[HN Gopher] Why a Slide Rule Works
       ___________________________________________________________________
        
       Why a Slide Rule Works
        
       Author : zdw
       Score  : 82 points
       Date   : 2022-04-11 13:50 UTC (9 hours ago)
        
 (HTM) web link (www.johndcook.com)
 (TXT) w3m dump (www.johndcook.com)
        
       | hilbert42 wrote:
       | I'm not commenting on this story and here's why (it's a copy of
       | my feedback to that web site):
       | 
       |  _" I have not yet read this article because it's too difficult
       | to read. Even the text I'm entering into this comment box is
       | almost illegible. I have to doublely check to see what I've
       | written.
       | 
       | Presumably the reason you've chosen a gray text which to me on my
       | smartphone looks to have no more than 20% saturation together
       | with a fine spindle like font is that it looks artistic on your
       | hi-res, high dynamic range monitor but it's essentially illegible
       | on my smartphone (1080x1920px). I'm not the only one who is
       | complaining, many have whinged about very feint essentially
       | illegible text on the web - it's a common complaint yet illegible
       | websites like yours still persist. Presumably, I could copy and
       | paste the text into a text editor to read it but then I'd lose
       | the images. It's messy and I shouldn't have to do it.
       | 
       | That said, the images of the slide rule are quite readable.
       | 
       | BTW, I'm not some casual narky reader who's being critical for
       | the sake of it. I am a regular slide rule user. In fact, I'm
       | looking at my two slide rules on my desk now - one's a Hemmi
       | Darmstadt No 130 and the other is a Faber Castell No 2/83 N. The
       | Hemmi was from my student days (before calculators), and the
       | F/Castell is about 60 years old and belonged to my father who was
       | an engineer. Both rules are still highly usable."_
        
         | willcipriano wrote:
         | Are you running a dark mode plugin or something? It works fine
         | for me.
        
           | hilbert42 wrote:
           | Absolutely not, this phone is stock standard Huawei Honor
           | (GR5) 2017
           | 
           | It's completely untweaked (unlike most of my rooted phones).
           | In fact, I use this phone as a workhorse because the screen
           | is very good for a cheap phone. (Even if we hate Huawei, we
           | have to admit the quality of its stuff is pretty good.)
           | 
           | It'd be interesting to know what you are using.
           | 
           | As soon as I post this I'll fire up the PC and see how it
           | looks there. I'll let you know.
        
           | hilbert42 wrote:
           | Update: See my reply to _dahardt_. Reckon the problem 's
           | (mostly) solved.
           | 
           | Thanks for your comment.
        
         | dahart wrote:
         | You might mention which device & browser. I don't see any
         | issues at all on an iPhone nor desktop. Could it be a bug in
         | your setup, and not something the site has much control over?
        
           | hilbert42 wrote:
           | OK, I'm now on the PC. My main PC with the hi-res monitor is
           | being refurbished so this 2nd PC will have to do, it only has
           | an old Dell E228WFP monitor (1680x1050) attached. The browser
           | is now Firefox.
           | 
           | This is a Windows PC with the browser font set to its default
           | size. The webpage is now readable but it's still low in
           | intensity (contrast) and the MS ClearType is having
           | considerable difficulty in keeping certain characters sharp--
           | in fact it's hardly working--the 'i' 'l' and 'm' look
           | annoyingly fuzzy.
           | 
           | When I increase the font (CTRL +) several sizes in the
           | browser it improves out of sight and the text becomes
           | completely and easily readable. It's a shame I can't post
           | some screen shots to show how significantly different that
           | typeface is under different viewing environments/conditions.
           | It only proves the point that web designers shouldn't just
           | take what they see on their own monitors and assume it's the
           | same as everyone else sees it.
           | 
           | As mentioned, I'm not alone in complaining about low contrast
           | grayish typefaces, here's the first other complaints I've
           | just found:
           | 
           | https://www.wired.com/2016/10/how-the-web-became-unreadable/
           | 
           | https://www.contrastrebellion.com/#page2
           | 
           | Incidentally, an interesting observation is that the
           | character pi, p, in the webpage is perfectly viewable on the
           | smartphone and has good contrast. Clearly it's from a
           | different typeface set, it also proves that the text's
           | typeface is the culprit in that it doesn't view well on all
           | displays.
           | 
           | I'll now go back to the smartphone and figure out what
           | typeface the phone is displaying the text in.
           | 
           | Thanks for your comment.
        
