Source: [Friden SBT10](https://youtu.be/1Bpnf17RRBQ)

Now tell it to divide by zero!

I actually saw a video on youtube where a guy asked such a mechanical calulator to divide by zero; the poor machine went into an infinite loop and didn´t stop until the guy turned the power off.

[This poor calculator!](https://www.youtube.com/watch?v=JU9ICaPZUCg) And my poor ears!

This is the expected result. This is kinda the result you expect to happen. Like a cartoon show when you ask the robot a paradox and it starts freaking out and explodes. These are all mechanical reactions. Electronics are not as fun in that regard. I expect my computer to explode or my robot to shoot itself in the head but it usually just crashes or tells me it cant.

I mean you can make them catch fire due to disabling the thermal limits but that shit hard

Mechanical…power off? (I thought the point was like before electricity)

Dude they had electricity in 1960

Mechanical referes to how it calculates. It uses gears and other physical mechanisms to generate calculations while regular calculators use circuits.

If you do that, it might catch on fire.

Halt or catch fire!

Halt and catch fire. And the show by the sane name was good but ignored, so shortlived, but they did complete all the story arcs

That was an amazing show. I rewatched again in the summer.

[OK, lets divide by zero](https://youtu.be/7Kd3R_RlXgc&t=103)

My grandfather had one at work back then. If you left it unattended people would make it multiply 99999999 times 9999999 and it would lock it up while it calculated

This is what I bring next day if my coworkers complain about my mechanical keyboard.

Was thinking to bring this to a maths exam or math class myself. Would be great to have if you worked in a business of adding numbers daily along with noise cancelling headphones for yourself.

No ANC headphone can get rid of this noise

Teacher "Of course you have to learn how to do long division on paper, your not going to be walking around with a calculator in your pocket" Hipster "Hold my Chai"

well if you had clicky switches then I would side with your coworkers

Cherry MX blue's!!

Least it's not box jades

box navies say hi

Oh Lord

*clicks in buckle spring*

I'll never be able to go back to non-mechanical keyboards for extended use. That being said, if your switches are loud enough to bother your coworkers then you're being an obnoxious prick.

I agree, **you** may like mechanical keyboards for their noise, that doesn't mean everybody around you does too. I find it quite distracting.

Most people don't buy mechanical keyboards because they like the noise

Granted, unfortunately the tactile feedback does translate into noise, at least on the most common ones.

inb4 your keyboard's still louder :\^)

I don't exactly know HOW my computer divides numbers, but I imagine it was based on one of these machines. It's like a physical algorithm, beautiful

multiple rounds of subtraction and decimal point shifting.

The mechanical engineering equivalent to the Towers of Hanoi recursion demo in software engineering, but like a lot more towers all at once.

Is that the thing that happens in Three Body Problem?

I both know more, and know less now.

it's long division, but with cogs an gears. or electrons and transistors, in the case of calculators

Wtf are you talking about?

Computers can only add, all the other arithmetic operations are permutations of adding operations. Search for "Slow division" and "fast division", these are the two families of division algorithms used in computers today (most modern computers use some variation of the [Goldschmidt method](https://lauri.võsandi.com/hdl/arithmetic/goldschmidt-division-algorithm.html), a Fast division algorithm).

> Computers can only add they can also divide or multiply by 2

Or powers of two, it's really sweet when you can, for example, divide by 128 super fast.

Multiplying by 2 (or anything) would just be adding, wouldn't it?

Multiplying (or dividing) by 2 can be done via a bit-shift. So, it could be done without doing the addition. While a CPU is going to have the bit-shift operators I doubt any would try to implement mult or div that way (that said, the complier could potentially optimize it to that).

Yeah I couldn't figure out dividing, but I'm not a 1960s computer programmer, but I was just pointing out multiplication is just addition.

Yeah, I haven't done embedded work in years and assembly in even longer. If I ever needed to do mult or div via bit-shift in my current work something has gone really wrong.

Imagine if you had to do it with punch cards.

That's the point though. Multiplication/division by a factor of 2 can be done *without* addition using a bitwise shift.

101000 is 40. Shift left by adding a bit (a zero on the RHS) 1010000 is 80.

