Numbers

Well,

how did we get here?

That's a question humans often ask

when they suddenly realise

that they are somewhere or other.

And that's particularly important with numbers,

because

numbers always need to be built from the beginning

be right from the start

or everything else will be wrong.

So they need to remember their foundations,

check them,

and re-cap what they know for sure so far.

And that can be really important when they are applying numbers to the world.

They have to look critically at what they are doing

to make sure that they have made no mistakes in what they know,

as well as how they got to where they are.

If their answers are based on questions

they have to re-examine them to see whether there was any bias in them,

any presumptions on which they were based.

The foundations need to be right if calculations and proofs

are to give a right answer.

So when people are collecting data

they need to know how to ask questions,

what to ask and how to ask it,

and for that they need to look inside themselves.

Then when they are organising their data

they need to look at the way they are grouping it.

The way things are named or labelled

can change the way that they are understood.

Words aren't numbers,

and different people understand them in different ways.

Even the way that data is displayed can make it give

quite different impressions.

Now, people who play with numbers soon get used to their basics,

the number line, fractions and decimals,

powers and roots and scientific notation

and of course, nowadays

much of the basic number crunching,

the time consuming side of things,

is done using a calculator or computer.

But then it is rather easy to lose track of the workings inside the machine,

so it can still be very useful to have

a printout or display of the calculation process.

By looking at a calculation as a whole,

it becomes possible to see patterns and sequences,

and estimate unknowns,

and to use those numbers in the world.

And those numbers can be used to give approximate estimations

to give a general idea,

or they can be exact calculations,

of length and area, perimeter and volume,

or the relationship between time and distance and speed.

Or calculations that follow the clock around the world,

along with the movement of money,

trade and exchange,

And of course, people use numbers

to describe the world around them

in terms of its geometry,

from two dimensions,

mapping and drawing to scale,

using compass and co-ordinates

or making patterns from tiles,

to the three dimensions of the world in which they live,

with its solid shapes and volumes.

So much of their world would never have existed

without the study of numbers.

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