Alafia

here's a little aside...
the Yoruba translation of "there are four stones." is nothing less than deep, for real.
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Sunday, December 23, 2001

It All Adds Up
SCIENCE AND AN AFRICAN LOGIC By Helen Verran University of Chicago
Press: 248 pp., $55

By MARGARET WERTHEIM


"Indigenous science." To many the phrase seems a contradiction
in terms. To a large degree the Western academy has accepted that
other cultures have sophisticated systems of philosophy and religion,
but science is still widely viewed as something unique to the West. A
growing body of scholars has begun to question this view and is
claiming that science is a multifaceted phenomenon manifesting in
many cultures.
On one level we are becoming used to such claims. Acupuncture,
Chinese herbalism and ayurvedic medicine have all gained huge
followings in the West. Major pharmaceutical companies are also
interested in "indigenous medicines," investing millions in
bioprospecting programs.
Other societies, most notably the Maya, developed their own very
different systems of astronomy. Where Western astronomy is based on
looking up, Maya astronomy was focused on the horizon. Where Western
astronomy is centered first on the Earth, then the sun, to Maya
astronomers, the most important celestial body was Venus.
Anthropologists and others have begun to examine a range of non-
Western knowledge systems with a view to investigating their
empirical and predictive power. In her book "Naked Science," UC
Berkeley anthropologist Laura Nader argues that in
rigidly "demarcating science from other systems of knowledge," we not
only misrepresent science, we also do ourselves a disservice by
failing to benefit from centuries of observation and insight by other
cultures.
In "Science and an African Logic," philosopher of science Helen
Verran takes the debate surrounding "indigenous science" much
further. A leader in the emerging field of what is also known
as "ethnoscience"--though she herself eschews both terms--Verran
focuses on the way the Yoruba people of Nigeria relate to numbers, a
relationship that she suggests is quite different from Western
patterns.
Between 1979 and 1986, Verran was a lecturer at Obafemi Awolowo
University in Ife-Ife, Nigeria, where she taught mathematics and
science teachers. She found that her African pupils would often
approach mathematical problems in what, to her Western-trained eyes,
seemed highly unorthodox ways. At first alarmed, then fascinated,
Verran began to investigate how Yoruba people interacted with numbers
in their daily lives.
It turns out that the Yoruba language has a particularly
flexible way of representing numbers. Although in English and other
Western languages, any given number has a unique verbal
representation, in Yoruba there will be many ways of speaking a large
number-- for the number 19,669, for example, Verran lists no fewer
than seven distinct ways. Each variation is a verbal encoding of a
different arithmetic pattern:
oke kan o din erinwo o le okaan dinlaaadorin
((20,000 x 1) - 400) + (-1 -10 + (20 x 4)) = 19,669
eedegbaawaa o le eedegberin o din okanlelogbon
(20,000 - 1,000) + (-100 + (200 x 4)) - (1 + 30) = 19,669
This flexibility comes about because, unlike our numerical
system, which is based on the number 10, the Yoruba language
recognizes three bases--10, 5 and 20. By playing around with
different combinations of these bases, one can produce different
spoken versions of the same numerical quantity. Being a good
enumerator in Yoruba takes long years of training and requires an
ability to quickly break down numbers into their components.
Yoruba enumerators must not only be adept at mental factoring,
they must also in a sense be poets, for Yoruba people consider some
verbalizations of numbers more elegant and aesthetically pleasing
than others. I have no idea how the words are meant to sound, but
from written examples, one cannot but be struck by the patterns and
clearly musical rhythms embedded in Yoruba number names. Even on
paper they look like songs.
More radically, Verran says, number words in Yoruba do not act
as nouns or adjectives but as adverbs. Numbers work not as attributes
of objects (as in: there are four oranges) but as modifiers of verbs.
Yoruba language conceives of number not as a static abstract quality
but as an active characteristic which changes the mode of what it
enumerates.
In English, for example, we would say "there are four stones."
The Yoruba translation would be something like "the matter with
characteristics of stoneness is manifesting here/now as a collection
divided to the extent of four."
Excited by such findings, Verran originally wrote some academic
papers that presented the formalities of this numbering system. But
by abstracting it, by treating this system as if it were an object
which could be put under a glass and studied in isolation away from
its everyday context within Yoruba life, Verran came to understand
that she was distorting the phenomena.
She realized that in a deeper sense she was guilty of the same
kind of colonialism and philosophical imperialism she had been so
trying to avoid. It was a similar notion to that of zoologists who
now understand that to comprehend animal behavior, creatures must be
studied in the wild; zoos are a very poor substitute.
After this realization--for her it was a philosophical crisis--
Verran embarked on a decade-long quest for a deeper understanding
that would do justice to Yoruba engagement with number in the context
of their lives. Crucial here was the insight that traditionally the
Yoruba had no written form for their numbers; their engagement with
number was never abstract but always verbal and always within the
context of practical activities like trading.
Verran argues that Yoruba understanding of the existence of
number is grounded in the body, those 10s, 5s and 20s reflect the
human arrangement of fingers and toes.
The importance of embodiment in our own relationship to number
has also been proposed by English mathematician and philosopher Brian
Rotman in his "Ad Infinitum: Taking God out of Mathematics and
Putting the Body Back In." Both these proposals are radical
departures from mainstream Western thinking about mathematics, which
sees numbers as transcendent entities existing independently from the
physical world.
The origin of number and the mysterious ability of humans to
manipulate numbers (that is, to do mathematics) has been a hot
research topic during the last few years. "Science and an African
Logic" makes a major contribution to this debate and will no doubt
keep philosophers arguing for years to come. Verran's chapters on
Yoruba life and classrooms are a delight, and anyone interested in
the subject of mathematics will have much to gain from this unusual
and, in the end, deeply personal book.

* * *
Margaret Wertheim is the author of "The Pearly Gates of
Cyberspace: A History of Space from Dante to the Internet."



Copyright 2001 Los Angeles Times


Shemhotep
************
"There is something dreadfully wrong
with an education/socialization process
that leaves us ignorant of our past,
strangers to our people, apes of our
oppressors, and creatures of habitual,
shallow thought, and trivial values."
-Dr. Asa G. Hilliard,III

"general group behavior patterns matter
more than individual exceptions. and
past group behavior is indicative of
future group behavior." - yuckwheat

"Everyone has their myths which is
fine. However when one parades "myth"
as "fact" especially concerning ANOTHER
group of people independent of the said
myth-making group then we have a
problem. The myth now becomes a LIE." -
Solarus