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Huygens' Clock Puzzle Solved
PhotoGuy writes "Okay, I haven't heard of this puzzle either until now, but it sounds like a fascinating phenomenon. According to this article:Huygens had two clocks side by side and he found that even when they began out of sync, they soon got into a rhythm where the pendulum on one moved as if it were a mirror image of the other.The article is pretty light on the explanation, noting only the conditions required (small relative mass of the pendulums [pendula?], relatively close speed of the clocks), and not really addressing the physics behind it.
" There's a great site at Georgia Tech that explains the puzzle in more detail.
[quote]The combined mass of the pendulums has to be very small compared to the combined mass of the entire clock assembly and frame - this was where Huygens was lucky. [/quote] i'm not sure where non linear dynamics and chaos theory come into this, but ah well... i probably wouldn't understand it, anyways. so... that which intrigues man has gone from undiscovered land masses, to redisocvered lost cities, and now to ancient riddles. i wonder what we're going to do for intrigue once we solve all these ancient riddles...
The GA tech column had an link to a picture of the wired article about it, I dug into Wired and found the text so it's more readable.. the link is: http://www.wired.com/wired/archive/9.03/eword.html ?pg=6
http://www.sciencenews.org/20001007/mathtrek.asp
Strangely enough, it didn't occur to them to test what happens if they put three clocks side by side... Antiphase synchronization seems somewhat hard with an odd number of clocks...
Say no to software patents.
When I was looking at this I was expecting something filled with tons of wizzbang scientific explainations. Sad that something that has stumped people since the 17th century turns out to be primarily luck.
( o ) one could say I'm rather baked
I'm interested to see if this may lead to a better understanding of how harmonics works with relation to high-rise buildings. Particularly in earthquake country. (see this)
We've got buildings that can withstand strong quakes -- but not necessarily those of long duration. I'll bet a shiny new penny that this reseach may be insightful in this field.
-jhon
My g/f in high school used to start her period on exactly the same day as all the other girls on her soccer team - amazing. I've also heard that girls often have their periods in sync with their mothers'. Has anyone formally attempted to relate this to the pendulum phenomenon?
...I heard that the reason the clocks go into synch is because they are connected to the same table. Now, when a pendulum stops swinging, it's momentarily "suspended" in the same way that a baseball is when it reaches its zenith just before it comes crashing down on you after you've thrown it directly up. At this point of 'suspension', there is /no/ force between the weight at the end of the pendulum and the rest of the pendulum. It's as if the weight weren't there at all. At all /other/ points, however (especially when the pendulum reaches its fastest point at the nadir of its swing), there obviously /is/ a force between the weight and the arm swinging it, if only because of the fact that the weight is moving (not momentarily suspended) and movement causes friction. This 'friction' manifests itself as vibrations between the arm of the pendulum and whatever it's connected with (even if it's just a nail that a rope is swinging from with a weight at the end of). Now let's say that because the whole frame isn't designed to take advantage of vibrations or treat them any special way, the net effect is just "random"... /more/: extreme example: if a comes to a stop just as b reaches its greatest momentum (nadir), then a has the greatest disturbance at it just when it counts the most. When they are in synch, however, a has the greatest disturbance at it just when it counts the last. Therefore, after a while the system will "settle" on disturbing itself only when it doesn't matter. (Since at all other times, it's an extremely unstable system, assuming that because of weird friction, etc, the 'noise' of the vibrations is more or less random.)
Now, then, we see why the two pendula come into synch: except for the points where the pendula are momentarily 'at rest', there is always a slight random noise they're giving out. This noise is greatest when their momentum is greatest, and, by coincidence, a pendulum is least able to be disturbed when its momentum is greatest.
(Okay, old physics puzzle: disregarding air resistance, how will two pennies behave with respect to each other if you throw down one, and then the second a tenth of a second later? Answer: they will grow farther and farther apart, and the speed of the first will at one point be more than a million miles per second faster than the speed of the second!)
So, to recap:
If a and b are in synch, then when b is moving fastest it's producing the most disturbance, but this disturbs a the least because its large momentum means that this change is minor for it. (And vice versa). At every other point, however, the disturbance tends to disturb a
Hope this helps.
Anonymous J. Coward.
Professor of Entymology,
University of Timbuktoo.
