Humans are bad at understanding large numbers.   Our education system successfully trains us to understand the relative magnitudes of small numbers,  but for larger numbers we tend to fall back on an intuitive logarithmic scale.  So we underestimate the real difference between, say, a million and a billion.

Here’s a wee table I put together, to help with visualising large numbers.  The table is based on the thickness of a New Zealand $1 coin.

  • We start with just one, which is 2.74mm thick (about twice as thick as a US quarter).
  • Then, imagine we make a stack of 1000 coins.  It would be about the height of a person (a tall person, with their arms up-stretched).
  • For a million coins, we would have to lie the stack on its side.  It would form a “sausage” of coins about the length of an airport runway.
  • For a billion coins, the sausage would be as long as a country (specifically, India).
  • For a trillion coins, we’d end up way out in space (almost 8 times as far away as the moon).  That’s hard to visualise, because there’s nothing there.  So how about we try $14 trillion instead (the size of the US public debt)?  If we had the US public debt in $1 coins, the stack would reach all the way to Venus.
Number   Length
$1k 10^3 person
$1 million 10^6 airport runway
$1 billion 10^9 India
$1 trillion 10^12 Moon * 8

So to visualise the difference between a thousand, a million and a billion, you can say: “person, runaway, India”.


Footnotes Nov 2011:

1. Here’s an amazing visualisation of dollar values at various scales

2. Further to the billion-coins-in-India example: what if we lined up a billion people, instead of a billion coins?  That’s approximately the actual population of India.   To get a line the same length as the  billion coins, we’d have to ask the people to stand about 500-abreast.  I.e. the population of India could stretch from the north to the south of the country, if they formed a long, skinny loosely-packed crowd approximately 500m wide.

3. A similar crowd in New Zealand, with the entire population of 4 million stretching the full length of the country, would be only 2 or 3 people wide – in part because the country is sparsely populated, and in part because it’s a long skinny country.

Jan 2012:

4. The number of stars in the observable universe is estimated at 7 x 1022.   Given the world population, that’s 10 trillion stars per person – which equates to one stack of coins, reaching most of the way to Venus, for every person alive today.

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