In the UK there was a time (late `70s) when slide-rules were allowed in examinations but calculators weren't, no-brainer to learn how to use one just for that. Even better, if you added "(SR)" after your calculations, that indicated that you had used a slide-rule so small errors were permitted.
To add to this, there's a great set of resources by Joe Pasquale explaining the mathematical theory behind how various functions can be computed by slide rules:
1. First, define a way to represent any univariate monotonic function f(x) on a graduated scale. (Specifically: select a discrete set of x values, and for each of these x values, place a mark with label x at a distance proportional to (f(x) - f(x_L)) from the left endpoint, where x_L is the leftmost x value.)
2. Then, if we have two such scales f(x) and g(x) that can slide relative to each other, we can compute functions of the form h(x, y, z) = f_inverse(f(x) + g(y) - g(z)).
It ends up being surprisingly versatile -- the above resources show how you can compute:
1. Multiplication: x * y using f(x) = log(x) and g(y) = log(y), with z fixed at 1
2. Hypotenuse: sqrt(x^2 + y^2) using f(x) = x^2 and g(y) = y^2, with z fixed at 0
3. Parallel resistors: 1/(1/x + 1/y) using f(x) = 1/x and g(y) = 1/y, with z fixed at +infinity
4. Exponentiation: x^(y/z) using f(x) = log(log(x)) and g(y) = log(y)
My Dad is a retired R&D chemist who worked at the DuPont corporation's Experimental Station. When I was a kid he would bring his old slide rules home from work when he got a new one, and at one point he explained to me how they work but I forgot it all long ago.
I still have the slide rules, so this post was a great rabbit hole to go down. In software there's no need for them but I still find them fascinating as a window into how engineers used to get their work done.
... but in the Real World they work pretty well for the sort of calculations you might need to do in the field (literally, in a field, sometimes) and don't require batteries, are reasonably waterproof, and reasonably robust if dropped.
Deep dive, for sure. I suspect Cliff Stoll is enjoying this site.
I played with creating a logarithmic slider thing [1] in Javascript that I hoped I could package up as a kind of "widget" people could use on their web pages. But I don't really know Javascript that well—or rather how to make an API out of a Javascript thing.
Anyway, to test it I tried to make an Ohm's Law calculator [2].
I would love to see a site like the one in this post have some kind of interactive slide rule on the web page itself.
It works well enough to get the idea of "set the voltage, set the resistance, read the current off the voltage scale above the 1 on the resistance scale". It might be a little easier to do if the rules were closer, which would probably require a little noodling about with the code to make the "resistance" box sit below the rule scale.
I have one at home, which is the one we had to buy to use in highschool. In the math classrooms we had a 6 feet version that could be mounted on the blackboard such that the teacher could used for instruction. See for a picture on the Dutch page https://rekenlat.barneveld.com/rekenliniaal.htm
While I'm a bit too young to have used one in school, my dad did give me his slide rule from when he was a student. It's one of my most prized possessions, if only to show how far humanity has come in terms of computing devices.
Slide rules are super cool. Such an easy gift to give the engineer in your life.
I never spent the time to get quick with it, but I could absolutely see it being quicker than a calculator. You’d just have to be aware of the limits to its precision if you were in a field that required it.
You still have to be aware of the difference between precision and accuracy, and how to propagate precision through calculations to maintain accuracy. It's a forgotten skill that lets us now create data out of whole cloth and call it actionable information but back when slide rules and log tables ruled the day the difference was stressed over and over in math and science classes and you would fail an assignment or a test question if you had the wrong precision in a result.
We have speed electronic calculators now instead of slide rules, but they give a wronger answer and people aren't even aware of it or know why.
Quicker than an algebraic calculator, maybe, but very few people could get. faster with a slide rule than an ergonomic RPN calculator. like the HP 41 series. And I say that as an enthusiastic and experienced slide rule user, before I switched to a calculator.