Not quite. Multiplying or dividing by 2 is just a bitwise shift. You move all the bits one bit to the left for multiplication by 2 and one bit to the right for division by 2. You're sort of correct about floating-point math though - for multiplication by 2 you add 1 to the exponent, and subtract 1 for division.

I’m gonna upvote you cause you sound right, but I really have no way of knowing.

Multiplying by two in base two is just a bit shift, just like multiplying by 10 in base 10 is just adding a 0 to the end.

Got it. Pretty cool

Of course left vs right depends on your endianess

That's not exactly right, endianness is about the order of the bytes, not the ordering of the bits within a single byte. Left/right shift stays the same.

Absolutely not. Encryption is done with huge prime numbers, imagine having to add some giant number up 3629647470100826378497 times. It would take AGES. No they use fast algorithms for multiplication.

There are 10 types of people in this world; those who understand binary, and those who don't.

More a reply in general rather than to you specifically: https://nandgame.com/ Building up a computer using nothing but nand gates. It is the very fundamentals of how that machine works. Starting with just nand gates you build out all the logic needed to build out adders and finally a basic computer.

Ok so computers should actually be called adders. TIL

Actually, we call the part of the processor that does this the ALU - arithmetic logic unit. It contains lots of adder circuits.

And computers used to refer to [people](https://english.stackexchange.com/questions/29470/etymology-of-computer-before-computer-referred-to-a-machine) who did calculations! Human computers were replaced by mechanical computers (like the one in this post), which were then replaced by electronic computers.

Don’t forget comparison operations

And bit shifting

Comparison is just subtracting and then jumping based on whether the result is less or more than or equal to zero.

I would venture to say that it isn’t like a physical algorithm, it ***IS*** a physical algorithm. Computers are nothing more than a particular pattern of electrons in fancy shaped wires Your CPU, the processor, the brains of the computer, works by letting the pattern of electrons flow like water through what’s called a computer “die.” Then, the CPU reinterprets the new pattern electrons on the other side and decides what to do with them All digital data also exists in a physical form on this planet (or in its orbit). They’re nothing more than electrons stored in a certain pattern and can be located on a physical machine

When you get to Calculus 2 and then Differential Equations, you actually perform the equations calculators use to find their answers. By that point, you’ve progressed past what a calculator can do for you. You just use them for the arithmetic.

Not quite e.g. I know my calculator uses CORDIC but I have never ever heard of a calc class that covers that and honestly if it showed up in a calc class it would be downright abusive.

Basically true for most calculators but isn’t there like a fancy TI-91(?) that can do calculus and equations? I think i remember seeing from the list of banned calculators but this was a few years ago when I was buying my graphing calc for school.

The TI-Nspire I was required to get for high school could solve multiple variable integrals.

None of this is true.

Honestly it seems like building an electronic digital calculator would be easier than making this electromechanical calculator.

Well you would disagree if you saw how complicated transistors were at this timeframe

Vacuum tube transistors acted similarly to MOSFETS didnt they?

This was the last gasp luxury end of mechanical calculators before electronics wiped them completely out.

It would be fucking badass to see virtual breakdowns and simulations of this!

Say no more! Here are some mechanical calculating components in naval firing computers that could tackle multi-variable calculus. Very educational! https://m.youtube.com/watch?v=s1i-dnAH9Y4

Thanks for sharing that, I love seeing this kind of stuff. We should show this kind of thing to all our kids coming up through school lest we forget. Reminds me of when I was 11 and dad got his army mos changed to data processing. We had an army training manual called "Digital Computers". I read it several times. Started with Boolean algebra - ands, ors, nors, fors, etc. -- then counting in binary I think, then on to building logic gates and fiip-flops with diodes, then how computers of the day used that technology to compute. I would pay a lot to have that manual.

If you hit Google images, was it either of these two titles? 1) FM 11-72 Digital Computers, Fundamentals 2) TC 9-72 COMMUNICATION-ELECTRONICS FUNDAMENTALS: DIGITAL COMPUTERS I think there's a way you can purchase reprints of these manuals from some government agency. If not, surplus military training manuals are sold by various outlets.

