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The Innovative Spirit fy17
A Smithsonian magazine special report
__________________________________________________________________
INNOVATION
How Humans Invented Numbers--And How Numbers Reshaped Our World
Anthropologist Caleb Everett explores the subject in his new book,
Numbers and the Making Of Us
Lorraine Boissoneault
Lorraine Boissoneault
March 13, 2017
__________________________________________________________________
counting-fingers.jpg "Numbers are a human invention, and they're not
something we get automatically from nature," says Caleb Everett.
Kwangmoozaa/iStock
Once you learn numbers, it's hard to unwrap your brain from their
embrace. They seem natural, innate, something all humans are born with.
But when University of Miami associate professor Caleb Everett and
other anthropologists worked with the indigenous Amazonian people known
as the Piraha, they realized the members of the tribe had no word used
consistently to identify any quantity, not even one.
Intrigued, the researchers developed further tests for the Piraha
adults, who were all mentally and biologically healthy. The
anthropologists lined up a row of batteries on a table and asked the
Piraha participants to place the same number in a parallel row on the
other side. When one, two or three batteries were presented, the task
was accomplished without any difficulty. But as soon as the initial
line included four or more batteries, the Piraha began to make
mistakes. As the number of batteries in the line increased, so did
their errors.
The researchers realized something extraordinary: the Piraha's lack of
numbers meant they couldn't distinguish exactly between quantities
above three. As Everett writes in his new book, Numbers and the Making
of Us, "Mathematical concepts are not wired into the human condition.
They are learned, acquired through cultural and linguistic
transmission. And if they are learned rather than inherited
genetically, then it follows that they are not a component of the human
mental hardware but are very much a part of our mental software--the
feature of an app we ourselves have developed."
To learn more about the invention of numbers and the enormous role
they've played in human society, Smithsonian.com talked to Everett
about his book.
How did you become interested in the invention of numbers?
It comes indirectly from my work on languages in the Amazon.
Confronting languages that don't have numbers or many numbers leads you
inevitably down this track of questioning what your world would be like
without numbers, and appreciating that numbers are a human invention
and they're not something we get automatically from nature.
In the book, you talk at length about how our fascination with our
hands--and five fingers on each--probably helped us invent numbers and
from there we could use numbers to make other discoveries. So what came
first--the numbers or the math?
I think it's a cause for some confusion when I talk about the invention
of numbers. There are obviously patterns in nature. Once we invent
numbers, they allow us access to these patterns in nature that we
wouldn't have otherwise. We can see that the circumference and diameter
of a circle have a consistent ratio across circles, but it's next to
impossible to realize that without numbers. There are lots of patterns
in nature, like pi, that are actually there. These things are there
regardless of whether or not we can consistently discriminate them.
When we have numbers we can consistently discriminate them, and that
allows us to find fascinating and useful patterns of nature that we
would never be able to pick up on otherwise, without precision.
Numbers are this really simple invention. These words that reify
concepts are a cognitive tool. But it's so amazing to think about what
they enable as a species. Without them we seem to struggle
differentiating seven from eight consistently; with them we can send
someone to the moon. All that can be traced back to someone, somewhere
saying, "Hey, I have a hand of things here." Without that first step,
or without similar first steps made to invent numbers, you don't get to
those other steps. A lot of people think because math is so elaborate,
and there are numbers that exist, they think these things are something
you come to recognize. I don't care how smart you are, if you don't
have numbers you're not going to make that realization. In most cases
the invention probably started with this ephemeral realization [that
you have five fingers on one hand], but if they don't ascribe a word to
it, that realization just passes very quickly and dies with them. It
doesn't get passed on to the next generation.
Preview thumbnail for Numbers and the Making of Us: Counting and the
Course of Human Cultures
Numbers and the Making of Us: Counting and the Course of Human Cultures
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Another interesting parallel is the connection between numbers and
agriculture and trade. What came first there?
