12 ms·

The Slide Rule

162 points by refrigerator 8y ago

sam_goody 8y ago
That IBM ad at the end is priceless on so many levels. (What did that massive computer do? How many female engineers do you count... etc,) Thanks for the article. My grandfather was an accountant who preferred the slide rule to a calculator. I grew up with slide rules around me, and never could understand the logic. Another tool lost in the past generation is the Abacus (here is a great story with Feynman[1]) and I would love more info as to how those compared in logic or use, if anyone can shed insight. [1]: https://www.ee.ryerson.ca/~elf/abacus/feynman.html https://www.ee.ryerson.ca/~elf/abacus/feynman.html
- sbradford26 8y ago
  I have some of the same experiences. Every older engineer would say "When I was in school we used slide rules" but no one would ever explain how they worked. This article was great for finally clearing that up for me.
  - perilunar 8y ago
    This surprises me. I went to school after electronic calculators replaced slide rules (and books of log and trig tables), but we still learned how logarithms worked and that they were the principle behind slide rules.
    - sbradford26 8y ago
      I graduated from college in 2016. We definitely covered logarithms but nobody really tied it back to slide rules. It definitely is a shame because understanding how problems were solved before can provide a lot of insight.
    - pbhjpbhj 8y ago
      We used log and trig tables in the 90s (UK) at a time when programmable graphing calculators were widely available.
    - true_religion 8y ago
      We learned about logarithms as well in the 2000s, but they never mentioned slide rules. Just lots of tables and charts to get a feel for it.
- jypepin 8y ago
  You can find videos of abacus competitions on youtube, and it's mind blowing how fast they go!
- dreamcompiler 8y ago
  > My grandfather was an accountant who preferred the slide rule to a calculator. This is hard for me to understand. Slide rules are inherently imprecise, in the same way floating point calculations are imprecise but much moreso. I'd expect an accountant to prefer integer (fixed point) math for the same reason banks do now.
  - lisper 8y ago
    > Slide rules are inherently imprecise And not particularly good for addition.
    - Someone 8y ago
      Depends on the scales used. With linear scales, they do addition. With logarithmic ones, multiplication.
      - lisper 8y ago
        Sure, in principle. Have you ever seen an actual slide rule with linear scales?
        zeveb 8y ago
        Mine had them. I don't think that I'd prefer it for accounting work, though.
        lisper 8y ago
        > Mine had them. I doubt that very much. Do you have a photograph? I used to collect slide rules. I have never seen one with a linear scale, and I can't find any evidence on the web that any such slide rule was ever manufactured. So if you can provide evidence that you possessed such a slide rule, that would be of significant historical interest.
        kens 8y ago
- lisper 8y ago
  > How many female engineers do you count Or non-white ones.
  - WorldMaker 8y ago
    The _Hidden Figures_ reminder there that women and people of color were job titled "computers" for a long time in the English language. The term for female/PoC programmers/mathematicians/engineers became the name of the machine built to replace them. It's a fact that feels increasingly strange with distance/hindsight, or at least it should to folks with a heart. (Just finished Mary Robinette Kowal's excellent "Lady Astronaut" books, and they are a fascinating retro-history of a timeline that fought to get to Mars faster than ours, and an interesting part of that success was getting more Computers in space, but by that it was meant women and people of color that could use a slide rule and do important math quickly in a crisis.)
    - gowld 8y ago
      you are conflating history with sexism/racism, though they overlap. "Computer" was essentially a "technician" who performed calculations, as today you'd have a technician to install parts in your machines or do other mechanistic tasks in an operation. It's not so unusual for a word that refers to a human job eventually becomes the name for the machine that replaces that job: dishwasher, messenger, agent. "computer" happens to be the job that is so easy to mechanise cheaply that the human job was made quickly obsolete once the opportunity arose. The term "Computer" long predated mechanical computers, by centuries. https://en.wikipedia.org/wiki/Human_computer https://en.wikipedia.org/wiki/Human_computer The earliest "computer" jobs tended to exclude women due to sexism. This photo shows an example of a human computer team that is mostly men (but may have a higher proportion of women than other technical teams in the larger organization) https://en.wikipedia.org/wiki/Human_computer#/media/File:NASA_human_computers_-_Mary_Jackson_on_far_right_-_Pressure_Tunnel_staff_taken_in_1950s.jpg https://en.wikipedia.org/wiki/Human_computer#/media/File:NAS... You're more likely to find women and PoC in "computer roles" than in scientist/engineer roles because they tended to be shut out from higher-level roles they may have been qualified for, leading to an oversupply of their demographic at the lower levels. And those overqualified women/PoC have more notable stories than the non-overqualified women and men in those roles.
- kens 8y ago
  > What did that massive computer do? I believe it's an IBM 604 Electronic Calculating Punch. This box was programmed with a plugboard and did BCD addition, subtraction, multiplication and division. It was built from 1100 vacuum tubes. It wasn't a computer in the modern sense. It read data from a card (the box in front is the card reader), ran through up to 60 steps of calculation, and then punched the result onto the same card, at the rate of 100 cards per minute. This system was introduced in 1948 and rented for $645 a month (about $5500 in current dollars). More info: http://www.columbia.edu/cu/computinghistory/604.html http://www.columbia.edu/cu/computinghistory/604.html
- walshemj 8y ago
  Actually back then the "girls" where the computers imagine typing pool that did maths calculations Los Alamos had a large number to do nuke calculations.
thanatropism 8y ago
Recently someone posted about a paper-based calculating tool where you had two or three scales and used a ruler to combine the numbers. There was even a Python package for producing them. What was the name?
- Jtsummers 8y ago
  Possibly this? https://en.wikipedia.org/wiki/Nomogram https://en.wikipedia.org/wiki/Nomogram A Python package for it: http://pynomo.org/wiki/index.php/Main_Page http://pynomo.org/wiki/index.php/Main_Page
  - function_seven 8y ago
    This example is one of the coolest things I've seen https://upload.wikimedia.org/wikipedia/en/a/a5/Risk_Based_Sampling_Nomogram_%283yr%29.png https://upload.wikimedia.org/wikipedia/en/a/a5/Risk_Based_Sa... I had some fun drawing lines and seeing how each factor influenced the chain of isopleths.
