Ice Under the Bridge

The BBC is renowned worldwide for the high quality of its journalism. Take this article from 2005:

A thirsty thief is being blamed for downing a bottle of water, valued at £42,500, at a literary festival.

The two-litre clear plastic bottle containing melted ice from the Antarctic was devised to highlight global warming by artist Wayne Hill…

Its value was worked out by the artist from the damage worldwide of the entire ice sheet melting – he estimates between £6 trillion and £9 trillion – and the relative amount of damage from two litres of water.

Hmm. Something seems off about those numbers. Let’s check them!

A two liter bottle of water weighs two kilograms. At £42,500 for a bottle, that’s about £21,250 per kilogram. A cubic meter of water weighs a metric ton, or 1,000 kilograms. So a cubic meter of Antarctic meltwater is worth, by this artist’s standard, a little over £21 million (as of 2005).

How much ice would £9 trillion buy at that exchange rate? £9,000,000,000,000 divided by £21,000,000/m^3 is roughly half a million cubic meters. That works out to an 80 meter cube (about enough to fill a football stadium) or a one meter thick iceberg with a surface area of half a square kilometer (something you might see a forlorn polar bear wandering around on in a BBC documentary). A football stadium full of ice is pretty big…but not really enough to cover an entire continentB-15, the largest iceberg on record, had a surface area of 11,000 square kilometers, and was probably more than 100 meters thicktake a look at the picture, and note that only about 10% of an iceberg is above water.

Well, maybe there’s a translation error. Maybe by ‘trillion’ the artist means not the American or scientific trillion, 10^12, but the continental trillion, 10^18, which is 1,000,000 times bigger. In that case, £9 trillion does buy you a few a big chunk of one B-15s worth of ice. That’s still not nearly enough to cover Antarctica; not even just the ice shelf around it. It’s also many orders of magnitude greater than the entire economic output of the human race since the dawn of recorded history.

Or, perhaps, the artist pulled the numbers out of thin air because they sounded impressive and he knew that nobody at a ‘literary festival’ would ever think to check. Certainly the BBC didn’t bother to.

He said: “The concept is to take something as dangerous as that and to bring it immediately into somebody’s presence.”

Or maybe the concept is to engage in hollow titillation of the audience’s self-concept as (in Neil Tennant’s words) The Persuaded We. If they actually gave a for-real damn, they’d apply simple arithmetic to test a contentious claim. Instead, they get to stare in mute, respectful silence at a bottle on a pedestal. This is how religions get started.

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5 thoughts on “Ice Under the Bridge

  1. By his estimate, how much is a two-liter bottle of water actually worth? I tried to figure this out, and if my math [nb: I have been awake for over 24 hours] and the estimate for the amount of ice in the Antarctic are both right, he’s off by about ten orders of magnitude and a two-liter bottle of Antarctic water isn’t even worth a rounding error.

    I don’t have a problem with believing that an artist would miss the truth in a very convenient direction for him and his message, but ten orders of magnitude is kind of a lot so I’m hoping I got something wrong.

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  2. http://www.willstegerfoundation.org/arcticantarctic-resources/antarctic-resources/item/113-how-much-ice-is-on-antarctica says there’s about 24,500 million billion or 24.5 x 10^18 kg of ice.

    9 trillion £ = 9 x 10^12 £.

    9 x 10^12 £ / 24.5 x 10^18 kg ~= 4 x 10^-7 £ per kg.

    A two-liter (two-kg) bottle will cost less than one millionth (10^-6) of a pound.

    It may be that he meant a continental trillion–10^18–rather than an American/scientific trillion. That gets you up to about 70 pence per bottle. But 9 x 10^18 £ is orders of magnitude greater than the total economic output of humanity (v. v. roughly 1 x 10^15 £) over all recorded history.

    In other words, you didn’t get anything wrong.

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