           | hilbert42 wrote:
           | See reply to _willipriano_. Browser Chrome.
           | 
           | As I said, I'll try my PC and get back. At this point, all I
           | can say is that everything else I've looked at on HN in the
           | last several is perfect.
           | 
           | ...Thinking, if OK with you this could be a typeface (font
           | substitution) problem. If so, it ought to show up on the PC
           | as the typefaces are mostly different.
        
             | [deleted]
        
         | khedoros1 wrote:
         | On both my desktop (Linux+Firefox @1440p) and phone
         | (Android+Firefox @2160x1080), the text is black on a white
         | background, in a reasonably-legible font, and at a reasonable
         | size. Trying it in Chrome doesn't look significantly different
         | on either device.
        
           | buescher wrote:
           | It doesn't work on my K&E or my Pickett either.
        
             | hilbert42 wrote:
             | As I've said to several other posters, I reckon it's a font
             | substitution problem - some fonts display much better than
             | others in certain environments.
             | 
             |  _BTW, an interesting observation, when I first posted the
             | comment it was up-voted, it 's now been down-voted to just
             | below where it started. I think this proves the point that
             | not everyone is viewing that page with equal ease._
        
       | throw0101a wrote:
       | A comment from a previous discussion:
       | 
       | ---
       | 
       | The Professor Herning YT channel has a bunch of videos on both
       | using slide rules and reviews/comparisons of various ones:
       | 
       | * https://www.youtube.com/c/ProfessorHerning/videos
       | 
       | The "Practical Slide Rule" [0] and "Basic slide rule theory and
       | use" [1] playlists are a good intro:
       | 
       | [0] https://www.youtube.com/playlist?list=PL_qcL_RF-
       | Zyu6ugp3E2nB...
       | 
       | [1] https://www.youtube.com/playlist?list=PL_qcL_RF-
       | ZyvJYtIr9NRX...
       | 
       | ---
       | 
       | https://news.ycombinator.com/item?id=30971066
        
       | bediger4000 wrote:
       | I tried to find a place to buy a new slide rule for my 15-year
       | old. I've got twins in different schools, one school doing a lot
       | more math than the other, and I wanted to get him going on
       | logarithms. Couldn't find a new one, just antiques on ebay, etc.
       | I ended up making one of the paper ones, but they're not the
       | same.
       | 
       | Does anybody make new slide rules?
        
         | wmwragg wrote:
         | Concise in Japan[1] still make circular slide rules (the 300,
         | 270N, 28N 27N). I bought a couple from them a few years ago.
         | Good quality, and work well.
         | 
         | [1] https://www.sliderule.tokyo/products/list.php
        
         | HappyJoy wrote:
         | Maybe an E6B would be helpful.
        
         | floren wrote:
         | I don't think anyone still makes new slide rules, except for
         | the E6B flight computer which is rather specialized. However,
         | you should be able to get a metal Pickett slide rule on ebay
         | for a reasonable price; they're great slide rules and being
         | metal rather than wood will tend to hold up better over the
         | years (moisture can really mess up a wood slide rule).
         | Something like this: https://www.ebay.com/itm/234503446574
        
         | derekp7 wrote:
         | You can buy refurbished and also new-in-box (a bit expensive
         | depending on the model) slide rules from various sites, such as
         | https://www.sphere.bc.ca/test/sruniverse.html.
         | 
         | I thought about getting into hand making them, figured out most
         | of the techniques that I can do in my garage with some
         | components (the end brackets, and cursor runners) being made on
         | a 3D printer. But I'm hung up on where to get the cursor
         | springs from, or what would be a good substitute. One of these
         | days I may revisit the topic.
        
       | goache wrote:
       | I recently created a web comic explaining slide rules!
       | https://randomlyunique.com/plancky/2021/slide-rules/index.ht...
        
       | agumonkey wrote:
       | I find this to be the most abstract yet primitive computing
       | device. Bands and marks and you hop right into logarithmic
       | relationships.
        
