Alex's Adventures in Numberland - Alex Bellos [80]
The slide-rule was a calculating machine of fantastic ingenuity, and while it may now be obsolete it still has fanatical devotees. I visited one of them, Peter Hopp, in Braintree, Essex. ‘Between the 1700s and 1975 every single technological innovation was invented using a slide-rule,’ he told me when he picked me up at the station. Hopp, a retired electrical engineer, is an extremely affable man with wispy eyebrows, blue eyes, and luxurious jowls. He was taking me to see his slide-rule collection, one of the world’s largest, which contains more than a thousand of these forgotten heroes of our scientific heritage. On the drive to his home we chatted about collecting. Hopp said the best stuff was auctioned directly on the internet, where competition inevitably pushed prices higher. A rare slide-rule, he said, can easily cost hundreds of pounds.
When we arrived at his house, his wife made us a cup of tea and we retired to his study, where he presented me with a wooden 1970s Faber-Castell slide-rule with a magnolia-coloured plastic finish. The rule was the size of a normal 30cm ruler and had a sliding middle section. On it, several different scales were marked in tiny writing. It also had a transparent movable cursor marked with a hairline. The shape and feel of the Faber-Castell were deeply evocative of a kind of post-war, pre-computer-age nerdiness – when geeks had shirts, ties and pocket protectors rather than T-shirts, sneakers and iPods.
I went to secondary school in the 1980s, by which time slide-rules were no longer used, so Hopp gave me a quick tutorial. He recommended that as a beginner I should use the log scale from 1 to 100 on the main ruler and adjacent log scale from 1 to 100 on the sliding middle section.
Multiplication of two numbers using a slide-rule – which also used to be called a slipstick in the US – is performed by lining up the first number marked out on one scale with the second number marked out on the other scale. You don’t even need to understand what logs are – you just need to slide the middle ruler to the correct position and read the scale.
For example, say I want to multiply 4.5 by 6.2. I need to add the length that is 4.5 on one ruler to the length that is 6.2 on the other. This is done by sliding the 1 on the middle ruler to the point where 4.5 is on the main ruler. The answer to the multiplication is the point on the main ruler adjacent to where 6.2 is on the middle ruler. The diagram below makes this clear:
How to multiply with a slide-rule.
Using the hairline cursor, it is easy to see where one scale meets the other. Moving up from 6.2 on the middle ruler, I can see that it crosses the main ruler at just under 28, which is a correct answer. Slide-rules are not precise machines. Or rather, we are imprecise in our use of them. In reading a slide-rule, we are estimating where a number is on an analogue scale, rather than finding a clear result. Yet despite their inherent imprecision, Hopp said that – for his purposes as an engineer, at least – slide-rules were accurate enough for most uses.
The log scale on the slide-rule I used went from 1 to 100. There are also scales that go from 1 to 10, which are used for greater accuracy because there is more space between the numbers. For this reason, whenever you use a slide-rule it’s always best to convert the original sum into numbers between 1 and 10 by moving the decimal point. For example, in order to multiply 4576 by 6231, I