Comment by coldpie | Hacker News Reader

Comment by coldpie | Hacker News Reader

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I dunno, man. I'm pretty well-versed in math and I find this page kind of baffling. I'm sure it's one of those things that is very easy to use once you learn it, but at least this introduction is very daunting. To do a basic multiplication (step 1 in the linked page) I need to use the C and D scales, each for two different purposes. Why not A and B? How do I remember it's C and D? Which part goes on C and which part goes on D? Then step 2 describes what to do if it goes off the edge of the scale, and it involves making an approximation. How do I know how accurate my approximation must be? Why is it to the tens digit? If I get larger numbers do I continue to use the tens digit, or some higher factor? We're only on step 2 and I'm already lost.

This definitely looks like a great tool, and I'm kind of sad I don't have one or understand how it works, but this kind of complex learning and memorization up against dropping a needle on a record you like isn't really a great comparison.

It works better if you know how the scales are constructed and get familiar with properties of logarithms (mainly variations on log ab = log a + log b)

C and D are plain log scales, where one decade is the length of the rule. They're sort of the default scales to use.

Multiplication is commutative, so you put either number on either scale. The important thing is that the distance from the left index of the scale is proportional to the log of the number (reading the scale as 1 to 10), so you want to arrange the scales to add the lengths corresponding to your numbers such that the lengths add up. (Or so that you subtract the length of the divisor from the dividend, if you're dividing).

You can get by without the approximation if you're willing to set up the multiplication, see that the product is out there in thin air, then move the slide to put the right index where you originally put the left index. (3 times 5: on the d scale find 3 and put the left index of the C scale there; opposite 5 on the C scale read nothing because there's no D scale there; try again using the right index of the C scale, which is the same thing as having another copy of the D scale out there to the right where the air was).

A and B are each 2 copies of a log scale. You can absolutely use the left side of A and B for your numbers to multiply, and the product will always be on the scale.

People normally use(d?) C and D because the precision is better and because the rest of the scales (like the trig and log-log) are constructed to work with them.

Nit: while multiplication is commutative, the property you meant to use was symmetry. I'm sure it was a mistake and you know this, I'm just pointing it out to prevent confusion for others.

Edit: s/competitive/commutative/

Huh. I heard (US high school algebra in a recent unspecified century) the fact that ab=ba called "the commutative property of multiplication", and the "symmetric property of equality" meant a=b <=> b=a, and didn't run across anything later on (comp sci from a department of the engineering college rather than the math department) inconsistent with that. Symmetry sounds like a reasonable term for both, but it sounds like there's a distinction I don't get?

https://en.wikipedia.org/wiki/Commutative_property

> In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

Are you saying you disagree?

No, I had a brainfart and was thinking of associativity. I have no idea how it happened. Very embarrassing.

Don't be fooled, slide rules are really easy to use. It took me less than a minute to learn how to do multiplication, and I wasn't an adult yet.

The A/B/C/D names are from Amédée Mannheim, who in 1851 designed the "modern" slide rule & give those scales those names. In practice, you normally just use the C & D scales when you want to multiply. Here's a history of the "cursor" on a slide rule, that also provides a clear history of the slide rule itself: https://www.nzeldes.com/HOC/Cursors.htm

I've never had a practical reason to use a slide rule over a calculator. But I've had fun with them, & that means something.

A lot of slide rules have a bunch of scales but there are only a few you routinely use. Using a slide rule is very easy to pick up. That said, you do need to handle the order of magnitudes mentally and precision is necessarily limited.

And slide rules don't do addition or subtraction.

So they were useful in the absence of calculators as a way to avoid using log and trig tables but you wouldn't realistically use them in place of calculators today. (But then I think vinyl records are pretty silly too; and I say that as someone who grew up with them and actually owns a turntable.)

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