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Chaotic Pendulum Clock

Chaotic toc
  [vote for,

Pendulum clocks are renowned for going tick-tock-tick- tock.

If the clock is out of beat, it can go ticktock - ticktock, or tocktick - tocktick, but it is nevertheless regular.

Semifamously, the fictional Lord Vetinari had a clock that ticked irregularly, but its mode of operation was never made quite clear. Electronic simulacra of this irregular clock have been built, but these are not really very satisfying.


A double pendulum (that is, a normal pendulum from which a second pendulum is suspended) swings chaotically, with energy being transferred back and forth between the two pendula.

I therefore propose a chaotic pendulum clock, being a normal pendulum clock with a small secondary pendulum dependent from the first. Such a clock should tick and tock completely irregularly, but can be tuned to keep correct time overall (for example, over the course of an hour, on average).

Potential problems: (1) The amplitude, as well as the period, of the primary pendulum will vary chaotically, within limits determined by the mass (mainly) of the small pendulum. A times of low amplitude, the escapement will not operate, and hence no maintaining energy will be supplied to the [primary] pendulum. Thus, the system must be sufficiently frictionless to ride out such low-amplitude intervals.

(2) Equally, at times the primary pendulum will have a larger-than-average amplitude. The escapement will need to be able to accommodate this (not difficult).

Overall, the chaotic clock will probably need a greater driving force than a regular pendulum clock, and hence will run for a shorter time for a given amount of winding energy; but this can be lived with. If the clock is spring- driven, it will probably be less isochronous than a normal clock - i.e. its rate (averaged over hours) will probably vary more between fully-wound and unwound than would a normal clock. This could be overcome either by using a fusee movement, or a weight-driven one.

The resulting clock would probably be extremely irritating (tick.. tockticktocktick... tock....... ticktock), and would randomly gain or lose minutes. In short, it would exhibit all those properties which are least desirable in a clock.

MaxwellBuchanan, Aug 29 2013

Quarter past chaos. http://www.bing.com...first=0&FORM=NVPFVR
[2 fries shy of a happy meal, Aug 30 2013]

The king of the swingers. http://www.futurity...-inverted-pendulum/
Chaos is largely dependent on order, and visa versus [4whom, Sep 03 2013]

Double Pendulum http://en.wikipedia...iki/Double_pendulum
wiki link [Loris, Sep 04 2013]

Chaotic rope http://www.youtube....watch?v=JXxn9Wc7sno
Ehh, not a great example but the basic idea. [doctorremulac3, Sep 04 2013]

Cat clock http://www.youtube....watch?v=RAPer8i6skY
Put that crazy pendulum on one of these and let the hilarity and mirth ensue [doctorremulac3, Sep 04 2013]


pocmloc, Aug 29 2013

       oh my, [+]
FlyingToaster, Aug 29 2013

       One that keeps time by grains of sand striking a tuning fork.   

       Clocks should be reconceptualized in relation to the exact phenomena they are timing and end the lie of time that leads to incongruency with the similar chronoscopic function of the body. A clock is nothing but a frivolous example of a basic thermodynamic process exibited in aeverything animate. Nothing but a roadshowman's perpetuum mobile that measures it own energy loss, that has mesmerized legions with a mechanical reliability that has dictated their lives.   

       But seriously about the time thing. Just because a clock can "be here on time" doesn't mean every person has to be an equivalent machine. Afterall, it's only the clock that can be so predictive of time. In fact, it's the device's utility that proves its asynchrony with anything other than immense planetary spheres, that it rarely measures itself. However, it measures the social simulacra of the design of itself; the hypnotized automaton.
rcarty, Aug 29 2013

       bifilar pendulum?
xenzag, Aug 29 2013

       //Such a clock should tick and tock completely irregularly, but can be tuned to keep correct time overall (for example, over the course of an hour, on average).//   

       If it were truly chaotic, it would not keep correct time over any period, even on average. Chaotic systems are chaotic at all scales.
spidermother, Aug 30 2013

       I seem to remember this as the topic of a mathematical recreations in Scientific American, some years ago.
Loris, Aug 30 2013

       Time is nothing but the rough divisions performed by an ancient orrery builder, the measured and rhythmic pendulum throws of the hypnotist, and the newspaperman trick of mass distributed media for spreading a cold and calculated outward object-oriented intersubjectivity.
rcarty, Aug 30 2013

       //Chaotic systems are chaotic at all scales.//   

       That is true. But is it true of a system with a finite amount of energy, finite friction etc? In watching chaotic pendula, it's clear that the pendulum never stops moving (except for the slow damping of friction), and never moves with more than a certain amount of vigor.
MaxwellBuchanan, Aug 30 2013

       // Lord Vetinari had a clock that ticked irregularly, but its mode of operation was never made quite clear. //   

       Probably designed by B.S, Johnson ... with interference, if not exactly help, no doubt, from Lu-Tze - or even Jeremy Clockson ...
8th of 7, Aug 30 2013

       Would you mind terribly making a wristwatch version (as opposed to cleverly making it), [MaxB]? I see the tiny weighted chain useful as either nunchaku or dental floss, and the chimes a nice break point during interminably boring movies. [+]
Grogster, Aug 30 2013

       I was thinking about that. It would be difficult, but I suspect it would be possible.   

       The solution would be to affix, to the rim of the balance wheel, a secondary balance wheel with an off-centre mass, freely pivoting.   

       My guess is that the balance wheel would then swing with a pseudo-chaotic period and amplitude. But it would be very tricky to engineer. For one thing, the secondary wheel would need jewelled bearings (like the balance wheel).   

