 So welcome to a historic talk, not historic because I do it for the first time, but it's more history lesson. We are jumping back 400 years. Here is a machine that has its 400th birthday as of today. So let's celebrate that. Wow. And yeah, it's only a replica. Sorry, it's not the original one. It's a replica. But this could be called the very, very first computer, computer to be defined. A machine that adds and multiplies on its own. Not a human person that knows how to add and to multiply, but only an operator that just moves parts and all the math is in there. So a few words about me. My name is Jürgen, Jürgen Weigert. I come from Nuremberg and we have a fab lab. Who knows what a fab lab is? What is a maker space? Somebody has a maker space seen here in Berlin? Not so many people. So that's nothing to do with vintage, obviously. Otherwise, you wouldn't know. A fab lab or a maker space is a place where people from different backgrounds come together like a technician, computer scientists, mechanical engineering. I'm kind of both. And electronics people or people who do something with cloths, like you could embroider something on a shirt and they do that here. And people who just come to have a relaxed time, talk together. And yeah, at the fab lab, you can see things like making Eiffel Tower. That's also something I did and it's done with a machine that is called a laser cutter, which is pretty cool. Laser cutter is a box where you put in a drawing and you get out a machine part. So what I want to talk about is a thing that is almost unknown, a 400 years old machine, and we can see that it was really well recognized in the past. They brought out a coin. There's a coin that German the Deutsche Münzpräger anstalt. They really made a silver coin, 20 euros worth, I hope so. And they say there was a computing machine, Rechenmaschine, that is now 400 years old. So it seems to be true. The inscription on the side is in Latin. I can better read it if I look that way. The inscription says Machinam extruxie quadatus numerus computed. So this machine seems to... Machinam extruxie, I built a machine. That's not me. That's a person quite older. That's a person named Wilhelm Schickert. This guy, he built that machine and it computes. So it does some math. It doesn't really mean computer in our sense with memory and with everything and with this data bus and timing. Computing just means I do some math. And the machine does it, not he himself. He built a machine and it computes given numbers. So let's see where we are in the history. What does it mean to be 400 years in the past? To give you a little bit of coordination in the timeline, let's do it in a binary. Jump 100, 200 and 400 years backwards. There we have a 13-year-old Conrad Susan in 1923. We have a wonderful painting of little Ada Lovelace. Her name wasn't Lovelace at that time. It was Ada Baron, the daughter of Lord Byron in 1823. That is eight-year-old Ada Lovelace in 1823. So half the way that we have to go back 200 years. And another 200 years. It's this Wilhelm Schickert that I want to talk about. What did he do? He says that he did the first Rechenhilfe. It says in German, so it's an aid for computing. We are at the edge where we cannot really tell it a computer or maybe it is a computer. It depends on your interpretation. This machine can multiply and it can add. It can subtract very easily. Maybe a division is also possible. I don't want to talk about that. That's not so easy. And he did the foundation work for the fully automated computing. What nowadays computers do. He was not a mathematician at all. By profession he was at the University of Tübingen and he had the chair for old languages. Hebraic, Aramaic and other biblical languages that the Catholic Church needed. Despite of all that, he had some time to think about mathematics and especially he had a friend, Johannes Kepler. Kepler is well known, astronomer. He is well known and he had to do a lot of math work. And that's the two factors. Kepler is well known. Schickert is not known at all. So we know about Schickert only through the heritage of Kepler. There are some letters from Kepler that we have but nothing directly from Schickert. Schickert was in Tübingen and everything he did there is lost. Very bad timing. 1623, that was the 30 years war and the city was burned. His workshop is lost and all his work is also lost. We have a few letters and nothing more. So let's go back what was happening at that time, 1623. Let's say we are tradespeople and we are on the market. Someone of us has to sell something and somebody else wants to buy something. So how do we compute? People have to compute. What is the amount of a total for paying? Let's assume a simple computation. I want to buy a lot of cloth. What is cider in English? Silk, a lot of silk. Like I say I want to buy 60 bunches of silk and each cost me 45 gold. Can I afford this? I have 789 gold coins or whatever the currency is and I want to know is that possible and can I still feed my family afterwards? At that time a salesman had no chance to compute that. They didn't know multiplication or addition. There was a profession. Computation works, I can do that, but I would not know that. There was a profession that is called the Rechenmeister, people who can compute and that was a profession. Like the very firm as Adam Ries, he was one of these human computers. That's really the term that one could say for that. And he came to the salesman and said, you want to buy this many silk for that