'Probable impossibilities are to be preferred to improbable possibilities.' Aristotle

I keep having flashbacks to my probability and statistics lectures. They're not pleasant. It's because probability is so much in the news.

We are told that the credit crunch happened because bankers thought they could measure risks, and securitize them, failing to realise that uncertainties are uncertain, that is they can't be measured. Or there's the discussion of swine flu with predictions about how many might die, on scales from dozens to tens of thousands: sounds pretty much like guessing to me. Or now, there're the curses being hurled at the British Met Office, who'd said we had a 65% chance of a 'barbecue summer', only now it's raining all the time. What did that 65% mean anyway?

The problem is that probabilities are very hard to interpret. This is what has been taking me back to the lectures. I remember very rapidly becoming very confused about the subject. You can almost envisage what's going on when thinking about coins being tossed. But that's barely the start of it. So I went to see my tutor, to ask for a heads up: what's it all about? And he told me this. Don't try to understand it. Just follow the formulae for working the probability out.

He wasn't being patronizing. He continued, explaining that no-one understands what probability means for sure. Different mathematicians have their preferred option. But maths itself can't tell you.

There're are a few who think probability is really just an expression of a feeling or hunch. It's quite likely to happen, or quite likely not to happen. So the 65% for a sunny summer is saying, just a bit more likely to be warm than not. But then, that doesn't sound very scientific. So most scientists want a more robust interpretation.

They may turn to the notion of frequencies. Here, 65% means that if you had 20 summers running in parallel, 13 of them would be hot, 7 overcast. That makes it seem pretty likely the summer would be nice. Except that it's entirely meaningless to talk of 20 summers running in parallel. There's only one summer. And this is it.

So, more again turn to the logical interpretation of probability. This rests on the idea that if you have one statement, then you can determine the probability of another. A coin has two sides, heads and tails (statement). Therefore, if I toss it, there is a 50% chance of heads (probability). It works fine in such simple situations. But quite how the logical interpretation can make sense of weather forecasting is beyond me. It's beyond most philosophers of probability too, who continually come up with different defenses of it. It's probably safest to say that they prefer this interpretation because it seems objective. Whether it is or not is anyone's guess. (No doubt, some wag has attached a probability to it.)

The thing is that for any subject to claim the status of a science, it needs to derive precise figures. So even though they may be strictly meaningless, scientists persist in coming up with exact probabilities.

Now, where's my crystal ball...