       | derekp7 wrote:
       | There are some things that a slide rule is superior for -- one
       | item I can think of is visualizing an arbitrary range of
       | fractional values. For example, lets say you need a capacitor and
       | a resistor with values in a particular ratio. Any pair will work
       | in your given circuit (within reason), as long as that ratio is
       | maintained. You have a drawer full of various resistors and
       | another of capacitors, and need to find a pair that will work. So
       | you set your slide rule to that fraction (let's say 1.7 / 3.3),
       | and you can then pull up any resistor and determine which size
       | capacitor can be used by glancing at the slide rule. (Of course
       | you still have to keep track of the magnitudes in your head, but
       | being in the habit of that makes you a better engineer anyway).
        
         | hilbert42 wrote:
         | _" There are some things that a slide rule is superior for --
         | one item I can think of is visualizing an arbitrary range of
         | fractional values."_
         | 
         | Exactly, similar to the way log scales make visualizing a range
         | of results across the slide rule no matter what one is doing.
         | 
         | Similarly, I have a number of good digital multimeters but I
         | also keep several analog AVO meters,
         | https://en.wikipedia.org/wiki/Avometer, to give me a sense of
         | proportion if I'm adjusting something (nulling a discriminator
         | etc.).
        
         | JKCalhoun wrote:
         | I implemented Ohm's Law as you describe for an iOS App some
         | years back [1]. Tried also to figure out how to do it in
         | Javascript (still learning, love it if someone could really
         | make it nice for the rest of us to use) [2].
         | 
         | [1] Perfboard (5th screenshot shows it):
         | https://apps.apple.com/us/app/perfboard/id46595187
         | 
         | [2] SlideRule.js: https://github.com/EngineersNeedArt/SlideRule
        
       | zabzonk wrote:
       | When I was in school in the late 60s a slide-rule company gave a
       | special offer to us, which all of our parents (wanting us to
       | succeed in the bright technological future) duly bought into. As
       | far as I know, none of us ever actually used them, preferring
       | paper log tables.
       | 
       | We were also taught how to use mechanical adding machines,
       | possibly the last people to be lumbered with this information,
       | which mercifully I have completely forgotten.
        
         | xyzzy21 wrote:
         | I was probably the last generation in the US in the 1970s to
         | willingly learn slide rules - the HP-35 had been out a few
         | years and new scientific calculators already made the demise of
         | slide rules pretty obvious to even us nerdlets.
         | 
         | One of my prized inheritances from my engineer father is his
         | slide rule (complete with leather case).
        
           | killjoywashere wrote:
           | I have a few slide rules at this point, including a Hemmi 200
           | "Made in Occupied Japan"
           | 
           | https://www.sliderulemuseum.com/Hemmi.htm
        
             | hilbert42 wrote:
             | Thanks for the link. I've just seen my _Sun Hemmi No. 130
             | System Darmstadt_ (which I 'm looking at now and that I
             | mentioned in my earlier post). It's still in excellent
             | condition except the glass in the cursor has a crack in
             | it).
        
       | dahart wrote:
       | Must be in the air, I just watched a YouTube recommended vid by
       | Mathologer on the circular slide rule that was interesting.
       | https://youtu.be/ZIQQvxSXLhI
        
         | function_seven wrote:
         | Definitely in the air. I just watched that video last week and
         | was blown away by the rubber band analogy. So simple and
         | intuitive what's happening as the wheel takes up the
         | infinitely-stretching rubber band.
         | 
         | I always thought I understood logarithms--and I actually did
         | somewhat--but that visual really drove home the "continuous
         | ratio-ing" that's happening as the scale is built.
        
         | szszrk wrote:
         | I love that it's still used in watches. Some brands have it
         | build into watches bezel, with some predefined marks for
         | popular conversions like galons/liters, miles/nautical
         | miles/kilometers and so on.
         | 
         | It looks fun and is fun. Of course the rule itself is very
         | limited as you basically have to figure out where is the
         | decimal point by yourself (even for small numbers) but it's
         | actually very precise and may be useful with practice.
         | 
         | Below some examples that are not very expensive [1], also a
         | Casio manual [3] I found very helpful and visually appealing.
         | 
         | [1] Seiko SSC632, Seiko SRPB59J1, Casio EF527D-1AV [2]
         | https://support.casio.com/answer.php?rgn=4&cid=002001009001&...
        