price? Let's see what remains. And you please give me two gold coins and then I compute that for you. So that was really a trade that was possible at that time, but as tradespeople we have to rely on that, that it's really correct what he tells us. Well, a machine would be better. So some people have to invent a machine for doing these computations. We have three faces here. Anybody recognize some of these faces? How do you know Shikert? It's written there. Ah, damned. Leibniz, correct. This gentleman over here is Leibniz, Gottfried Wilhelm Leibniz. Then there's a little bit younger person that is Blais Pascal in the middle. And there's Shikert. They invented something. What did they invent? The computer or a computing machine. All three of that did that. So yeah, if you ask like 10 years ago who really invented, then Shikert was not known. The best guest you get in Germany would be Leibniz. The best bet you get in France would be Pascal. So let's put in the correct historical order. You see the machines like they do. Leibniz has a wonderful one, Pascal has a wonderful one. Leibniz one is of course better. I'm German, sorry. It's much better. It can multiply. Pascal's can only do add and subtract. And from Shikert we have a nice drawing and a replica. So timing. Yeah, Leibniz was, oh, I did it the wrong way. I think it did it the wrong way. Leibniz was in 1642. I got the swapped, I'm afraid. Leibniz did it in 1642 and Pascal was in 1673. But as you can see, the first of all is Shikert. He did it 20 years earlier than any of these two. But Shikert is unknown. So I have to talk about that. Here's no background in math, as I already said. And he went for the university career. He was what they call a magister. So really good status to start by age of 19. And he was in the church active by age of 22. And he was professor already was 27. So he had not much time to lose and was busy with yeah, things. But then the church is not so easy. You see their little image of a witch and they try to guess the weight of the Mitch. If she's heavy or not heavy, that would be her fate if she's really a witch. If she's too light, she would swim. That would mean she would survive if you drown her in water. But then she's a witch. And if she goes down in water, then she's probably not a witch, but she's dead anyway. So that's the problem with these things. And actually, one of the witches that were at a trial at these times was a woman called Katarina Kepler. And that happened to be the mother of Johannes Kepler, the astronomer. So these two men got together and became friends because Kepler obviously wanted to defend his mother. And she said, yeah, it seems to be logical what is happening here. That's nothing, no witchery, no devil's work, nothing involved. That's very normal what happens here. And he helped to defend. So they came together and discussed obviously also astronomy with all these bad problems, but they also discussed astronomy and the amount of computation that Kepler has to do to prove what he wanted to prove. And yeah, when they were together in Tübingen, nothing written is there. But after the trial was over, Katarina was innocent. They proved it. Kepler went back to Linz. And everything that happened in Linz is well preserved. And there's a Kepler researcher. His name is Franz Hammer, who really studied everything that came from Kepler, and he found a few letters, which obviously don't do anything with astronomy. That's something else. You don't see any reference of astronomy. You see a strange drawing that roughly resembles that machine. And you see some Latin and German texts there in a bad handwriting. And some details. But that's about all the corpus of material that we have from this machine. There's one more page and one more photo, nothing else. That's the other one that we have. So it's very bad foundation. But Franz Hammer managed to present that in 1957 to a group of mathematicians in Schwarzwald in Germany, where they wanted to have a congress about the history of math. And they said, I have something that looks like math. It comes from Kepler, but it looks like math. Let me present that to you. And two days later, three days later, this young gentleman, he was much younger at that time, Professor Loringhoff, Bruno Freitag from Loringhoff, he says, I think I understand what this is all about. And he built the machine according to these old drawings in 1960 that's a photo from that time there. And his machine is a bit larger than mine. You can see that looks from the shape quite similar. So we all have no really idea what these strange bulbs, what that means. So I did the same. So probably Schickert's original drawing was very much simplified. But yeah, it could be some ornaments that belong to the 1700s area. We don't know that. And he built a replica and got it working and presented that to close the loop. I managed Konrad Zuse in the beginning when he was 13 years old. And this was to Konrad Zuse's 50th birthday. I managed Konrad Zuse twice here, but he has nothing to do with the machine. He presented that as a birthday gift to Konrad Zuse and he proved that it really works. So the machine exists. We have some from his replica. We have some in the museums around mostly around Germany. Some went out of Germany, looks like this. And we have obviously a view inside of the machine because it still exists. That's what Loringhoff did. He has some gears up there. He has some paper tapes with numbers on them and some very strange gears with their