I don't know if he mentioned, the name doesn't show up in the transcript, it but this seems to be very close to an unrolled Curta, the main difference being that it doesn't use 9s complement for subtraction so it has a more complex bidirectional carry mechanism. Otherwise the function is very similar down to shifting the turns and output accumulator to multiply the entry number. The big drum he makes many of is just one in the Curta that actuates every output dial through a full rotation.
9s complement makes subtraction extremely satisfying on the Curta because it causes a carry on (almost) every single output and turn accumulator dial.
Hi, I made the calculator and this video. As I discuss throughout and particularly towards the end of the video, my design is based on Thomas de Colmar's Arithmometer (~1820-1860) and Leibniz's Stepped Reckoner (late 1600s), both of which predate the Curta (1930s). Or rather, the Curta is a super cool and elegant refinement of those (and other) designs. I think it is more accurate to say the Curta is like a rolled up version of those (and my) calculator.
The "big drum" you mention is sometimes called a Leibniz Wheel, though this naming convention is misleading in some ways: http://journals.cambridge.org/abstract_S0007087414000429. As that article argues (though I disagree with some points), the history of calculating machines is more nuanced than a linear progress narrative suggests. So, I tried to keep my narrative a little tighter and not go much into the calculators of the late 19th century and the designs in the 20th century like the Curta. Also, the Curta's (awesome!) story has been told many times, so I did not feel the need to go into it. Sorry to go on this long, but I think this history is fascinating and how we tell it speaks to how we understand how technology changes through time.
I just want to say that this is one of my favorite YT videos of all-time. Content, presentation, project, execution, pace, music : all perfect. That is NO exaggeration. You have made my day better, young man.
Well done, young sir! Thank you for your hard, difficult work, and sharing it with us.
The carry propagation hardware is the hardest to make work right. The low-digit add has to power the entire chain of carries. As the number of digits increases, it gets harder to do that, because so much mechanism has to be pushed.
There are carry mechanisms which use an external power source for carry propagation. Babbage's Difference Engine has one.[1] All the pending carry values are stored in a latch for each number wheel. Then a cam system applies the carries one at a time. This scales to large numbers of wheels.
Yeah carry propogation is tricky. Matthew Jones (the historian who wrote the book I discuss in the video) calls it the "Sufficient Force" problem. Babbage certainly did solve the problem, but so did Thomas de Colmar in his calculator and all the derivatives it spawned (including mine). This is because the mechanism that performs the carry is driven by the central drivetrain and furthermore each column is offset in the cycle (by 1 tooth of the drive sprockets) so that carries ripple, instead of happening all at once. See 20:35 in the video. This means that a low-digit add does not directly power the entire chain of carries, it just triggers them. And furthermore, you can basically keep adding columns without worrying about the force increasing drastically: Thomas de Colmar even made a "piano Arithmometer" with a 30 digit capacity.
While carry propagation is certainly a hard problem to solve (just ask Leibniz), I had much more difficulty getting the zeroing mechanism to work smoothly - in a way it's a similar issue because you need to move a bunch of parts all at once, which from a force perspective is difficult.
Oh I should mention that Pascal also solved the sufficient force carry propagation issue in the Pascaline with his "sautoir" mechanism.
You can definitely feel it when doing subtraction on a Curta, there's significantly more drag involved in it both because you're generally adding a larger number so more teeth interact but also the wave of the carries going around. However the low digit doesn't have to power all the carries though on a Curta because all the carry does it shift a gear up that then interacts with a single tooth (or 9 during subtraction) on the drum that performs the carry for the next digit up.
There's a whole page of Curta info [0] and a 3d simulator [1] where you can see how similar the setup is and some of the ingenious tricks to fit all of the functions of this machine into a little larger than a grenade sized package.
Yes, as the number of wheels scales up, powered carry becomes necessary.
Another mechanism that's been used is sort of analog - differential gears, with two inputs and one output. Race track totalizators used that to add multiple unsynchronized inputs. Here's one from Adelade.[1] The machines were huge and heavy, but reliable.
(It is a tradition and a contract term in the gambling industry that gambling equipment companies are strictly liable for errors. As a result, that industry builds unusually reliable equipment. GTech once mentioned in an annual report that they paid out about 3% of revenue in error payments.)
