I designed and 3D-printed my own slide rule to help me play Balatro!
Balatro is a roguelike survival game where you need to multiply "chips" and "mult" together to meet a requirement each round. You get three chances to draft enough resources to survive. I designed my own slide rule to help with the mental multiplication - most of the fun of the game comes from the mechanics being slightly obscured from the player.
Since I designed this slide rule myself, I was able to make a couple unconventional design choices that fit my needs. For instance, mine has three octaves so it can represent numbers within the ones, thousands, or millions' range, for example; no need to track arbitrary powers of ten. Since it's a rotary rule, it wraps around. Eg. 353×24 shows on the device as 8.47, so you can think of it as 8.47 thousand, for example.
Holding a physical object in my hands while playing helps more than I thought it would. Should I take a card that increases chips by 600 or increases mult by 1.3×? Do I need to take a card to clear the blind in the short term, or do I have enough resources to draft a slower card that will scale better over time? Even just looking at how densely packed the marks are on the "Chips" side vs the "Mult" side of the device gives a visceral physical sense of what my build needs to focus on.
I do not use, and have never used, a slide rule. My grandfather was an aeronautical engineering / materials scientist for McDonnell Aircraft, and did a lot of foundational work on heat shields for early space flight (or so I am told). He was eventually named a McDonnell Douglas Fellow, back when there were fewer than 15 Fellows - the company, at the time, took out a full-page ad in Aerospace Magazine announcing it.
I have his slide rule, that he used for ages. It's a mystery in a box to me - I have not the foggiest clue how it is used - but I cherish it.
> I have not the foggiest clue how it is used - but I cherish it.
It's easier and more straightforward than you might expect. I encourage you to learn to use his slide rule, in large part because you might find it fun, but also to honor your grandfather's legacy.
I agree. In fact you should make a (YouTube?) video showing the slide rule and how to use it and your grandfather’s history to preserve this bit of history for your family and family’s future descendants.
A key idea is that addition for logs is equivalent to multiplication. To multiply two numbers you line them up on a log scale and then read out the sum, which is equivalent to the product. There is much more they can do but that was one aha moment when my dad showed me his.
I've never used a slide rule but recently developed an interest in them (and also in nomograms [1])
My fascination stems from a belief: that slide rule usage helps users develop a certain intuition for numbers whereas the calculator doesn't. To illustrate, suppose someone tries to multiply 123 and 987 with a calculator but incorrectly punches in 123 and 187. My hypothesis is they'll look at the result but won't suspect any problem. The equivalent operation on a slide rule requires fewer physical actions and hence, is less error prone.
Nomograms are cool. They're little charts that let you compute a function physically, e.g. by lining up a ruler. A nomogram isn't a picture of a function: it is the function. If you're clever, you can make a nomogram that encodes complicated nonlinear mappings or even complex-valued relationships on a 2D plane.
Occasionally nomograms are just better too: because they're continuous and analog, they can naturally express things digital logic people can do only awkwardly, just like Rust people can only awkward approximate things natural in Verilog (e.g. truly parallel CAM search).
Nomograms are basically the tabletop gaming of math. Like a good tabletop game, a good nomogram requires a special kind of cleverness. Sure, coding something like Factorio is also hard: but it runs on a CPU. Something as rich and complex as Power Grid and High Frontier? Running on cardboard? Whole other level.
I recall one tabletop two-player game that featured a single-player mode in which you played against an "AI" that you ran by hand by moving cardboard pieces around on a game-provided template under pseudocode-ish rules from the game manual. It's hard enough to code a decent game AI with all the resources of a CPU at your disposal. It's an OOM harder to do it when you're limited to physically-realized lookup tables, a literal handful of registers, and a scant few clock cycles of logic per turn.
Coming full circle, some of these tabletop game "AI"s incorporate nomograms to help them fit their logic within the constraints.
Example of a cool nomogram: https://en.wikipedia.org/wiki/Smith_chart. Smith charts let you compute complex (pun intended) relationships in RF signal processing with just a compass and straightedge.
Also: part of the fun in making nomograms is that there's no general procedure you can follow to make a good one, just like there's no general compiler from computer game to tabletop game. They're art: specifically, one of those forms of art that, like architecture, has to meet functional requirements while tickling our aesthetic sense. It's kind of funny how when you optimize this kind of art for aesthetics under their functional constraints, you end up supercharging the functional part by side effect somehow.
With a slide rule you always have to estimate the expected answer in your head before you begin any calculation. So you develop a feel for how quantities scale with multiplication.
With a slide rule you can only multiply the significant digits, not the magnitudes -- which you have to do in your head. So you do exactly the same thing with the slide rule to multiply 123 and 987, 1.23 and 9.87, and 1,230 and 9,870. In all three cases, you get exactly the same answer: 121 or maybe just 120 (you only get 3 digits of precision at best). You still have to multiply the powers of ten in your head, to get the answers 121,000, 12.1, and 12,100,000.
I am just old enough to belong to the last generation of slide rule users. I used them in high school and college, then scientific calculators came along.
You don't have to multiply the powers of ten in your head. In your examples, the slider of the slide rule must be moved to the left of the body of the rule. This means the number of digits left of the decimal point in the answer is the sum of the number of digits left of the decimal point in the two multiplicands.
If the slider had been to the right of the body, the number of digits left of the decimal point in the answer is the sum of the number of digits left of the decimal point in the two multiplicands MINUS 1.
.
Yes. I don't recall doing this, though. Maybe because in scientific and engineering calculations we often worked in scientific notation so 'digits to the left of the decimal point' wasn't meaningful - we had to keep track of the exponents.
It's not the number of actions, it's because the slide rule is analog and physical. The smaller numbers are to the left, the larger to the right, and you have to slide the rule to the first number, then the hairline cursor to the second number. There's no way you could mix up a large number like 987 with a small number like 187.
Exactly. Using a slide rule shows how some complex operations in one domain can be made much easier in another.
One you understand slide rules and logarithms, it is easier to understand convolutions in the FFT (frequency) domain...
Almost like programming in APL, where you can solve a problem by expanding it in extra dimensions and getting the answer by re-compacting the complex object using a different view.
I had a similar experience! My grandfather worked at a paper company for years and years as a chemical engineer. He was a hot head, but lightened up as I got older. We started to connect well later in life because I was the only other "engineering type" in my family.
