4 ms·
This essay is pretty sensationalized and doesn't really paint an accurate picture. Leibniz did build the first 4-operation calculator: https://en.wikipedia.org
by olooney 8y ago
This essay is pretty sensationalized and doesn't really paint an accurate picture. Leibniz did build the first 4-operation calculator:
https://en.wikipedia.org/wiki/Stepped_reckoner https://en.wikipedia.org/wiki/Stepped_reckoner
https://en.wikipedia.org/wiki/Leibniz_wheel https://en.wikipedia.org/wiki/Leibniz_wheel
http://history-computer.com/MechanicalCalculators/Pioneers/Lebniz.html http://history-computer.com/MechanicalCalculators/Pioneers/L...
And he did demonstrate it in England and Paris - but framing it as "faltering through live demonstrations" ignores the fact that this was in the 17th century and the only similar thing they would have seen was Pascal's calculator which was limited to addition and subtraction. A device which could also multiply and divide was seen as a huge advance. While it does seem likely that early versions did not work very well (seeing as Liebniz would go on to commission a brass version from a master clockmaker after lamenting, "If only a craftsman could execute the instrument as I had thought the model!") these early demonstrations were still successful enough to illustrate the principle and in fact brought Leibniz considerable fame: to quote Wikipedia, "This 'stepped reckoner' attracted fair attention and was the basis of his election to the Royal Society in 1673."
https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz#Computation https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz#Comp...
http://history-computer.com/MechanicalCalculators/Pioneers/Lebniz.html http://history-computer.com/MechanicalCalculators/Pioneers/L...
While the story of an early version of the machine being lost and recovered is true, this is pretty much just a piece of trivia. The important ideas were never forgotten because Liebniz wrote several books about his machine. His design was well known and many successors worked on their own versions of it. In fact, for the next two centuries, the Liebniz wheel and the pinwheel calculator (another Liebniz design) would dominate the field and most machines produced in this time derived from one of Liebniz's designs.
https://en.wikipedia.org/wiki/Mechanical_calculator#The_18th_century https://en.wikipedia.org/wiki/Mechanical_calculator#The_18th...
Two centuries later, the Liebniz wheel would form the basis of the first commercially successful mechanical calculator:
https://en.wikipedia.org/wiki/Arithmometer https://en.wikipedia.org/wiki/Arithmometer
The essay's insinuation that "the machine never worked as intended" seems to be based on this statement: "Burkhardt reported that, while the gadget worked in general, it failed to carry tens when the multiplier was a two- or three-digit number." We know that Burkhardt only had access to an early version of the machine, but even assuming the problem persisted in later versions, this is extremely binary thinking. You don't dismiss an innovative and fundamentally successful design because the proof-of-concept implementation has a minor bug.
I did learn one thing from the essay though - Liebniz could not catch a break. I knew that Voltare had viciously satirized him as Professor Pangloss in Candide, but I didn't realize that Swift had also mocked him. I did know attacking formalists as somehow damaging the "creative" side of thinking has a long history and the argument was still being leveled at Frege and Boole centuries later. Just as you have to define the rules of chess before you can get a Bobby Fisher, you have to have a trivial procedure for verifying a given proof before mathematicians can fully exercise their own creativity in inventing and proving new theorems. Liebniz's "art of infallibility" is of course about the proof verification/checking, as the full quote makes clear:
"if controversies were to arise, there would be no more need of disputation between two philosophers than between two calculators. For it would suffice for them to take their pencils in their hands and to sit down at the abacus, and say to each other (and if they so wish also to a friend called to help): Let us calculate."
If two mathematicians have arrived at opposite conclusions on the same theorem, then they simply need to check their work and formally verify each of their proofs to decide who is right.
- nanna 8y agoSwift's satire of Leibniz wasn't premised on science, it came down to them each occupying opposing political stances at the time in respect of the Whigs and Torys. Remember they were both heavily invested politically. Wiener argues that Swift also had a go at Leibniz through his satire of the little people who tie up Gulliver, which can be read as mocking his concept of infinitely divisible substances. Had a go looking for the refference but can't find. Might be in the manuscript to his last unpublished lectures... What really damaged his reputation for centuries was not Swift though, but the debacle with Newton over the invention of calculus.
- olooney 8y agoThat's not surprising. Voltaire's caricature of Leibniz was politically motivated too, or religious, which was all tangled together during the enlightenment. Basically a liberal/atheist criticizing a conservative/religious thinker. And the Leibniz/Newton debate seems to me to have been primarily political too, dividing neatly on national lines. Politics is always with us, it seems. Regardless of who came first, Leibniz's work on calculus was excellent. He knew the chain rule, product and quotient rule, linearity, and how to differentiate powers of x; he defined both integration and differentiation and was aware of (but did not prove) the fundamental theorem of calculus (that integration and differentiation are opposites) We still use his notation today: sigma f(x) dx for integration, and dx/dy for differentiation. In fact, even the word for function, in the sense "f is a function of x", seems original to Leibniz and came directly out of his work on calculus. Leibniz could walk into a classroom today and lecture on his calculus and it wouldn't look much different than a modern Intro to Calculus class. If it hadn't been for the climate of German/English intellectual rivalry it wouldn't have even been an issue. https://www.maa.org/book/export/html/641727 https://www.maa.org/book/export/html/641727
- nanna 8y agoWish I understood calculus as well as you obviously do. I guess the one thing I'd add is that it was a far broader art than just for maths. The classroom today would be pretty surprised to hear how its continuous with metaphysics too. Regarding Leibniz/Newton, not exactly the case that it divided on national lines, because the lines didn't exist in the same way as today. He worked as archivist for the Elector of Hanover George Ludwig, who would be brought over to the UK to become King George I towards the end of Leibniz's life. To Leibniz's consternation, George I would leave him behind in Hanover, where he would die. Lots of theories about why this was the case, but one reason is that Newton and his supporters via the Royal Academy ensured he wouldn't be brought over. Their spat (with Clarke as Newton's mouthpiece) was in the general context of that, hence its rancorous tone. Norbert Wiener at least considered the two centuries of suppression of Leibniz and his calculus and its superior notation in Britain to have held back the British and American sciences.