I found my slide rule the other day while moving into my new home office. While made obsolete by hand-held calculators, a slide rule still teaches a valuable lesson in precision, or more specifically, false precision in the digital age.
Divide 4 by 7 on a calculator, your smartphone, or in Excel and something like 0.57142857 will be returned. Now, perform the same operation on a slide rule, and (after some squeezing and squinting) 0.572 will be returned. Wow…the digital age is so much more precise!
Not so fast. Granted, the calculator returns more decimal places but the answer may or may not be more precise. How can that be? Good engineering practice is to express results to the same number of significant digits as the measured value with the least number of significant digits. Since it is unlikely that both our “4” and “7” were measured out to 9 decimal places, the digital age’s greater precision is an illusion.
Excel formulas to truncate significant digits are tricky and I don’t know anyone who uses them. Even so, we can all easily limit decimal points to something more reasonable than nine places.
So that’s the lesson on precision. Curious as to how a slide rule works?
Slide rules are based on base 10 logarithms. A logarithm is the power to which a number must be raised to equal another number. The base 10 logarithm of 100 is 2 because it takes exactly 2 tens (10 x 10) to equal 100. Adding the logarithms of two numbers is the same as multiplying the two numbers. Similarly, subtracting logarithms is the same as dividing one number by another. By sliding the scales and cursor relative to each other, logarithms are added or subtracted to perform multiplication and division.
A slide rule can also calculate square roots, cube roots, sines, tangents, etc. If I remember correctly, I did not use my slide rule for the trig functions. I looked them up in tables like this one from my CRC Standard Mathematical Tables, a reference book full of way too much information. Calculators are much easier!
Here’s a link to an NPR article on slide rules including a demo:
The slide rule jockeys of the 1960’s had it right: they put a man on the moon to three significant digits.