[BITList] Fwd: Re: Human calculator. [VIDEO]

[HUGH]

Frank, David,

>From what I read on him, Trachtenberg analysed the steps employed in multiplying numbers, using memory (a lot) and the basic tools. The basic tools are the memorised multiplication tables.  I got up to 12x12 in primary school (1938-1945), my grandchildren got up to 10x10, my father got up to 15x15. I got mental arithmetic in primary school, and I was never any good at it, since much of it consisted of calculating the cost of 15 eggs if an egg cost 1/2d, or some such. My mind was always on other things than eggs, and I couldn't be bothered.  I recall we got a rule for multipying 2-digit numbers by 11 in our heads. Eg, 98 x 11.   >From R to L : 1 x 8 = 8, and partial answer is 8 ; add 9+8 = 17, put 7 with 8 and partial answer is 78 ; add the 1 and the 9 = 10 ; answer is 1078.  But it's easier with a pencil and paper and less chance of error.

The chap who took us for HNC maths, Dr Whatsisname, forbade us to inflict arithmetic on him, so once a problem reached numbers we had to stop and write no more on it. I didn't object.  His favourite approach in the calculus was to ask us to write a short piece on how we'd solve a problem, instead of actually solving it. That was the point at which my brain started to realise there was something to maths apart from bloody quadratic equations and arithmetic.

Squaring numbers, incidentally, follows the same trick as multiplying by 11.  A set of steps from R to L, memorising the last results and carrying over numbers.  Unfortunately, the rule for 3 digits is not quite the same as that for 2, and so on.

Dave,  I'm sure you used as much maths in navigation as I ever used in engineering.

Hugh. 
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