- scrooched_moose 8y ago
  Historically I believe they were just "computers" but that is just about impossible to search for these days. "Slide charts" is what I have the most luck with. I've inadvertently picked up a couple (usually tucked into old engineering books I've purchased)so looked into them a while ago. This page has a great collection of them: http://www.mathsinstruments.me.uk/page66.html http://www.mathsinstruments.me.uk/page66.html That search term also pulls up a ton on ebay.
tr352 8y ago
I got familiar with a slide rule when I studied for my pilot's license, through the "E6B flight computer"[1]. This is essentially a slide rule for specialised calculations (knots-km/h, gallons-litres, density altitude, etc). The E6B is still a mandatory piece of equipment for student pilots but generally regarded as outdated, even by instructors. As an early millennial I'd never ran into this 17th century marvel called slide rule. When I asked the instructor how it works (rather than how to use it) he answered along the lines of "don't ask, it just does". [1] https://en.wikipedia.org/wiki/E6B https://en.wikipedia.org/wiki/E6B
- pc86 8y ago
  I got largely the same answer during my PPL. For my check ride the DPE just wanted to make sure I knew how to use it for one simple calculation (estimating fuel remaining after a diversion) then we just used the figures in ForeFlight for the rest of the ride.
- dbcurtis 8y ago
  Is this the device referred to as the “circular prayer wheel”?
- skykooler 8y ago
  I think the E6B contradicts the article's assertion that the last slide rule in the US was made in 1976; when I was taking flying lessons a few years ago, I was required to buy a new E6B, and I doubt that was from some massive overstock in the 70's.
  - tr352 8y ago
    True. ASA still makes them but I suppose the only reason they're still made is that it's been considered standard classroom equipment for the past 70 years, combined with the well known universal dislike for change in the aviation world. I don't know anyone who kept using the E6B after getting licensed.
spreiti 8y ago
A practical implementation of a slide rule can be found on watches such as the Breitling Navitimer. I like to use it for quick currency conversions when traveling.
- z2 8y ago
  And most are helpfully marked for unit conversions as well! I have mine set for restaurant tipping by default (North America).
kqr 8y ago
I grew up long after slide rules went out of fashion, but I really like them. And not only for their signaling value; I genuinely think they make working with specifically ratios easier. For example if you have a recipe calling for 150 g of butter, but you want to use all of your 250 g, you can just align 150 and 250 on the slide rule, and then read off the correct amounts of the other ingredients, without ever touching the slide rule again. No multiplication performed. I understand people don't use slide rules for more things, but I'm baffled they aren't considered standard kitchen equipment, in one shape or another.
- jimktrains2 8y ago
  I'm not great with mine, but I really love using them. I took some of my engineering finals with it and finished well and quickly. They just make the calculation more "real" and I feel like I'm actually working out the problem instead of just punching numbers into a thing that gives numbers back.
- madcaptenor 8y ago
  That wouldn't work in the US, because we measure a lot of things by volume, don't use the same units for everything (small volumes are measured in teaspoons or tablespoons, larger volumes in cups), and tend to use lots of fractions in cooking. So a recipe wouldn't call for 150 g of butter, it would call for 2/3 of a cup. I suppose you could have multiple scales on a kitchen slide rule though.
  - madcaptenor 8y ago
    For American-style recipes you could use something like this: https://www.reddit.com/r/woodworking/comments/5y1r4h/kitchen_slide_rule_for_converting_recipes_for/ https://www.reddit.com/r/woodworking/comments/5y1r4h/kitchen...
  - contravariant 8y ago
    Wouldn't that all still be the same ratio though? If you set the slide rule to convert 250 to 150, shouldn't it e.g. also convert 2 cups to 1.2 cups?
derekp7 8y ago
There is a fairly good writeup on various slide rule types and scales, on http://www.quadibloc.com/math/slrint.htm http://www.quadibloc.com/math/slrint.htm (the rest of this guy's site is worth exploring on its own too, there seems to be a huge dump of various bits of knowledge on it).
dbcurtis 8y ago
The transition was nearly instantaneous. We all used slide rules in high school chemistry and physics. Two years before I entered freshman engineering, “engineering computation” was taught with slide rules. The next year, you could optionally take the traditional course or the new version based around calculators. My freshman year, the calculator-based course was required. As a senior, I bought the most high-end Post slide rule at the campus bookstore at the clearance sale for $3.00.
- ghaff 8y ago
  >The transition was nearly instantaneous. The first pocket scientific calculator was the HP-35 in 1972 (costing about $2,500 in today's dollars). Within 3 years, at least for most university engineering programs in the US, slide rules were completely gone. [That's incredibly fast.]
  - 7402 8y ago
    In my freshman physics class (1972-73) that price was a brief ethical issue. The professor said that for a midterm we could use one page of written notes and a slide rule. One student asked if he could use a calculator instead of a slide rule. "Are you going to buy calculators for everyone else in the class, too?" the professor asked. He felt it would be unfair to give such a big advantage to those few who could afford an HP-35 at that time.
    - ghaff 8y ago
      I’m now a bit curious when the switch flipped at the school I attended. There was no question when I started in 1975 that you needed a calculator. I suspect that those in the class ahead did as well. But that must have been very new.
zokier 8y ago
> The last slide rule manufactured in the US was produced on July 11, 1976 This is bit surprising to me. Does it imply that slide rule production had shifted to other countries, or did it really fall out of fashion so very rapidly? For reference, HP-35 calculator was released only in 1972 (for launch price of $395), and TIs competing SR-50 ("slide rule calculator") in 1974 (at $170). I would expect slide rules to be significantly cheaper and fairly entrenched (especially in colleges etc), so being killed in only few years is remarkable if true.
- asynchronous13 8y ago
  I'm guessing that's a bit of hyperbole, since new sliderules are still available for purchase today. Obviously manufacture of sliderules dropped precipitously, but there's still a niche market for them.
  - macintux 8y ago
    "manufactured in the US" I wouldn't be surprised if the quote is accurate.
    - ghaff 8y ago
