I inherited two or three slide rules from my father. One of them is circular shaped. Once or twice he showed me how to do some basic calculations, and I've spent ten minutes here and there with various online tutorials, but I've never put the time in to actually understand it, so I always instantly forget how they work. Kind of a shame, but I hang on to them anyway. They're cool artifacts from the pre-computer world.
Hm, I wonder if it could be a handy way to do fractional computation while I'm doing woodworking? If so, that could be a good excuse to finally learn how to use one.
(Strangely, my work's proxy blocks this domain as "pornography." Interpret that as you will.)
> They're cool artifacts from the pre-computer world.
I like slide rules, and abaci, and jigs, protractors, T squares, or other nifty tools for measuring and computing from "before" the computer age because they represent something of a unique tool.
Every tool exists to perform some action better than can be done by some other tool or set of tools. And the interesting side of tools for solving math problems or measuring things directly or indirectly is that it's the foundation of abstraction. Breaking down a big problem into a smaller one that can be trivially done with another tool is foundational to how we develop technology.
Like a pump moves water or a lever amplifies force, tools like a slide rule let us do less work but instead of manipulating physical forces they're reducing the amount of working memory and information we need to solve a problem.
It's a level of ingenuity that's worth respecting.
Give you a woodworking example where it matters, see if it reaonates..
You’ve got a box 10" high, 15" wide, you want to decorate the side with a few raised panels with borders, whatever. You decide that they're going to be inset ¾" from the sides, middle one will be maybe 10% larger on each side, the double spacing of 1½" between seems too wide so you want to fudge to 1⅛".
So all told width-wise you have a 15" span of which ¾ + 1⅛ + 1⅛ + ¾ is margin, so that’s 1½ + 2¼ = 3¾, you'll have 11¼ left over. You want to divide it into 1 + 1.1 + 1 = 3.1 pieces.
So you locate axes A and B on your slide rule, these should be double log-log, going from 1 - 100, fine for multiplications. You will also see C and D, single log-log going from 1 to 10, higher in precision, also having them next to A and B allows you to perform square roots, use the hairline on the cursor to confirm that the square root of 16 is 4 for example. You also probably have a red series that is single log-log but backwards called CI, this can sometimes be helpful for divisions, and a maybe a K scale that is triple log-log allowing cubing or cube roots. Flip it over, you might have S for sine, t for tan, L for logarithm being a linear scale.
Anyway, move the hairline on the cursor over A=11.25 to “remember” it, then put B=3.1 under the hairline and look at the place where B=1, it's around 3.625. Of course we would rather have this in eighths or 16ths, but look at (no sliding!) B=8 to find this is nearly A=29 or 29/8 inches, that 3.625 is 3⅝". And looking at B=1.1 you get that 10% larger is just 4".
So you want a 4"×8½" panel in the middle, two 3⅝"×7¼" panels on the sides, you can again get that 7¼" by moving B=1.1 next to A=8.5 and then B=1 shows 7 and change, peek up at B = 4,8,16 to see if it's best written as a quarter or eighth or sixteenth fraction.
So they're great at
- multiplying or dividing numbers, especially if they are not round
- converting those decimals to eighths or sixteenths, calculators just give you digits usually, slide rules you can quickly see what is 1x this number, 2x, 4x, 8x, 16x, makes it a snap.
Most slide rules will do many operations, but the basic operation is multiplication.
Multiplication on a slide rule works because you can turn multiplication into addition with
X * Y = 10 ^ (log(X) + log(Y))
(Edit: i had e and ln up here, but 10 and log is a better match the slide rules from 1 to 10l
The rules are log scaled, so you find X on one rule and line up 1 on the other rule, then look at what number on the first rule is where Y is on the second rule.
Run a couple examples you know the answer to, and you'll get it. As I recall, wrapping/bounding is tricky, you might need to reverse X and Y or go the opposite way to get your answer.
You'll need to do it like scientific notation as well, the rules only have numbers between 1 and 10.
