What I learned at Cambridge University: approximation

I think I probably learnt a lot more than just one thing, but I would argue that the most important thing I learnt was the ability to approximate, and to feel confident working with approximations.

I suspect I do approximate calculations every working day of my life: maybe I am comparing 'by eye' whether a client's gross profit margin has gone up or down, what the revenue per person is (one of my favourite metrics), what a client's tax bill is, what the sum of a column of numbers is, roughly…sometimes accuracy is needed, but often it is not.

A case in point. I recently gave a lunchtime training session in which we had to calculate 36*45. Alas, my audience reached for their calculators, ready to tap away: it's about 1,600, I said to incredulity. I decided to ban the use of calculators for the remainder of my session: they get in the way of thinking.

36 can be rounded up to 40: it's pretty close, about 10% different; and so can 45, here by chance 10% different too, so 36*45 is probably pretty close to 1,600: and of course it is, 1,620. The error, 20, is about 1%, being roughly 10% of 10%. That's pretty close enough, and even if the example is quite a good selection, the ability to be roughly right is an important skill to learn.

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