      Missed that. Yes, that makes it plausible as Post and K&E had both ceased production by then and, presumably, most of the cheaper plastic ones were either made in Japan or in places like the Soviet Union for domestic use.
- ghaff 8y ago
  Although that date is all over the Internet, I don't believe it and some detailed timelines for individual companies suggest a few years later. [1] [ADDED: As the sibling notes, I'm sure at least cheap slide rules were available perhaps even today. But that date is plausible for "in the US."] They were killed off pretty quickly though. When I started college in fall on 1975 I got a TI scientific calculator which was somewhere around $100-$200. (It was required.) Prices were in sharp decline. A five function TI calculator was about the same price the year before. A year or two later an older HP model (which were higher-end calculators) was also about the same amount. Calculators were fairly expensive at first but remember that slide rules weren't useful for adding and for a lot of calculations anyway. [They're not precise enough for everything.] So once engineers, in particular, switched to calculators, there wasn't much of a market for slide rules. [1] http://www.sliderulemuseum.com/SR_Dates.htm http://www.sliderulemuseum.com/SR_Dates.htm
jhallenworld 8y ago
People on eBay are selling these Soviet pocket-watch style rotary slide rules: https://www.youtube.com/watch?v=Kuzdjy3HpWg https://www.youtube.com/watch?v=Kuzdjy3HpWg I think they were made into the 80s.
unethical_ban 8y ago
First, the positive note: This is an awesome, accessible article. Now the error: In the paragraph beginning "By converting numbers into their logarithm", log(4)=2 should be log2(4)=2 - it's been a while since I was in mathematics academically, but isn't it a necessity to show the base of the log if it's not 10?
- robmoore 8y ago
  In general, log(x) does not refer to one base (although 10 is common). In this case, they specify that log(x) is referring to base 2 in the paragraph above, but yeah it could definitely be more spelled out.
- gowld 8y ago
  It's a convention, not a law. If the base is known (or irrelevant) in context (as it is explicitly laid out for several paragraphs), no need to show the base in every expresion. The article says: "In the world of 2s, log(x) tells you how many times you have to multiply 2 by itself to get x."
- roywiggins 8y ago
  I think it's convention, but it would have been good to explain this a bit more. The previous sentence seems to say "from now on we mean base 2" ("In the world of 2s, log(x) tells you how many times you have to multiply 2 by itself to get x.") Which base gets to be special depends. Log on its own often means base e; sometimes base 10; and sometimes base 2 (and sometimes 'base whatever, it's not important')
- WorldMaker 8y ago
  It's an interesting debate in notation. Not all log notations show the base, as they mostly assume you know which base you are in (even/especially in the slide rule era, to my understanding, where the base was always assumed by the slide rule in use; which stories posit was fun when mathematicians would default to natural log slide rules and engineers to base-10 log). This article would be better if showed the base in its notation, but for the most part the bases are determinant in context of each paragraph, and that's roughly par for the slide rule course.
cafard 8y ago
Some of the last people using them for work may have been graphic artists, who called them "proportion wheels". I don't know how many of the folks sizing photos knew that they were using circular slide rules.
- ghaff 8y ago
  At one time there were a lot of industry specific tools to calculate various things (usually made out of cardboard) that were effectively slide rules or slide rules combined with lookup tables.
sizzzzlerz 8y ago
Growing up at a time B.C. (before calculators), we learned to use the slide rule in high school trig. I also used it during my freshman year in college. My dad bought me a Pickett trig slide rule that I still have in a drawer at home. I've taken it out occasionally to play with and I am always impressed by how simple and yet powerful it is. Very elegant. Very dated.
puetzk 8y ago
> The last slide rule manufactured in the US was produced on July 11, 1976 Actually, ThinkGeek made a production run a couple years back (though I guess I don't know that they were US-made). Doesn't seem to still be on their website, but I have one so it definitely existed. https://www.amazon.com/ThinkGeek-Slide-Rule/dp/B003M5B84C https://www.amazon.com/ThinkGeek-Slide-Rule/dp/B003M5B84C still shows a listing.
- tzs 8y ago
  I have a couple, too. They were not very good though. I'd be interested if someone made a new good slide rule. And not just slide rules--there are at least a couple of other older computing devices I'd like a good quality working replica or reproduction of. 1. A Curta calculator. https://en.wikipedia.org/wiki/Curta https://en.wikipedia.org/wiki/Curta 2. The Antikythera mechanism. https://en.wikipedia.org/wiki/Antikythera_mechanism https://en.wikipedia.org/wiki/Antikythera_mechanism
  - function_seven 8y ago
    I'm sure you've seen this already, but if not: https://www.youtube.com/watch?v=j9uRckJLqLk https://www.youtube.com/watch?v=j9uRckJLqLk A 3:1 scale replica of the Curta, 3D printed.
  - masklinn 8y ago
    > 1. A Curta calculator. https://en.wikipedia.org/wiki/Curta https://en.wikipedia.org/wiki/Curta The article notes that Marcus Wu has published a printable 3D model of a curta (at 3:1 size due to printer precision issues, though there are comments about people attempting 2:1 builds). You can also find actual curtas on ebay, though they're not cheap ($500~$1500 depending on condition and the like).
  - ghaff 8y ago
    You can find all sorts of slide rules on eBay (e.g. K&E). The really good ones can get pricey but they're readily available.
- ghaff 8y ago
gepoch 8y ago
Reading about the usefulness of logs reminded me of another spatial math tool: The Triangle of Power! https://www.youtube.com/watch?v=sULa9Lc4pck https://www.youtube.com/watch?v=sULa9Lc4pck
- thunderbong 8y ago
  This one was seriously awesome! Thanks. Most times when people say Math is hard they are actually talking about this. All the different ways to memorize stuff which doesn't help them get intuitive in Math.
Sniffnoy 8y ago
Another precursor to logarithms was prosthaphaeresis[1], based on trigonometric functions. Of course, like the quarter-square method, this required lookup tables, not a nifty device. But even with logarithms, log tables were pretty commonly used as well. [1] https://en.wikipedia.org/wiki/Prosthaphaeresis https://en.wikipedia.org/wiki/Prosthaphaeresis
- jacobolus 8y ago
  Angle measure is just the bivector (‘imaginary’) part of the complex logarithm.
combatentropy 8y ago
"A movable pointer called a 'cursor' was developed to make it easier to read numbers off more precisely. (This is likely the origin of the computer cursor!)" Etymonline corroborates this, https://www.etymonline.com/word/cursor#etymonline_v_494 https://www.etymonline.com/word/cursor#etymonline_v_494. So its cursor was the precursor to our cursor.