Great video, I really enjoyed how down to earth it was. It reminded me of The Secret Life of Machines [1], where we get to peek behind the curtain and see how seemingly "magical" machines (in your case a digital computer) emerges from simple fundamental concepts.
I love thinking about the "what if?" universe where we never figured out semiconductors and transistors, but still had roughly the same level of human progress. Would everything be clockwork like Syberia [1]? Would we have something akin to iPhones but done entirely with electro-mechanical stuff with antennas? I guess this is sort of the appeal of something like Steampunk.
Mechanical calculators are ridiculously cool to me. If I ever become an eccentric billionaire, I really want to buy an original Curta calculator [2], just because I respect the genius and engineering required to design such a thing.
The one in this video is also very cool. Very satisfying to watch all the gears turn at once.
£850 is actually cheaper than I thought it was, but it's still a bit much for me to justify right now. If I spent a grand on a fidget toy, I think my wife would be pretty mad at me.
Whatever patents that they had have to be expired, I kind of wish someone would make reproductions. I know there's the 3D printed ones, which are cool in their own right, but since 3D printers aren't super precise the parts have to be huge to compensate. I want as close to a one-to-one reproduction as possible, but I guess there's not much money in it.
It doesn’t help that they made an absolute ton of them: something like 140,000! That means that they’re not particularly rare, and it holds the price down.
Add in the fact that authenticity is part of the appeal, plus the fairly expensive process to make a decent replica, it’s not shocking that no replicas have emerged, even though cheap-ish CNCs mean it’s probably easier to do than it ever has been.
I'm sure they would not have been less than £850 in whatever currency it was sold in back then, inflation adjusted. But the justification was much better than being a fidget toy.
Update it with USB so that it can take input and return results. Hook it up to a cash register for something like an antique store. Ideally one selling small items so that the customer can marvel at the display adding things up.
I also have always wanted one of those mechanical vintage cash registers, for the same reason I have always wanted a Curta. They always seemed like they would be fun to play with.
I could probably get one of those cash registers to play with for not a ton of money, but my house isn't huge and it's hard to justify the space.
I have had an interest in building a mechanical computer for a long time. It has not ever gotten farther that some research into what route to take. There are lots and lots of simple logic mechanisms (many, many in use in real world applications). It can go as far and be as capable as you have time for.
Mechanical computers are a great reminder of what computation is and what it isn't.
Computation as studied by computer science is not a physical phenomenon, but a mathematical construct that claims to formalize the notion of an effective method. This claim is perhaps most tangibly expressed in the form of the Church-Turing thesis.
Computing devices are not objectively computing. They simulate the formal construct. Anything that can be used "computer-wise" can be said to be a computer in the same manner that anything that can be used chair-wise can be said to be a chair. But there is nothing inherently computational about the device itself.
> Computing devices are not objectively computing. They simulate the formal construct.
Isn't it backwards? I don't think that e.g. herding sheep into the pen while making a mark on the door for each sheep "simulates counting sheep". Instead, you can use the formal construct "counting sheep" to describe this physical process: "doing this and this will count the sheep".
Otherwise you may very easily end up puzzled why maths is so unreasonably effective in natural sciences.
I don't know if he mentioned, the name doesn't show up in the transcript, it but this seems to be very close to an unrolled Curta, the main difference being that it doesn't use 9s complement for subtraction so it has a more complex bidirectional carry mechanism. Otherwise the function is very similar down to shifting the turns and output accumulator to multiply the entry number. The big drum he makes many of is just one in the Curta that actuates every output dial through a full rotation.
9s complement makes subtraction extremely satisfying on the Curta because it causes a carry on (almost) every single output and turn accumulator dial.
Hi, I made the calculator and this video. As I discuss throughout and particularly towards the end of the video, my design is based on Thomas de Colmar's Arithmometer (~1820-1860) and Leibniz's Stepped Reckoner (late 1600s), both of which predate the Curta (1930s). Or rather, the Curta is a super cool and elegant refinement of those (and other) designs. I think it is more accurate to say the Curta is like a rolled up version of those (and my) calculator.
