Three Figures

One of the “features” of being an old guy is that I remember how to use a slide rule. My university days and in fact my early career with General Foods were filled with slide rule calculations. There was no other way unless you used a desktop sized transistorized calculator or a Friden mechanical crashbox based in the analytical lab.

Well I suppose there was always longhand multiplication and division. I remember my times tables after all.

But the slide rule was king. I learned all the scales and techniques for trig calculation and logarithm addition. I had a really good Pickett aluminum slide rule. Still have it, for that matter.

Of course that has all gone the way of the dodo. A lovely instrument and a finely honed skill made obsolete by a two buck computer chip and an LED. After 1974 there was no need for it.

Something else went away too. The concept of “three figure accuracy.” It was important to keep in mind back in the 1960s because the best you could do with a slide rule was three figures. For example my slide rule couldn’t calculate any closer than 4.25 42.5 or 425 so the number of digits in your answer determined how many decimal places you could write accurately. A number like 4250 presumed an accuracy you didn’t have, so the scientifically correct thing to do was write it in exponential form e.g. 4.25 X 10^3.

This may have seemed like a limitation but for all my university years I had only one situation where three figure accuracy wouldn’t do – and that was a spectroscopy experiment that required 7 figure calculations. Today we’d use a calculator but then I had a set of 7 place log tables. Go figure.

In the food labs we almost always went with three figures or less. A lab balance couldn’t weigh much more accurately than that. A typical package of Jell-O weighed 56.7 grams – three figures. Our lab color and texture instruments were mostly analog and not all that accurate either.

Nowadays we can calculate to eight figures easily, and probably 15-17 with a computer. But that doesn’t mean all those extra decimal places mean anything. Certainly the machines that fill packages of noodles can’t do it any more accurately than 5 decades ago.

The only place where we wrote a product formula to 4 decimal places was for product costing. Some of the numbers there purported to be accurate to six figures, and others like a colouring or a vitamin maybe only one. But it was totally an accounting trick. Nothing actually got weighed or added to a product that way.

In engineering, airplanes like the B-52 and Boeing’s early passenger jets were designed to three figure accuracy. You needed a bit more precision for long range space navigation, but Buzz Aldren took a slide rule along to check the final calculations to land the lunar module. The big picture for getting to the moon was also calculated with slide rules.

In short, we can calculate much more quickly and efficiently with today’s computational resources but does writing an answer as 4.2496667 mean anything more physically than 4.25? I don’t think so.

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