- lurquer 8y ago
  I concur, sir.
abecedarius 8y ago
The intro about Kepler is inaccurate, so I distrusted the claim about Newton too. It seems he did use a kind of slide rule: http://www.oughtred.org/history.shtml http://www.oughtred.org/history.shtml > In 1675 Sir Isaac Newton solves cubic equations using three parallel logarithmic scales and makes the first suggestion toward the use of the cursor. > In 1677, two years after Newton invents the cursor, Henry Coggeshall perfects the timber and carpenter's rule. Newton's cursor fails to catch on at the time.
- refrigerator 8y ago
  Thanks for raising this — what part of the intro was inaccurate? This was the source we used for the Kepler info: https://www.jstor.org/stable/27838992?seq=1#page_scan_tab_contents https://www.jstor.org/stable/27838992?seq=1#page_scan_tab_co...
  - abecedarius 8y ago
    > Kepler first formulated his hypothesis: planets had elliptical orbits with two foci, and then set out to prove it mathematically. He didn't start with that hypothesis, he came to it after multiple tries at fitting other models like an equant (an offset circle with angular speed controlled from the opposite offset, which is actually a good first-order approximation to the Kepler-law motion at small eccentricity). > Only after repeating his procedures 70 times did he offset his computational errors. With a little less patience, he wouldn’t have proved his theory, and elliptical orbits would have eluded us for longer. I skimmed the paper, and it seems to be about Kepler fitting an equant instead of an ellipse. Apparently he used an iterative method, stopping after 70 iterations? And his numerical errors seem to be responsible for it not converging faster. That makes more sense to me than my misunderstanding that you were saying he ran through the whole calculation from the start 70 times. I jumped to a conclusion about that part, and I'm sorry. Julian Barbour's The Discovery of Dynamics explains what Kepler did in detail (it's not the whole topic of the book, but a big chunk of it). A great book -- I didn't really appreciate Kepler before reading it. Both brilliant and very human.
skatanski 8y ago
This reminds of my uncle who had them in his university and later at work (studying in the 70s in the communist Poland). I remember him mentioning that when first calculators came, skilled slide rule users were much much fasters, than anyone using a calculator.
todd8 8y ago
I've noticed that my daughter, despite being an engineering student, isn't nearly as comfortable with the properties of logarithms as I am. Of course, she studied them in Calculus classes, but they were just abstract functions to her since she always had computers or calculators to perform calculations. For me, they were a part of the standard education for technical or science related fields. Even in high school we were expected to use slide rules or tables of logarithms to perform calculations. I bought my first slide rule around 1964 (with money I made delivering the Detroit Free Press newspaper every morning before school). It was a bright yellow Pickett like those available on EBay[1]. It was possible to do multiplication, division, roots, trig, exponentials, etc. to just less than 3 significant digits of accuracy. If this wasn't enough accuracy, I had to recast the computation as addition or subtraction of logs from log tables, which could with some interpolation yield around 6 significant digits of accuracy. I just recently pulled out my old slide rule to show my accountant how they worked. At MIT I saw circular slide rules, and some of my fellow students used them (more accuracy on the outer scales, less on the inner most scales). The most interesting slide rules I've seen are cylindrical. The scales wrap around the cylinder in a helix and are much longer giving an extra digit or two of accuracy (but requiring more mental work on the user to figure out which reading of the cursor to use because the cursor was parallel to the axis of the cylinder). See [2] By the time I was finished using my slide rule, I'd started working with computers. Even today, I have a fancy overpriced TI calculator that just sits in a drawer. I'd much rather fire up a Python REPL to do most calculations. [1] https://www.ebay.com/itm/VINTAGE-1959-PICKETT-DUAL-BASE-SLIDE-RULE-MODEL-N4-ES-WITH-LEATHER-CASE/113321672651?hash=item1a627f7fcb:g:tCMAAOSwWotbwn12:rk:10:pf:0 https://www.ebay.com/itm/VINTAGE-1959-PICKETT-DUAL-BASE-SLID... [2] https://ocw.mit.edu/courses/edgerton-center/ec-050-recreate-experiments-from-history-inform-the-future-from-the-past-galileo-january-iap-2010/image-galleries/slide-rule/ https://ocw.mit.edu/courses/edgerton-center/ec-050-recreate-...
- rmason 8y ago
  I bring out the slide rule pretty much these days to give history lessons to young folks. Last time I showed how it worked to a pair of GenZ kids they looked at me with a healthy bit of skepticism. Like somehow this was some sort of fake contraption. I felt a bit like my late father explaining what it was like to crank a car to start it.
draw_down 8y ago
I get that this is meant to demonstrate the elegance of the slide rule, but boy oh boy am I glad I can just punch some numbers into a device and get the answer. What a pain in the butt this looks like.
carapace 8y ago
I have my grandfather's slide rule. I don't often handle it because it has a patina on it from the thousands of calculations he must have carried out on it. It has several rulings on it and a sliding cursor. Studying it, I realized that, once set, it shows the multiplication of the whole continuum. In other words, a given setting of the rule to some n shows nm for all m. (Actually all mnEk for all m and k.) Some slide rules are circular or tubular. See also: https://en.wikipedia.org/wiki/Nomogram https://en.wikipedia.org/wiki/Nomogram
gshubert17 8y ago
A nice reference is Clifford Stoll's (author of A Cuckoo's Egg) article in Scientific American 2006: http://www.uvm.edu/pdodds/files/papers/others/2006/stoll2006a.pdf http://www.uvm.edu/pdodds/files/papers/others/2006/stoll2006... And a way to make your own sliderule: https://static.scientificamerican.com/sciam/assets/media/pdf/Slide_rule.pdf https://static.scientificamerican.com/sciam/assets/media/pdf... The article has the same IBM ad and says it's from 1953.
philiplu 8y ago
I've got a slide rule to thank for my precocious early math studies. I was always interested in math as a young kid, and my parents got me a Post slide rule for Christmas 1970, when I was in 5th grade/10 years old. I didn't know what the S and T scales on the back side of the main slide were for, so went looking up info in the local library. Turns out they were sine/tangent scales, which led to reading about trigonometry, which led to me realizing I needed to know algebra first. Over the next couple years, those library trips led to teaching myself algebra, geometry, trigonometry, and calculus, thanks mostly to TutorText books. For a nerdy little kid in the early 70s, that was heaven.

