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I'd love to see a watch manufacturer try to build a watch-sized purely mechanical computer


That's clearly feasible; the mechanical complexity for a mechanical computer is on the order of a Curta calculator, and I outlined some promising approaches to macroscopic mechanical digital logic 15 years ago in https://dercuano.github.io/notes/mechanical-computers.html. Since then MEMS has advanced significantly and gone mainstream, and photolithographic and reactive-ion-etching-based silicon fabrication has been used for other purposes, including watchmaking, with macroscopic silicon flexure components going into first TAG Heuer's Guy Sémon's Zenith Oscillator in the Zenith Defy Lab https://www.hodinkee.com/articles/zenith-defy-lab-oscillator... and then mainstream watches:

https://wornandwound.com/no-escapement-an-overview-of-obtain...

https://monochrome-watches.com/in-depth-the-future-of-silico...

https://www.chrono24.com/magazine/innovative-escapements-fro... (warning, GDPR mugging)

https://www.azom.com/article.aspx?ArticleID=21921

https://www.europastar.com/the-watch-files/those-who-innovat...




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