MATHEMATICS
INTRODUCTION TO NUMBERS
v 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
were those statistics 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 are
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 maths 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.
v 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
dies 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
How Did Mathematics Begin?
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.
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. 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.
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.
The early Romans created a number system 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 XIXXIX.
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 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
