcgl.228
Posted: Tue Dec  2 13:45:22 1986
Date-Received: Tue, 2-Dec-86 22:54:45 EST
References: <1509@ihlpl.UUCP> <1335@hoptoad.uucp> <1364@hoptoad.uucp> <399@viper.UUCP>
Reply-To: awpaeth@watcgl.UUCP (Alan W. Paeth)
Organization: U of Waterloo, Ontario
Lines: 27

In article <399@viper.UUCP> dave@viper.UUCP (David Messer) writes:
> ...Also the number would be translated into words as "three and twenty and
> one hundred" instead of "One hundred and twenty three."  Obviously, the
> people who originally started using arabic numbers made a major mistake!

The Old English convention for two digit numbers puts the units before the
tens. Surviving forms exist in nursury rhymes: "four and twenty blackbirds"
or in the "teens". German still maintains this "backward" convention, e.g.
Dreiundseibzig (three and seventy). It has the very nice advantage than
when doing additions and multiplications, the two digit sum or product can
be spoken out, with the first digit spoken immediately written down as the
correct partial result, and the second digit carried.

I was an exchange student in Bavaria, the problem of conceptualizing
numbers "backwards" when thinking in German quickly melted away during math
classes when at the blackboard. I realized that (in English) I'd grown up
with a mental reversal step when hand multipling, with its slight increase
in cognitive burden.

Unfortunately, the convention doesn't extend beyond the first two digits,
(e.g. "three hundred, one and twenty", transliterated) but two digits are
adequate manual multiplication. English speakers can use the same convention,
but only when doing addition, because the digit reversal is good only up to
ninteen. Does this make German a more efficient language for mental reckoning?
(Memorize log tables and its all the same anyway!)

    /Alan Paeth