He gave me his slide rule probably a year or so before he passed away. I've got it sitting on my desk and always makes me think of him. Like you, I've got no idea how to use it (even though he tried to explain it to me), so maybe the other comments here can fill in the gaps for me :)
My grandfather was a computational meteorologist for the US Air Force who passed when I was a kid. I inherited both his slide rule and his laptop (a 486dx with a math coprocessor!) It felt cool being the only kid at the school with a laptop, but the slide rule languished in a box under my bed until I got it out and figured out how to work it in college. I wish I'd figured it out sooner because it gave a more visceral understanding of the mathematical relationships that I'd been lacking before. Granted, the slide rule has sat mostly idle since then, but it was definitely worth it. I'd encourage you to give it a go.
Me too! My grandfather worked in construction among other things and gave me his slide rule some years before he died. He showed me how to use it but I don't remember (though what he gave me came with instructions).
A big 6-foot K&E sliderule hung at the front of my high-school chemistry classroom, but was never used. At graduation ('91) I asked the teacher if I could have the slide rule and she said "sure".
I keep it now in my office, and once a year I bring to the data visualization class I teach at UChicago, to show how it works, and to show it as an example of a visual device in aid of computational thinking (nomographs being another great example).
I love the Vernier scales! But I honestly hadn't known about the sense in which slide rules have a Venier scale until your comment, which led me to [1]. In another class on laser-cutting I had students make a kerf-meter, which became more accurate with a Vernier scale.
I have one on my watch. It’s a citizen with a circular slide rule /E6B flight computer. I need my reading glasses to use it, but it’s fun.
It can reliably get me 2 sig figs, and a decent guess at a third. But… if I think about it for a minute, I can usually get that in my head anyway. Being able to setup a ratio is great though for unit conversions and things.
It’s also really good for answering that question when driving where you’re like, ok if I go 10mph faster how much sooner will I get there which is otherwise hard to do mentally.
Most of the benefit of using a slide rule in my experience comes not from using it, but from thinking LIKE you’re going to use a slide rule. You learn to freely use scientific notation with ease, and mental estimation to get the order of magnitude right.
And just my 2 cents, but circular slide rules are where it’s at.
I used them in high school in the late 1990s... just to get an extra challenge. I had my dad's and grandfather's and I picked up a couple at garage sales. I still have a collection, but haven't really used them in years. I'll probably break them out again when my kids get in middle school / high school math for fun. They are great for learning the rules of logs.
Knew a mechanical engineer at a place where I interned. Asked him about it and he joked that he didn't trust those transistors before explaining that it's just muscle memory to him and while a calculator would be faster he'd still earn the same per hour. Apparently I was the first to ask him in over a decade as everyone had moved on to do stuff in software and no one was pushing him to use a calculator anymore. Interns didn't inquire because they thought it must be some esoteric/religious practice. Last I heard he was still working there, management asked him to stay on past retirement age for his invaluable skillset. While its probably some other skill I just like to imagine the suits in a meeting where they decided to keep him on for this particular "skill" that no one else in the company had anymore.
Although slide rules are a "dead skill," Aviators typically learn to use something called an E6B Flight Computer, which works on the same principle as a round slide rule.
I have one in my flight bag and was required to demonstrate proficiency in its use. Of course we fly with connected digital devices these days, but having an analogue backup that operates even if the power fails is important.
I have a couple of EB6s to show to my students but ever since scientific calculators were allowed in written tests, I have never used one myself. Law of cosines is good enough for wind triangles :). Worked for a commercial test as well as the ATP. It is a beautiful device though ...
Similar point applies to being able to use a sextant for celestial navigation in bluewater sailing. GPS is great, until you lose power or your equipment malfunctions. Of course, you can have double or triple redundancy to make such cases vanishingly rare, but still — it’s nice to have a backup that relies on nothing outside your control.
Some of it is pure nostalgia, though, I’ll admit. It a way to honor how people solved similar problems in the past. In the 18th century a sextant plus accurate chronometer or lunar distance table was one of the pivotal technologies of the age; you could use it to pinpoint your location on the boundless ocean within a few miles. That demands respect, and it’s also just really cool it was possible in an era before electricity and radio.
> Some of it is pure nostalgia, though, I’ll admit. It a way to honor how people solved similar problems in the past. In the 18th century a sextant plus accurate chronometer or lunar distance table was one of the pivotal technologies of the age; you could use it to pinpoint your location on the boundless ocean within a few miles. That demands respect, and it’s also just really cool it was possible in an era before electricity and radio.
Heh heh, I was in the Sailing Cub in high school, and our Sailing Master (RIP Master Gibb) said literally the same thing about learning to navigate with sextant and chronometer even though we never sailed out of sight of land. It was all about deep respect for the history and tradition of being a Mariner.
Now I fly gliders, "the purest form of flight," and while you can get a glider with electrically operated landing gear, a jet sustainer engine, and digital navigation and flight computing devices...
There is something extraordinarily pure about the exercise of flying with everything electrical turned off (except for the transponder and radio for safety). And even purer... Flying with covered instruments so we don't even get analogue airspeed and altitude.
Circling back to slide rules... Sometimes we crave that simplicity, that direct experience of a thing.
I used a calculator throughout college; they had just become relatively affordable. But I still generally brought a slide rule to exams in case something happened to my calculator. (They were LED displays and things weren't as generally reliable at that time.)
Somewhere around here, I have a Proportion Calculator wheel which I used for determining the size/scaling of graphics --- I was the only person in the shop who could use it though, everyone else used calculators or once I showed them how, did math in the size field of the applications such as Freehand/MX which allowed math.
When I was in high school, (early 1990s,) there was a giant one mounted above the blackboard. It was clearly used for instruction in the past, but it looked so cool that no one wanted to remove it.
Every once in awhile a teacher would spend about 10-15 minutes showing how to use it. Everyone would "oooh" and "awww" and then we would all laugh about how we didn't need to use them now that we all had calculators in our pocket that were more powerful than the computers that put people on the moon.
It's always nice to learn about the past so we can appreciate what we have now.
I was issued one at King's Point Merchant Marine Academy in 1957 and used it constantly. A side benefit was the learned ability to estimate an answer and decimal point a skill which I still use. As I recall I mostly used multiplication, division, logs, and trig. I think I quit using it when I purchased a HP scientific calculator years later.
My mom found my shellback card among some stuff in her basement and asked if I’d like her to send it to me. Yes, please! Darned if I want to earn a replacement card.
