Subject: Which-endian identification?

From: Graham Klyne <[email-masked]>
Date: Fri, 22 Jan 1999 12:20:33 +0000

At 22:41 21/01/99 -0800, Mohsen BANAN wrote:

[...]
>It is about a fundamental architectural design
>decision.  Based on what we have learned over
>the past 15 years, the "right" and the
>"wrong" are quite clear now. 
>
>Key architectural attributes for "right" and
>"wrong" are consistency, uniformity, cohesion,
>fitness in bigger pictures, usability,  ...

*If* there is a definitive right or wrong here (which I doubt), there are
arguments either way.  You make one based in part on consistency with
numeric formats.

If my (admittedly poor) knowledge of history of science is correct, use of
positional number systems was first widely adopted by Arabic speaking
societies where the normal written script goes right-to-left.  But (even
when using their own digits) Arabic nations write the most significant
digit at the left (i.e. "last") -- this is something that has often puzzled
me, but I think you have helped me to see that in developing a positional
number system from scratch, it was maybe more natural to write the *least*
significant digit first.  We in the West adopted the arabic numbering
structure without fundamental change, and have grown used to most
significant digit first;  I suspect that's a matter of learning, not
fundamentals.

One technical reason that I believe favours least-significant-first is
abbreviation:  people like to truncate things.  I speculate that what is
required is that the most *relevant* information comes first, so that less
relevant details can be dropped off the "end".  Here, "relevant" is not
(necessarily) the same as "significant":  by "relevant" I mean the
information that is most likely to distinguish one datum from another.
Maybe this is why Japanese use a different postal addressing order to most
Westerners, because of what their culture deems most relevant?

#g

------------
Graham Klyne
([email-masked])

---

From: Michael McNeil <[email-masked]>
Date: Sun, 24 Jan 1999 10:50:29 -0800

Graham Klyne wrote:
>*If* there is a definitive right or wrong here (which I doubt),
>there are arguments either way.  You make one based in part on
>consistency with numeric formats.
>
>If my (admittedly poor) knowledge of history of science is correct,
>use of positional number systems was first widely adopted by Arabic
>speaking societies where the normal written script goes right-to-left.  

If we are to delve into the history of mathematics, the first widely
used positional numbering system, in the Old World, was the base-60,
"sexagesimal" numbering system developed around 2,000 B.C. by the
Babylonians.  This Babylonian positional system is still in wide use
today, by virtually everyone -- in the hours-minutes-seconds used to
represent time, and degrees-minutes-seconds used for angular measure.

During its entire history the sexagesimal system incorporated base-60
fractions (it's really an early example of floating point).  A zero
symbol was added by Hellenistic times, following which the system
spread over virtually the entire civilized world, excepting China.

Users of sexagesimal -- mostly astronomers and mathematicians --
performed computations such as long division by close analogy to
what is done today using base-10.  Ptolemy's famous _Almagest_ of
140 A.D., for example, utilized a zero symbol in conjunction with
sexagesimal numerals and fractions exactly as we do today.  Usage of
sexagesimals by astronomers and mathematicians continued throughout
the Byzantine and Islamic periods into the modern mathematical era.

Decimal numerals, contrariwise, developed much later, during the
middle of the first millennium A.D. -- in India, not Arabic lands.
Until 1000 A.D. or so, the decimal system, unlike the sexagesimal,
did not include a zero symbol but used only nine digits.  Moreover,
until the age of modern mathematics (the 16th century), decimals had
not been extended to include base-10 fractions, and as a result, for
scientific computations decimals were far inferior to sexagesimals.

Once both a zero symbol and decimal fractions had been incorporated
into the system, however, decimal numerals proved more convenient
to use than sexagesimal -- which, after all, requires a times table
60 columns wide and deep.  Decimal computations gradually replaced
sexagesimal after this in the astronomical and mathematical worlds.

Remember, though, even today we use minutes and seconds to express
time and angular position, so the change is not complete.  Minutes
and seconds were not, you see, originally _units_ of time and angle,
but are first- and second-order base-60 fractions, what Ptolemy
called _partes minutae primae_ and _partes minutae secundae_.

(Back to your regular station....)

>But (even when using their own digits) Arabic nations write
>the most significant digit at the left (i.e. "last") -- this is
>something that has often puzzled me, but I think you have helped me
>to see that in developing a positional number system from scratch,
>it was maybe more natural to write the *least* significant digit
>first.  We in the West adopted the arabic numbering structure
>without fundamental change, and have grown used to most significant
>digit first;  I suspect that's a matter of learning, not
>fundamentals.
> 
>One technical reason that I believe favours least-significant-first
>is abbreviation:  people like to truncate things.  I speculate that
>what is required is that the most *relevant* information comes first,
>so that less relevant details can be dropped off the "end".  Here,
>"relevant" is not (necessarily) the same as "significant":  by
>"relevant" I mean the information that is most likely to distinguish
>one datum from another.  Maybe this is why Japanese use a different
>postal addressing order to most Westerners, because of what their
>culture deems most relevant?
>
>#g
>
>Graham Klyne ([email-masked])

--
Michael McNeil
[email-masked]

P.S.  Sorry for the diversion from the usual weighty topics, but at
times I'm tempted to do something about the low level of knowledge
about the history of science.  When an opportunity presents itself
(such as someone touching on the subject), sometimes I'll grab it.

P.P.S.  An excellent guide to this subject is Carl B. Boyer's
_A_History_of_Mathematics_ (Second Edition, 1991, John Wiley
and Sons Inc., New York, 715 pages, ISBN 0-471-54397-7 (pbk)).

---

From: Michael McNeil <[email-masked]>
Date: Sun, 24 Jan 1999 10:50:29 -0800

--
Michael McNeil
[email-masked]