Professor Stewart's Hoard of Mathematical Treasures (31 page)

A popular British journalist wrote, in his regular column, something to the effect ‘How come they can be so specific about the date, but they don’t know the year?’ Now, to be fair, it was a humorous column, and it’s quite an amusing question. But it has a serious answer.

Enlighten the journalist. [Hint: What is a year, astronomically speaking?]

 

Mathophila takes a pack of cards, and places the four aces on the table, face down. So two (spades, clubs) are black; the other two (hearts, diamonds) are red.

Shuffle, place face down, pick two.

‘Innumeratus?’

‘Yes?’

‘If you pick two of these cards at random, what is the probability that they have different colours?’

‘Ummm . . . ’

‘Well, either the colours are the same, or they’re not, right?’

‘Yes.’

‘And there’s the same number of cards of each colour.’

‘Yes.’

‘So the chances of your two cards being the same, or different, must be equal - so both are equal to
. Right?’

‘Ummm . . . ’

Is Mathophila right?

 

Let ε < 0.

If you don’t understand this one, see the note in the Answers section, page 317. If you do understand it and don’t find it funny, congratulations.

Mathematical models are central to the study of global warming, because they help us understand how the Earth’s atmosphere would behave with different levels of incoming radiation from the Sun, different levels of greenhouse gases such as carbon dioxide (CO
₂
) and methane, and whatever else might go into the model. I’ll ignore the effect of methane - basically, it just makes everything worse. Climate change is a very complex topic, and this is just a quick look at one common misunderstanding.

Nearly all scientists working on climate are now convinced that human activities have increased the amount of CO
₂
in the atmosphere, and that this increase has caused temperatures to rise. A few still disagree, and in March 2007 Channel 4 Television broadcast a documentary, The Great Global Warming Swindle, about these dissident opinions. One of the more puzzling pieces of evidence put forward in this programme was the observed long-term relation between temperature and CO
₂
. Former presidential candidate Al Gore, who has been very active trying to persuade the public that climate change is real, was shown delivering a lecture in front of a huge display of how temperature and CO
₂
have changed in the past. These figures can be deduced from natural records such as ice cores.

Historical records of temperature and CO
₂
, based on: J. R. Petit and others, ‘Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica’, Nature, vol. 399, pp. 429-436 (1999).

The two curves go up and down almost together, a convincing association. But the programme pointed out that the temperature increases start and end before the CO
₂
ones do, especially if you look closely at the most recent data. Clearly it is rising temperature that causes CO
₂
to increase, not the other way round. This argument seems quite convincing, and the programme placed a lot of emphasis on it.