MATHEMATICS
INTRODUCTION TO
NUMBERS
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Visualizing Numbers
Numbers
are central to the statistics you just saw. In fact, most of these numbers are
so large that they aren’t easy to visualize. While it might have been difficult
to visualize 7,500,000,000, which the approximate world population, you might
have found it somewhat easier to visualize the fact that the Chinese make up
about 20% of the world’s population because that’s a fraction of about 1515. You might also have
found it much easier to visualize the number 7 which is
Nigeria’s position on the list of world’s most populous countries.
Why
those statistics were shared using numbers? Would it have been as impressive if
we had just said that there is a huge number of people currently living in the
world today and that a large percentage come from China? Or what if we had said
that a lot of the massively enormous number of people in the world today is
Chinese?
Without numbers we can’t quantify things in the
world. For instance, how would you be able to determine if the many people that
live in the world today are up to a million, which is a huge number in itself,
let alone 7.5 billion? Quantifying things is a way to test things against
others, and to comprehend the world.Even though mathematics as a
discipline is much broader than just visualizing and manipulating numbers, you
don’t have to be a math wizard who sees numbers or Greek symbols when you
close your eyes at night in order to be a good mathematician or scientist.
Working with numbers is about practice, daily experience and familiarity with a
few basic concepts. It gets easier as you spend more time doing some
number-based tasks.
If you can tell time, count how many bananas are in a bunch or
figure out how many biscuits you can buy with the little change in your pocket,
then you’re probably better with numbers than you think.
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We all use mathematics in the world today
Consider how the world was 150 years ago. You would probably
have lived quite well without understanding numbers greater than 100. That was
a world with relatively less technology than we have today, a world of about
one and a half billion people (1,500,000,000), compared to the almost seven and
a half billion people (7,500,000,000) today.
Babies die at a very high rate, with about 10 to 15 infants
dying before their first birthday. Disease was much more common with about
500,000 malaria cases being recorded a year in the South of the United States
in the early 1900s.
However, a lot has changed since then and most of our modern
comforts and some amazing scientific discoveries have come about through the
application of scientific thinking in medicine, engineering, and food science.
This is wonderful but not without its risks. As astronomer, Carl Sagan
describes, “we live in a society exquisitely dependent on science and
technology, in which hardly anyone knows anything about science and technology.”
Numbers are everywhere, not just for us to count items from 1 to
20, or even to 500, but to describe the masses of atoms, the basis of matter
all around us, or the amount of electric charge carried by electrons, the basis
of electricity.
We see numbers everywhere today, not just in our schools, but in
the media, in the market, and even in our daily lives. Numbers do really
matter, and scientists expend a lot of effort quantifying the world in order to
understand it. Because we all have to deal with numbers in today’s world and
attempt to understand what they might mean, in some sense, we’re all
mathematicians and scientists.
Exercise: Manipulating Numbers to Figure Out Number of Days
Try counting how many days there are until next week Friday. The
answer will vary depending on what day it is today for you. The point is for
you to think about how we approach this kind of tasks. How did you arrive at
your answer? Did you use your fingers? Or, did you have a unique method? You
can share your method in the comments section below.
A Brief History
Human
beings from our earliest beginnings have searched for solutions to basic
problems such as building homes, measuring space, keeping track of seasons and
counting objects.
Over 30,000 years ago,
early Paleolithic people kept track of the passing seasons and the changes of
weather for planting. To represent the passing of time, they carved tally
marks (||||||)(||||||) on cave walls or slash (/)(/) tallies on bones, wood or stone. See the image
below.
Each tally stood for one. However, this system
was awkward when it came to large amounts, so symbols were eventually created
that stood for groups of objects. In fact, Sumerian clay stones have been found
to date back to fourth millennium BC. A small clay stone was used for 1, a clay
ball was used for ten and a large cone stood for 60
Written records from around 3300 BC show that Babylonians inscribed amounts on
clay tablets with a reed (see
image above). They used a nail shape for ones and a “V” on its side
for tens (<) (<), combining these symbols to write other
numbers. For example, see the way the Babylonians wrote the number 12 in the image
above.
The
ancient Egyptians used objects from everyday life as symbols. A rod stood for
one. A cattle hobble was ten. A coiled rope was 100. A lotus flower was a
thousand and so on. The number 12 was a cattle hobble and two rods. See
the figure below for an illustration.
The early Romans created
a number system (see
figure below) that we
still see today. Along with other symbols, they used an XX for 1010 and an II for 11. By the Middle Ages, Romans were putting
the II to the right of the XX for 1111 and to the left for 99, so they wrote 1919 as XXXIX.
All these creative number systems show groups of objects as well
as individual objects. Some of the oldest human counting systems rely on
fingers and toes, so they were based on ones, fives, tens and twenties. The
Zulu words for six means “to take the thumb of the right hand” meaning that all
the fingers on the left hand had been added up and the other thumb was needed.
Other systems evolved from commerce. The Yoruba in Nigeria used
calorie shells (see image below) as
currency and developed an amazingly complex number system which was based on
twenties and on the operations of multiplication, subtraction and addition. For
example, they thought of 45 as three
times twenty minus ten minus five.
Knots tied in cords and
strings were used for recording amounts by many cultures like the Persians. The
Incas used a more refined version called a “quipu” or “khipu”, a thick cord
held horizontally from which hung a knotted string. The kind of knot the Incas
used along with the length and colour of the cord represented ones, tens and
hundreds. See the image below.
