Don’t talk homeopathy to a mathematician

A friend and I once spent a confused few minutes trying to make sense of the mental numbers that fall out of analysing homeopathy. We’d read that a centilitre of magical ingredient, diluted at ’30C’, is equivalent to 1cl of ingredient mixed into a cube of water with dimensions of over 100 light years. We weren’t disputing the claim – it doesn’t take much to realise some pretty large numbers are involved – but we were confused as to how homeopathic solutions are manufactured. Even if the water is re-used12, they aren’t using 1003 light years’ worth – so what’s going on? We eventually realised the amount of magical ingredient must be incredibly tiny – small enough to counter the insane dilution exponentials.

So a centilitre is obviously way too much, but how about just one molecule? In yesterday’s Times, mathematician Matt Parker runs the numbers:

…the process of consuming enough pills to get that one molecule also boggles the mind. You can try imagining Wembley Stadium completely filled with people, all drinking pints of medicine at the rate of two an hour. For just one of these people to eventually consume one molecule, you would need a million Wembley Stadiums all at full capacity with people who have drinking pints constantly since the Earth formed 4.5 billion years ago. Oh, and you’d need 737 million such Earths.

That’s only for one molecule. Molecules are tiny: it takes about a billion of them to cover a standard metric full-stop. To put homeopathy in a medicinal context, if you wanted to consume a normal 500mg paracetamol dose you would need ten million billion homeopathic pills. Where each pill is the same mass as the Milky Way galaxy. There is actually not enough matter in the entire known Universe to make the homeopathic equivalent of a single paracetamol pill.

The charming working-out is here. It seems like you’d still need a stupid amount of water to produce a 30C dilution by homeopathic methods, though.

This is part of a media blitz around the 10:23 campaign, which will see 300 skeptics taking simultaneous homeopathic ‘overdoses’. 10:23 is very nicely put together – the strapline is particularly excellent – and hopefully it’ll help embarrass Boots into taking homeopathy off the shelves. My only worry is the solutions themselves: it’s been known for ‘homepathic’ treatments to actually contain active ingredients – totally against the nature of the treatment, obviously – but hopefully the campaign has taken this into account.

Via New Humanist.

  1. which would be a bit dodgy []
  2. what with water supposedly having a memory and all []
  3. not really a footnote []