WHY MATHS?
Everybody moans at the very mention of “maths”. People think that the world is divided into two kinds of folks. The “brainy” lot who understand mathematics but are not the kind of people one wants to meet at parties...
But all of us need to understand maths to some extent. Without mathematics, life would be inconceivable.
Indeed, mathematics has become a guide to the world in which we live, the world which we shape and change, and of which we are a part. And as the world becomes more and more complex, and uncertainties in our environment become more urgent and threatening, we need mathematics to describe the risks we face and to plan our remedies.
The ability to deal with mathematics does require a special talent and skill – like any other field of human endeavour, such as dancing. Just as an accomplished ballet performance is sophisticated and exquisite, so is mathematics in its essence very elegant and beautiful.
But even though most of us cannot become fully-fledged ballet performers, all of us know what it is to dance and virtually all of us can dance. Similarly, all of us should know what mathematics is about, and be able to understand and handle certain basic steps.
COUNTING
At school, children learn to count, to calculate, and to measure. Once they have been learned, these techniques may seem “elementary”. But for the learners they are full of mystery.
The naming of numbers becomes an incantation, especially when we get to the bigger ones. Counting to a hundred becomes tedious, but getting to a thousand is like climbing a mountain! What is the last number, the biggest one of all?
How do we name the numbers, as we call them out one after another? Perhaps just a few numbers are enough. Some animals can recognize different collections up to five or seven – beyond that it’s just “many”. But if we know that numbers go on continuously, we can’t just keep inventing new names indefinitely as we go along.
The language of the Dakota Indians was not written down.
It is made of cloth and the pictographs are drawn in black ink. Each year a new pictograph was added to show the main event of the past year.
The best way to systematize naming and counting is to have a “base”, a number that marks the beginning of counting again. The simplest base is just two. For example, the Gumulgal, an Australian indigenous people, counted like this:
1 = urapon
2 = ukasar
3 = urapon-ukasar
4 = ukasar-ukasar
5 = ukasar-ukasar-urapon
The fingers of the hands are useful for defining bases. Some systems use five, more common is ten. But many other bases can be used. The old British currency had several: twelve (pence per shilling) and then twenty (shillings per pound) and even twenty-one (shillings per guinea!). Shop assistants needed to keep reckoning books by their sides. And when people bought in instalments, they might be told that th...