[HN Gopher] Why a Slide Rule Works
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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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