From the Article:
>
As Huygens surmised, the platform motion is the culprit: if we prevent the platform from moving, there is no synchronization at all
Can you believe it took this long to solve this problem? I admit I'm sceptical. Am I missing something?
Here's how I interpret the phenomenon:
Imagine two pendulums hanging side by side (on a rocking boat (I tried to make ASCii art, but the lameness filters don't like whitespace) Align the pendulums so that they swing in the direction of the boat rocking side to side.
Pull the pendulums apart and release simultaneously (assume they don't collide).
Initially they are 180 degrees out of phase, but as the boat starts rocking, its like giving one an extra push (in phase), while the other (out of phase) pendulum a tug to shift its sinewave in the opposite direction. Eventually both pendulums will have the same phase shift and will be affected by the rocking boat equally.
A slightly more complicated example could include two children on a swingset put into phase by giving each a strategically timed push or by loosely comparing it to the harmonics that caused the destruction of the Tacoma Narrows Bridge in those old film clips.
Sounds more like vibes 101 problem than a 336 year old unsolved problem.
Am I overlooking something?
The first time I heard of this was in a book called _Drumming at the Edge of Magic_, written by former Greatful Dead drummer Mickey Hart.
He was discussing the pervasiveness of rhythm, and used this as an example.
Of course, he didn't try to explain the science, and I wondered why at the time.
Writers imply. Readers infer.
It seems that Huygens' was the first observation of a phenomenon known now at the subatomic scale as particle coupling. The youngsters (Hawking et al) can still learn a few tricks from the guys of the past. 8-)
Yesterday was the time to do it right. Are we having a REVOLUTION yet?
The synchronizing of the female reproductive cycle is thought to be the result of pheremones. I suppose it's some prehistoric competitive thing that ensures the male never has to resort to the less dominant females.
That has nothing to do with pendulums. The key point of the phenomenon is that the two clocks must be on a base which is wobbly enough to transmit the "equal and opposite reaction" of the pendulum from one clock to the other while being strong enough to prevent the pendulum from swinging the clock.
Black magic... nothing more...
We really have no clue how any action at a distance works. There's plenty of hypotheses out there, but nothing with a shred of proof.
Doesn't mean they're wrong though... Who knows, the explanation with the most truth could involve tiny little quantum midgets on horseback sending messages between particles...
But what are the quantum midgets made out of?!?!?
Oh dear, the search never ends,
~Loren
If anyone is interested in accuracy in time keeping, a trip to the Royal Observatory in Grenwich is a must for you. You can see Huygens' parabolic pendulum located there.
Get to know about John Harrison, who made the first 'accurate' timekeeper, for use at sea to measure longitude. See Harrisons first accurate time peices of the world, H1 thru H4, where H1-H3 still ticks today.
A must is to stand on the prime meridian of the world, which represents 0 degree longitude, also located there. At night, a green laser can be seen streaking across the sky marking the zero parallel.
Check out the Royal Observatory, you won't regret it!
That's a weird clock you have:)
The most common form of this problem is two pendulums hanging from a string. Stretch a string, the tightness is not important. hang two strings from the first string. put weights on the bottoms of the hanging string. swing the pendula across the axis of the first string. voila! coupled pendulums. It's a standard problem in hamiltonian dynamics, and taught in most university physics courses.
another example is a pendulum with one or more hinges in the middle of a stiff rod.
This whacky guy observed and measured the effect in his own clocks.
BugBear
Ignorance is curable. Stupid is forever.
No, simple linear dynamics won't help you (and if they work out with your perl-script, then probably because of nonlinearities creeping in due to rounding). That is, because you can only get linear behaviour out of a linear system. That means a linear system can be described by a matrix, and the eigenvalues of that matrix will give you the frequencies of oscillations that may happen (given the System oscillates about a stable state). If you couple linear systems in a linear fashion (like with a force k(x1-x2) as you suppose) you only get a bigger linear system, with more oscillation modes.
In a purely linear system all these modes of oscillation are independent of each other. But the clocks manage to get from one mode of oscillation into another. This can only happen, if energy is somehow transferred between the modes, and to get that you need a (nonlinear, or you get just another linear system with slightly different modes) coupling between the modes.