The "big drum" you mention is sometimes called a Leibniz Wheel, though this naming convention is misleading in some ways: http://journals.cambridge.org/abstract_S0007087414000429. As that article argues (though I disagree with some points), the history of calculating machines is more nuanced than a linear progress narrative suggests. So, I tried to keep my narrative a little tighter and not go much into the calculators of the late 19th century and the designs in the 20th century like the Curta. Also, the Curta's (awesome!) story has been told many times, so I did not feel the need to go into it. Sorry to go on this long, but I think this history is fascinating and how we tell it speaks to how we understand how technology changes through time.
Your machine, and the video, are astounding. The complexity and precision of your design, and the clarity of the explanation were all marvelous.
Thanks so much for bringing this to us.
Just wanted to say, fantastic work and video. I really enjoyed watching it.
I just want to say that this is one of my favorite YT videos of all-time. Content, presentation, project, execution, pace, music : all perfect. That is NO exaggeration. You have made my day better, young man.
Well done, young sir! Thank you for your hard, difficult work, and sharing it with us.
ETA: And you got a lol from me at the end!
Thank you all for the kind words! I appreciate all the wonderful comments and support from people - It is so encouraging and makes me very gratified.
Great video! Very instructive.
The carry propagation hardware is the hardest to make work right. The low-digit add has to power the entire chain of carries. As the number of digits increases, it gets harder to do that, because so much mechanism has to be pushed.
There are carry mechanisms which use an external power source for carry propagation. Babbage's Difference Engine has one.[1] All the pending carry values are stored in a latch for each number wheel. Then a cam system applies the carries one at a time. This scales to large numbers of wheels.
[1] https://youtu.be/vdra5Ms__9s?t=247
Yeah carry propogation is tricky. Matthew Jones (the historian who wrote the book I discuss in the video) calls it the "Sufficient Force" problem. Babbage certainly did solve the problem, but so did Thomas de Colmar in his calculator and all the derivatives it spawned (including mine). This is because the mechanism that performs the carry is driven by the central drivetrain and furthermore each column is offset in the cycle (by 1 tooth of the drive sprockets) so that carries ripple, instead of happening all at once. See 20:35 in the video. This means that a low-digit add does not directly power the entire chain of carries, it just triggers them. And furthermore, you can basically keep adding columns without worrying about the force increasing drastically: Thomas de Colmar even made a "piano Arithmometer" with a 30 digit capacity.
While carry propagation is certainly a hard problem to solve (just ask Leibniz), I had much more difficulty getting the zeroing mechanism to work smoothly - in a way it's a similar issue because you need to move a bunch of parts all at once, which from a force perspective is difficult.
Oh I should mention that Pascal also solved the sufficient force carry propagation issue in the Pascaline with his "sautoir" mechanism.
You can definitely feel it when doing subtraction on a Curta, there's significantly more drag involved in it both because you're generally adding a larger number so more teeth interact but also the wave of the carries going around. However the low digit doesn't have to power all the carries though on a Curta because all the carry does it shift a gear up that then interacts with a single tooth (or 9 during subtraction) on the drum that performs the carry for the next digit up.
There's a whole page of Curta info [0] and a 3d simulator [1] where you can see how similar the setup is and some of the ingenious tricks to fit all of the functions of this machine into a little larger than a grenade sized package.
[0] https://www.vcalc.net/cu.htm
[1] https://www.satadorus.eu/x_ite/yacs_2_0/yacs_2_0.html
Yes, as the number of wheels scales up, powered carry becomes necessary.
Another mechanism that's been used is sort of analog - differential gears, with two inputs and one output. Race track totalizators used that to add multiple unsynchronized inputs. Here's one from Adelade.[1] The machines were huge and heavy, but reliable.
(It is a tradition and a contract term in the gambling industry that gambling equipment companies are strictly liable for errors. As a result, that industry builds unusually reliable equipment. GTech once mentioned in an annual report that they paid out about 3% of revenue in error payments.)
[1] https://www.cs.auckland.ac.nz/historydisplays/SecondFloor/To...
Great video, I really enjoyed how down to earth it was. It reminded me of The Secret Life of Machines [1], where we get to peek behind the curtain and see how seemingly "magical" machines (in your case a digital computer) emerges from simple fundamental concepts.
