Are we very big or very small?

How small is the smallest thing in the universe? How small is a quark? A superstring? Actually, no one knows but the smallest possible length in the universe is the universe is called the Planck length of about 0.000000000000000000000000000000000001 metres. This figure is a fundamental axiom of quantum mechanics and represents the 'lumpiness' of the universe that means that in quantum mechanics you can never be entirely certain of where something is.

How big is the biggest thing in the universe? That must be the universe itself. Latest figures suggest it is about 10,000,000,000 years old. It started from a point at the Big Bang and so the size of the whole universe is the distance that light could have travelled in the 10 billion years available. Light being very fast, this comes to about 100,000,000,000,000,000,000,000,000 metres.

Of course, these big numbers are very unwieldy so we tend to use exponentials to tidy things up a bit. The Planck length is expressed as 10^-35 metres, the size of the universe 10^25 metres. How big are we? About 1 metre tall or 10^0 metres. So comparing our absolute size to the smallest and biggest possible things in the universe, we are about three fifths of the way up the scale. In other words, we are of medium to large size using the exponential scale, the only scale that makes any sense in physics.

All this makes nonsense of one of Carl Sagan's arguments, also picked up by Richard Dawkins, Stephen Hawking and lots of others who should know better. In Pale Blue Dot and elsewhere, Sagan invites us to believe that the universe is very large (true) and that we are very small (not true, as we have seen). This apparently means that we are not very important and God doesn't exist. Not only does this argument assume that value and physical size are directly comparable (which, obviously, they are not), but it also uses the wrong scale to determine what is big and what is small. Given that Sagan spent his career trying to explain why science sometimes doesn't say what common sense says, it is annoying that here he uses the everyday arithmetical scale to make a silly point which is invalidated by a scientific view of the universe anyway.

Another of Sagan's mistakes was to assume that when Copernicus moved the Earth from the centre of the universe, he was demoting it. This is also untrue as this paper shows. My thanks to the correspondent who sent me this link and thus inspired this post (which picks up on a point in the second half of the linked paper).

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