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."
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”.
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).
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].
"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.).
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).
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
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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...
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.
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.
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).
In our high school physics class in early 80s, the teacher didn't care for calculators, so you'd have to do your calculations by hand, or learn to use a slide rule. I learned to use a slide rule, along with a buddy. I don't remember others in the class using slide rules, but looking back now, I have a hard time believing everybody else used pencil & paper. So there were probably others.
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.
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).
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.
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
> except for the E6B flight computer which is rather specialized
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.
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.
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.
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?
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.
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."
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.
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.
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?
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:
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.
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.
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.