That was amazing! Thanks

That was awesome. You just sent me down a rabbit hole of mechanical computer videos.

I’ll do you one better: [here’s a physical demonstration of a simpler machine, presented by the the most charismatic math enthusiast you’ve ever seen](https://youtu.be/wwh0KH-ICCw)

My thesis advisor told me a story about when he was in grad school and bought his first electronic calculator. He was so excited he woke up a few times during the night, did some square roots, and went back to bed

This actually made my giggle. Definitely one of those things that makes you appreciate the technology we have now.

*yawn* just gonna do sum square roots...

As much as I can only fool myself into thinking I could theoretically understand how electrons interacting with metal and silicon to create 0s and 1s could possibly be used to perform calculations, the idea that someone could create a system of gears and other things that go "clicky click" to do the same thing is beyond me.

Well, if it makes it easier, they took the same concept and implemented it in the reverse direction! All we did was make the pieces smaller.

Battleships used to use analog computers that were the size of about two big desks back to back, which could be fed a target range, bearing, and velocity, and then automatically track the turrets to compensate for the battleship's speed, target's speed, and battleship pitch and roll from the waves. The turrets would just automatically track whatever they were pointed at, and were devastatingly accurate.

>and were devastatingly accurate. Well, for that time they were. But it was still only a 5-10% hit rate. Mostly because of physics being a bitch, and/or rangefinding errors.

They did that in the Air Force with a mechanical wonder called the Norden Bombsight. They used it to lock in on targets after 6 seconds or something. My dad was in the Army Air Corps (the Air Force in WW2 before it was a separate division). He was a bombsight mechanic and too valuable to go into combat. He said it had a bunch of gyros in it and every time you took out a screw you had to put it back in the exact same hole because of the precision of balancing the weights. He enlisted at Ellington Field and took a bunch of tests. To qualify to be a bombsight mechanic you had to score in the top 1% on IQ and the top 1% on mechanical aptitude. His bombardment group got 2 Distinguished Unit Citations and he personally got 2 Bronze Stars.

Its the same processes, but so much more insane. Hell even those old school vacuum tube computers are so insane to think about. Way more insane then the chips that replaced them.

This. I'm in absolute awe at anyone who can understand how it works and even more so when they _created it_

Fruit machines (mechanical gambling machines/one armed bandits) work in a similar way, I've rebuilt one before, and it's fascinating how it works, a big mechanical computer with 7 bits of ram. Amazing considering how old they are, pretty sure they predate mechanical calculators.

Good thing for you they had to train sailors on how they work https://www.youtube.com/watch?v=gwf5mAlI7Ug

It's electric, but not electronic.

🎵Boogie woogie woogie🎵

It depresses me to think about the skills that men developed over their careers to build something like that, only for it to be completely obsolete a short time later.

Eh it’s all a process of building better methods on top of what’s already know. We might not have gotten more efficient calculators until later without earlier devices such as this.

We stand on the shoulders of giants.

Seriously. Major props to those who came before us and forced the road ahead

As I said in another comment, I'm skeptical that's true. Mechanical calculators don't seem like an evolutionary step toward electronic computers. Although there is some overlap in what they accomplish, they are entirely different technologies. I doubt much of what we learned by building mechanical calculators helped us to build electronic computers.

I thoroughly enjoyed reading this. I could almost feel your excitement on the subject and it definitely projected onto me.

I love stuff like this! I'm glad you enjoyed it. If you want more content, here's a great channel on mechanical calculators and typewriters and just general retro computing: [TechTangents](https://m.youtube.com/c/AkBKukU)

Yes thank you, it’s like saying punch cards don’t lead to computers

You deserve a r/bestof post my dude

Someone did it! https://www.reddit.com/r/bestof/comments/r1pbg6/ufirewolf420_explains_the_significance_of_older/

Wow! Didn't expect this!! <3 This was nice to see after my Thanksgiving meal

Thank you!!!

Thanks for the link!

Probably didn't help physically, but maybe some of the ideas behind logic and the process could've helped.

Or you know, not having to do all the math by hand might have sped things up a bit

both great points!

