Why a Slide Rule Works
johndcook.com
johndcook.com
[1] Perfboard (5th screenshot shows it): https://apps.apple.com/us/app/perfboard/id46595187
[2] SlideRule.js: https://github.com/EngineersNeedArt/SlideRule
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.).
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).
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&...
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.
Ha. The famous E6B flight computer is a circular slide rule.
Edit: it's mentioned in the video.
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.
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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.
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.
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.
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.
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...
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.
One of my prized inheritances from my engineer father is his slide rule (complete with leather case).
I think that teacher didn't retire for another 20 years, so he may have had kids in the 21st century still learning to use slide rules for his class.
Does anybody make new slide rules?
That's a positive, not a negative, since it demonstrates a whole host of practical problems that can be solved quickly with a slide rule. And they still work fine for general multiplication, and they are cheap and easy to get.
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.
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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...
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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.
"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."
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.
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, π, 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.
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.
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.
Thanks for your comment.