Large Numbers

I am a physicist. We deal in large numbers, some of them so ludicrously big that even we cannot comprehend them. But a physicist learns tricks to be able to imagine them (you know the idea - "If the Sun were the size of a pea then the Earth would be in Newport Pagnel service station", poor darling).

During a brief stint as a secondary school teacher (ages 12 to 19 years), I came up with a couple of tricks which might be of use...

Big Populations, Big Money

I'm not concerned with exact numbers in this, just a feeling for size.


The population of the UK is between 50 and 60 million, call it 50 million. So an (American) billion (1,000,000,000) pounds is 20 pounds per person. If the government gives one million pounds to a cause, that's two pence per person. An (American) trillion (1,000,000,000,000) pounds is 20 thousand pounds per man woman and child.

Larger Regions

The European Union (which includes the British Isles), the USA, and the former USSR (roughly, the CIS) each have populations of between 200 million and 400 million. Call it 333 million. Then one (American) billion Euros/dollars/roubles is 3 Euros/dollars/roubles per person. One (USA) trillion is 3,000 E/d/r per person.(In fact, the population of the EU is nearly 400 million, and that of the US nearly 300.

Well, it puts governmental budgets in context for me.

So How Big Is a Million?

Ah, well I'm glad you asked me that.

Take hold of a ruler, marked in millimetres. Imagine a cube one millimetre on a side. Now find or imagine a metre rule (maybe two computer-widths long). For those who haven't caught up yet, a metre is one tenth longer than a yard.

Right, there are one thousand (1,000) millimetres in a metre.

So, imagine a square, each side of which is a metre long. Cover that square with millimetre cubes. There are a million of them. (1,000 x 1,000 = 1,000,000, count the zeros!)

Now imagine a cube, each edge of which is one metre long. Fill it (probably only in your imagination) with those little millimetre cubes. There are one (American) billion of them. (1,000 x 1,000 x 1,000 = 1,000,000,000.)

At the time of writing, the human population of the Earth is about 7,000,000,000 people.

That's 7 of those metre cubes (if filled with water they weight a tonne each, which is close to the UK and USA tons).

The populations of the EU, USA and CIS added together are about one of those cubes. The other six and a quarter are... African, Chinese, Indian, South American... Check out the figures yourselves!

And back to the UK. Central London, I think of as having about 5 million, about the population of Norway. That's a 5 millimetre thick layer of one of those cubes. The entire UK is a layer about 56 millimetres thick (say 2 inches), out of a 39-inch high cube, which is itself a seventh of the world.

Age of the Earth?

Is roughly 4 (American) billion years. So that's 4 of those metre cubes, each year being a millimetre cube.

The last ice age ended about 10,000 years ago. That's a 1 cm WIDE layer, only one millimetre thick. All known civilisation fits in there.

Homo Sapiens Sapiens appeared in Europe 40,000 years ago. Coo, thats a full 4 cm wide shaving.

Human-like species have been around 1-3 million years (pick your definition of human-like, and your favourite paleoanthropologist), that's a shaving 1-3 millimetres thick from one of those 4 blocks.

Oh, yes, and if you took one of those metre cubes and put all of the millimetre cubes which it contains in line to form a chain, and magnified all the millimetre cubes until they were full metre cubes, then 150 of those chains would be needed to reach the Sun.

Space is big.


© M.D.Cahill, 2002 CE. (Population data corrected Dec. 2002.)