One problem with a slide rule is that it only performs operations on normalized mantissas. You have to keep a parallel exponent calculation in your head, and that slows you down. Also, maintaining best precision slows you down.
When using a slide rule, keeping track of the number of digits to the left of the decimal point (DLDP) in the result is fairly simple if you know the basic rule:
For multiplication, the DLDP in the result is:
- the sum of the DLDPs of the multiplicands MINUS 1 if the multiplication is done with the slide sticking out to the right of the ruler's body (for example 2.0 x 3.0 = 6.0).
- the sum of the DLDPs of the multiplicands if the multiplication is done with the slide sticking out to the left of the ruler's body (for example 5.0 x 4.0 = 20.0).
There's a similar rule for division, but that's left as an exercise for the student.
I used an HP-41CV for many years. I needed the financial calcs module which I used in place of the dedicated HP financial calculator in grad school. Eventually gav out on me but was a good calculator for a long time.
I did keep a slide rule as a backup for exams in college when calculators were still LED but never really used one after a couple of years in high school.
Last week I donated several slide rules to Goodwill; a few were very nice. Meanwhile, I still have a pristine HP-41cx and HP-15c, and an HP-25 app on my iPhone.
I have an HP-15c as well as a 16c and I've been using the latter on a daily basis while writing a byte-level network protocol client. I'm getting faster by the day and on the verge of writing some programs for shortcuts on the calculator. I still use the excellent PCalc as well, but seem to be faster on the physical calculator, which is kind of surprising.
A sort of non-logarithmic slide rule, the E6B Flight Computer, was still in use when I was a student pilot 20 years ago. I still carry one: they don't require electricity (although using one in the dark requires a light source).
When the "cloud" is raining and your laptop and phone batteries are drained and you suddenly need to navigate your 4823 times table - its got you covered.
You will also need to work out how to write with a pen or pencil on paper or try and fix up your atrophied ability to remember arbitrary "facts" short term.
Honestly the scenarios where this becomes likely are dwindling with the advent of solar and batteries. Offline knowledgebases and the ability to use them long term are getting increasingly stable, and the likely low point in a societal collapse is probably getting high enough that a slide rule would not be necessary.
I have a Casio fx-991ES calculator, and twenty years later I have yet to need to replace the button cell in it thanks to the tiny solar cell.
I still have the wooden 10" Keuffel and Esser that I inherited from my father and that I used in college. These days I use my HP15C unless I want to provoke glee and amusement in my younger colleagues by sporting my Pickett slide rule in my shirt pocket.
For the past 10 years, I've worn a slide rule every day. It's a small circular one modeled after the E6B aviation slide rule, with markers for common aviation conversions.
In the UK there was a time (late `70s) when slide-rules were allowed in examinations but calculators weren't, no-brainer to learn how to use one just for that. Even better, if you added "(SR)" after your calculations, that indicated that you had used a slide-rule so small errors were permitted.
This education film from 1957 gives a good overview of using one:
* https://www.youtube.com/watch?v=oYQdKbQ-sgM
"Professor Herning" (?) also has a good series of videos on the use of various scales as well:
* https://www.youtube.com/@ProfessorHerning/videos
His playlist starting at the beginning (C and D scales) with a Manheim layout:
* https://www.youtube.com/playlist?list=PL_qcL_RF-ZyvWJJkJOk_O...
* https://sliderulemuseum.com/Manuals/M37_Post_Manheim_Instruc...
Some manuals / books on slide rules:
* 1909: https://archive.org/details/mannheimsliderul00coxwrich
* 1922: https://archive.org/details/cu31924002978561/mode/2up
To add to this, there's a great set of resources by Joe Pasquale explaining the mathematical theory behind how various functions can be computed by slide rules:
* https://cseweb.ucsd.edu/~pasquale/Classes/SlideRule/
* Mathematical Foundations of the Slide Rule (PDF): https://cseweb.ucsd.edu/~pasquale/Papers/IM11.pdf
* Why Does A Slide Rule Work? (PDF): https://cseweb.ucsd.edu/~pasquale/SlideRuleTalkLasVegas14.pd...