Division is inverted multiplication, so for X / Y, line up the rules so X and Y match, the quotient is what is on the X rule where Y is 1.
I don't know much about woodworking, are you doing multiplication or division with fractions, or adding? Do you want fractional results or decimals?
A lot of woodworking is done in inches and fractions of inches. Doing joinery where you have to consider things like the kerf of the blade often requires many annoying additions and subtractions of power-of-two denominators. While adding 3/16 and 5/32 is trivial, trying to do that while focusing on making a good cut and taking accurate measurements can be distracting.
Usually adding and division. For example "7 3/4 plus 8 1/8" or "15 3/4 divided by 4." Fractional result would be ideal. I don't know if a sliderule is a good tool for this is or not :)
You'll still need to do the addition, and then you'd need to eyeball 15 3/4 as a number between 1 and 2, do the division, and then eyeball the result into a fraction.
I think I've only seen decimal marked slide rules, you could certainly have a fraction marked rule, but it wouldn't be that helpful, because 15 3/4 is not easy to turn into
10 * (1 + 1/2 + 3/4 * 1/5 )
And then you're not at a power of two fraction anymore either. Some other tool would be better; probably a pocket calculator that's taken advantage of half a century of computational advances and can manage fractions.
Yeah, there's a ton of perfectly good fractional calculator apps and so on out there. I was just looking for an excuse to use my dad's old thing. Thanks again for the explanations.
No. A slide rule is all scientific notation (2 or 3 significant digits on the rule and you carry the mantissa in your head). Very good for accuracy but not so much for precision.
At school I was introduced to several calculation aids:
* Slide rule
* Mechanical adder
* IBM Schools Computer
The IBM wasn't actually much of an aid; it had no persistent storage, and you had to program it in hex, from the console.
The mechanical adder was marvelous; you toggled in the arguments using metal wheels, and then cranked a handle on the side to do additions. We actually used them to do sums; there was a cupboard in the maths classroom, with enough machines to have one on each desk.
My father left me a Faber slide rule from the twenties. Wood, with ivory lamination, and a nice, delicately-sprung cursor. We never used slide rules at school to do computations, we only used them to learn how to use slide rules (which was therefore a complete waste of time).
It's really worth looking at a few of the collections. There are lots of slide rules on display, and many if not most are far beyond plain linear slide rules. (Most are special purpose and application specific.)
There are still a few companies that make them. Called "slide charts", since they come in many forms besides just the "rule" form.
I look into having them made every now and then, but it seems like the minimum order quantity is almost universally 500. It would be nice if there was a modern style of e-print service for smaller quantities.
I've been meaning to dust off my old slide rule for a long time. Learning to use one circa 8th grade made future science so much easier. Had to think of significant figures ahead of time, spend a few moments to plan the computation, and get comfortable with when to approximate and how. Pretty soon I was able to get a sense for what answers ought to be, at least to within a factor of 2-5. Anything outside of that and I knew I'd made a mistake somewhere.
I also loved the old HP calculators of the late 1970s to late 1980s and eventually set the slipstick aside but am ever grateful for what it did for me. And for fellow RPNthusiasts, there is the Museum of HP Calculators at
https://hpmuseum.org/
I feel like being gen x i might have been part of the first wave of kids never to learn to use a slide rule. I'm actually not even totally clear on what they are even for.
I am really digging some of the other mechanical calculators in the collections though. Always love to see a curta.
> I'm actually not even totally clear on what they are even for.
The same way you can pick a point on amap, measure a certain distance away on the map and "automatically" know how far away to locations are in really life - you can pick a number on a side rule, move a certain distance away and it will "automatically" multiply or divide two numbers.
It will have a small amount of error in it, the same way measuring distance on a map will have a small amount of error in it.
Hm, I wonder if it could be a handy way to do fractional computation while I'm doing woodworking? If so, that could be a good excuse to finally learn how to use one.
(Strangely, my work's proxy blocks this domain as "pornography." Interpret that as you will.)