I have two or three that I inherited from my dad. I've never learned to use them because I haven't thought of something I'd use them for. The one thing I could think of is quickly doing fractional math while woodworking (what width will I have if I rip this 7.5" board into 4 pieces?) but in reality I just don't actually do that much math while woodworking.
As mentioned elsewhere you can use them in the kitchen if you start wanting to scale recipes at will - it's easy to double, but with a slide rule you can quickly get other ratios.
Works better when you do things by weight and metrically, no doubt.
I used a circular slide rule when I first started flight training. It was used in flight planing to calculate ground speed and a few other things. You can still buy one.
Back in 1969 I had a summer job in the engineering department of a factory. The Chief Engineer was an old guy who was a slide rule artist. He taught me how to solve second degree equations (ax^2 + bx + c = 0) with just a slide rule. The standard formula that I had learned in high school includes adding and subtracting, which a slide rule cannot do. His method involved pulling out the slider of the slide rule and inserting it backwards. Then, through some clever manipulation using the D and B scales (which now faced each other) and the A and C scales, he could actually solve the equation with just the slide rule. I wish I could remember exactly how it was done.
We learned to use them in high school (in Canada) in the mid-late '70s. Electronic calculators were just becoming widespread, and not everyone had them.
I think I can do basic calculations with them, although I really haven't touched one in many years.
I just did so yesterday. I was discussing with the ophthalmologist how to estimate when a very opaque bottle of eye drops was near-empty. (I find this user-hostile)
I've been weighing the bottle on a kitchen scale, and the tare weight is 8 grams, (from the previous bottle) while a full bottle is 23 grams, (from the next bottle) agreeing with the 15 gram (milliliter) stated contents. Assume density of 1.0 g/ml.
So, the fun part was estimating the droplet volume. From the measured rate of decline (7 grams in 40 days) the drop size was 45 microliters. (4 drops per day) Easy slide rule math, but the important thing is that the slide rule requires you to understand orders of magnitude (we had a whole bunch of lessons on this in high school) and units.
I have some from my father, but even though he showed me how to use them a long time ago, I never actually used them. I do however encourage anyone with an interest to go to the Arithmeum in Bonn (Germany) if you have the chance. It houses an large collection of regular and specialized sliderules as well as other (mechanical) computational devices.
I have a kitchen slide rule that I use to scale recipes and do simple conversions. I used it last week when inflating a ball that had a target diameter in centimeters, but measuring the circumference was much easier and my measuring tape was in inches.
Yep. I have one and I keep showing off how to do math using it, to kids.I have also replaced the broken slider with a plastic piece after etching the log scale onto it.
The physics prof who gave me my start would always get this kind of fond, nostalgic look in his eye whenever anyone mentioned "the days of punch card programming". So, naturally, I took an old slide rule and mounted it in a shadowbox with lettering that said "IN CASE OF EMERGENCY BREAK GLASS" when I got ready to graduate. He got a tremendous kick out of it.
I have a little collection of slide rules. I love those things.
I'm not old enough to have used them to do calculations, but I find them extremely useful to explain logarithms and how multiplication can be represented by the sum of logarithms. I actually work with grad students who should know these things, but watching it in a slide rule on their hands really helps to build intuition.
Now that's a properly dead skill, surely. I have my dad's one somewhere, and know roughly how it works, but I've not touched it this century.
I also have one of these: https://archive.org/details/spencersdecimalr0000unse ; I believe they were popular around the time of the UK converting to decimal currency, to save people having to do the transitional arithmetic. Had a bunch of other tables in. A physical LUT.
I wonder if there's anyone with abacus skills here. I hear that held out against calculators a lot longer, for shopkeeper uses.
I've picked it back up as an intentional way of slowing myself down during calculations.
Typically to do a calc I fire up Excel or the calc on my phone, bang in the numbers and accept the result without thinking. It's that "without thinking" part that is dangerous. The slide rule is slow and physical and forces my brain to think about the inputs. Another nice feature is that it can give you quick answers when you aren't sure of the accuracy of the inputs. eg if 2 * 4 was really 1.8*4.1, what would the answer be? It's quicker to see that on a slide rule (one tap on the ruler) than punch in 7 characters.
I have one as a watch bezel that I use in a pinch. Anything you need to scale, divide, or multiply in the real word doesn't need more than 2 significant digits of precision so it works. For example, I've used it to calculate how many grams of coffee will give me a 1:16 to the amount of water/coffee I want.
Following a post on HN a few weeks ago, I bought a used one to use in the kitchen for scaling recipes. It has to be a linear one for that, not circular, so you can set it and read it without touching it again. I also have one in my "apocalypse kit" in case of, I dunno, an EMP?
My dad was an engineer in the slide rule era and taught me how to use one when I was a kid. He said when he was in college all the engineering students had them hanging from their belts in leather sheaths like gladiator swords and they would slap when they walked.
When I was in high school, calculators had just hit the scene. Some teachers allowed them, others didn't.
One of our teachers allowed us to bring a single page of notes to the exam. I wrote my notes on a photocopy of a slide rule. At exam time, I tore the sheet in half.
Of course the teacher thought I was being a smart-ass, and given that the tests were written when calculators were not allowed, they were never really all that useful.
In college chemistry, at each exam, they handed out a sheet that had the periodic table on one side, and a table of logarithms on the other.
I used a slide rule for some of my high school physics tests in the 2010s, just for fun. I lost a few points from messing up order of magnitude calculations, but it was totally worth it. I've since collected a few more slide rules from estate sales in my neighborhood. I wish more people knew about them—they're such a neat and elegant part of engineering history, which is why I keep them around.
I have no use for them on a day-to-day basis, though. An abacus is more useful for things like counting board game points and adding up taxes.
I inherited and know how to use a couple slide rules, including a spiral one that’s 46 feet long (1). But if I need to actually calculate something, I use a RPN calculator. Or Python.
Yes, I have a few, and I do use them from time to time. I keep one in my daily backpack along with an abacus; mostly just to surprise people when I don't pull out my phone to some more complex calculations that I can't easily do in my head.
The children's maths/puzzle book "Nut-Crackers" (John Jaworski and Ian Stewart, 1971) had a slide rule printed at the back of the book - two strips each numbered 1-50 - to cut out and try out.
The authors commented "If you get really interested you can make much more accurate slide rules, or you can buy them for about £1." I fear not any more...