The gist of it is:
1. First, define a way to represent any univariate monotonic function f(x) on a graduated scale. (Specifically: select a discrete set of x values, and for each of these x values, place a mark with label x at a distance proportional to (f(x) - f(x_L)) from the left endpoint, where x_L is the leftmost x value.)
2. Then, if we have two such scales f(x) and g(x) that can slide relative to each other, we can compute functions of the form h(x, y, z) = f_inverse(f(x) + g(y) - g(z)).
It ends up being surprisingly versatile -- the above resources show how you can compute:
1. Multiplication: x * y using f(x) = log(x) and g(y) = log(y), with z fixed at 1
2. Hypotenuse: sqrt(x^2 + y^2) using f(x) = x^2 and g(y) = y^2, with z fixed at 0
3. Parallel resistors: 1/(1/x + 1/y) using f(x) = 1/x and g(y) = 1/y, with z fixed at +infinity
4. Exponentiation: x^(y/z) using f(x) = log(log(x)) and g(y) = log(y)
My Dad is a retired R&D chemist who worked at the DuPont corporation's Experimental Station. When I was a kid he would bring his old slide rules home from work when he got a new one, and at one point he explained to me how they work but I forgot it all long ago.
I still have the slide rules, so this post was a great rabbit hole to go down. In software there's no need for them but I still find them fascinating as a window into how engineers used to get their work done.
> In software there's no need for them...
... but in the Real World they work pretty well for the sort of calculations you might need to do in the field (literally, in a field, sometimes) and don't require batteries, are reasonably waterproof, and reasonably robust if dropped.
Here one can play with many slide rules in the browser https://www.sliderulemuseum.com/VirtualSR.shtml
For people into watches, check out this video (and the whole series of watch and learn) on slide rules on watches: https://www.youtube.com/watch?v=RuK_77DEUfw
Deep dive, for sure. I suspect Cliff Stoll is enjoying this site.
I played with creating a logarithmic slider thing [1] in Javascript that I hoped I could package up as a kind of "widget" people could use on their web pages. But I don't really know Javascript that well—or rather how to make an API out of a Javascript thing.
Anyway, to test it I tried to make an Ohm's Law calculator [2].
I would love to see a site like the one in this post have some kind of interactive slide rule on the web page itself.
[1] https://github.com/EngineersNeedArt/SlideRule
[2] https://www.engineersneedart.com/ohmslaw/index.html (the yellow slider is not directly user-moveable in this example)
It works well enough to get the idea of "set the voltage, set the resistance, read the current off the voltage scale above the 1 on the resistance scale". It might be a little easier to do if the rules were closer, which would probably require a little noodling about with the code to make the "resistance" box sit below the rule scale.
In my head: “Oh yeah, I forgot how to use one of those”
This article: “lol, is that the depth of your commitment”
I have one at home, which is the one we had to buy to use in highschool. In the math classrooms we had a 6 feet version that could be mounted on the blackboard such that the teacher could used for instruction. See for a picture on the Dutch page https://rekenlat.barneveld.com/rekenliniaal.htm
Wow that's fascinating! Crazy how things change, no wonder my grandma thinks math is black magic!
These TMSLs were also reasonably common in classrooms in the United States in the 1950s.
Two Meter Slide Rule
While I'm a bit too young to have used one in school, my dad did give me his slide rule from when he was a student. It's one of my most prized possessions, if only to show how far humanity has come in terms of computing devices.
Slide rules are super cool. Such an easy gift to give the engineer in your life.
I never spent the time to get quick with it, but I could absolutely see it being quicker than a calculator. You’d just have to be aware of the limits to its precision if you were in a field that required it.