162 points by refrigerator 8y ago

That IBM ad at the end is priceless on so many levels. (What did that massive computer do? How many female engineers do you count... etc,) Thanks for the article. My grandfather was an accountant who preferred the slide rule to a calculator. I grew up with slide rules around me, and never could understand the logic. Another tool lost in the past generation is the Abacus (here is a great story with Feynman[1]) and I would love more info as to how those compared in logic or use, if anyone can shed insight. [1]: https://www.ee.ryerson.ca/~elf/abacus/feynman.html https://www.ee.ryerson.ca/~elf/abacus/feynman.html

sbradford26 8y ago
I have some of the same experiences. Every older engineer would say "When I was in school we used slide rules" but no one would ever explain how they worked. This article was great for finally clearing that up for me.
- perilunar 8y ago
  This surprises me. I went to school after electronic calculators replaced slide rules (and books of log and trig tables), but we still learned how logarithms worked and that they were the principle behind slide rules.
  - sbradford26 8y ago
    I graduated from college in 2016. We definitely covered logarithms but nobody really tied it back to slide rules. It definitely is a shame because understanding how problems were solved before can provide a lot of insight.
  - pbhjpbhj 8y ago
    We used log and trig tables in the 90s (UK) at a time when programmable graphing calculators were widely available.
  - true_religion 8y ago
    We learned about logarithms as well in the 2000s, but they never mentioned slide rules. Just lots of tables and charts to get a feel for it.
jypepin 8y ago
You can find videos of abacus competitions on youtube, and it's mind blowing how fast they go!
dreamcompiler 8y ago
> My grandfather was an accountant who preferred the slide rule to a calculator. This is hard for me to understand. Slide rules are inherently imprecise, in the same way floating point calculations are imprecise but much moreso. I'd expect an accountant to prefer integer (fixed point) math for the same reason banks do now.
- lisper 8y ago
  > Slide rules are inherently imprecise And not particularly good for addition.
  - Someone 8y ago
    Depends on the scales used. With linear scales, they do addition. With logarithmic ones, multiplication.
    - lisper 8y ago
      Sure, in principle. Have you ever seen an actual slide rule with linear scales?
      - zeveb 8y ago
        Mine had them. I don't think that I'd prefer it for accounting work, though.
        lisper 8y ago
        > Mine had them. I doubt that very much. Do you have a photograph? I used to collect slide rules. I have never seen one with a linear scale, and I can't find any evidence on the web that any such slide rule was ever manufactured. So if you can provide evidence that you possessed such a slide rule, that would be of significant historical interest.
        kens 8y ago
lisper 8y ago
> How many female engineers do you count Or non-white ones.
- WorldMaker 8y ago
  The _Hidden Figures_ reminder there that women and people of color were job titled "computers" for a long time in the English language. The term for female/PoC programmers/mathematicians/engineers became the name of the machine built to replace them. It's a fact that feels increasingly strange with distance/hindsight, or at least it should to folks with a heart. (Just finished Mary Robinette Kowal's excellent "Lady Astronaut" books, and they are a fascinating retro-history of a timeline that fought to get to Mars faster than ours, and an interesting part of that success was getting more Computers in space, but by that it was meant women and people of color that could use a slide rule and do important math quickly in a crisis.)
  - gowld 8y ago
    you are conflating history with sexism/racism, though they overlap. "Computer" was essentially a "technician" who performed calculations, as today you'd have a technician to install parts in your machines or do other mechanistic tasks in an operation. It's not so unusual for a word that refers to a human job eventually becomes the name for the machine that replaces that job: dishwasher, messenger, agent. "computer" happens to be the job that is so easy to mechanise cheaply that the human job was made quickly obsolete once the opportunity arose. The term "Computer" long predated mechanical computers, by centuries. https://en.wikipedia.org/wiki/Human_computer https://en.wikipedia.org/wiki/Human_computer The earliest "computer" jobs tended to exclude women due to sexism. This photo shows an example of a human computer team that is mostly men (but may have a higher proportion of women than other technical teams in the larger organization) https://en.wikipedia.org/wiki/Human_computer#/media/File:NASA_human_computers_-_Mary_Jackson_on_far_right_-_Pressure_Tunnel_staff_taken_in_1950s.jpg https://en.wikipedia.org/wiki/Human_computer#/media/File:NAS... You're more likely to find women and PoC in "computer roles" than in scientist/engineer roles because they tended to be shut out from higher-level roles they may have been qualified for, leading to an oversupply of their demographic at the lower levels. And those overqualified women/PoC have more notable stories than the non-overqualified women and men in those roles.
kens 8y ago
> What did that massive computer do? I believe it's an IBM 604 Electronic Calculating Punch. This box was programmed with a plugboard and did BCD addition, subtraction, multiplication and division. It was built from 1100 vacuum tubes. It wasn't a computer in the modern sense. It read data from a card (the box in front is the card reader), ran through up to 60 steps of calculation, and then punched the result onto the same card, at the rate of 100 cards per minute. This system was introduced in 1948 and rented for $645 a month (about $5500 in current dollars). More info: http://www.columbia.edu/cu/computinghistory/604.html http://www.columbia.edu/cu/computinghistory/604.html
walshemj 8y ago
Actually back then the "girls" where the computers imagine typing pool that did maths calculations Los Alamos had a large number to do nuke calculations.

thanatropism 8y ago

Recently someone posted about a paper-based calculating tool where you had two or three scales and used a ruler to combine the numbers. There was even a Python package for producing them. What was the name?