I mean, this is the kind of thing IBM was building before they built mainframes... typewriters and calculators like this. The engineering process, business process, information process, all evolving to the digital computer.

Not just development of the mechanism, development of the entire concept of a desktop calculator. Would an electronic calculator in it's current form (numeric keypad, with digits and operators input in sequence and an answer produced on explicit command) even exist if there were not already a market for such a device? If all that was available when discrete ICs became available were abaci or two/three function digit-wheel iterative counting machines, it would be a lot harder to both develop the concept of a modern calculator, and to drum up the funding to implement it (it's much easier to fund "X, but smaller and cheaper" than "imagine if you had a machine that could manipulate numbers, but did not require a skilled operator"). e.g. we see this with the way mechanical semaphore towers predated electrical telegraphs, but laid the groundwork not only for the concept of coding schemes but for the concept of sending ephemeral duplicates of messages over predetermined shared physical channels in the first place.

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I was going to say. On a modern processor you can probably find a transistor allegory to any of the mechanical systems in that early calculator. Early attempts at designing digital circuits pretty much certainly drew from the knowledge of mechanical circuits since the logic pathways and algorithms already existed and just needed to be adapted to a transistor layout.

It paved the way. We couldn’t skip that step, what they did was lay the crucial foundation for what we work with now.

The analogy of a foundation doesn't seem apt. I doubt much of what we learned from building mechanical calculators like this one translated well to electronic computers. edit: that's part of why I find it depressing, actually. Despite the skill these guys possessed and the refinements they made over the years of producing mechanical calculators, it was a dead end, technologically. Electronic computers work on a completely different set of physical principles, and are superior in practically every way.

You are going to shit on the caveman because he didn't have a bic lighter already?

I gotta try and find it for you but I think you would really dig this one old reel about the last days of the old New York Times printing press, before it switched to a computer controlled system. Edit: here you go. I hope you enjoy it. https://youtu.be/1MGjFKs9bnU

I don’t know why you’re being downvoted, you’re right.

They aren't right. Mechanical computing came before electrical.

Yes it came first, but that’s not what he argued against. He said that these miraculous mathematical mechanisms aren’t what electronic calculators are based on, which is accurate: though these devices are awesome, their electronic counterparts were designed with different principles (optimized for the relays that constituted the machines).

No,they aren't right Have you heard of the analytical machine?Lady Ada Lovelace wrote the first algorithm ever for that machine,but the analytical computer was too slow to run it properly.However her techniques paved the way for more modern algorithms on Modern computers used today.Similiarly,these machines,in essence, use the same techniques to add and subtract that modern computers and calculators do,just using mechanical components instead of transistors.

The understanding and insights such machines provided were definitely integral to the creation of electronic computing but the methods of operation are not the same (thus why electronic computers are so fundamentally different). No one is saying that the mechanical predecessors were unimportant (that importance is part of what we’re emphasizing). What we’re saying is that the electronic computers’ fundamental operation is too different from the mechanical for them to be the foundation. The mechanical computers were more like the testing ground for concepts before being adapted for electricity.

He's not right. In fact he's so wrong that it's frustrating. He said that mechanical computations had no bearing on digital programming of the same computations when in fact the original computer programmers first used the analog computations to program the first digital calculators (i.e. using the methods of analog in digital) and they simplified from there.

> He said that mechanical computations had no bearing on digital programming of the same computations He most certainly did not, and neither have I. We are saying that, the fundamental operations of the two are different: though they share concepts, one is confined to logic gates and binary while the other works with decimals and decimal shifting.

> He most certainly did not, He said >I doubt much of what we learned from building mechanical calculators like this one translated well to electronic computers. Which is pretty much saying that mechanical computations had no bearing on digital programming of the same computations

Don't be depressed! The journey sometimes makes it all the worth while.

It's not really a short time though. These calculators were relevant and used into the 90s, especially at older small businesses. They saw a ton of use. I used to travel with my old man for work and I remember different versions of these still being on the desks of every crusty old proprietor we dealt with. So if you think about it, many of these probably had long and productive service lives just like their designers and builders intended, and there were a ton of other electro-mechanical devices that benefited from their development.