Linear Systems are, in a sense, boring, once you have worked out all the coupling constants, put them in a matrix and found it's eigenvalues you know all about it (for large enough systems, say a crystall with 10^23 Atoms that can be quite a feat and can get you some interesting results nevertheless) and can predict it into all eternity. The interesting stuff happens when nonlinearities creep in.
You could describe our solar system in a linear manner, and you will learn much about it by that, mainly that the planets orbit about the sun and are themselves orbited by moons. But if you want to know why some orbits more stable than others, for example why there are gaps in the saturn rings for orbits in sync (with w being a multiple of the W of the moon) with the moons, you have to look into the nonlinearities.
--
"By the way if anyone here is in advertising or marketing... kill yourself." -- Bill Hicks
In a piano, some of the keys strike a pair (or three) strings when struck. Piano tuners tune each of the strings independently, but also realize that one string affects its mate. Even if they are tuned just a titch off from one another, they will try to sycnh up. Instead of seeking to tune the pair perfectly together, detuning one from the other very slightly will affect the loger-term 'envelope" of the note.
You get it with piano strings too. Where two or more are tuned to the same note. The delta in tuning has an important on the sustain-decay profile of the notes.
Huygens figured out the general principle. If you have two things that are matched in frequency, and capable of influencing each other, then any influence, however tiny, will eventually drag them into some preferred phase relationship. If there is some difference in frequency, then this may destroy the coupling effect, if it is too small. You get it with piano strings too. Where two or more are tuned to the same note. The delta in tuning has an important on the sustain-decay profile of the notes. Arguing that entrainment must exist to some degree between two clocks is easy. Showing exactly what causes it is a lot harder. That is what the recent paper was about.
Could the pendulums be iron ferrite or have trace elements of magnetic metals?
This must be Thursday, I never could get the hang of Thursdays.
Oh please. "A few loose ends in non-linear dynamics"? If you're sitting on some magical framework to predict the details of turbulent flow, there are probably a couple of people at Boeing or Lockheed who'd like to see it.
I forget who I'm misquoting here, but someone said "talking about non-linear dynamics is like talking about non-elephant biology".
gravitational attraction between objects that weigh a couple ounces? You have to be kidding.
Not really, Although you have a valid point, the article specifically states that the effect only worked on smaller weighted pendulums - larger ones would have a stronger gravitational effect. On top of this, if both pendulums were started in the same direction, then they would not be moving away from each other and thus the gravitational effects on each other would be unchanging. Thus gravitational effect would have no bearing at all. In the article at Science News (http://www.sciencenews.org/20001007/mathtrek.asp) they specifically mention that the pendulums were started in opposite directions, and also in the same direction.
Am I the only person who was instantly reminded of menstrual cycle synchronization?
Did YOU know it? Then I guess it's news to you, eh?
I've always favored the idea of magical pixies living inside the particles. If the physicists ever prove the existence of the pixies, the pixies will be obligated to grant us three wishes. Then we can wish for the pixies to alter the very workings of reality to make faster than light travel and all sorts of other useful things possible.
My only political goal is to see to it that no political party achieves its goals.
This phenomenon is known as rythym entrainment, and a few of us 'Old Ones' Grok it in fullness.
"As Huygens surmised, the platform motion is the culprit: if we prevent the platform from moving, there is no synchronization at all."
This statement is, of course, patently absurd. There simply does not appear to be any sync because of limited tools for observation. If one had patience one could wait for fullness and observe the effect.
And as far as claiming that they stopped the platform from moving goes, did someone achieve the temperature my name describes and forget to tell me???
Those who want a better understanding of this, and many other secrets of the universe may want to read
Guns don't kill people; Physics kills people! - John Lithgow as Dick Solomon on Third Rock From The Sun
[snip]
"As Huygens surmised, the platform motion is the culprit"
Summary:
Huygens, 1657: "I think the frame is wiggling."
GATech, 1995: "Yes, the frame is wiggling."
What an amazing scientific mystery that was...
=)
-BK
Chemical Blog
Unfortunately, the Royal Observatory has gone a little soft in the science in the attempt to attract tourists. It's not quite as bad as Disney, but it's definitely enough that people who actually care about this stuff will go quietly mad. (Disclaimer: the following comments are based on reports I've seen in various locations over the past few years - it's possible they finally got their act together.)