You still have to be aware of the difference between precision and accuracy, and how to propagate precision through calculations to maintain accuracy. It's a forgotten skill that lets us now create data out of whole cloth and call it actionable information but back when slide rules and log tables ruled the day the difference was stressed over and over in math and science classes and you would fail an assignment or a test question if you had the wrong precision in a result.
We have speed electronic calculators now instead of slide rules, but they give a wronger answer and people aren't even aware of it or know why.
Quicker than an algebraic calculator, maybe, but very few people could get. faster with a slide rule than an ergonomic RPN calculator. like the HP 41 series. And I say that as an enthusiastic and experienced slide rule user, before I switched to a calculator.
One problem with a slide rule is that it only performs operations on normalized mantissas. You have to keep a parallel exponent calculation in your head, and that slows you down. Also, maintaining best precision slows you down.
When using a slide rule, keeping track of the number of digits to the left of the decimal point (DLDP) in the result is fairly simple if you know the basic rule:
For multiplication, the DLDP in the result is:
- the sum of the DLDPs of the multiplicands MINUS 1 if the multiplication is done with the slide sticking out to the right of the ruler's body (for example 2.0 x 3.0 = 6.0).
- the sum of the DLDPs of the multiplicands if the multiplication is done with the slide sticking out to the left of the ruler's body (for example 5.0 x 4.0 = 20.0).
There's a similar rule for division, but that's left as an exercise for the student.
I used an HP-41CV for many years. I needed the financial calcs module which I used in place of the dedicated HP financial calculator in grad school. Eventually gav out on me but was a good calculator for a long time.
I did keep a slide rule as a backup for exams in college when calculators were still LED but never really used one after a couple of years in high school.
Last week I donated several slide rules to Goodwill; a few were very nice. Meanwhile, I still have a pristine HP-41cx and HP-15c, and an HP-25 app on my iPhone.
I have an HP-15c as well as a 16c and I've been using the latter on a daily basis while writing a byte-level network protocol client. I'm getting faster by the day and on the verge of writing some programs for shortcuts on the calculator. I still use the excellent PCalc as well, but seem to be faster on the physical calculator, which is kind of surprising.
A sort of non-logarithmic slide rule, the E6B Flight Computer, was still in use when I was a student pilot 20 years ago. I still carry one: they don't require electricity (although using one in the dark requires a light source).
https://en.wikipedia.org/wiki/E6B
The main part of the E6B is a very standard logarithmic slide rule. Having it loop unto itself is a neat trick but very ancient.
But perhaps you were referring to one of the many other parts of the E6B which I am not familiar with.
I have a little collection of them. I keep the small Hemmi bamboo on the navigation table at all time.
https://wiki.xxiivv.com/site/slide_rule
It is worth keeping one around.
When the "cloud" is raining and your laptop and phone batteries are drained and you suddenly need to navigate your 4823 times table - its got you covered.
You will also need to work out how to write with a pen or pencil on paper or try and fix up your atrophied ability to remember arbitrary "facts" short term.
Honestly the scenarios where this becomes likely are dwindling with the advent of solar and batteries. Offline knowledgebases and the ability to use them long term are getting increasingly stable, and the likely low point in a societal collapse is probably getting high enough that a slide rule would not be necessary.
I have a Casio fx-991ES calculator, and twenty years later I have yet to need to replace the button cell in it thanks to the tiny solar cell.
I still have the wooden 10" Keuffel and Esser that I inherited from my father and that I used in college. These days I use my HP15C unless I want to provoke glee and amusement in my younger colleagues by sporting my Pickett slide rule in my shirt pocket.
K&E's are classic. What do you think was the most popular Pickett model?
For the past 10 years, I've worn a slide rule every day. It's a small circular one modeled after the E6B aviation slide rule, with markers for common aviation conversions.
The HP-35 wasn’t programmable- it was just a scientific calculator.
This would have been helpful for Sam Cooke.