slide rules OK

I may have bought the last slide-rule in Ireland in about 1974.  I had cherished one all through my high-school career in England and had it lost/stolen sometime shortly after I came to College in Dublin.  I was attached, I thought it was an essential tool for science, so I went round the corner to Lincoln Place and bought another.  Not half so nice as my old Faber-Castell 50/82 but functional.  Almost immediately the price of pocket calculators collapsed and slide-rules fell into the dustbin of history.  So much so that very few people under the age of 50 will know what I am blithering on about.

Slide rules were wooden tables of logarithms, about 30cm long, built with appropriate technology to have only two moving parts (a slidey bit and a cursor to help line things up) and the batteries never run out.

On a slide-rule the table of logarithms I showed earlier are represented as lengths.  To multiply two numbers using log tables, you look up two numbers and add them together.  A slide rule comes with a pair of identical wooden rules where each number from 1 to 10 is etched at the logarithm of its distance from the left-hand end. The diagram above shows how to multiply 2 by 3, by adding the distance representing log(2) to the distance representing log(3).  And here's a chap with a beard (must be clever) showing how it's done.  Slide rules don't only work with whole numbers: you can do 1.2 x 3.65 using the same method and for a slide rule small enough to fit in a brief-case, typically you can work with about 3 significant figures and take an informed punt for the 4th.  Good enough for engineers!

Now here's the rub.  You use the slide-rule in exactly the same way (and get the same answer!) whether you are multiplying 2 x 3 or 20 x 3 or 200 x 3 million. So you had to estimate the answer you expected before you started tricking about with the apparatus. When you read off the significant figures from the slide-rule, you knew whether you were talking 6 or 60 or 6/10ths of a billion. I just showed how to do this by estimating the seconds in a calendar year. So with the tools of more than 40 years ago, you knew how to ball-park, got experience in estimating and developed a feeling for numbers and magnitude.  The calculator generation tend not to have this skill particularly well polished.  The other great advantage is that you're not tempted to write down an answer like 3.1415926 for Pi, when 22/7 is good enough for your present purpose.