pins sticking out and touching another gear. So he describes the machine. He explains how it works. But there's a problem. This machine is already... Yeah, what is it? 60 years old? More than 60 years. And it's a museum. It's usually either with a label don't touch it or it is in a glass cabinet where you just cannot touch it. And I happen to be in Kiel in the very north of Germany and visit a Konrad Zuse... I managed him three times. A Konrad Zuse museum in Kiel where they brought together a lot of after-war things that they came back to Germany, collected that in Kiel. And there was in a cabinet in a room that was especially for children where they had an abacus and some Boolean logic boards where you can plug and play with cables and study how and and all logic works for kids. In the same room this thing was in a glass cabinet. That cannot be true. That's such a very simple and educative machine if kids could just play around with these knobs and see how it works. But they would not allow that because if it breaks, it's 60 years old. It's definitely vintage. Nobody can repair it. It's an original rebuild. So my plan was go to the lab, take the laser cutter and try to make the best and build one in wood and only wood. So we have a three millimeter board of birchwood plywood and the laser cutter can cut that very nicely and see if I can make this happen. Software wise, I only did it in 2D. I would not do it that way again. I did it in inkscape only. It's much better to use something in 3D where you can really arrange the parts in space and see how it works. I did not do that in the in the when I started today. I would probably use free kit for that. But it was possible to do and I had all this internal knowledge from Leninghof how to how to construct the gears. I made some simplified versions and tried to think about yeah, there's some springs. That little thing here is a spring from here to here. It moves up and down as needed. So how can I do a spring in wood? Yeah, it works. If you take a longer piece of wood, it also works as a spring. And I studied how the gears work and actually that was the challenge that I put for myself. Is it possible to do that all with the laser cutter and everything out of one material? And yeah, first of all, the most important part, we have some gears that have to turn correctly. And that's the most important part of the machine. The carry over from when you go from nine to 10, that you have that carry that does the other digit. So I just place some gears on the board and play with them back and forth and I can see how that works. And yeah, it works quite nice. It goes like this. Maybe like 10 or 12 or 15 of these boards. Then I know it was possible. The springs that I mentioned look in my version look like this. It's a very, very long arm with a little roller at the end that goes into this tooth gear. And yeah, it works like a spring. Some experiments there. Mechanics, a lot of gears. They have to be offset a little bit and constructed in the correct way. Now we are in the third dimension, how to arrange that really in a box. I found a way to do that and yeah, works. So what are the components of that machine? In the middle is the adder. That's the middle part. And let's start with that. This has dials, like these six rings that you see. And I use a pin like this one. I use that pin to point into one of these holes and turn it around for addition. That's the instruction that says here, put the pin in one of the holes and turn it clockwise until you get to a stop. Clockwise means to add. Counterclock works just the same. It subtracts. And the carry, you don't have to think about that. It just works. That's one of the nicest things about these machines that the carry, just forget about it. You don't have to think about that. I have that as a pre-made animation here. But let's try to do it live on the machine. That would be much nicer, I think. If I could have a camera operator to point at the gears, then we can switch over. You tell me if it doesn't work in the back rows, then I switch back to the animation to do that. So the camera is there. And we have to have a view that you can also see in here what happens there. That's the results. So let's make a very simple adding. I'm adding four plus four, okay? So I point in the position where there's a four, and I crank down until the stop. Obviously you get a four. That's very nice. And plus four means I do it again. Here's the four. And I crank. And obviously the wheel just continues, and we see the eight. You can see that, right? Okay, great. If I continue with another four, what should I get? 12. That doesn't work on the single digit position. We need a carry. See how that happens. Just by itself. Backwards? Forward. No problem. It does carry. So that's what this part of the machine does. Let's imagine there was already a nine at that position. And I'm going forward here also to the nine. Then our carry does two digits. The machine can do that. We can turn it around. You can study how it works. I don't do it right now. You can have a look later. That's what the adder does. Okay? I'm going back to the laptop. That's the little animation for that. Oh, there we are. And then you have a look inside. I do that by the animation because that gets very wobbly in the backside. Backside view, when we do that, what we just did, you see there's one tooth that is larger, and that goes to the side and touches the little gear, and then it catches the gear, moves, and then it's out