One of my regular deliveries, until the early 2000s, was an old store that was still using a crank-lever cash register. Not even electric; you pulled a handle on the side to execute each operation. The proprietor told me he never intended to get rid of it. He remembered being the only store in town able to operate as normal one time during a prolonged blackout.

I used to work for NCR in Dayton OH. Their campus still had the old buildings that were the steel and brass foundries and held the massive plate presses. Beautiful cash registers were created by master craftsmen and massive production shops. They are prized collectibles now, with their brass NCR nameplates and wooden cash drawers. But they were the super reliable workhorses of the retail world. Their sales pitch was to keep all employees honest by creating a visible ring-up and printed receipt record of each transaction. Before these machines, an owner couldn’t be certain if his employees were skimming a bit of the till. NCR then looked at the labor involved in pricing each item in the store (remember the old labeling machine to put a price sticker on each can of green beans!) and with the growing “just in time” inventory concept, and along came electronic databases and fully computerized systems. NCR even had the first wireless multipoint network (called WaveLan) that allowed employees to walk around with handheld price scanners that were constantly linked to the store’s central database. Talk about a stepping stone on the way to WiFi! Just looked it up on wiki - “WaveLAN laid the important foundation for the formation of IEEE 802.11 working group and the resultant creation of Wi-Fi.”

Reminds me of VCR's.

Those were seriously underappreciated by everyone who never opened one up and watched it work.

Seriously. Check this out. 3MHz of bandwidth on a half-inch ferromagnetic tape running at only 1.3in/sec (0.9 in Europe) and sometimes only a third of that at SLP https://youtu.be/KfuARMCyTvg

I was hoping it would be a Technology Connection video.

This is why they had to go find one in Cowboy Bebop. Future tech couldn't handle that shit.

So what ya working on now? SURPRISE it's going to be obsolete in 10 years so you can stop working on it now

Not obsolete. People would have created algorithms based on the processes used to make this machine work. chances are the work that went into this saved a ton of time later on.

"Short Time" Do you also feel bad that the NES was made because ~10 years later the N64 was released? Seems like creating the NES was a waste, right?

That's not the same thing. Skills that people honed working on the NES were undoubtedly very directly applicable to the N64. Probably a lot of people worked on both.

Complicated mechanical machines are still around, too.

When I was a small child my father was a draftsman. In the draftsmen's office there was a mechanical calculator similar to this one. To watch it work was mesmerizing, needless to say. Jesus. That was only 57 years ago....

In the 1960s-70s, my father occasionally brought one home - he worked at a bank, so he was roped in to help out with the church accounts - only it wasn't even electric. It had a crank handle like an old-style one-armed bandit slot machine. Hit "clear", crank the handle Enter first number, press operation, e.g. + - \* or /, crank handle Enter next number, and operator, crank handle Repeat until ready to generate the answer, press '=', crank handle. I forget how many numbers could be entered before you had to hit the '=', and I don't think you could mix operators within one calculation, i.e. it was all +, or all \*

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You probably haven't been a real_human_person for as long.

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You'll get there friend.

I was a kid then. A *long* time is relative: my memories from then are as clear as yesterday's, yet since then people have gone into space, created artificial mechanical organs, invented handheld computers. I recall talking to my favorite aunt. She saw the electrification of her parents' neighborhood, their first televisions, the birth and growth of the automotive, aerospace, chemical and electronics industries, civil aviation, the moon landing, and computers, e-mail, etc. A lot happens.

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You and me both. What happens next is more often good than bad, so I'm kind of looking forward to it.

I had a fleeeeting glimpse

If I still had a job where I worked in a cubicle, I would absolutely take this into work and have this thing on my desk. Like when Ron Swanson got the old typewriter in Parks & Rec.

“I’m going to calculate every number I know!” “Pi!” “Euler’s!” “Butthole!”

"Euler's Butthole Pi!"

New band name! CALLED IT!

Imagine taking an exam with one of these. And punching in 2+2, you know just to be sure.

Wow super glad people built this stuff in the past. Also double super glad that we don't have to use this shit now.

