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My brother asked me how I might build a functioning alethiometer, which is a fictional device superficially resembling an analog pocket watch, but with essentially random movements. I told him I would use electronics rather than clockwork ("clockwork" is colloquially synonymous with predictable mechanical motion, after all). But that didn't stop me from wondering how it might be done in a purely mechanical way.

A larger, immobile device might combine a pendulum clock with a chaotic double pendulum system, for example. What other mechanical randomness source might work for a smaller, portable device?

monguin
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    This is an interesting question and has me thinking. My first thoughts are that it would require some external "noise" such as temperature fluctuations, wind, solar, tidal, rain, volcanic or other natural phenomena to provide some variation. Let's see what comes up. – Transistor Mar 14 '21 at 21:33
  • I'm also curious about a pseudorandom solution. Perhaps something like a series of oddly-shaped cams with relatively prime periods? I'm not sure what would be a reasonable way to construct something like that. – monguin Mar 15 '21 at 03:59
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    There is a 2012 paper titled "Chaos in coupled clocks" which leads me to believe that it might be possible to build two watches with mainsprings, coupled in a way somehow analogous to coupled pendulums. Also, it strikes me that the Antikythera mechanism exhibits what looks like pseudorandom behavior, if you aren't aware of what it represents. – monguin Mar 15 '21 at 04:12
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    @monguin I agree - that was my first thought, to couple one hairspring to another. (Not the mainspring; that's just the power source). That at least gives you a random elapsed "real time" per ratchet step. randomizing forward/backward would be more tricky. – Carl Witthoft Mar 15 '21 at 12:18
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    There's a very interesting experiment (magnetic pendulum) you could look into. You take some magnets and fix them to a table. Then swing a pendulum (iron mass) and wait to see at which magnet it stops. No matter where you start the pendulum, you cannot predict where it will stop. Maybe that could give you some ideas? – Suryetto Mar 16 '21 at 12:42

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If you want a mechanical movement, something vaguely pseudorandom that uses chaotic behavior similar to the double pendulum idea is the best you are going to do.

Looking at the alethiometer web site, it sounds the hands should go both forward and backwards, not necessarily with each other. One could go forward slow now and back fast later at the same time as another goes back slow now and forward slow later (and forward fast after that). A set of four bar linkages with link lengths affected by cams could accomplish this. There would be a central clock style escapement that would cause things to move and drive a cam and a four bar linkage. The cam would limit, reverse the linkage. The web site shows four hands, stacking up four mechanisms like that is more than.

In the old days, we had these 45 rpm phonograph records with big center holes. If you put one of those on the turntable without the centering device, it played ... interestingly, slow now, fast later. Something similar with the central clock, ticking part combined with a cam that would switch lengths of the linkages would result in apparent random behavior. You get the idea.

Such a thing could be built but you'd need an awesome watchmaker to get all the pieces in something the size of a pocket watch.

Keep in mind Donald Knuth's recommendation that "random [values] should not be generated with a method chosen at random." He was talking about random number generators on a computer but it applies equally well to mechanisms.

user1683793
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