h a l f b a k e r yOn the one hand, true. On the other hand, bollocks.
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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.
So.
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.
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]
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Annotation:
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One that keeps time by grains of sand striking a tuning
fork. |
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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. |
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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. |
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//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).// |
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If it were truly chaotic, it would not keep correct time over any period, even on average. Chaotic systems are chaotic at all scales. |
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I seem to remember this as the topic of a mathematical recreations in Scientific American, some years ago. |
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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. |
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//Chaotic systems are chaotic at all scales.// |
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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. |
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// Lord Vetinari had a clock that ticked irregularly, but its mode of operation was never made quite clear. // |
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Probably designed by B.S, Johnson ... with interference, if not exactly help, no doubt, from Lu-Tze - or even Jeremy Clockson ... |
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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. [+] |
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I was thinking about that. It would be difficult,
but I suspect it would be possible. |
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The solution would be to affix, to the rim of the
balance wheel, a secondary balance wheel with an
off-centre mass, freely pivoting. |
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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). |
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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. |
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//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. |
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With random watches, our police forces would have
the ability to catch those whom are able to work
system weaknesses. |
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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. |
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I am pondering how one might mechanically turn a chaotic rhythm into a regular rhythm. |
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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? |
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Tree branches rubbing, bird or insect calling. ? |
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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. |
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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. |
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// 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. |
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//a heavy chain as a pendulum?// That's an
interesting idea. I wonder what the physics is for a
heavy uniform chain? |
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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. |
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Ah, that paints a picture good enough to eat. |
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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. |
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*3/4 of a bottle of seriousness. |
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One thing you can say for chaos....it is awfully consistent
over time... |
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// //a heavy chain as a pendulum?// That's an
interesting idea. I wonder what the physics is for a
heavy uniform chain?// |
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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. |
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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. |
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I'll see if I can find a link to an example of rope
swinging animation to show what I'm talking
about. |
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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. |
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Obligatorily ornamented with a spiked metal ball
on the end. |
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This is turning into a community art project. I like it. |
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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. |
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At the moment, my two imaginings are: |
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(1) A single-link pendulum, with weights both at
and below the link, and with the link being a low-
friction, low-wobble bearing. |
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(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. |
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How about some kind of yo-yo arrangement? |
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// a chaotic double spring analog for wrist
watches?// Not yet. But it was mentioned in the
annos up ^^there. |
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Re: the wristwatch idea, it should be possible to achieve pseudo-random movement from a pair of balance wheels and a system of differentials. |
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