I’m an electronics engineer how tf does this work

Gears go clickety clack

22 \----- 7 Might be just a liiiiiiiitle big easier.

a.k.a. [Yuelü](https://en.wikipedia.org/wiki/Mil%C3%BC)

Just use 3

I’ve spotted the engineer

https://www.forbes.com/sites/kionasmith/2018/02/05/indianas-state-legislature-once-tried-to-legislate-the-value-of-pi/

22/7 only gives 2 decimal points of pi (3.14) 335/113 gives 6 decimal points of pi (3.141592) So it just depends how much accuracy you need. 22/7 works for a lot of things and it's good to know, but 335/113 is accurate for pretty much anything conventional (or exceeds the accuracy needed). About the only things I can think of that really commonly use significantly more decimal places of pi would be NASA, they use 15 or 16 decimal places when calculating various things for the guidance control system in the ISS. It's been calculated that you could determine the circumference of the known universe with 39 decimal places of pi and be accurate to within an atom's width.

~~So out of curiosity I did the napkin math. If the universe is about 93 light years, that is a circumference of around 5.5e18 meters. A proton, which is muuuuch smaller than an atom is less than a femtometer, but let's just say 1e-15 meters. So that means the circumference of the universe would roughly be 5.5e33 protons around, which means 39 decimal places of pi would allow you to split hairs on the back of a proton.~~ Edit: tired brain. Universe bigger than 93 ly and is actually 93e9 ly. Universe is then around 5.5e42 protons around, so need a few more decimal places of pi to split those hairs

But that's only accurate to 2 decimal places. 355/113 is accurate to six !

Agree and I hear you. I think we BOTH hate them both. It's like, *"My god man use π and stay in school long enough to know how to use it. It's not asking that much."*

My Dad used a slide rule to design airplanes...genius level stuff but tripped over the iterative process of modern engineering... The refinement, tolerances and safety factors unimaginable to his generation. He's passed now but damn they were amazing engineers. Our generation is too, just different tools and narrower roads to follow on the way to solutions.

If you like this look up the curta calculator from WW2

Now imagine you are tasked with fixing one.

You call a watch maker.

Mechanical calculators are so fascinating! Here's a Monro-Matic CSA-10 that I restored last year [doing the same thing](https://imgur.com/a/195OZ8z).

Damn, that's hot

What are you doing step-calculator? Divides by 0

It’s whisper quiet.

Crazy. Would not want to be the repair guy.

if that's a calculator, their iphones must have been big as buicks!

i wonder what /r/typewriters would think of this

This reminds me of a calculator someone built in Minecraft. I wonder if someone could build a computer inside of Minecraft

Can and has. Don’t have link put someone built the equivalent of a c64 in MC

I'm old enough to have played with these - restoring one and making them operational sounds like a terrifying task...

"You can bring a calculator to the test"

My [great-grandfather](https://en.wikipedia.org/wiki/Carl_Friden) invented this! Wild seeing it on Reddit! We had one of these in our home when I was growing up.

This mf gonna subtract a finger if you’re not careful

The sounds it makes are fabulous.

That is a thing of beauty. All the parts were hand drawn, thought out by mere humans.

I want to know.how it works, but I don't have a week of free time.

60 years from now we will be looking at tablets,smart phones,and laptops the same way we look at this interesting but antiquated device...and don’t get me started in gaming devices,all consoles today 60 years from now will look like PONG compared to what they’ll have.

Okay, so this is something that amazes me. There's simple aglorithms to add, subtract, multiply and even divide. It's no big deal to program these algorithms on a computer in machine code. There's internal combustion engines with a simple timing chain that controls the valves to make sure there's fuel/air mixture inside the cylinders at the right time which gets ignited at the exactly right point. And then there's THIS THING. It's basically something in between and yet completely different. It's multiple algorithms cast into a mechanical machine. Blows my mind.

Wow, this thing looks like it was a nightmare to manufacture and produce lol.

Do 420/69 next.

When the class you're taking requires a TI-84, but all you have is your grandpa's TI-1

Back when you could lose a finger trying to use a calculator.

But can it play Doom?

I desperately want to see someone tackle this challenge.