The most obvious to most people is the fact that a GPS shows that the PM is marked by an unlabeled garbage can (read: ignored) while the PM marker is a substantial distance off - as much as 100m?.
There's actually an easy and fascinating explanation. Geographical positions were originally determined by astronomy, and this implicitly took into account the actual complex shape of the earth. Most slashdot readers know about the equatorial bulge, but there are other bumps and valleys as well. But modern positioning uses GPS and a simplified model of the earth's shape, and the coordinates do not match exactly. Minimizing the differences worldwide required a sizeable jump in the London area.
This then brings up the difference between astronomical time and atomic time, how GMT tracks the former and UTC tracks the latter, and the need for leap seasons.
I think it's reasonable to expect anyone who knows enough science to visit the RO would find this interesting, but the RO apparently doesn't. Most people think the positioning of a garbage can on the true PM was an accident, I'm not so sure.
Even more bizarre was their behavior around January 1st, 2000. It wasn't Y2K until it was Y2K in London. Except it was. Except it wasn't. I don't think anyone ever figured out what their position was, except that all celebrations should somehow refer to them. (It got so bad I half expected to see a claim that the RO patented Y2K.)
Ironically, I never heard of any reference to the reason why this time zone was first among equals - the fact that UTC is widely used in computers, telecommunications, etc. Half of the world (by definitition!) may have been in 2000 by the time it hit midnight in London, but much of the technology of the world would turn over at that time. That's why I was glued to the TV at 5 pm local time, with CNN on one TV and BBC America on another.
If you have a chance to visit the RO, take it. But think of it as "Royal Observatory World," the theme park.
For every complex problem there is an answer that is clear, simple, and wrong. -- H L Mencken
I used to demonstrate this with a pair of 555 timer chips on a solderless breadboard. If set up to oscillate at the same frequency, they would phase-lock, because when the output transistor switched, it would cause a power dip. These things would lock up even at different frequencies; I was able to obtain locking at ratios like 6:7.
This also occurs with periodic polling programs, like mailers. Programs that poll, then wait for a fixed time will, if polling the same server, lock into synchronization. Then they all poll at about the same time. This phenomenon was discovered in Sendmail in the early 1980s, by someone at Lawrence Livermore Labs.
the decades old question of why Guinness bubbles 'float' down the glass has been solved. Actually took some high end fluid modelling software to figure it out :)1 31010,00.html
http://articles.thetechmag.com/articles/?0,0372,0
Also a press release here: http://www.fluent.com/about/news/pr/pr5.htm
That's called the Harem effect (or something like that). Basically you get any number of women, greater than 1, put them into close contact with each other and they all have their period at the (nearly) same time. Well documented phenomeon(sp?)
It MAY be related to the fact that roughly half the estrogen in the body is produced by cells in the lungs. (It's the particular cell type that sometimes becomes cancerous, which is why lung cancers often have effects on secondary sexual characteristics, such as breast enlargement.)
Now I don't KNOW of any proven causual relationship. But the location of these cells in the lungs makes me wonder if they might be acting as chemosensors, with their estrogen output modulated by some airborne signaling chemical. This in turn could be responsible for all sorts of interesting and advantageous effects (both in humans and other animals), such as ovulation and/or coming into heat in response to proximity to a fertile male.
One such effect might be synchronization of periods of women in long-term proximity, via estrogen release by these cells in response to a signaling pheromone emitted by the other women. Synchronized periods would help maintain pair bonding by reducing the temptation for a man to mate with other women when his usual mate was having a period and the other women were not.
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way
From time to time,I hear stories of clocks stopping when their owners die. I consider a few of them reliable accounts. I wonder if these type of things are coincidential, or if there would be some sort of interaction going on here as well?
An obvious interaction:
The grandfater clock stops when grandfather dies because grandfather is the fellow who WOUND the darned thing.
So it's not unreasonable for it to stop at roughly the time grandfather does. And if he's dying in the house with the clock, the family is likely to be around the bed when he goes or otherwise distracted.
When they start paying attention to anything but granddad it's likely that they'll notice the stopped clock. They won't KNOW if it stopped EXACTLY when grandpa's heart did. But since it stopped roughly at that time, to the limits of their measurement (running when grandpa cried out, stopped next time we wanted to know the time), it's easy to believe it stopped right when grandpa did.
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way