       | tedunangst wrote:
       | > Notice that the 1 of the bottom is under p on the top bar.
       | 
       | I spent a long time staring at the picture until I figured out
       | the bottom is the second row, and there are four rows of numbers
       | below the bottom.
        
       | dragontamer wrote:
       | So I've known about slide-rules for a while.
       | 
       | What I didn't realize was that the mechanical principles of
       | slide-rules were applied to fire-control computers on WW2-era
       | Battleships.
       | 
       | https://en.wikipedia.org/wiki/Mark_I_Fire_Control_Computer
       | 
       | These computers had slide-rule like cylinders that would rotate.
       | As you aimed the gun sights "at" a target, the gun's coordinates
       | were being mapped to a cylinder, which would move the gun a
       | different direction (you have to aim the gun "higher" the further
       | away the target is, to account for gravity "drooping" the
       | bullet).
       | 
       | In effect; the weirdly shaped cylinder inside the fire-control
       | computer is a pre-computed solution that maps x/y coordinate
       | inputs to a z-coordinate output (where "z" would be fed into the
       | gun's raw aiming system).
       | 
       | The different parameters of the gun were programmed in with gears
       | and cranks, moving the cylinder around physically.
       | 
       | For more details, see:
       | https://www.youtube.com/watch?v=gwf5mAlI7Ug
       | 
       | Its a 20-minute video. The cylinder mechanism (of 2x inputs
       | mapped to 1x output) is specifically talked about here:
       | https://youtu.be/gwf5mAlI7Ug?t=636 . Carefully crafted cylinders
       | could be any pre-computed 2-input / 1-output function.
       | 
       | ---------
       | 
       | Mechanical computers are fun. Slide rules are but the simplest
       | kind. People were using more complicated "mechanical computers"
       | for very serious combat / rangefinding / etc. systems just a few
       | decades ago, before the advent of modern digital computers.
        
         | wlesieutre wrote:
         | I don't have one because they go for $1000+, but speaking of
         | cylinders, the Curta mechanical calculator is fascinating
         | 
         | https://en.wikipedia.org/wiki/Curta
         | 
         | https://www.youtube.com/watch?v=loI1Kwed8Pk
        
         | pugworthy wrote:
         | Another cylindrical rule is the Thacher Cylindrical Slide Rule.
         | It's a cylinder with many rules marked out on it, that rotates
         | in a set of fixed rules. All told it is the equivalent of a 66
         | foot long conventional slide rule.
         | 
         | https://www2.humboldt.edu/scimus/NorthCoastInst/ThacherCalcu...
         | 
         | I actually picked one up out of the garbage bin at the
         | university I worked at. It didn't have an inventory sticker so
         | they had to toss it according to the rules.
        
         | 7thaccount wrote:
         | Mechanical computers are really cool. Veritasium just did a 2
         | part video on them. The second goes over some ML applications
         | for the future. You can make a really tiny and energy efficient
         | mechanical chip to do some cool things.
        
           | HideousKojima wrote:
           | Technically Veritasium's videos were about analog computers
           | (of which some mechanical computers are a subset, it's
           | entirely possible to make a digital mechanical computer
           | though it would be extremely slow).
        
