## Thursday, 5 November 2015

### Back to back?

The BBC news announced recently that New Zealand had won two rugby world cups 'back to back'. Well done, New Zealand. But not so well done, BBC.

How has it happened that 'back to back' has come to mean 'in succession'? Given that this question is about the language we use to describe spatial or temporal relationships, I think that, as a mathematician, I am entitled to a little light-hearted rant.

I hear people talking about watching successive episodes of a TV programme they have recorded and saying that they watched them 'back to back'. That's just daft. The back of the first episode (i.e. the end) is not followed by the back of the second episode, but by the front of it (i.e. the beginning). So, if anything, they are watching the two programmes 'back to front'.

The pastor in our church announces that we are going to sing two songs 'back to back'. It would clearly make more sense to say that we'll sing them 'back to front'! But 'in succession' or 'one straight after the other' would perhaps be less ambiguous.

When I was a lad, growing up on a council estate in London, 'back to back' described houses, where the back of one house faced the back of another, often with very little space between them for our 'back yards'. Those were the days when the phrase 'back to back' actually meant something; when we got the geometry right.

This phrase 'back to back' seems to be associated with the image of books or DVDs stacked on a shelf, cover to cover. But when they are stacked like this the back of one book is touching the front of the next book.  This is related to a well-known little mathematical puzzle ...

There are ten paperbacks, each width one centimetre, standing neatly and upright on a bookshelf, with no gaps between them. Working left to right, a bookworm starts at the beginning of the first book and chews horizontally through to the end of the tenth book. How far does the bookworm travel?

No, it's not 10 cm!

I enjoyed Tim Vine's one liner about this irritating phrase: 'my wife and I watched two episodes of Downton Abbey back to back; fortunately I was the one facing the television.'

By the way, the bookworm travels about only 8 cm.

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