Counting in Circlemaths

Arithmetic

It's All about

YOU

Most people understand

that arithmetic is

a very useful tool

which accountants, scientists

and commercial people

use.

That's true.

But we're going a bit deeper here.

Actually

Number

is

about

YOU.

It's a description

of how you look

feel and think.

So let's start

by seeing how that is.

by looking at what

number really is.

YOU

What are you?

Mind and body

Two opposites

packaged together

like

Mountain and Valley

Opposites which can't be pulled apart

Body is solid.

Flesh and blood.

Heavy. Very Real.

Mind is like a ghost.

Thought. Feelings.

Ideas.

They are opposites.

Yet they come together, naturally.

Number comes from YOU.

And so its no surprise

it works this way too.

The Birth of Number

is 0 and 1

They're special

They're not real numbers!

Let's say you look out your window

and are suprised to see

a number of cows

have walked onto your lawn.

You tell your friend

There's a number of cows on our lawn

How many cows?

they ask.

None.

Zero cows.

Does that really make sense?

Not really.

Because a number

is

a group.

How about they ask

How many cows?

and you reply:

One.

One cows.

Oops.

That's not quite right either, is it?

It should just be:

One cow.

Cows

is plural

meaning many

a group of them

more than

one.

So in one way of looking at things

zero and one

are not numbers.

They are what the other numbers are made of.

Bricks aren't made of brick.

Sheep aren't made of sheep.

They're a bit different

to all the other

numbers.

Zero and one are the parents

of all the other numbers.

How is that?

Think of the number 3.

It is ONE 3.

For after all, two three's are six.

So it's a one

by being one three.

What's inside it?

Not the three little pigs,

but three little ones.

3 = 1 + 1 + 1

On the left is ONE number, the 3.

On the right, three numbers, each of them ONEs.

And you can do that with all numbers.

So all numbers are ones.

Do all numbers have a zero in them?

Yes!

The 3 is 3 steps up from zero.

5 is 5 steps up from zero

and so on.

The size of a number

is measured

from

zero.

Without zero

number couldn't exist!

Look how bad our rulers would be

without a zero:

So every number

inherits from 0 and 1

which are the parents.

They are special

semi-numbers.

There is another side to this story.

There usually is to all stories…

In another way

we can say:

Think of a number between 0 and 10

and you could answer

one

or

zero

and that would be perfectly fine.

So although

strictly speaking

as we have just shown,

0 and 1 are

not numbers,

in normal everyday usage

they are.

So are 0 and 1 numbers?

You take your pick!

:-)

Anyway,

like the atom

which is very small

but made the atomic bomb

and makes up everything we see

0 and 1 are very small

but

they make up all the bigger numbers.

So being special we'd better become

atomic numberists

and look at them

more closely!

ZERO or NOUGHT

Let's start with some exercises.

Exercise 1:

Point to 2 things you can see.

Exercise 2:

Point to 1 thing you can see.

Exercise 3:

(the futile exercise)

Point to 0 things you can see.

You could do them all except the last, right?

That was a trick question!

How can you point to no things

Nothing.

You can't.

Which tells us something about zero.

Zero

is the nothing

of number

It doesn't exist out there

in the real world.

If you point to it

you've got it wrong.

It's simply

not out there!

You can't find

zero things

in the world!

So where does zero live?

It's inside you!

0 is an idea

in your mind.

It is actually your idea!

Its in you.

ONE

You come as a

double pair of opposites.

Mind and body.

So the ideas inside you

do likewise.

0 is like YOU as mind.

1 is like YOU as body.

0 vanishes away.

1 is solid.

They are both ideas.

0 attaches to nothing.

1 attaches to everything.

They are opposites.

But they naturally exist together.

When we say

think of a number between 0 and 10

and we answer

0

we are saying

nought is a number.

We give it an existence

(well, it exists as an idea)

we make it a reality.

Something real.

A ONE.

What is the

First One?

That would have to be

Oneself

You.

See.

You are actually

an expert in number!

That's quite right actually.

You don't know it, but you use numbers

all day long

(not just counting sheep at night!)

Let's find out how that is so

by finding out

what exactly

is

ONE?

Firstly

one can be anything.

Everything is a one.

One star, one grain of sand, one cat.

Even one football game.

What do they have in common

that makes them all the same,

that makes them

all ones?

Actually they don't have a lot in common…

That's a tough question…

Let's look at an example of ONE.

Suppose we look at

ONE

bike:

What's it got in common

with a star, a grain of sand

and a football game?

Nothing.

Except this.

YOU

can observe

the bike and

all of those things.

Actually

that's the only thing

they have in common!

Your attention.

Every time you've ever seen

any of those things

YOU"VE

been there

watching

right?

YOU

are the

ONE

common factor

linking

all those things!

So in search of

What ONE means

let's look at your

attention!

Exercise

Look at ONE word.

Notice it is made up of

lots of letters

inside it.

And there are

lots of other words

outside it.

But the moment YOU selected it

as your focus of attention

you made it

The ONE

Pick another word

on the same page

a bit away from it.

Focus on that.

Did you notice

how the original word

got lost

blended in to the background

and faded away

from your attention?

If not, have another look.

When YOU change

the focus of your attention

and select

another ONE word

the original word

blends and fades

from view.

End of Exercise

That's your attention at work.

Casting the net of ONEness

here, there and everywhere

it looks.

Let's get back to our bike example.

Here is a prime example of a ONE.

ONE bike:

One bike is just one bike.

But also it can be exploded into many parts.

It has little ONEs

inside it.

The wheels, the seat, the bell

and so on.

Each of these

is a ONE in its own right:

Inside the ONE

we find its made of

lots of little ONEs.

You could switch your attention

to the bell

and see you have

ONE

bell.

ONE chain

ONE frame

ONE wheel

Another ONE wheel

ONE seat

and so on.

All of them are equally ONEs.

Inside the ONE bike.

But notice

they don't split off

and become

ONE's

until

someONE

namely

YOU

pays them

attention!

Your brain is so clever!

It takes all these little parts

and FUSES them together

to make

just ONE bike

you are looking at!

We forget, dismiss, ignore

the differences between the parts

and fuse them together

in our minds eye

to make

just

ONE

bike.

That's an interesting idea.

Ignoring, dismissing, forgetting

is actually

part of the process

by which your mind

focuses and pays attention

in order to select

a

ONE.

That's making

nothing out of something.

NOUGHT.

There's another side to this story too.

(There usually is, to most stories)

The bike could be sitting next to other bikes.

Behind it might be a mountain, some clouds in the sky

some grass…

All sorts of things.

But when we point to the bike

as the example of ONE

we don't include them.

We EXCLUDE them.

This