I collect and use them. There are several on my desk right now. There's something about the immediacy that I find very appealing. They don't simply spit out an answer, they display entire relations, which I think is a beneficial intuition.
I don't use one "seriously", or even really know how to use one to be honest. But I did buy one last year, with the intention to learn to use it. Why? Novelty mostly, and just general intellectual curiosity. I haven't really had time to dig into working with it yet though. :-(
I found usage really helps you learn how to WAG (Wild Ass Guess).
It also scares the crap out of me to think about what infinity is: you see your slide manipulate incredible numbers, then you imagine a slide that is twice as big. Or a few feet long.
I have four now, and even go out of my way to use them a bit.
My favorites from my collection are a little Dietzgen No 1773, which is surprisingly featureful for something that can fit in a pocket, and a Faber-Castell Novo-Biplex 2/83N, which is kind of one of the big guns for slide rules.
I have half a dozen of them (including my father's from college) that I cherish, but do not use. I love the simplicity and elegance of the design. (Slide rules do a lot with operations that essentially boil down to addition, subtraction, and looking up function values in tables.)
I worked at a countertop shop and used a sliding rule a bit. But I also used a sticky paper with marks to get measurements off my screen. A lot of blueprints provide no dimensions for cabinets and desks.
Countertops is an industry with all the modern tools but 5000yo approach.
My grandfather taught me, I have long since forgotten. But I do recall that the killer use case was cube roots, which as opposed to multiplication or even square roots is difficult to do with pen and paper and much harder to mentally estimate.
Yes, but just as a ruler. It belonged to my Dad who was an avionics engineer starting back in the 1950s. He worked all over the world seeing out the end of the British Empire. It smells of old cigarettes and is very worn and chipped.
I built my own slide rule in school for fun! It looked pretty cool to me at the time. The template is still out there if you search something like "paper slide rule".
I've collected some links for building regular slide rules ([1] & [2]) as well as a circular slide rule [3]. Someone might also like the slide rule simulator [4].
I sort of did for a lark a few years ago, then promptly forgot how to since I could do reasonable math approximations in my head. But my father used his pretty effectively.
Yes, but only as a fun retro thing. Not for most calculations, although I have to say for back of the napkin, almost all in your head style things, they can be handy.
I bought one a few months ago off of ebay after I realized how important logarithms are in many different domains (including machine learning & information theory)
in spite of my age, I'm one of first digital native. I never used it and nobody explained me how to use. At same time I avoid most of analog instruments: multimeters, scope meters, calipers.
"The Analytical Rule might be considered a distant relation – as a skyscraper is to a shack – of that kindergarten toy, the logarithmic Slide Rule. Darell used it with the wristflip of long practice. He made freehand drawings of the result and, as Anthor stated, there were featureless plateaus in frontal lobe regions where strong swings should have been expected."
I'd really love an Analytical Rule, this hoverboard of the early atomic era.
I designed and 3D-printed my own slide rule to help me play Balatro!
Balatro is a roguelike survival game where you need to multiply "chips" and "mult" together to meet a requirement each round. You get three chances to draft enough resources to survive. I designed my own slide rule to help with the mental multiplication - most of the fun of the game comes from the mechanics being slightly obscured from the player.
Since I designed this slide rule myself, I was able to make a couple unconventional design choices that fit my needs. For instance, mine has three octaves so it can represent numbers within the ones, thousands, or millions' range, for example; no need to track arbitrary powers of ten. Since it's a rotary rule, it wraps around. Eg. 353×24 shows on the device as 8.47, so you can think of it as 8.47 thousand, for example.
Holding a physical object in my hands while playing helps more than I thought it would. Should I take a card that increases chips by 600 or increases mult by 1.3×? Do I need to take a card to clear the blind in the short term, or do I have enough resources to draft a slower card that will scale better over time? Even just looking at how densely packed the marks are on the "Chips" side vs the "Mult" side of the device gives a visceral physical sense of what my build needs to focus on.
Pictures and .STL: https://www.printables.com/model/1026662-jimbos-rotary-slide...
Github repository: https://github.com/gcr/balatro-slide-rule
The actual plotting code used Marimo notebooks, which host a python in your browser via WASM. Take a look here: https://marimo.app/l/4i15d7
I entered it in Printables’ educational tools competition but the other entries were cooler. Maybe HN might like it. :-)
As a bonus, multiplication and division can feel like operating a Stargate ;)
You almost have to do this, or buy a used one at a markup, as nobody seems to make them anymore (except circular ones).
Still available in Germany („Rechenschieber“), eg https://www.wissenladen.de/products/der-rechenschieber
Its really cool, appreciate the typeface choice.
"cool" is not an Absolute. i think it's extremely cool. like close to εK
How much did it help? How far have you ascended?
right, i'm still absolute rubbish at the game but it's been a great learning experience!
Wow, this is incredible.
I do not use, and have never used, a slide rule. My grandfather was an aeronautical engineering / materials scientist for McDonnell Aircraft, and did a lot of foundational work on heat shields for early space flight (or so I am told). He was eventually named a McDonnell Douglas Fellow, back when there were fewer than 15 Fellows - the company, at the time, took out a full-page ad in Aerospace Magazine announcing it.
I have his slide rule, that he used for ages. It's a mystery in a box to me - I have not the foggiest clue how it is used - but I cherish it.
> I have not the foggiest clue how it is used - but I cherish it.
It's easier and more straightforward than you might expect. I encourage you to learn to use his slide rule, in large part because you might find it fun, but also to honor your grandfather's legacy.
I agree. In fact you should make a (YouTube?) video showing the slide rule and how to use it and your grandfather’s history to preserve this bit of history for your family and family’s future descendants.
A key idea is that addition for logs is equivalent to multiplication. To multiply two numbers you line them up on a log scale and then read out the sum, which is equivalent to the product. There is much more they can do but that was one aha moment when my dad showed me his.
I've never used a slide rule but recently developed an interest in them (and also in nomograms [1])
My fascination stems from a belief: that slide rule usage helps users develop a certain intuition for numbers whereas the calculator doesn't. To illustrate, suppose someone tries to multiply 123 and 987 with a calculator but incorrectly punches in 123 and 187. My hypothesis is they'll look at the result but won't suspect any problem. The equivalent operation on a slide rule requires fewer physical actions and hence, is less error prone.
Do you think there's anything to this hypothesis?
