Flavin's Corner

Wrong Numbers

     The September 23rd loss of NASA's Mars Climate Orbiter was avoidable.
As the $125 million dollar spacecraft began to circle Mars, attempting to
become the first interplanetary weather station, its onboard navigational system
malfunctioned.  The spacecraft hit the Martian atmosphere at the wrong angle
and burned up.  Why the malfunction?  Wrong numbers...  NASA claims they're
overworked and underfunded, neglected to check the units of measurement used
by one of their many contractors, and when it came time for the spacecraft to
enter into orbit, it couldn't process the conflicting measurements of International
Units (e.g., meters and kilometers) and the quaint, isolationist American system
(e.g., feet and miles).  Well, considering America's conflicting, self-inflecting,
degrees of stubbornness regarding most things, maybe the malfunction wasn't so
uncommon after all.

An Ice Age notational artifact.

     Though dedicated researchers, such as Alexander Marshack (The Roots of
Civilization, 1972 & 1991), have advanced our understanding of the cognitive
abilities of early modern humans, linguists and anthropologists have failed to
uncover any evidence of a prehistoric numbering system or any remnant names
for numerals beyond 'three'.  It appears our prehistoric ancestors counted "one,"
followed by "two," and then used some variation of "a whole bunch!"  Though
the concept of number was undoubtedly recognized early, as evidenced by
notational tally counts from around the globe, imparting names to numbers
appears to have been a rather late development.

   The renowned historian of mathematics, Dr. Otto Neugebauer, drew
attention to the general inability of most ancients to name their numbers by citing
the "Spell for Obtaining a Ferry-Boat" from the Egyptian Book of the Dead, a
section which was derived from material contained in the earlier, so-called
"Pyramid Texts" of the Old Kingdom period.  The section tells of an underworld
ferryman who asks: "Did you bring me a man who cannot number his fingers?"
Apparently the ability to name numbers was usually limited to kings (or
pharaohs) and magicians (or priests). [See: The Exact Sciences in Antiquity by
O. Neugebauer, p. 9, Second Edition, 1957, Brown University Press; reprinted
(and still in print) 1969, Dover Books, as well as a cheapie, hardcover edition
(sans plates), by Barnes and Noble Books, which is widely available.]

     Owing much to the pioneering and still controversial work of Dr. Denise
Schmandt-Besserat, Professor of Art and Middle Eastern Studies at the
University of Texas at Austin, many now understand the emergence of the
earliest writing system (Sumerian cuneiform) to have developed from an archaic
counting system which used tokens and identifying character marks.  According
to Schmandt-Besserat, then, the act of numbering gave rise to the associative
process of assigning character marks to communicative ideas and language.  It
may be assumed that the preliterate Sumerians "named" their numbers, but those
"words" remain unknown. [For more on Schmandt-Besserat click  here.]

     While today's graphic expressions of numbers are traced through Hindu and
Arabic characters, and the Classical Greeks are widely credited with having
initiated "science" and mathematics, in actuality both were extremely dependent
on the continuation of the archaic counting system of the preliterate Sumerians.
The Sumerian culture, through conquest and population influx, is now divided
into such "historical" periods as Akkad, Ur, the Hammurabi Dynasty or "Old
Babylonian," Cassite, Assyrian, Persian or "Neo-Babylonian," contemporary
Iraq, and the like.  Very early, probably from the beginnings of numeration, there
were conflicting systems of counting, as evidenced by the diverse base-systems
of extant cuneiform texts.  We know of the popularity of the sexagesimal
system, as it survives in our 60 minute hour and 360° circle, but what is not
widely known is that this awkward system was only used in astronomical
calculations, and many other systems (e.g., based on 10, 5, 4, etc.) were used in
commonplace numbering.  It's most confusing to comprehend today, it must've
taken a "king" or "magician" to understand such in its day, and the difficulty
seems to survive in the work of some of the private contractors hired by NASA!
[For a thorough (though somewhat "out-of-date"" discussion of terms and
periods, see: Science Awaking II  by B. L. van der Waerden, 1974,
Noordhoff/Oxford, Chapter Two, "Old Babylonian Astronomy."]

     It remains folly to suggest why the Sumerian culture and their later offshoots
elected to utilize a numbering system based on 60.  Some have advanced the
origin of the 60-base system as a division of the measurement of silver, as a
mana was divided into 60 shekels, but this is "putting the cart in front of the
horse," and the answer remains elusive.  What is plain and demonstrable is the
biological happenstance of our species possessing ten fingers and choosing 10 as
our common, or "base," counting system.  The base-10 system developed,
seemingly independent in Sumeria, Egypt, and elsewhere, the early Greek
mathematicians continued the confluence of different systems (e.g., 60 for
astronomy and 10 for commonplace notations), and this diffused eastward to
Arabia, India, and beyond, which later returned as "our" notational system.
Yup, the world keeps getting smaller!

     What Alexander the Great attempted, the Romans idealized, the Catholic
church nearly realized, and Napoleon Bonaparte foolishly struggled for--a
uniting of us all--is ultimately a grand and hopeful goal.  Fortunately, so far,
when despots, governments, and religions make the attempt it fails, because
subtle distinctions proudly separate us and major commonalties enjoin us.  It's up
to us to define our own way in the modern world and not be beholden to the
past.  The 18th century invention of the "metric" system has steadily united
much of our planet with its straightforward simplicity.  Oh, except America, that
is, even though we've been told todo so for some time now.  See, we don't like
being told what to do, even if it means crashing a $125 million dollar spacecraft,
"walking a mile for a Camel" cigarette, and buying a gallon of milk, a quart of
beer, or a pint of booze.  We don't appreciate ...being told what to do!
Americans are Coke, McDonald's, and Gap commercials (read: spoiled,
self-centered adolescents), and we'll waste our money and technology as we see
fit.  Got it? [Click here  for an overview of the metric system.]

     The upcoming Mars Polar Lander, scheduled for December 3rd, 1999, is
susceptible to the same software problems as the Climate Orbiter.  NASA has
promised it will correct everything, ...mumbled something about how their
immediate mission will continue without the Climate Orbiter, and is trying to put
the best face on a really embarrassing event.  NASA?  Forget embarrassment...
Birds have feet as well as wings...  Get back to work!


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