Monday, 27 July 2009

Two inaccurate things before lunch

This is off-topic, but I'm currently reading Six Impossible Things Before Breakfast which has been a massive disappointment given the potentially fascinating topic. There's no coherent argument sustained throughout it, it's more like a stream of consciousness, and whilst there are some interesting individual bits of research referred to in the text the lack of footnotes (though there are endnotes) adds to the feeling it has been thrown together. In short, I don't like it.

But there are also a couple of examples given in the text that I think are actually plain wrong. So I'm posting them up to check if I'm being a dumbo or not. First up (and I notice this one has been picked up by an Amazon reviewer) is on page 6:
No unhealthy food have cholestorol.
Some unhealthy foods are fried foods.
Therefore no fried foods have cholestorol.

Valid or not? My guess is that your left frontal and temporal lobe belief system was activated, and so the conclusion seemed invalid. But it is valid logically.
Errr... no it isn't, is it? Based on the premises the conclusion is not valid. You can say 'some fried foods have no cholestorol' because it is stated that 'Some unhealthy foods are fried foods'. But it is not stated that 'all fried foods are unhealthy foods'. So how can you reach the conclusion that no fried foods have cholestorol? Am I missing something, or has he got it wrong? There are certainly examples of logic puzzles like this where we tend to accept or reject the logic depending on what the conclusion is - but this isn't one as far as I can see.

Similarly on page 96 I think he gets the 'four card problem' wrong. He says:
In Peter Wason's classic experiment, subjects are asked which card to turn over to test the rule that if there is a vowel on one side, there is an even number on the other. The four cards are Ace, King, 2 and 7. Most turn over the ace, just trying to confirm the rule. But then they can try one more card, and most turn over the 2, which tells us nothing; only 4% turn over the 7, which could falsify the rule.
There is something wrong with his version, surely? In the original experiment two cards had a letter facing up, one with a vowel and one with a consonant (say an A and a B), and two had a number facing up, one odd and one even (say 2 and 7). So the correct way to approach it is to turn over the vowel and the 7.

In his version you can't disprove the rule from the letter perspective, since no cards are letter-up. So effectively by turning over the Ace and 7 you are trying to disprove the rule the same way twice. So it's not the same as the orginal experiment, where people tend to turn over the A and the 2, because they wrongly seek only to confirm the rule. By turning over just two odd numbers you may well end up still not having disproved it if both cards have a consonant on the other side.

But that's assuming he thinks the Ace is an odd number card (which it always is, isn't it?) Actually, and more fundamentally, he seems to think an Ace is an even number card ("Most turn over the ace, just trying to confirm the rule.") and in doing so I think he demonstrates that he hasn't grasped the point of the experiment in first place. Because turning over the even number card can't disprove the rule (whereas turning over the A and the 7 can).

Innit? Or have I missed summink? Is the point that "Ace" and "King" are spelt out rather than being the card itself, and as such both contain a vowel in the word on the card? But then there's no consonant only card.

NB - the headline is slightly misleading as I actually posted this after eating my lunch. I was thinking of going with the alternative 'Dude, where's my proof-reader?' but hey.


Tom Freeman said...

I think he has got the cards one right (in his head), although he's made a real hash of presenting it. Talking about playing cards ruins the reader's ability to see what he's getting at. I think he's imagining a situation where the cards have just "A", "K", "2" and "7" facing up, in which case it works.

But if I didn't already know this one I would never have understood what he meant.

And you're spot on about the foods one.

Tom Powdrill said...

Yeah I think that must be it!