[1] https://news.ycombinator.com/item?id=28690298
> nomograms
Me too!
Nomograms are cool. They're little charts that let you compute a function physically, e.g. by lining up a ruler. A nomogram isn't a picture of a function: it is the function. If you're clever, you can make a nomogram that encodes complicated nonlinear mappings or even complex-valued relationships on a 2D plane.
Occasionally nomograms are just better too: because they're continuous and analog, they can naturally express things digital logic people can do only awkwardly, just like Rust people can only awkward approximate things natural in Verilog (e.g. truly parallel CAM search).
Nomograms are basically the tabletop gaming of math. Like a good tabletop game, a good nomogram requires a special kind of cleverness. Sure, coding something like Factorio is also hard: but it runs on a CPU. Something as rich and complex as Power Grid and High Frontier? Running on cardboard? Whole other level.
I recall one tabletop two-player game that featured a single-player mode in which you played against an "AI" that you ran by hand by moving cardboard pieces around on a game-provided template under pseudocode-ish rules from the game manual. It's hard enough to code a decent game AI with all the resources of a CPU at your disposal. It's an OOM harder to do it when you're limited to physically-realized lookup tables, a literal handful of registers, and a scant few clock cycles of logic per turn.
Coming full circle, some of these tabletop game "AI"s incorporate nomograms to help them fit their logic within the constraints.
Example of a cool nomogram: https://en.wikipedia.org/wiki/Smith_chart. Smith charts let you compute complex (pun intended) relationships in RF signal processing with just a compass and straightedge.
Also: part of the fun in making nomograms is that there's no general procedure you can follow to make a good one, just like there's no general compiler from computer game to tabletop game. They're art: specifically, one of those forms of art that, like architecture, has to meet functional requirements while tickling our aesthetic sense. It's kind of funny how when you optimize this kind of art for aesthetics under their functional constraints, you end up supercharging the functional part by side effect somehow.
With a slide rule you always have to estimate the expected answer in your head before you begin any calculation. So you develop a feel for how quantities scale with multiplication.
With a slide rule you can only multiply the significant digits, not the magnitudes -- which you have to do in your head. So you do exactly the same thing with the slide rule to multiply 123 and 987, 1.23 and 9.87, and 1,230 and 9,870. In all three cases, you get exactly the same answer: 121 or maybe just 120 (you only get 3 digits of precision at best). You still have to multiply the powers of ten in your head, to get the answers 121,000, 12.1, and 12,100,000.
I am just old enough to belong to the last generation of slide rule users. I used them in high school and college, then scientific calculators came along.
You don't have to multiply the powers of ten in your head. In your examples, the slider of the slide rule must be moved to the left of the body of the rule. This means the number of digits left of the decimal point in the answer is the sum of the number of digits left of the decimal point in the two multiplicands.
If the slider had been to the right of the body, the number of digits left of the decimal point in the answer is the sum of the number of digits left of the decimal point in the two multiplicands MINUS 1. .
Yes. I don't recall doing this, though. Maybe because in scientific and engineering calculations we often worked in scientific notation so 'digits to the left of the decimal point' wasn't meaningful - we had to keep track of the exponents.
It's not the number of actions, it's because the slide rule is analog and physical. The smaller numbers are to the left, the larger to the right, and you have to slide the rule to the first number, then the hairline cursor to the second number. There's no way you could mix up a large number like 987 with a small number like 187.
Exactly. Using a slide rule shows how some complex operations in one domain can be made much easier in another.
One you understand slide rules and logarithms, it is easier to understand convolutions in the FFT (frequency) domain...
Almost like programming in APL, where you can solve a problem by expanding it in extra dimensions and getting the answer by re-compacting the complex object using a different view.
I had a similar experience! My grandfather worked at a paper company for years and years as a chemical engineer. He was a hot head, but lightened up as I got older. We started to connect well later in life because I was the only other "engineering type" in my family.
He gave me his slide rule probably a year or so before he passed away. I've got it sitting on my desk and always makes me think of him. Like you, I've got no idea how to use it (even though he tried to explain it to me), so maybe the other comments here can fill in the gaps for me :)
My grandfather was a computational meteorologist for the US Air Force who passed when I was a kid. I inherited both his slide rule and his laptop (a 486dx with a math coprocessor!) It felt cool being the only kid at the school with a laptop, but the slide rule languished in a box under my bed until I got it out and figured out how to work it in college. I wish I'd figured it out sooner because it gave a more visceral understanding of the mathematical relationships that I'd been lacking before. Granted, the slide rule has sat mostly idle since then, but it was definitely worth it. I'd encourage you to give it a go.
If you ever want to try using it, I recommend this page: http://www.goodmath.org/blog/2006/09/12/manual-calculation-u...
Me too! My grandfather worked in construction among other things and gave me his slide rule some years before he died. He showed me how to use it but I don't remember (though what he gave me came with instructions).
I too cherish it.
echoing others' suggestions to take it out and play with it a little !!
slide rules are happiest when they're used and worn out. they need exercise and sunlight
A big 6-foot K&E sliderule hung at the front of my high-school chemistry classroom, but was never used. At graduation ('91) I asked the teacher if I could have the slide rule and she said "sure".
I keep it now in my office, and once a year I bring to the data visualization class I teach at UChicago, to show how it works, and to show it as an example of a visual device in aid of computational thinking (nomographs being another great example).
There is also the Vernier scale on certain styles of mechanical calipers.
I love the Vernier scales! But I honestly hadn't known about the sense in which slide rules have a Venier scale until your comment, which led me to [1]. In another class on laser-cutting I had students make a kerf-meter, which became more accurate with a Vernier scale.
[1] https://dram.page/p/slide-rule-vernier/
Oh my God that is so clever. Thanks for sharing!
I have one on my watch. It’s a citizen with a circular slide rule /E6B flight computer. I need my reading glasses to use it, but it’s fun.
It can reliably get me 2 sig figs, and a decent guess at a third. But… if I think about it for a minute, I can usually get that in my head anyway. Being able to setup a ratio is great though for unit conversions and things.
It’s also really good for answering that question when driving where you’re like, ok if I go 10mph faster how much sooner will I get there which is otherwise hard to do mentally.
Most of the benefit of using a slide rule in my experience comes not from using it, but from thinking LIKE you’re going to use a slide rule. You learn to freely use scientific notation with ease, and mental estimation to get the order of magnitude right.
And just my 2 cents, but circular slide rules are where it’s at.