I think the most likely scenario is one of coevolution. You develop
numbers that allow you to trade in more precise ways. As that
facilitates things like trade and agriculture, that puts pressure to
invent more numbers. In turn those refined number systems are going to
enable new kinds of trade and more precise maps, so it all feeds back
on each other. It seems like a chicken and egg situation, maybe the
numbers came first but they didn't have to be there in a very robust
form to enable certain kinds of behaviors. It seems like in a lot of
cultures once people get the number five, it kickstarts them. Once they
realize they can build on things, like five, they can ratchet up their
numerical awareness over time. This pivotal awareness of "a hand is
five things," in many cultures is a cognitive accelerant.
How big a role did numbers play in the development of our culture and
societies?
We know that they must play some huge role. They enable all kinds of
material technologies. Just apart from how they help us think about
quantities and change our mental lives, they allow us to do things to
create agriculture. The Piraha have slash and burn techniques, but if
you're going to have systematic agriculture, they need more. If you
look at the Maya and the Inca, they were clearly really reliant on
numbers and mathematics. Numbers seem to be a gateway that are crucial
and necessary for these other kinds of lifestyles and material cultures
that we all share now but that at some point humans didn't have. At
some point over 10,000 years ago, all humans lived in relatively small
bands before we started developing chiefdoms. Chiefdoms come directly
or indirectly from agriculture. Numbers are crucial for about
everything that you see around you because of all the technology and
medicine. All this comes from behaviors that are due directly or
indirectly to numbers, including writing systems. We don't develop
writing without first developing numbers.
How did numbers lead to writing?
Writing has only been invented in a few cases. Central America,
Mesopotamia, China, then lots of writing systems evolved out of those
systems. I think it's interesting that numbers were sort of the first
symbols. Those writings are highly numeric centered. We have
5,000-year-old writing tokens from Mesopotamia, and they're centered
around quantities. I have to be honest, because writing has only been
invented in a few cases, [the link to numbers] could be coincidental.
That's a more contentious case. I think there are good reasons to think
numbers led to writing, but I suspect some scholars would say it's
possible but we don't know that for sure.
Something else you touch on is whether numbers are innately human, or
if other animals could share this ability. Could birds or primates
create numbers, too?
It doesn't seem like on their own they can do it. We don't know for
sure, but we don't have any concrete evidence they can do it on their
own. If you look at Alex the African grey parrot [and subject of a
30-year study by animal psychologist Irene Pepperberg], what he was
capable of doing was pretty remarkable, counting consistently and
adding, but he only developed that ability when it was taught over and
over, those number words. In some ways this is transferrable to other
species--some chimps seem able to learn some basic numbers and basic
arithmetic, but they don't do it on their own. They're like us in that
they seem capable of it if given number words. It's an open question of
how easy it is. It seems easy to us because we've had it from such an
early age, but if you look at kids it doesn't come really naturally.
What further research would you like to see done on this subject?
When you look at populations that are the basis for what we know about
the brain, it's a narrow range of human cultures: a lot of American
undergrads, European undergrads, some Japanese. People from a certain
society and culture are well represented. It would be nice to have
Amazonian and indigenous people be subject to fMRI studies to get an
idea of how much this varies across cultures. Given how plastic the
cortex is, culture plays a role in the development of the brain.
What do you hope people will get out of this book?
I hope people get a fascinating read from it, and I hope they
appreciate to a greater extent how much of their lives that they think
is basic is actually the result of particular cultural lineages. We've
been inheriting for thousands of years things from particular cultures:
the Indo-Europeans whose number system we still have, base ten. I hope
people will see that and realize this isn't something that just
happens. People over thousands of years had to refine and develop the
system. We're the benefactors of that.
I think one of the underlying things in the book is we tend to think of
ourselves as a special species, and we are, but we think that we have
really big brains. While there's some truth to that, there's a lot of
truth to the idea that we're not so special in terms of what we bring
to the table genetically; culture and language are what enable us to be
special. The struggles that some of those groups have with quantities
is not because there's anything genetically barren about them. That's
how we all are as people. We just have numbers.
Lorraine Boissoneault
Lorraine Boissoneault | | READ MORE
Lorraine Boissoneault is a contributing writer to SmithsonianMag.com
covering history and archaeology. She has previously written for The
Atlantic, Salon, Nautilus and others. She is also the author of The
Last Voyageurs: Retracing La Salle's Journey Across America. Website:
http://www.lboissoneault.com/
Anthropology Books Inventions Mathematics The Innovative Spirit
Education
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