Number
&
Measure

People have always liked playing with numbers,

seeing them as not just to be used

but to be explored in ways that have no apparent use,

exploring the world of numbers

just for fun,

and that means exploring wherever you can go,

searching out the limits,

up and down, and through and around,

large and small numbers,

fractions and decimals,

roots and squares and higher powers.

They looked at the way certain kinds of numbers can be similar, or different

like primes,

and if they can be put in groups, or recognised as patterns,

and what they ended up with was a system of numbers,

some parts of which may not only seem to have no use,

but also seem impossible

apart from in the world of their imaginations.

Negative numbers of things can't be seen,

but the numbers can be imagined,

and the calculations done with them can be very useful,

and the limits of numbers, like infinity and zero,

can end up being equally useful

though in different ways.

Or they use letters for unknown numbers,

variable or constant,

and symbols and marks and letters

to write down the various actions

that take place between numbers

in a system of scientific notation.

They even use different systems of numbers for different things.

So for a system that is simple enough for a machine to work with they use binary,

as that way it only has to recognise zeros and ones.

And it is very useful

to get a machine to do the calculations,

as working with the relationships between the numbers

is really the most fun part.

Actually doing the calculations with the numbers can be very boring,

especially when the numbers are large.

It takes patience and concentration,

as one mistake and no matter how much more calculation is gone through

the answer is going to be wrong.

So it makes sense to use a calculator or computer

to do the calculations,

and just deal with the bit that takes place in the imagination.

The imagination can see patterns

and sequences in numbers,

and see them as linear or quadratic graphs.

And the system ends up with

algebraic conventions

and precedence and functions

and equations and inequations

and formulae and proofs.

And that world of the imagination spreads out

through the world of creation,

to measure and estimate,

to describe length and area,

perimeter and volume,

and to describe the relationship between time and distance and speed.

And the same number system is used

all around the world,

even though other things vary.

Different times of day need to be

co-ordinated when people travel,

and different types of money need to be traded

and exchanged,

and one mathematical language does it all.

How amazing.

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