> " You learn to freely use scientific notation with ease, and mental estimation to get the order of magnitude right."
This is what I was trying to get at in my other comment [1]!
[1] https://news.ycombinator.com/item?id=46872141
I have one of these Citizens, it was my first "nice" watch.
They're really cool
I have a Rotary Henley Chronograph and love using it for baking ratios.
I used them in high school in the late 1990s... just to get an extra challenge. I had my dad's and grandfather's and I picked up a couple at garage sales. I still have a collection, but haven't really used them in years. I'll probably break them out again when my kids get in middle school / high school math for fun. They are great for learning the rules of logs.
Knew a mechanical engineer at a place where I interned. Asked him about it and he joked that he didn't trust those transistors before explaining that it's just muscle memory to him and while a calculator would be faster he'd still earn the same per hour. Apparently I was the first to ask him in over a decade as everyone had moved on to do stuff in software and no one was pushing him to use a calculator anymore. Interns didn't inquire because they thought it must be some esoteric/religious practice. Last I heard he was still working there, management asked him to stay on past retirement age for his invaluable skillset. While its probably some other skill I just like to imagine the suits in a meeting where they decided to keep him on for this particular "skill" that no one else in the company had anymore.
> while a calculator would be faster he'd still earn the same per hour.
This guy gets it.
I did a little nostalgia threat on Mastodon recently. The sixth picture is of the slide rule I took to High School in 1973.
https://social.bau-ha.us/@raganwald/115979168665997624
Although slide rules are a "dead skill," Aviators typically learn to use something called an E6B Flight Computer, which works on the same principle as a round slide rule.
https://pilotinstitute.com/e6b-made-easy/
I have one in my flight bag and was required to demonstrate proficiency in its use. Of course we fly with connected digital devices these days, but having an analogue backup that operates even if the power fails is important.
I splurged on the metal E6B for my private training: https://asa2fly.com/metal-e6b-flight-computer/
A beautiful device... though I have to admit after getting the certificate I exclusively use Foreflight.
I have a couple of EB6s to show to my students but ever since scientific calculators were allowed in written tests, I have never used one myself. Law of cosines is good enough for wind triangles :). Worked for a commercial test as well as the ATP. It is a beautiful device though ...
Similar point applies to being able to use a sextant for celestial navigation in bluewater sailing. GPS is great, until you lose power or your equipment malfunctions. Of course, you can have double or triple redundancy to make such cases vanishingly rare, but still — it’s nice to have a backup that relies on nothing outside your control.
Some of it is pure nostalgia, though, I’ll admit. It a way to honor how people solved similar problems in the past. In the 18th century a sextant plus accurate chronometer or lunar distance table was one of the pivotal technologies of the age; you could use it to pinpoint your location on the boundless ocean within a few miles. That demands respect, and it’s also just really cool it was possible in an era before electricity and radio.
> Some of it is pure nostalgia, though, I’ll admit. It a way to honor how people solved similar problems in the past. In the 18th century a sextant plus accurate chronometer or lunar distance table was one of the pivotal technologies of the age; you could use it to pinpoint your location on the boundless ocean within a few miles. That demands respect, and it’s also just really cool it was possible in an era before electricity and radio.
Heh heh, I was in the Sailing Cub in high school, and our Sailing Master (RIP Master Gibb) said literally the same thing about learning to navigate with sextant and chronometer even though we never sailed out of sight of land. It was all about deep respect for the history and tradition of being a Mariner.
Now I fly gliders, "the purest form of flight," and while you can get a glider with electrically operated landing gear, a jet sustainer engine, and digital navigation and flight computing devices...
There is something extraordinarily pure about the exercise of flying with everything electrical turned off (except for the transponder and radio for safety). And even purer... Flying with covered instruments so we don't even get analogue airspeed and altitude.
Circling back to slide rules... Sometimes we crave that simplicity, that direct experience of a thing.
I used a calculator throughout college; they had just become relatively affordable. But I still generally brought a slide rule to exams in case something happened to my calculator. (They were LED displays and things weren't as generally reliable at that time.)
Spock still uses one in the 23rd century.
https://www.youtube.com/watch?v=V1nKBrkPUeA&t=90s
"My eyes are dim, I cannot see. I have not brought my E6-B" -- submarines used a similar "Is/Was" circular slide rule for torpedoes. https://www.dreadnoughtproject.org/tfs/index.php/Is-Was
Somewhere around here, I have a Proportion Calculator wheel which I used for determining the size/scaling of graphics --- I was the only person in the shop who could use it though, everyone else used calculators or once I showed them how, did math in the size field of the applications such as Freehand/MX which allowed math.
When I was in high school, (early 1990s,) there was a giant one mounted above the blackboard. It was clearly used for instruction in the past, but it looked so cool that no one wanted to remove it.
Every once in awhile a teacher would spend about 10-15 minutes showing how to use it. Everyone would "oooh" and "awww" and then we would all laugh about how we didn't need to use them now that we all had calculators in our pocket that were more powerful than the computers that put people on the moon.
It's always nice to learn about the past so we can appreciate what we have now.
> we all had calculators in our pocket that were more powerful than the computers that put people on the moon.
Pencils and slide rules are what got us to the moon, and back to Earth. Pencils and slide rules.
Yes, but also very early microchips!
https://en.wikipedia.org/wiki/Apollo_Guidance_Computer
And “computers,” the people kind.
Seen yesterday on someone's blog
[You Need A Kitchen Slide Rule](https://entropicthoughts.com/kitchen-slide-rule)
I was issued one at King's Point Merchant Marine Academy in 1957 and used it constantly. A side benefit was the learned ability to estimate an answer and decimal point a skill which I still use. As I recall I mostly used multiplication, division, logs, and trig. I think I quit using it when I purchased a HP scientific calculator years later.
Re: your username
My mom found my shellback card among some stuff in her basement and asked if I’d like her to send it to me. Yes, please! Darned if I want to earn a replacement card.
Shwllback3 was my radio callsign in Vietnam in '67 & '68.
Nice. I got mine 4 miles off the coast of Mogadishu in '94.
I got mine on the way home from Australia in 1985.
Did you fly out and then sail home?
Nah, it was the tail end of a WESTPAC, we were on our way home from liberty in Perth. We skipped it on the way down.
Similar here! Except we got it going out on WESTPAC, not on our way home from Perth.
