### Chopping logic

 These are twins. The one on our left is older.
I have had an interesting discussion with Paul Nahin, the author of The Logician and the Engineer, which I'm currently reading to review.

Nahin quotes a logic problem that is apparently well known amongst mathematicians. In it, one person is trying to guess the (integer) ages of the other's three daughters. He is given some information that allows him to narrow the possible ages down 1, 6 and 6 or 2, 2, and  9. Then the first gives an additional pieces of information. 'My oldest daughter,' he says, 'likes bananas.' Immediately the second person knows the girls' ages.

The accepted correct solution goes that the daughters can't be 1, 6 and 6 because there isn't an oldest daughter in this scenario, so our logician can deduce they are 2, 2 and 9. But I say that this is rubbish - at the very least poor logic.

Why? It is perfectly possible to have two six-year-old daughters born 10 months apart. Clearly one is older than the other. However even with twins, one is always older than the other for legal reasons.

Prof. Nahin counters with two points. One is that integer ages were specified, and the other than this is a pure maths problem so legality doesn't enter into it.

I would say it doesn't matter about the 'integer' ages bit - both daughters have the integer age of six in both my counter examples. (And even if they literally had to be six that day, they could still be twins). As for the 'pure maths problem' argument, that doesn't hold up either. This clearly isn't a pure maths problem. It features a person liking bananas. Pure maths? I think not. It is an attempt to apply logic to a (admittedly rather odd) real world situation. In the real world it would be perfectly acceptable for the father to comment about his 'oldest daughter' even if the six-year-olds were twins, because she is accepted as such. As a father of twin daughters, I have done this.

If logic is being applied to a real world problem, I'd suggest it should take into account the way that the real world describes things.

### Why I hate opera

If I'm honest, the title of this post is an exaggeration to make a point. I don't really hate opera. There are a couple of operas - notably Monteverdi's Incoranazione di Poppea and Purcell's Dido & Aeneas - that I quite like. But what I do find truly sickening is the reverence with which opera is treated, as if it were some particularly great art form. Nowhere was this more obvious than in ITV's recent gut-wrenchingly awful series Pop Star to Opera Star , where the likes of Alan Tichmarsh treated the real opera singers as if they were fragile pieces on Antiques Roadshow, and the music as if it were a gift of the gods. In my opinion - and I know not everyone agrees - opera is: Mediocre music Melodramatic plots Amateurishly hammy acting A forced and unpleasant singing style Ridiculously over-supported by public funds I won't even bother to go into any detail on the plots and the acting - this is just self-evident. But the other aspects need some ex

### Is 5x3 the same as 3x5?

The Internet has gone mildly bonkers over a child in America who was marked down in a test because when asked to work out 5x3 by repeated addition he/she used 5+5+5 instead of 3+3+3+3+3. Those who support the teacher say that 5x3 means 'five lots of 3' where the complainants say that 'times' is commutative (reversible) so the distinction is meaningless as 5x3 and 3x5 are indistinguishable. It's certainly true that not all mathematical operations are commutative. I think we are all comfortable that 5-3 is not the same as 3-5.  However. This not true of multiplication (of numbers). And so if there is to be any distinction, it has to be in the use of English to interpret the 'x' sign. Unfortunately, even here there is no logical way of coming up with a definitive answer. I suspect most primary school teachers would expands 'times' as 'lots of' as mentioned above. So we get 5 x 3 as '5 lots of 3'. Unfortunately that only wor

### Which idiot came up with percentage-based gradient signs

Rant warning: the contents of this post could sound like something produced by UKIP. I wish to make it clear that I do not in any way support or endorse that political party. In fact it gives me the creeps. Once upon a time, the signs for a steep hill on British roads displayed the gradient in a simple, easy-to-understand form. If the hill went up, say, one yard for every three yards forward it said '1 in 3'. Then some bureaucrat came along and decided that it would be a good idea to state the slope as a percentage. So now the sign for (say) a 1 in 10 slope says 10% (I think). That 'I think' is because the percentage-based slope is so unnatural. There are two ways we conventionally measure slopes. Either on X/Y coordiates (as in 1 in 4) or using degrees - say at a 15° angle. We don't measure them in percentages. It's easy to visualize a 1 in 3 slope, or a 30 degree angle. Much less obvious what a 33.333 recurring percent slope is. And what's a 100% slope