Imagining big numbers

I am trying to imagine a million

Not just the number a million

But a million objects grouped or stacked together

How would they look?

How much space would they occupy?

Is the notion of a million something that can be imagined?

Or is it too vast to visualise?

I think of a mass of objects of identical size

Let these objects be cubes that can be neatly stacked

One upon the other without gaps

What if these object were sugar cubes

Each measuring one centimetre square

I could arrange a line of such cubes

One meter long

That would comprise one hundred cubes

Easy to envisage

Now I arrange another ninety- nine such lines

Above my first to form a meter square

Comprising one hundred times one hundred cubes

This makes ten thousand cubes

A very large number but easy to visualise

And now I add another ninety-nine such square meters

Above the first to form a cubic meter

I can imagine a cubic meter as topsoil or sand

Is often delivered in bags of a cubic meter

To calculate the number of cubes in my cubic meter

I remember I have to multiply the height by the width by height

That’s one hundred, times one hundred times one hundred

That’s a million!

So now I can envisage this vast number

As a tangible mass of objects

I am now intrigued to know if I can imagine

As tangible objects, a far vaster number

How about a billion?

Which is one thousand times one million

So I imagine a line of one thousand objects

Each measuring one cubic millimetre

Of which there would be one thousand in a cubic centimetre

A cubic millimetre is roughly the size of a grain of sand

So still imaginable

I add to this line of one thousand cubic millimetres

Another identical nine hundred and ninety-nine rows

One above the other

I now have a square meter comprising

One million cubic millimetres

And as many as the cubic meter of cubic centimetres!

As before, I add another nine hundred and ninety-nine such square meters

One above the other to form a cubic meter

Which this time comprises

One thousand, times one thousand times one thousand cubic millimetres

Which is one billion!

And just about imaginable as a tangible arrangement

So these two vast numbers of one million and one billion

Can now be envisaged in the mind’s eye

More meaningful that a set of unrelated digits

But there is no point in these musings

They serve no useful purpose

Other than to amuse the writer

And bore the reader!