Monday, 14 January 2008

Dodgy Mathematics Exposed: #1, The Perils of The Incorrect Underlying Assumption

I meant to mention this before now, but hadn't got round to it. As a mathematician, I am often appalled by some of the ways in which The Glorious Discipline is manhandled in the popular media. So I have decided to expose such lapses when I come across them, for the sake of your education. Our subject today is what we shall call The Incorrect Underlying Assumption. An Underlying Assumption occurs when you assume something and then use that in the process of your analysis; if this Underlying Assumption is Incorrect, your analysis becomes nonsense.

On Boxing Day I was reading The Times (you can't buy The Guardian in Ballywalter; it took a certain level of persuasion to convince my dad that The Daily Mail was not an adequate substitute before we finally settled on The Times, which had a splendid pull-out puzzle section that day) and there was an article about the complexity of various recipe books (clearly a Boxing Day filler).

What they had done was to analyse various recipe books and see how easy they were to understand. So far, so good. But the way they had done this (I say 'they', I mean some scientists with too much time on their hands, not the people at The Times, who were just reporting the story) was that they had compared the number of big words in each, where a 'big word' was one with three or more syllables. They also counted what they described as 'technical terms', such as 'simmering'. The one with the least number of big words and technical terms was deemed the simplest, and therefore the winner.

So the Underlying Assumption here is that words with 3 or more syllables are more complicated than words with less than 3 syllables. Hence, broccolli is more complicated to cook than duck.
To use mathematical parlance, complexity of cooking is directly proportional to complexity of spelling.

One can back up the Underlying Assumption by pointing out that beans on toast is quite simple to cook, whereas ratatouille is rather more complex.

Now the difficulty which arises here should be fairly obvious: if your recipe requires the cook to simmer cauliflower, for instance, you need to tell people to... well... simmer the cauliflower. There is no way to say 'cauliflower' in a way that has less than 3 syllables; indeed, some of our English viewers will pronounce it with 4. Likewise, if you need an aubergine, you need an aubergine, and you can't just tell people to chuck in a kipper instead, even for the sake of simplicity.

This approach will lead to a recipe for coq au vin being simpler than one for mashed potato, which would be nice if only it were true. In fact, on this basis, a bowl of Weetabix is the height of sophisticated cuisine, especially if you throw a handful of sultanas on top and wash it down with a lingonberry smoothie. You are not advised to even attempt to use tortellini, avocados or coriander without supervision; any attempt at anything vegetarian and you could do yourself a mischief. On the other hand, you're quite safe to plough ahead with souffles, meringues and pastry, which are all straighforward.

Now, clearly this is nonsense, and the reason is that our Underlying Assumption is Incorrect. Sauerkraut may be more complicated to cook than peas, but this is not because it is a longer word.

All of this reminded me of a piece of GCSE coursework where we had to compare two newspapers and decide which was more complicated to read. So we all bought our copies of The Sun and The Times, and hypothesised that 'The Times will be more complicated so it will have more big words' and then proceeded to chart pretty graphs of how many letters there were in each word of a corresponding story in each paper. But of course The Sun had more big words, mainly things like 'babelicious' and 'snogtastic', which blew our hypothesis right out of the water; this was because it rested on our Underlying Assumption that a big word is more complicated than a little word, which was Incorrect (if you're still having doubts, please define both 'qat' and 'caravan' for me, without reference to a dictionary or thesaurus, using the comments link below).

And so we see how the Incorrect Underlying Assumption leads us to nonsense, and I hope we have all learned to question what we think is true before we start drawing conclusions from it.


lilytodd said...

Great post! Very funny!

I must confess I now teach that very same lesson. I may even use this blog in class (with your permission) to show I'm one step ahead of the additional maths genius pupils who have taken journalism as a filler.

My defence will be 'English is not maths', feel the spirit of the text, big words in The Sun will undoubtedly be made up, silly words, 'lowest common denominator' humour. (like what I did there?)

whynotsmile said...

Use my blog however you want!

Now, you see, we need to introduce a distinction here between the literary document, and the technical one. The literary document has a more or less free choice of words to use, whereas the technical one has a certain vocabulary which it must draw on.

For example. The fact that one is making cauliflower soup means that one must use the word cauliflower, as I suggested. Whereas, in literature, one could describe the cauliflower in artistic ways, such as 'the white thing that is a bit like broccoli' which is all simple words and sounds rubbish, or in some other, more artistic way which I can't think of 'cos I'm a mathematician. This is good in literature, but would make for a very complicated recipe book.

So you could do a lesson on technical documents vs literary documents, and get them to make up other ways of saying 'snogtastic' which would appeal to different audiences. I could come and do that lesson; it'd be class.

I liked the lowest common denominator comment, very clever, heh heh.

cawb said...

Genius! This makes aubergine harder to cook than egg plant, and courgette easier than zuccini!

I have a friend who has made programming this underlying assumption a possibility in dependently typed languages.

He says you should be happy to state that 3 = banana, so long as you cannot abstract from it, or substitute it until you have actually proven it. He called it John Major equality.