             | ddingus wrote:
             | Yes, but when reading the parent comment I was struck by
             | the parallelism in that analog computers and mechanical
             | ones run on the rules of the world.
             | 
             | Take a cam and follower, perhaps with a mechanical or
             | hydraulic means to hold or change or respond to a state.
             | That is not really different from a periodic signal fed
             | into a trigger and or a flop or gate.
             | 
             | And somewhere on here we all had a discussion about math
             | and someone ran the test and determined the "simulation" we
             | are living in is a twos complement machine. (That's really
             | an artifact of our math and set of axioms we are working
             | on), but it was fun to think about.
             | 
             | By default, these kinds of computation systems are robust
             | because the world is robust. And they can respond as things
             | in the world, running on the world "simulation" tend to
             | do.[1]
             | 
             | Another related thought are those PONG games lacking a CPU.
             | First time I encountered a schematic, I realized the
             | circuit was the game!
             | 
             | Robustness can be high value and fast!
             | 
             | Extending it a little, one could take lookup tables, simple
             | ADD operations and software that runs mostly out of a ROM.
             | The old Atari 2600 (VCS) was like that having only 128
             | bytes of RAM!
             | 
             | The Apollo flight computer was not powerful, in the sense
             | of having exotic math functions, or tons of speed to throw
             | at a problem. But they ran in real time, able to control a
             | lot of I/O and such.
             | 
             | These kinds of systems are remarkable in that they tend to
             | be able to perform their designed for tasks well, and will
             | always do that in a lean way, and we could always package
             | that up, provide interfaces to far more complex systems and
             | get way more out of it than one might expect.
             | 
             | The other way we tend to get at these benefits is by
             | putting things into custom silicon. A look back at some
             | powerful, low latency solutions shows just what really
             | understanding a need or problem well enough to make a
             | circuit, or mechanism to deliver can do. (A lot)
             | 
             | A while back I was setting up some advanced CNC CAM
             | software for an injection mold shop specializing in high
             | volume production. For a while they had an absolutely huge
             | demand for 3.5" floppy disk cases, for example! They
             | developed top notch, high performance mold tooling and had
             | the process very highly automated.
             | 
             | The vast majority of that automation was done with cams,
             | both linear and rotational types, simple electrical valves
             | to operate the necessary effectors, grips, pushers, and the
             | occasional PLC here and there, and those were mostly about
             | space and sometimes ease of development by newer engineers
             | who just did not think in that way more than it was a
             | requirement of some kind the mechanical means could not
             | address.
             | 
             | Similar means were in the machines themselves, analog
             | computers taking inputs from thermocouple, more cams and
             | such would maintain process consistency in a robust, will
             | run for a few decades with no worries kind of way.
             | 
             | I find this particular line of reasoning compelling. It is,
             | in some ways, much harder than the familiar run code on a
             | CPU connected to electromechanical devices and sensors way
             | we see today. But, it is also easier in ways too.
             | 
             | One notable ease was simply being able to understand what
             | the intended behavior was just by looking! I, being a lay
             | person with only at that time a shallow understanding of
             | the concepts, was brought up to speed quickly by the older
             | engineer teaching all this stuff to new team members, got
             | it quicker than I expected.
             | 
             | And it all can be done using ordinary tools, means,
             | methods.
             | 
             | Again, I find it interesting and compelling to learn about
             | this stuff. We can do a lot, and did amazing things on what
             | we could easily view as "stones and chisels" type tech,
             | given a modern perspective.
             | 
             | And take something like an EMP or some serious event or
             | other. People with these kinds of reasoning skills and
             | means, tools, methods could build, repair, and or engineer
             | solutions to tough problems without anywhere near the
             | degree of bootstrapping needed to get going from a "reset"
             | class event.
             | 
             | [1] - Not that I believe we are in some sort of simulation
             | or meta world space. I frankly do not know and tend to
             | focus my thoughts toward things that matter more to me and
             | also found all this to be convenient and lean such that I
             | need a lot less poking about on my mobile touch screen to
             | express my thoughts.
        
       | marcodiego wrote:
       | I asked this once. The answer I got was: because "Log(x) + Log(y)
       | = Log(XY), and the scales of a slide rule are logarithmic."
        
       | s0teri0s wrote:
       | I love slide rules. I'm old enough to have had one with a belt
       | case that I brought to school. But I have to ask, what is wrong
       | with a ridiculous amount of precision?
        
       | zwieback wrote:
       | My sister is 3 years older and she still learned slide rule in
       | high school but I didn't. Being a nerd I had my dad teach me
       | though. One of the key things is just the right amount of grease
       | in the tracks.
        