Jtsummers 8y ago
Possibly this? https://en.wikipedia.org/wiki/Nomogram https://en.wikipedia.org/wiki/Nomogram A Python package for it: http://pynomo.org/wiki/index.php/Main_Page http://pynomo.org/wiki/index.php/Main_Page
- function_seven 8y ago
  This example is one of the coolest things I've seen https://upload.wikimedia.org/wikipedia/en/a/a5/Risk_Based_Sampling_Nomogram_%283yr%29.png https://upload.wikimedia.org/wikipedia/en/a/a5/Risk_Based_Sa... I had some fun drawing lines and seeing how each factor influenced the chain of isopleths.
scrooched_moose 8y ago
Historically I believe they were just "computers" but that is just about impossible to search for these days. "Slide charts" is what I have the most luck with. I've inadvertently picked up a couple (usually tucked into old engineering books I've purchased)so looked into them a while ago. This page has a great collection of them: http://www.mathsinstruments.me.uk/page66.html http://www.mathsinstruments.me.uk/page66.html That search term also pulls up a ton on ebay.

tr352 8y ago

I got familiar with a slide rule when I studied for my pilot's license, through the "E6B flight computer"[1]. This is essentially a slide rule for specialised calculations (knots-km/h, gallons-litres, density altitude, etc). The E6B is still a mandatory piece of equipment for student pilots but generally regarded as outdated, even by instructors. As an early millennial I'd never ran into this 17th century marvel called slide rule. When I asked the instructor how it works (rather than how to use it) he answered along the lines of "don't ask, it just does". [1] https://en.wikipedia.org/wiki/E6B https://en.wikipedia.org/wiki/E6B

pc86 8y ago
I got largely the same answer during my PPL. For my check ride the DPE just wanted to make sure I knew how to use it for one simple calculation (estimating fuel remaining after a diversion) then we just used the figures in ForeFlight for the rest of the ride.
dbcurtis 8y ago
Is this the device referred to as the “circular prayer wheel”?
skykooler 8y ago
I think the E6B contradicts the article's assertion that the last slide rule in the US was made in 1976; when I was taking flying lessons a few years ago, I was required to buy a new E6B, and I doubt that was from some massive overstock in the 70's.
- tr352 8y ago
  True. ASA still makes them but I suppose the only reason they're still made is that it's been considered standard classroom equipment for the past 70 years, combined with the well known universal dislike for change in the aviation world. I don't know anyone who kept using the E6B after getting licensed.

spreiti 8y ago

A practical implementation of a slide rule can be found on watches such as the Breitling Navitimer. I like to use it for quick currency conversions when traveling.

z2 8y ago
And most are helpfully marked for unit conversions as well! I have mine set for restaurant tipping by default (North America).

kqr 8y ago

I grew up long after slide rules went out of fashion, but I really like them. And not only for their signaling value; I genuinely think they make working with specifically ratios easier. For example if you have a recipe calling for 150 g of butter, but you want to use all of your 250 g, you can just align 150 and 250 on the slide rule, and then read off the correct amounts of the other ingredients, without ever touching the slide rule again. No multiplication performed. I understand people don't use slide rules for more things, but I'm baffled they aren't considered standard kitchen equipment, in one shape or another.

jimktrains2 8y ago
I'm not great with mine, but I really love using them. I took some of my engineering finals with it and finished well and quickly. They just make the calculation more "real" and I feel like I'm actually working out the problem instead of just punching numbers into a thing that gives numbers back.
madcaptenor 8y ago
That wouldn't work in the US, because we measure a lot of things by volume, don't use the same units for everything (small volumes are measured in teaspoons or tablespoons, larger volumes in cups), and tend to use lots of fractions in cooking. So a recipe wouldn't call for 150 g of butter, it would call for 2/3 of a cup. I suppose you could have multiple scales on a kitchen slide rule though.
- madcaptenor 8y ago
  For American-style recipes you could use something like this: https://www.reddit.com/r/woodworking/comments/5y1r4h/kitchen_slide_rule_for_converting_recipes_for/ https://www.reddit.com/r/woodworking/comments/5y1r4h/kitchen...
- contravariant 8y ago
  Wouldn't that all still be the same ratio though? If you set the slide rule to convert 250 to 150, shouldn't it e.g. also convert 2 cups to 1.2 cups?

derekp7 8y ago

There is a fairly good writeup on various slide rule types and scales, on http://www.quadibloc.com/math/slrint.htm http://www.quadibloc.com/math/slrint.htm (the rest of this guy's site is worth exploring on its own too, there seems to be a huge dump of various bits of knowledge on it).

dbcurtis 8y ago

The transition was nearly instantaneous. We all used slide rules in high school chemistry and physics. Two years before I entered freshman engineering, “engineering computation” was taught with slide rules. The next year, you could optionally take the traditional course or the new version based around calculators. My freshman year, the calculator-based course was required. As a senior, I bought the most high-end Post slide rule at the campus bookstore at the clearance sale for $3.00.

ghaff 8y ago
>The transition was nearly instantaneous. The first pocket scientific calculator was the HP-35 in 1972 (costing about $2,500 in today's dollars). Within 3 years, at least for most university engineering programs in the US, slide rules were completely gone. [That's incredibly fast.]
- 7402 8y ago
  In my freshman physics class (1972-73) that price was a brief ethical issue. The professor said that for a midterm we could use one page of written notes and a slide rule. One student asked if he could use a calculator instead of a slide rule. "Are you going to buy calculators for everyone else in the class, too?" the professor asked. He felt it would be unfair to give such a big advantage to those few who could afford an HP-35 at that time.
  - ghaff 8y ago
    I’m now a bit curious when the switch flipped at the school I attended. There was no question when I started in 1975 that you needed a calculator. I suspect that those in the class ahead did as well. But that must have been very new.

zokier 8y ago

> The last slide rule manufactured in the US was produced on July 11, 1976 This is bit surprising to me. Does it imply that slide rule production had shifted to other countries, or did it really fall out of fashion so very rapidly? For reference, HP-35 calculator was released only in 1972 (for launch price of $395), and TIs competing SR-50 ("slide rule calculator") in 1974 (at $170). I would expect slide rules to be significantly cheaper and fairly entrenched (especially in colleges etc), so being killed in only few years is remarkable if true.

