[rtkwe]

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.

[WilliamG52]

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.

[MrMcCall]

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!

[WilliamG52]

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.

[mjd]

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.

[gregschlom]

Just wanted to say, fantastic work and video. I really enjoyed watching it.

[glth]

Great video! Very instructive.

[Animats]

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

[WilliamG52]

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.

[rtkwe]

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

[Animats]

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...

[matt-attack]

Yep. The whole time I kept thinking, “oh so that’s why I have to that to the curta” or “oh so now I get what’s happening in my curta!”