I have two or three that I inherited from my dad. I've never learned to use them because I haven't thought of something I'd use them for. The one thing I could think of is quickly doing fractional math while woodworking (what width will I have if I rip this 7.5" board into 4 pieces?) but in reality I just don't actually do that much math while woodworking.
As mentioned elsewhere you can use them in the kitchen if you start wanting to scale recipes at will - it's easy to double, but with a slide rule you can quickly get other ratios.
Works better when you do things by weight and metrically, no doubt.
(Raises aged hand sheepishly)
I have one on my desk that I often use for quick estimations. It boots up in zero seconds.
I used a circular slide rule when I first started flight training. It was used in flight planing to calculate ground speed and a few other things. You can still buy one.
https://en.wikipedia.org/wiki/E6B
Back in 1969 I had a summer job in the engineering department of a factory. The Chief Engineer was an old guy who was a slide rule artist. He taught me how to solve second degree equations (ax^2 + bx + c = 0) with just a slide rule. The standard formula that I had learned in high school includes adding and subtracting, which a slide rule cannot do. His method involved pulling out the slider of the slide rule and inserting it backwards. Then, through some clever manipulation using the D and B scales (which now faced each other) and the A and C scales, he could actually solve the equation with just the slide rule. I wish I could remember exactly how it was done.
I had a Keuffel & Esser slide rule, but it has long since disappeared. Check out some of the other stuff they made:
https://en.wikipedia.org/wiki/Keuffel_and_Esser
I still use one of mine on occasion. I would say 2-6 times a month.
We learned to use them in high school (in Canada) in the mid-late '70s. Electronic calculators were just becoming widespread, and not everyone had them.
I think I can do basic calculations with them, although I really haven't touched one in many years.
Yeah. Pickett N600-ES. Sometimes I will solve a problem with it just because I can. Keeps the mental model fresh. Mostly just use an HP 42s though.
I will note I didn't get it or use it until about 1998.
I just did so yesterday. I was discussing with the ophthalmologist how to estimate when a very opaque bottle of eye drops was near-empty. (I find this user-hostile)
I've been weighing the bottle on a kitchen scale, and the tare weight is 8 grams, (from the previous bottle) while a full bottle is 23 grams, (from the next bottle) agreeing with the 15 gram (milliliter) stated contents. Assume density of 1.0 g/ml.
So, the fun part was estimating the droplet volume. From the measured rate of decline (7 grams in 40 days) the drop size was 45 microliters. (4 drops per day) Easy slide rule math, but the important thing is that the slide rule requires you to understand orders of magnitude (we had a whole bunch of lessons on this in high school) and units.
The latter two are winners.
Internet lookup only to check results, of course.
Yes. Still use my E6B, no matter how much hate I get from other pilots.
I feel like it's actually a little faster than a digital computer. I don't have a lot of experience yet, though.
I have some from my father, but even though he showed me how to use them a long time ago, I never actually used them. I do however encourage anyone with an interest to go to the Arithmeum in Bonn (Germany) if you have the chance. It houses an large collection of regular and specialized sliderules as well as other (mechanical) computational devices.
https://www.arithmeum.uni-bonn.de/en/arithmeum.html
I have a kitchen slide rule that I use to scale recipes and do simple conversions. I used it last week when inflating a ball that had a target diameter in centimeters, but measuring the circumference was much easier and my measuring tape was in inches.
Yep. I have one and I keep showing off how to do math using it, to kids.I have also replaced the broken slider with a plastic piece after etching the log scale onto it.
The physics prof who gave me my start would always get this kind of fond, nostalgic look in his eye whenever anyone mentioned "the days of punch card programming". So, naturally, I took an old slide rule and mounted it in a shadowbox with lettering that said "IN CASE OF EMERGENCY BREAK GLASS" when I got ready to graduate. He got a tremendous kick out of it.
I have a little collection of slide rules. I love those things.
I'm not old enough to have used them to do calculations, but I find them extremely useful to explain logarithms and how multiplication can be represented by the sum of logarithms. I actually work with grad students who should know these things, but watching it in a slide rule on their hands really helps to build intuition.
I own my grandfather's slide rule, he was a master toolmaker for Rolls Royce (aerospace engines) in North London during WW2.
Now that's a properly dead skill, surely. I have my dad's one somewhere, and know roughly how it works, but I've not touched it this century.
I also have one of these: https://archive.org/details/spencersdecimalr0000unse ; I believe they were popular around the time of the UK converting to decimal currency, to save people having to do the transitional arithmetic. Had a bunch of other tables in. A physical LUT.
I wonder if there's anyone with abacus skills here. I hear that held out against calculators a lot longer, for shopkeeper uses.
I've picked it back up as an intentional way of slowing myself down during calculations.
Typically to do a calc I fire up Excel or the calc on my phone, bang in the numbers and accept the result without thinking. It's that "without thinking" part that is dangerous. The slide rule is slow and physical and forces my brain to think about the inputs. Another nice feature is that it can give you quick answers when you aren't sure of the accuracy of the inputs. eg if 2 * 4 was really 1.8*4.1, what would the answer be? It's quicker to see that on a slide rule (one tap on the ruler) than punch in 7 characters.
I have one as a watch bezel that I use in a pinch. Anything you need to scale, divide, or multiply in the real word doesn't need more than 2 significant digits of precision so it works. For example, I've used it to calculate how many grams of coffee will give me a 1:16 to the amount of water/coffee I want.
Following a post on HN a few weeks ago, I bought a used one to use in the kitchen for scaling recipes. It has to be a linear one for that, not circular, so you can set it and read it without touching it again. I also have one in my "apocalypse kit" in case of, I dunno, an EMP?
My dad was an engineer in the slide rule era and taught me how to use one when I was a kid. He said when he was in college all the engineering students had them hanging from their belts in leather sheaths like gladiator swords and they would slap when they walked.
When I was in high school, calculators had just hit the scene. Some teachers allowed them, others didn't.
One of our teachers allowed us to bring a single page of notes to the exam. I wrote my notes on a photocopy of a slide rule. At exam time, I tore the sheet in half.
Of course the teacher thought I was being a smart-ass, and given that the tests were written when calculators were not allowed, they were never really all that useful.
In college chemistry, at each exam, they handed out a sheet that had the periodic table on one side, and a table of logarithms on the other.