asynchronous13 8y ago
I'm guessing that's a bit of hyperbole, since new sliderules are still available for purchase today. Obviously manufacture of sliderules dropped precipitously, but there's still a niche market for them.
- macintux 8y ago
  "manufactured in the US" I wouldn't be surprised if the quote is accurate.
  - ghaff 8y ago
    Missed that. Yes, that makes it plausible as Post and K&E had both ceased production by then and, presumably, most of the cheaper plastic ones were either made in Japan or in places like the Soviet Union for domestic use.
ghaff 8y ago
Although that date is all over the Internet, I don't believe it and some detailed timelines for individual companies suggest a few years later. [1] [ADDED: As the sibling notes, I'm sure at least cheap slide rules were available perhaps even today. But that date is plausible for "in the US."] They were killed off pretty quickly though. When I started college in fall on 1975 I got a TI scientific calculator which was somewhere around $100-$200. (It was required.) Prices were in sharp decline. A five function TI calculator was about the same price the year before. A year or two later an older HP model (which were higher-end calculators) was also about the same amount. Calculators were fairly expensive at first but remember that slide rules weren't useful for adding and for a lot of calculations anyway. [They're not precise enough for everything.] So once engineers, in particular, switched to calculators, there wasn't much of a market for slide rules. [1] http://www.sliderulemuseum.com/SR_Dates.htm http://www.sliderulemuseum.com/SR_Dates.htm

jhallenworld 8y ago

People on eBay are selling these Soviet pocket-watch style rotary slide rules: https://www.youtube.com/watch?v=Kuzdjy3HpWg https://www.youtube.com/watch?v=Kuzdjy3HpWg I think they were made into the 80s.

unethical_ban 8y ago

First, the positive note: This is an awesome, accessible article. Now the error: In the paragraph beginning "By converting numbers into their logarithm", log(4)=2 should be log2(4)=2 - it's been a while since I was in mathematics academically, but isn't it a necessity to show the base of the log if it's not 10?

robmoore 8y ago
In general, log(x) does not refer to one base (although 10 is common). In this case, they specify that log(x) is referring to base 2 in the paragraph above, but yeah it could definitely be more spelled out.
gowld 8y ago
It's a convention, not a law. If the base is known (or irrelevant) in context (as it is explicitly laid out for several paragraphs), no need to show the base in every expresion. The article says: "In the world of 2s, log(x) tells you how many times you have to multiply 2 by itself to get x."
roywiggins 8y ago
I think it's convention, but it would have been good to explain this a bit more. The previous sentence seems to say "from now on we mean base 2" ("In the world of 2s, log(x) tells you how many times you have to multiply 2 by itself to get x.") Which base gets to be special depends. Log on its own often means base e; sometimes base 10; and sometimes base 2 (and sometimes 'base whatever, it's not important')
WorldMaker 8y ago
It's an interesting debate in notation. Not all log notations show the base, as they mostly assume you know which base you are in (even/especially in the slide rule era, to my understanding, where the base was always assumed by the slide rule in use; which stories posit was fun when mathematicians would default to natural log slide rules and engineers to base-10 log). This article would be better if showed the base in its notation, but for the most part the bases are determinant in context of each paragraph, and that's roughly par for the slide rule course.

cafard 8y ago

Some of the last people using them for work may have been graphic artists, who called them "proportion wheels". I don't know how many of the folks sizing photos knew that they were using circular slide rules.

ghaff 8y ago
At one time there were a lot of industry specific tools to calculate various things (usually made out of cardboard) that were effectively slide rules or slide rules combined with lookup tables.

sizzzzlerz 8y ago

Growing up at a time B.C. (before calculators), we learned to use the slide rule in high school trig. I also used it during my freshman year in college. My dad bought me a Pickett trig slide rule that I still have in a drawer at home. I've taken it out occasionally to play with and I am always impressed by how simple and yet powerful it is. Very elegant. Very dated.

puetzk 8y ago

> The last slide rule manufactured in the US was produced on July 11, 1976 Actually, ThinkGeek made a production run a couple years back (though I guess I don't know that they were US-made). Doesn't seem to still be on their website, but I have one so it definitely existed. https://www.amazon.com/ThinkGeek-Slide-Rule/dp/B003M5B84C https://www.amazon.com/ThinkGeek-Slide-Rule/dp/B003M5B84C still shows a listing.

tzs 8y ago
I have a couple, too. They were not very good though. I'd be interested if someone made a new good slide rule. And not just slide rules--there are at least a couple of other older computing devices I'd like a good quality working replica or reproduction of. 1. A Curta calculator. https://en.wikipedia.org/wiki/Curta https://en.wikipedia.org/wiki/Curta 2. The Antikythera mechanism. https://en.wikipedia.org/wiki/Antikythera_mechanism https://en.wikipedia.org/wiki/Antikythera_mechanism
- function_seven 8y ago
  I'm sure you've seen this already, but if not: https://www.youtube.com/watch?v=j9uRckJLqLk https://www.youtube.com/watch?v=j9uRckJLqLk A 3:1 scale replica of the Curta, 3D printed.
- masklinn 8y ago
  > 1. A Curta calculator. https://en.wikipedia.org/wiki/Curta https://en.wikipedia.org/wiki/Curta The article notes that Marcus Wu has published a printable 3D model of a curta (at 3:1 size due to printer precision issues, though there are comments about people attempting 2:1 builds). You can also find actual curtas on ebay, though they're not cheap ($500~$1500 depending on condition and the like).
- ghaff 8y ago
  You can find all sorts of slide rules on eBay (e.g. K&E). The really good ones can get pricey but they're readily available.
ghaff 8y ago

gepoch 8y ago

Reading about the usefulness of logs reminded me of another spatial math tool: The Triangle of Power! https://www.youtube.com/watch?v=sULa9Lc4pck https://www.youtube.com/watch?v=sULa9Lc4pck

thunderbong 8y ago
This one was seriously awesome! Thanks. Most times when people say Math is hard they are actually talking about this. All the different ways to memorize stuff which doesn't help them get intuitive in Math.

