### Another poke in the QI

I love the BBC TV show QI dearly, but since they so delight in the misunderstandings of others, they are fair game when they get something a trifle wrong. Recently they did just this - or to be precise, they omitted an important part and focused on an answer that, while true, was not the best picture.

Specifically, they were asking about Sherlock Holmes and what kind of reasoning he employed. Inevitably, someone fell into the trap of saying 'deduction', because we associate phrases like 'And what can we deduce, Watson?' with old SH, even if never said. 'No,' said the awesome Stephen Fry, 'he used abduction.' Now I would like to suggest that this is an incorrect remark on several levels. Firstly, occasionally Holmes did use deduction. And, yes, he did sometimes use abduction. But I think his main technique was, in fact, induction.

Here's a quick summary of the three, using that most delightful of reasoning tools, the logical swan. (These examples are probably not perfect if you are a nitpicking logician, but good enough for QI purposes.)

Deduction: Mr Davies makes model swans. He only makes white model swans. I have in this box one of Mr Davies' swans. I can deduce (without looking at it) that it is a white swan.

Induction: I have been down to the river and all the swans I examined (possibly with a magnifying glass) were white. I form the hypothesis 'all swans are white' (and it holds up pretty well until I visit Australia).

Abductive: All the swans I have observed are white and the most likely explanation for this is that 'all swans are white'.

The distinction between induction and abduction is extremely subtle. Both go beyond what is logically proved by the evidence (known in the trade as being 'ampliative') but abduction specifically requires an explanation - the reason that the swans I have observed are white is that all swans are white, where induction is more statistical: 100% of the swans I have observed are white, so I will use the hypothesis that swans are white without worrying about the reason why this is the case.

So when Sherlock does his party trick of saying something to the effect of 'I see you are an ex-military medical man, recently returned from Afghanistan,' Holmes is almost certainly using abduction, but when he does his day job, using cigar ash or a footprint in the soil, it is likely that he is using induction.

Back to QI, to be fair and logical they did not say that what Holmes did wasn't induction, because no one brought it up - but to state plonkingly that what Holmes used was abduction is no better answer than the 'deduction' that got so derided.

Image from Wikipedia

### 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