I used a slide rule for some of my high school physics tests in the 2010s, just for fun. I lost a few points from messing up order of magnitude calculations, but it was totally worth it. I've since collected a few more slide rules from estate sales in my neighborhood. I wish more people knew about them—they're such a neat and elegant part of engineering history, which is why I keep them around.
I have no use for them on a day-to-day basis, though. An abacus is more useful for things like counting board game points and adding up taxes.
You mean like this one:
https://www.flickr.com/photos/jonsphotos/218609214/
Funny you ask ... I lieterally just now pulled out one of my slide rules to keep track of the required run rate for a cricket T20 game.
Fastest and best feedback for whether the batting team is ahead of the rate.
Does it implement Duckworth-Lewis-Stern ;)
No, but a friend of mine made a nomogram to do that.
Yeah, to intimidate kids when they don't deliver academically :)
Related (60 comments, How slide rules work)
https://news.ycombinator.com/item?id=45985196
I inherited and know how to use a couple slide rules, including a spiral one that’s 46 feet long (1). But if I need to actually calculate something, I use a RPN calculator. Or Python.
(1) https://www.sliderulemuseum.com/Circular/Gilson_Atlas_Calcul...
Yes, I have a few, and I do use them from time to time. I keep one in my daily backpack along with an abacus; mostly just to surprise people when I don't pull out my phone to some more complex calculations that I can't easily do in my head.
The children's maths/puzzle book "Nut-Crackers" (John Jaworski and Ian Stewart, 1971) had a slide rule printed at the back of the book - two strips each numbered 1-50 - to cut out and try out.
The authors commented "If you get really interested you can make much more accurate slide rules, or you can buy them for about £1." I fear not any more...
I bought a vintage (pre-WW1) circular slide rule. But it's too much of an "artifact" to use - I'm afraid I'd damage it.
Naw. I used to, but it's so long ago, I'm not sure I could do it now if you put one in front of me. What you don't use atrophies.
I collect and use them. There are several on my desk right now. There's something about the immediacy that I find very appealing. They don't simply spit out an answer, they display entire relations, which I think is a beneficial intuition.
I don't use one "seriously", or even really know how to use one to be honest. But I did buy one last year, with the intention to learn to use it. Why? Novelty mostly, and just general intellectual curiosity. I haven't really had time to dig into working with it yet though. :-(
I found usage really helps you learn how to WAG (Wild Ass Guess).
It also scares the crap out of me to think about what infinity is: you see your slide manipulate incredible numbers, then you imagine a slide that is twice as big. Or a few feet long.
I have four now, and even go out of my way to use them a bit.
My favorites from my collection are a little Dietzgen No 1773, which is surprisingly featureful for something that can fit in a pocket, and a Faber-Castell Novo-Biplex 2/83N, which is kind of one of the big guns for slide rules.
What I _really_ want, now that I have the Faber-Castell, is a Curta.
https://en.wikipedia.org/wiki/Curta
I have half a dozen of them (including my father's from college) that I cherish, but do not use. I love the simplicity and elegance of the design. (Slide rules do a lot with operations that essentially boil down to addition, subtraction, and looking up function values in tables.)
I worked at a countertop shop and used a sliding rule a bit. But I also used a sticky paper with marks to get measurements off my screen. A lot of blueprints provide no dimensions for cabinets and desks.
Countertops is an industry with all the modern tools but 5000yo approach.
I've acquired one for curiosity (a relative used to teach engineering, he was thrilled I wanted one, gave me his own)
I used it a few times, it works, of course, ... but it's not fast and not precise so I don't think anybody would use it to be productive in 2026
It sits in a box
My grandfather taught me, I have long since forgotten. But I do recall that the killer use case was cube roots, which as opposed to multiplication or even square roots is difficult to do with pen and paper and much harder to mentally estimate.
Yes, but just as a ruler. It belonged to my Dad who was an avionics engineer starting back in the 1950s. He worked all over the world seeing out the end of the British Empire. It smells of old cigarettes and is very worn and chipped.
I built my own slide rule in school for fun! It looked pretty cool to me at the time. The template is still out there if you search something like "paper slide rule".
I've collected some links for building regular slide rules ([1] & [2]) as well as a circular slide rule [3]. Someone might also like the slide rule simulator [4].
[1] https://www.sliderulemuseum.com/REF/scales/MakeYourOwnSlideR...
[2] http://leewm.freeshell.org/origami/card-slide.pdf
[3] https://www.sliderulemuseum.com/SR_Scales.shtml#YingHum
[4] http://www.antiquark.com/sliderule/sim/virtual-slide-rule.ht...
I sort of did for a lark a few years ago, then promptly forgot how to since I could do reasonable math approximations in my head. But my father used his pretty effectively.
Yes, but only as a fun retro thing. Not for most calculations, although I have to say for back of the napkin, almost all in your head style things, they can be handy.
I bought one a few months ago off of ebay after I realized how important logarithms are in many different domains (including machine learning & information theory)
I don't use it, but if you are interested in math, it's a nice device to take a look and try to understand, at least for the basic operations.
Knowing how they work can be useful when imagining machinations of an algorithm and if the code is really necessary to do all the steps that way. :)
I had to learn how to use a circular slide rule for my pilot school (CRP-5). Easily top 5 exciting pieces of technology I had the opportunity to use
I'm building a slide rule in my head: https://magworld.pw
I was not allowed to use a calculator in my high school calculus class but I was permitted to (and did) use a slide rule.
My grandfather taught me the basics of using it and I still have his, but haven’t used it in decades and need a refresher.
As a pilot, I'm using it all the time. Even got a fancy watch with physical dials to spin
Not in a few years, but now that you've reminded me, I should pick the habit back up.
in spite of my age, I'm one of first digital native. I never used it and nobody explained me how to use. At same time I avoid most of analog instruments: multimeters, scope meters, calipers.
A slide rule is casually used by the General in "Fantastic Voyage"
Obligatory Asimov quote:
"The Analytical Rule might be considered a distant relation – as a skyscraper is to a shack – of that kindergarten toy, the logarithmic Slide Rule. Darell used it with the wristflip of long practice. He made freehand drawings of the result and, as Anthor stated, there were featureless plateaus in frontal lobe regions where strong swings should have been expected."
I'd really love an Analytical Rule, this hoverboard of the early atomic era.
In 1995 I used slide rules in Fort Sill, Ok. Haven't used them since.
My father is an electrical engineer and uses one
Besides Cliff Stoll? ;-)
Slide rules are awesome.