       | jhallenworld wrote:
       | For old calculating machines I want to recommend Prof. Chris
       | Staecker's YouTube channel, his videos are enjoyable. Here is a
       | play-list:
       | 
       | https://www.youtube.com/watch?v=swCy6pQSEpk&list=PLLFpXNanTP...
       | 
       | Inspired me to buy a Comptometer:
       | 
       | https://en.wikipedia.org/wiki/Comptometer
       | 
       | If all you need to do is add, Comptometers are the fastest
       | machines so far invented. They are fast because you can enter
       | entire numbers at once (as a "chord" with multiple fingers
       | pressing multiple digits at once). No need to hit "+" key or pull
       | a lever between numbers, each button press is an immediate
       | addition.
       | 
       | I'm thinking of making an electronic version- it would have the
       | same Comptometer key layout, but have more operations (for
       | example, hold multiply "shift" key down while entering number for
       | a multiply).
        
         | pwr-electronics wrote:
         | For graphical computation, I recommend Nomographer's YouTube
         | channel
         | https://www.youtube.com/channel/UCOLYtsL4ge6QfaAvBDeG1IA
        
       | xyzzy21 wrote:
       | Mathologer has a nice video about this via "log wheels".
       | 
       | https://www.youtube.com/watch?v=ZIQQvxSXLhI
        
       | GeorgeTirebiter wrote:
       | https://www.sliderulemuseum.com/Manuals/M220_AnEasyIntroduct...
       | is the best book ever for a beginning slide rule user.
        
       | pkaye wrote:
       | I think these are essentially nomograms. I seem to recall in
       | college engineering back in 90s they taught us how to design
       | nomograms for simple functions.
        
       | albert_e wrote:
       | For those who prefer this concept explained to you with a video
       | and examples -- https://www.youtube.com/watch?v=waiprjueVpQ
        
       | jhallenworld wrote:
       | A nice casual use case for a slide rule is metric conversion:
       | 
       | https://americanhistory.si.edu/collections/search/object/nma....
       | 
       | Consider that this slide is doing two things for you: it
       | remembers the conversion factor (for a bunch of difference
       | conversions), and it does the multiplication or division.
        
         | ddingus wrote:
         | I want one of these. Right now, I do this conversion a lot more
         | than usual. Over time, I have mapped many of my familiar
         | Imperial unit touchstone type references onto Standard
         | International units, so I am largely good to go, but this would
         | have been very useful during the process.
         | 
         | And what I mean here is just ones sense of scale and ability to
         | mentally estimate and work with familiar ratios to arrive at
         | solid first order approximations. These are important, in that
         | one can set expectations about the answer quickly and
         | accurately. Doing that is a great check on the problem overall
         | and or makes mental analysis quick and robust.
         | 
         | It is all the little things, like a sheet of paper being 0.004"
         | or 0.1mm. Looking at something, say to understand whether it
         | can be manufactured, or maybe features are too small or large
         | and fall outside process limits.
         | 
         | Or, given a force, something happening, or one suspects may
         | have happened, working backward to arrive at root cause of
         | failure, having that kind of info "in head", useable directly
         | in that internal way, knowing how it might appear, feel, be
         | seen, sound like, is high value.
         | 
         | Tools like this really help with all that. Combining the data
         | with motions, the slide, how far, etc all build robust mental
         | connections. It just starts happening. For me at least, I just
         | begin to "know" whether it make sense, will fit, break, etc...
        
           | spc476 wrote:
           | I have four slide rulers, and all of them I picked up at
           | various antique shops. The latest one I bought is the same
           | type that the Apollo astronauts took to the moon (Picket
           | N600-ES, about 6" (15.5cm) long). I paid about US$5 for it.
        
       | zanethomas wrote:
       | That's what I had for a calculator in chemistry.
        
       | evilotto wrote:
       | _The ark lands after The Flood. Noah lets all the animals out.
       | Says, "Go and multiply." Several months pass. Noah decides to
       | check up on the animals. All are doing fine except a pair of
       | snakes. "What's the problem?" says Noah. "Cut down some trees and
       | let us live there", say the snakes. Noah follows their advice.
       | Several more weeks pass. Noah checks on the snakes again. Lots of
       | little snakes, everybody is happy. Noah asks, "Want to tell me
       | how the trees helped?" "Certainly", say the snakes. "We're
       | adders, and we need logs to multiply."_
        
         | vincent-manis wrote:
         | This reminds me of the cartoon diagram of a computer posted in
         | our university's IBM 7044 computer room circa 1968. I've
         | forgotten most of it, but I still remember the snake swimming
         | in a little pool of water, subtitled "Floating-point adder".
        
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