of the gear again. So for the transition from nine to zero, this tooth grabs the next digit. Before that, the digit is free. Afterwards, the digit is free. That's the trick that you have to implement here. Okay? So let's do something bigger. I think you can see that you're just fine. Let's do something bigger. Let's add three digit numbers, two of them. We have the instructions up here. It's easier for me because I don't have to think and speak at the same time. 753 plus 296 should be 1049. So we just add, we just input, we don't add the input, one digit, one of these numbers. Like the seven goes here, the five and the three. It's the hundreds, hundreds, tens, and units, digits. I have my number. Now for the next number. I do just the same, but I should not look at these. I should look where I'm pointing to because there's already something in the accumulator. And we don't have to take that into account. We have to have absolute numbers. We start with a two because it's 296. I point into the two and crank it around until the stop. So there was a seven. I'm adding two. It seems like it's a nine now. On the other one, yeah, there's another carry happening because a nine goes all the way around. And the last one is a six that works without a carry. You get a nine. And interesting enough, the result is already there. So there's no additional step like making a crank movement somewhere. Just input the numbers. It adds them up automatically. Which has some problems, but works quite nice. Now the next thing I'm showing the animation first and then I'm showing the simplified version that I really like to do is to multiply numbers. Let's take the same numbers. Very same numbers that we had before. And multiplying works quite different in the beginning, but it uses the same mechanisms in the end. The first number goes to the top and the second number goes to the bottom. So you can see the 753 in the top row and you can see the two. That's a nine. You have to look a bit more from the top. 296 in the bottom. And that's our input, how we start for multiplication. The instruction says look at the far lower right corner. What digit do we have here? And open the slider for that digit. So I open the slider and I get some row of... Let's zoom in on that. I get some row of numbers. There's a 42. There's a 13. There's an 18. Back in 1623, nobody knew why these strange numbers appear here. For you, it's probably very easy to understand that here's a seven in that column. There's a six in this column. So that's the product. Six times seven is 42. But let's imagine you have no idea why that happens. We just see these numbers. Written strangely with a little flash in the middle that has a reason. The reason is that I have to split that number up because it's a two digit number most of the time in this little window. So on the first window, we have the 18 and it goes a one here and an eight there. That doesn't mean on a slash shift it to the next position. Same thing on the other position. The 30 with the zero have to do nothing there. If I point my pin down there where the zero is, I'm already stopped. So I know I don't have to do anything. But the three goes one to the side. And the last position is a 42 that splits into these two. And it doesn't have a two here because there was already a three. So there's some summing up is already happening inside the machine. And the next digit, we have the two. Now we have the nine. So we open up the lowest slider where we have the nines. And we basically do the same. Read what is there and put it into the dials. But with one extra complication, we have to understand that this is the tenth digit. The nine is a 90. So everything we read, we have to offset by one position. Don't forget to do that. That's very important. But it's horrible. People will forget it, of course. Read your two and your seven and put this in these two dials. And read the four and the five and put them in those dials. And the others there. And it gets even worse if we have the hundreds digit. Now it's 296. So for that, we open the slider of the two that's very up to the top. And we have to go to the side by two positions. That's even worse. So most of the time, I would bet that people will do that wrong. So it could be that some very skilled person does it very often. Understand that pattern. But it doesn't really, really work up so nicely. If I do it correctly, then, of course, I get the correct result. 753 times 926 is this funny number chosen by on purpose. So let's do it in real and with an improvement. Same computation. I need my numbers back. 753. Can you see that? 753. And on the bottom, we have 296. 296. Oh, and I have to reset my counter. Otherwise, the result will be off. That was designed like that on purpose. If a salesman has multiple positions and as a merchant, I'm buying all these positions, we can multiply the small sums and all that adds up to a total bill and I have the end result already there. So the adder just puts on more multiplications if I don't reset in between. Okay, let's do it like what we did just before. And I see here in the corner, there's a six. So I open the slider. It's already open. I open the slider for the six and I read the numbers in here. That's a little 18. You can see that? Yeah, we can see that nicely. So I'm going to the wheels down, grab the eight, down here and grab the one. I'm reading 30 in here. So I don't do anything here and I'm putting a three in there. Next one is a 42. So I go down, have the two in here