       For another, watch balance wheels generally have an amplitude of around 270°, and it's difficult to engineer things to allow for much more of a rotation. Therefore, if the chaos tried to drive the wheel to an amplitude of 300° or more, things would go badly.
MaxwellBuchanan, Aug 30 2013

       //pseudo-chaotic// That's the bit I like. After a few weeks it wouldn't impinge on the owner's conscious mind, but a visitor would be climbing the walls.
FlyingToaster, Aug 30 2013

       With random watches, our police forces would have the ability to catch those whom are able to work system weaknesses.
wjt, Sep 03 2013

       For a wristwatch I suggest that the pendulum would be impractical in the modern world, and perhaps a source of annoyance.
I propose a set of cogs with relatively prime numbers of teeth. A subset of these cogs would have one or more side-pins, polling of these would increment the display time. As the cogs poll at different frequencies the reported time will vary as desired, yet it is straightforward to ensure the average progress matches the rest of the world. It would even be reasonable to syncronise multiple such watches so they routinely showed the same time.
Loris, Sep 03 2013

       I am pondering how one might mechanically turn a chaotic rhythm into a regular rhythm.
bungston, Sep 03 2013

       Is/was there a regular clicking in the forests or plains of Africa that our evolving ancestors grew to like because it signaled safety or time to sleep or something?   

       Tree branches rubbing, bird or insect calling. ?
popbottle, Sep 03 2013

       I think you'd need to put more energy into the device to keep it moving since the second pendulum's movement would just take momentum away from the primary pendulum. Nothing wrong with that though. It would be a neat effect.   

       Could you take it a step further and use a heavy chain as a pendulum? Then you could sit in a waiting room and count how many cycles it took to do the same move. Handy for DMV waiting rooms and such.
doctorremulac3, Sep 03 2013

       // you'd need to put more energy into the device to keep it moving// Yes, as indicated in the post. But the secondary pendulum eventually returns its momentum to the primary, so you only need a little extra, to allow for times when there's no net driving force from the escapement.   

       //a heavy chain as a pendulum?// That's an interesting idea. I wonder what the physics is for a heavy uniform chain?
MaxwellBuchanan, Sep 03 2013

       The chatter was lively as drinks were served, until for apparently no reason, a lull spread across the room. Something was wrong. I realized the chaotic ticking of the grandfather clock characteristic of the Buchanan parlor had been replaced by a steady tick-tock. Tick-tock. Surely that wasn't why all conversation had suddenly stopped, but as my eyes drifted to the clock, so too did every other pair in the room. The butler just entering stopped short, looking for the source of trouble until his eyes too followed the others to the clock. The pendulums were in sync. The uniform ticking continued for what seemed like forever as everyone watched. And waited. But before words could be said or steps taken to see what had changed, the inherent instability of the system overcame, bringing a slightly fast tick, an extended pause and a double-tock. A few nervous chuckles were heard as conversations were sheepishly resumed, no one wishing to admit they could be distracted by such a thing. I was just looking at the clock because everyone else was.
scad mientist, Sep 03 2013

       Ah, that paints a picture good enough to eat.   

       As I write, I am listening to the steady tick-tock of a 1920's Gledhill Brookes Time Recorder with fusee movement. It has a massive cast-iron and brass pendulum, and I am seriously* contemplating fashioning a hinged pendulum for it.   

       *3/4 of a bottle of seriousness.
MaxwellBuchanan, Sep 03 2013

       One thing you can say for chaos....it is awfully consistent over time...
4whom, Sep 03 2013

       // //a heavy chain as a pendulum?// That's an interesting idea. I wonder what the physics is for a heavy uniform chain?//   

       A buddy of mine once wrote a program to animate a hanging rope moving through it's various cycles of waves and swings. This was a while ago and I thought it was pretty neat. Now incredibly complicated movement algorithms are standard plugins for off the shelf animation programs, but at the time I thought it was magic.   

       Anyway, a swinging chain pendulum might be very relaxing to watch. Maybe put it on one of those cat clocks so it looked like a mad cat twitching it's tail.   

       I'll see if I can find a link to an example of rope swinging animation to show what I'm talking about.
doctorremulac3, Sep 04 2013

       Have a long steel chain such that it is suspended through the center of a pair of hoops. Each hoop has an electromagnet at one point; the hoop rotates such that the electromagnet travels around the chain, changing the direction of attraction. The hoop's motions are independent of each other. If at any point the chain makes contact with a hoop, the power is momentarily cut off to that electromagnet so the chain won't stick there.   

       Obligatorily ornamented with a spiked metal ball on the end.
lurch, Sep 04 2013

       This is turning into a community art project. I like it.
doctorremulac3, Sep 04 2013

       One of the important things is to limit back-and- forth (as distinct from side-to-side) motion, since this is effectively lost to the system.   

       At the moment, my two imaginings are:   

       (1) A single-link pendulum, with weights both at and below the link, and with the link being a low- friction, low-wobble bearing.   

       (2) A freely-rotating wheel mounted on the end of the pendulum, with an off-centre mass on the wheel, so that energy is traded between the to- and-fro swing of the whole wheel, and rotation of the wheel.
MaxwellBuchanan, Sep 04 2013

       How about some kind of yo-yo arrangement?
doctorremulac3, Sep 04 2013

       // a chaotic double spring analog for wrist watches?// Not yet. But it was mentioned in the annos up ^^there.
MaxwellBuchanan, Sep 04 2013

       Re: the wristwatch idea, it should be possible to achieve pseudo-random movement from a pair of balance wheels and a system of differentials.
mitxela, Sep 04 2013


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