When 10-3 = 13

Posted:
14 May 2010 06:02 AM PDT

Recently, an American from the University of   was
conducting research on the Suya Indians of Mato Grosso, Brazil, attempting to
determine how they count.  This group of Amazonian Indians are largely famous
for their music; , a at the
, , who has produced a book called Why Suya
Sing, says that their singing is used to create community, establish
relationships and social identity and also formulate ideas about time and
space. 

Singing, to a Suya, is hard and soft science.

Math lesson
This was
investigating
the level of sophistication of the Suya concerning mathematics.  Many
scientists
examining cultural differences over operate on the
assumption
that many native cultures basically don’t have language to describe
quantities
of things; for instance, the Piraha people use the same word ‘hoi’ to
describe
‘about one’ and ‘about two’; the only difference is a subtle alteration
in
inflection of pronunciation.  The much-studied Munduruku in the
have
words for numbers only up to 5.

This has led many scientists to examine whether human beings have
innate
numerical skills or whether it is simply a part of cultural
conditioning.  Is it
possible to operate entirely without numbers?

So asked a member of the Suya tribe what
was the
correct answer to the following numerical problems:  If you had 10 fish
and gave
away three fish, how many would you have?

The Suya answered without hesitation and as though the researcher
were a bit
dull-witted to have even asked the question. 

As anybody in the village could tell you, the answer, of course, is
13. 

Minus equals plus
This was how he worked it out. 
In the
Suya tradition, whenever you give something away to someone else, the
recipient
pays you back double.  So if he gave three fish to his brother, he said,
his
brother would have to give him back two times three fish, or six.  So
added to
his 10 original fish he would first have 16 fish.

Once he deducted the three fish he originally gave his brother, he
would have
a net increase of three, or 13. 

So, 10-3 = 7 in Western mathematics transforms into 10 + (2×3) – 3 =
13 in
Suya mathematics.

In fact, the native was dismayed at the American version of the
equation.  He
does not view giving away as equivalent to subtraction.  He finds the
entire
notion of it abhorrent. 

“Why is it that ‘giving’ is always seen as a ‘minus’ for white
people?’
another member of the tribe asked.  “I know that you want me to use the
minus
sign instead of the plus sign, but I don’t understand why.”

This was a little shocking to Alex Bellos, the of the recently
published Alex’s Adventures in Numberland (Bloomsbury, 2010), a study of
cultural differences in mathematics.  He began the study of his
fascinating book
with the belief that numbers are a universal language – the way in which
we
could, say, communicate with extra terrestrials — only to find that our
basic
understanding of arithmetical relationships depends upon cultural
context.

Relationships in the numbers
I find the story
delightful
for several reasons. 

It reveals something very profound not simply about mathematics but
about how
different cultures view relationships in general, particularly how we
view
ourselves in relation to other things.

Our sense of mathematics very much depends upon how we define our
world, and
whether we view ourselves and all the things around us as individual
entities
separate from each other or inherently intertwined.

Many non-Western societies — pre-literate cultures such as the
Aborigines,
the ancient Greeks and the Egyptians, the adherents of Eastern religions
such as
Buddhism, Zen and Taoism, and a number of modern indigenous cultures  — 
conceive of the universe as inseparable, connected by some universal
energy
‘life force’. The beliefs of many tribal societies about this central
energy
force have many similarities, suggesting that an intuitive understanding
of the
interconnectedness of all things is fundamental to human experience.

This central belief breeds an extraordinarily different way of seeing
and
interacting with the world.  These traditional cultures believe that we
are in
relationship with all of life – even with the earth itself.  They hold a
very
different notion of time and space as one vast continuum of ‘now’ and
‘here’.

They even perceive the world out there very differently.  We see the
thing;
they see the totality, the relationship between the things.  To an
indigenous
native, math and the song are equivalent —  all about the plus sign, the
connection, in this instance, between the man with the fish and his
brother. 

We would do well to take a few math lessons from the Amazon.