and the four over there and all the other positions are zero. We are done here. And now look closely to that. I said I have to start in that corner and for the tenth digit, I'm not going to make this mental movement but I'm moving instead this box. So now I have a nine in the same position that I was before. So let's just do the same thing again. Open that slider for the nine. We have a 27 there. So the seven comes over here and the two is there. We have a 48, is it? No 45 in here. So the five goes in there and the four goes here and we have a 63 in the next position. So the three goes again in that wheel and the six goes over here. 63 it was, right here. Six goes in here. Then we are done with that. And now it's very easy. What we just did with one shift we can do with another, the hundredth position. We put it here and we need the slider for the two. And there's the six up there and I go straight down and at the six. There's a 10 so I don't have to do anything here. The one goes one to the side. I have a 14 up there so in the same wheel I have the four. You don't see the 14 up there? Yeah, now we see everything. And a little one in here. Did I do it right? Did something wrong? I'm afraid I did something wrong. I missed something. You're right. So the end result is off. That's why I'm saying I did something wrong. We have a 122,888. It should be one more. Sorry for that. Yeah, I missed one. Did it. Okay, so that's the multiplication. Adding and subtracting is very simple in the other unit and multiplication is combination of things. I would say it's not a full computer because I have to read things and move them downwards. Let's assume over the history this simplification would have happened because right afterwards 20 years later when Leibniz came around, he did that on his machine. He had that little moving part and all the adding up just goes down and not sideways because the machine does that. And Leibniz also did the connection between the upper body and the lower body of the machine. So this is his famous invention in Germany. It's called Staffelwalze. He did that in the back of the machine. Here these parts are not connected at all. So a human has to read numbers and write numbers down there. Seems like Leibniz did the very same concept just better. The difference is that this machine probably really worked and Leibniz machine was too complicated and probably never really worked in his lifetime. So maybe Leibniz knew about Schickert or maybe Leibniz invented everything again. We can assume that he was capable of inventing all that. But yeah. So this is just a summary who wants to really study that. That's the summary of how the multiplication works. This is the algorithm. That's the thing you have to learn. But there's no math in that algorithm. It's just moving things in the right way. So that's about it, what I wanted to show. Except that there's one thing I did that difference to the original machine. My slide here is movable. That is probably not part of the original machine having that movable. So yes, I did that. It seems to work well. So that is my contribution to a 400 years old machine. I think it's plausible to do it like that. Okay, thank you very much for that. I'm about to close with that. You see some references where everything is. The URLs are also written on the machine itself. If you come over to the booth, it's booth number six. Where I am, you can see what I have. And if you like, there's the plan directly at GitHub. You find the complete plans to rebuild your machine. The investment got quite high. You need to add 50 euros of plywood these times. I started with like 20 euros a few years ago. Prices went up. And the other thing you need to find is a laser cutter at your nearest FabLab or Makerspace. And the final thing is what I can say. Use it yourself. Try it out. It's for playing around. If you break something, well, I'm a maker. I fix it. It's just plywood. Laser cutter does give them replacement parts. That's the key difference to the old machines from Leninghof. Those are in a glass cabinet and cannot be touched. All right. Thank you very much. The gears of Antiqueter could be viewed as a computer. That's true. It's more a planetary thing. It's definitely an analog computer. So it's not a digital computer. We are entering the world of digital computers. Okay. That was a question back in the article which were brought out around the submission of the coin. There was also mentioned that this machine could do division. Is that really true? Don't mention it. Yes, it can. The division is a more complex algorithm than multiplication. You saw a full page of description how to multiply. And the instructions to do division is two pages of very small writing. And it's actually the same algorithm that you know for dividing on paper. Like, write the numbers down and do all these. Does it fit? No, I need something smaller, something bigger. And you have to do all that without writing down the intermediate steps. You don't see your intermediate steps. So it's much more harder to do the division with that machine than to do it on paper. It's the same algorithm. The machine doesn't really help that much with division. But in the words of Schickert, yes, it's a four-species machine. It can do multiply, divide, add, and subtract. I would say, no, don't do it. Thank you. Other questions? Okay, you come over to my booth. We have plenty of more time. I'm here also tomorrow. So let's make room for the next speaker. Thank you very much.