[1] https://en.wikipedia.org/wiki/The_Secret_Life_of_Machines
For a second video, this is amazing. It also took me to their first video which is a mechanical hand, also out of wood https://youtu.be/gxT8TfI5DaE
I love thinking about the "what if?" universe where we never figured out semiconductors and transistors, but still had roughly the same level of human progress. Would everything be clockwork like Syberia [1]? Would we have something akin to iPhones but done entirely with electro-mechanical stuff with antennas? I guess this is sort of the appeal of something like Steampunk.
Mechanical calculators are ridiculously cool to me. If I ever become an eccentric billionaire, I really want to buy an original Curta calculator [2], just because I respect the genius and engineering required to design such a thing.
The one in this video is also very cool. Very satisfying to watch all the gears turn at once.
[1] https://en.wikipedia.org/wiki/Syberia
[2] https://en.wikipedia.org/wiki/Curta
Maybe without semiconductors we would stumble upon something better sooner.
Maybe optical/biological/quantum computing.
You don't have to be a billionaire, I got a Curta mark I for ~£850 on ebay and it's like the world's greatest fidget toy.
£850 is actually cheaper than I thought it was, but it's still a bit much for me to justify right now. If I spent a grand on a fidget toy, I think my wife would be pretty mad at me.
Whatever patents that they had have to be expired, I kind of wish someone would make reproductions. I know there's the 3D printed ones, which are cool in their own right, but since 3D printers aren't super precise the parts have to be huge to compensate. I want as close to a one-to-one reproduction as possible, but I guess there's not much money in it.
It doesn’t help that they made an absolute ton of them: something like 140,000! That means that they’re not particularly rare, and it holds the price down.
Add in the fact that authenticity is part of the appeal, plus the fairly expensive process to make a decent replica, it’s not shocking that no replicas have emerged, even though cheap-ish CNCs mean it’s probably easier to do than it ever has been.
I'm sure they would not have been less than £850 in whatever currency it was sold in back then, inflation adjusted. But the justification was much better than being a fidget toy.
Oh definitely, prior to having cheap computers that can compute gigaflops, I would definitely have bought one to do number crunching.
The problem is that if I bought one now, it would simply be a toy and nothing else. That's just a bit more than I'm willing to spend.
Update it with USB so that it can take input and return results. Hook it up to a cash register for something like an antique store. Ideally one selling small items so that the customer can marvel at the display adding things up.
I also have always wanted one of those mechanical vintage cash registers, for the same reason I have always wanted a Curta. They always seemed like they would be fun to play with.
I could probably get one of those cash registers to play with for not a ton of money, but my house isn't huge and it's hard to justify the space.
What is the simplest way to do mechanical logic? Without all those fancy looking gears. I wonder how far it can go if you actually optimize it.
An interesting option is rod logic, which is the mechanical equivalent to a PLA (programmable logic array).
https://www.jamiekawabatarobotics.com/?p=40
https://www.youtube.com/watch?v=G_SC7oWL78A
The Whiffletree was used in mechanical calculators. It's an interesting way to encode digital data mechanically.
I have had an interest in building a mechanical computer for a long time. It has not ever gotten farther that some research into what route to take. There are lots and lots of simple logic mechanisms (many, many in use in real world applications). It can go as far and be as capable as you have time for.
the madness of cutting hundreds of gears by hand, many with a 45 degree bevel, I couldn't even imagine.
madness!
Great work, excellent video.
You can just continue the division by inputting the remainer i think?
Mechanical computers are a great reminder of what computation is and what it isn't.
Computation as studied by computer science is not a physical phenomenon, but a mathematical construct that claims to formalize the notion of an effective method. This claim is perhaps most tangibly expressed in the form of the Church-Turing thesis.
Computing devices are not objectively computing. They simulate the formal construct. Anything that can be used "computer-wise" can be said to be a computer in the same manner that anything that can be used chair-wise can be said to be a chair. But there is nothing inherently computational about the device itself.
> Computing devices are not objectively computing. They simulate the formal construct.
Isn't it backwards? I don't think that e.g. herding sheep into the pen while making a mark on the door for each sheep "simulates counting sheep". Instead, you can use the formal construct "counting sheep" to describe this physical process: "doing this and this will count the sheep".
Otherwise you may very easily end up puzzled why maths is so unreasonably effective in natural sciences.
Great work !