Sniffnoy 8y ago

Another precursor to logarithms was prosthaphaeresis[1], based on trigonometric functions. Of course, like the quarter-square method, this required lookup tables, not a nifty device. But even with logarithms, log tables were pretty commonly used as well. [1] https://en.wikipedia.org/wiki/Prosthaphaeresis https://en.wikipedia.org/wiki/Prosthaphaeresis

jacobolus 8y ago
Angle measure is just the bivector (‘imaginary’) part of the complex logarithm.

combatentropy 8y ago

"A movable pointer called a 'cursor' was developed to make it easier to read numbers off more precisely. (This is likely the origin of the computer cursor!)" Etymonline corroborates this, https://www.etymonline.com/word/cursor#etymonline_v_494 https://www.etymonline.com/word/cursor#etymonline_v_494. So its cursor was the precursor to our cursor.

lurquer 8y ago
I concur, sir.

abecedarius 8y ago

The intro about Kepler is inaccurate, so I distrusted the claim about Newton too. It seems he did use a kind of slide rule: http://www.oughtred.org/history.shtml http://www.oughtred.org/history.shtml > In 1675 Sir Isaac Newton solves cubic equations using three parallel logarithmic scales and makes the first suggestion toward the use of the cursor. > In 1677, two years after Newton invents the cursor, Henry Coggeshall perfects the timber and carpenter's rule. Newton's cursor fails to catch on at the time.

refrigerator 8y ago
Thanks for raising this — what part of the intro was inaccurate? This was the source we used for the Kepler info: https://www.jstor.org/stable/27838992?seq=1#page_scan_tab_contents https://www.jstor.org/stable/27838992?seq=1#page_scan_tab_co...
- abecedarius 8y ago
  > Kepler first formulated his hypothesis: planets had elliptical orbits with two foci, and then set out to prove it mathematically. He didn't start with that hypothesis, he came to it after multiple tries at fitting other models like an equant (an offset circle with angular speed controlled from the opposite offset, which is actually a good first-order approximation to the Kepler-law motion at small eccentricity). > Only after repeating his procedures 70 times did he offset his computational errors. With a little less patience, he wouldn’t have proved his theory, and elliptical orbits would have eluded us for longer. I skimmed the paper, and it seems to be about Kepler fitting an equant instead of an ellipse. Apparently he used an iterative method, stopping after 70 iterations? And his numerical errors seem to be responsible for it not converging faster. That makes more sense to me than my misunderstanding that you were saying he ran through the whole calculation from the start 70 times. I jumped to a conclusion about that part, and I'm sorry. Julian Barbour's The Discovery of Dynamics explains what Kepler did in detail (it's not the whole topic of the book, but a big chunk of it). A great book -- I didn't really appreciate Kepler before reading it. Both brilliant and very human.

skatanski 8y ago

This reminds of my uncle who had them in his university and later at work (studying in the 70s in the communist Poland). I remember him mentioning that when first calculators came, skilled slide rule users were much much fasters, than anyone using a calculator.

todd8 8y ago

I've noticed that my daughter, despite being an engineering student, isn't nearly as comfortable with the properties of logarithms as I am. Of course, she studied them in Calculus classes, but they were just abstract functions to her since she always had computers or calculators to perform calculations. For me, they were a part of the standard education for technical or science related fields. Even in high school we were expected to use slide rules or tables of logarithms to perform calculations. I bought my first slide rule around 1964 (with money I made delivering the Detroit Free Press newspaper every morning before school). It was a bright yellow Pickett like those available on EBay[1]. It was possible to do multiplication, division, roots, trig, exponentials, etc. to just less than 3 significant digits of accuracy. If this wasn't enough accuracy, I had to recast the computation as addition or subtraction of logs from log tables, which could with some interpolation yield around 6 significant digits of accuracy. I just recently pulled out my old slide rule to show my accountant how they worked. At MIT I saw circular slide rules, and some of my fellow students used them (more accuracy on the outer scales, less on the inner most scales). The most interesting slide rules I've seen are cylindrical. The scales wrap around the cylinder in a helix and are much longer giving an extra digit or two of accuracy (but requiring more mental work on the user to figure out which reading of the cursor to use because the cursor was parallel to the axis of the cylinder). See [2] By the time I was finished using my slide rule, I'd started working with computers. Even today, I have a fancy overpriced TI calculator that just sits in a drawer. I'd much rather fire up a Python REPL to do most calculations. [1] https://www.ebay.com/itm/VINTAGE-1959-PICKETT-DUAL-BASE-SLIDE-RULE-MODEL-N4-ES-WITH-LEATHER-CASE/113321672651?hash=item1a627f7fcb:g:tCMAAOSwWotbwn12:rk:10:pf:0 https://www.ebay.com/itm/VINTAGE-1959-PICKETT-DUAL-BASE-SLID... [2] https://ocw.mit.edu/courses/edgerton-center/ec-050-recreate-experiments-from-history-inform-the-future-from-the-past-galileo-january-iap-2010/image-galleries/slide-rule/ https://ocw.mit.edu/courses/edgerton-center/ec-050-recreate-...

rmason 8y ago
I bring out the slide rule pretty much these days to give history lessons to young folks. Last time I showed how it worked to a pair of GenZ kids they looked at me with a healthy bit of skepticism. Like somehow this was some sort of fake contraption. I felt a bit like my late father explaining what it was like to crank a car to start it.

draw_down 8y ago

I get that this is meant to demonstrate the elegance of the slide rule, but boy oh boy am I glad I can just punch some numbers into a device and get the answer. What a pain in the butt this looks like.

carapace 8y ago

I have my grandfather's slide rule. I don't often handle it because it has a patina on it from the thousands of calculations he must have carried out on it. It has several rulings on it and a sliding cursor. Studying it, I realized that, once set, it shows the multiplication of the whole continuum. In other words, a given setting of the rule to some n shows nm for all m. (Actually all mnEk for all m and k.) Some slide rules are circular or tubular. See also: https://en.wikipedia.org/wiki/Nomogram https://en.wikipedia.org/wiki/Nomogram

gshubert17 8y ago

A nice reference is Clifford Stoll's (author of A Cuckoo's Egg) article in Scientific American 2006: http://www.uvm.edu/pdodds/files/papers/others/2006/stoll2006a.pdf http://www.uvm.edu/pdodds/files/papers/others/2006/stoll2006... And a way to make your own sliderule: https://static.scientificamerican.com/sciam/assets/media/pdf/Slide_rule.pdf https://static.scientificamerican.com/sciam/assets/media/pdf... The article has the same IBM ad and says it's from 1953.

philiplu 8y ago

I've got a slide rule to thank for my precocious early math studies. I was always interested in math as a young kid, and my parents got me a Post slide rule for Christmas 1970, when I was in 5th grade/10 years old. I didn't know what the S and T scales on the back side of the main slide were for, so went looking up info in the local library. Turns out they were sine/tangent scales, which led to reading about trigonometry, which led to me realizing I needed to know algebra first. Over the next couple years, those library trips led to teaching myself algebra, geometry, trigonometry, and calculus, thanks mostly to TutorText books. For a nerdy little kid in the early 70s, that was heaven.