Synchronized Chaos

December 14, 2005 2:50 PM

The synchronizationof two pendulum clocks was discovered in 1665 by Huygens. Two pendulum clocks mounted on the same wall always fell exactly out of phase with each other no matter what the starting conditions. Regardless of the initial conditions the system always ended up the same. In stark contrast, a chaotic system is extremely sensitive to initial conditions. How can these two seemingly seperate things be tied together? The synchronization of chaos. When two chaotic systems are synchronized together, information can be shared between them. It immediatly brings to mind applications for encryption, but it is still far away from everyday use.
posted by ozomatli (49 comments total)

I would be remiss if I did not mention that Kevin Cuomo and Alan Oppenhiem were the first to publish details of a successful transmitter-receiver circuit. They used the findings of Pecora and Carroll.
posted by ozomatli at 2:59 PM on December 14, 2005

Very interesting, thanks.
posted by sour cream at 3:05 PM on December 14, 2005

that is awesome.
posted by unknowncommand at 3:13 PM on December 14, 2005

AWESOME post. For anyone interested in this topic, I recommend Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life by Steven Strogatz
posted by anomie at 3:38 PM on December 14, 2005

This something new and unique that I didn't know much about before, thank you.

(The name Huygens sounds familiar. Is there another reason I should know this name other than this pendulum issue?)
posted by dios at 3:42 PM on December 14, 2005

Thanks, ozomatli, that was a great post!
posted by solotoro at 3:42 PM on December 14, 2005

I was about to post the book that anomie posted, it's a great book that goes through all this cool stuff and more.
posted by Mach5 at 3:43 PM on December 14, 2005

The criticalness of the masses of the system in the original 1665 observation is an amazing part for me. I always wonder how many things are waiting to be discovered just because we've standardized on a clock hanger that is a hair to heavy or light.

Of course it shows that the most exciting phrase in science isn't "Eureka!" but instead "Hmm, that's weird".
posted by Mitheral at 3:48 PM on December 14, 2005

Huygens
posted by dash_slot- at 3:53 PM on December 14, 2005

dios: Well, he was a fairly famous contemporary of Newton, but the likely reason you've heard the name recently is the Huygens probe of the Cassini mission to Saturn and its moons (notably Titan, in the case of the probe).
posted by jedicus at 3:53 PM on December 14, 2005

dios: The Hyugens probe named after Christiaans Huygens, who I assume is the same as the Huygens mentioned above.
posted by Freen at 3:53 PM on December 14, 2005

Curses, foiled again!
posted by jedicus at 3:53 PM on December 14, 2005

If you want see the coupling of angular momentum first hand, make a coupled pendulum. Simple make 2 indentical pendulas (a weight hanging from a string) then, a short distance down, connect the two by tying a between them. Now start one or both swinging (along the axis that connects them). What is interesting is that after a while one pendulum will stop swinging then start again and vice versa.
posted by 445supermag at 3:54 PM on December 14, 2005

wow. Jinx!

Great series of links though. Thanks!
posted by Freen at 3:54 PM on December 14, 2005

More posts of this kind would be great. Thanks, that's all.
posted by killdevil at 4:05 PM on December 14, 2005

Anyone have any knowledge of, or even better links to this:

Coupled oscillators are even more ubiquitous in nature, showing up, for example, in the synchronized flashing of fireflies and chirping of crickets, and in the pacemaker cells that regulate heartbeats. "The theme of synchronization between coupled oscillators is one of the most pervasive in nature

?
posted by batou_ at 4:07 PM on December 14, 2005

Hmm.

I have heard of that Huygens probe, but in my mind, I am hearing a specific reference to Huygens. And if you put a gun to my head, I'd want to say that I remembering his name from a Chomsky speech on his theory of linguistics. I can just hear that word in Chomsky's voice. Any guesses as to whether that is a name Chomsky would have used?
posted by dios at 4:10 PM on December 14, 2005

"Two pendulum clocks mounted on the same wall always fell exactly out of phase with each other no matter what the starting conditions."

Actually, from the first link, there was a fairly precise set of starting conditions that had to be met before he saw the anti-synchronization. "Because Huygens intended his clocks to go on board a ship, where the rolling motion might easily topple them, he had placed two 100-pound weights inside their case to keep them stable. This put the weight ratio in the range for antisynchronization to arise. "If the situation hadn't been exactly right, Huygens wouldn't have seen what he saw," Wiesenfeld says."

But still, fascinating stuff. I'd definitely like to see more posts of this nature.
posted by fenriq at 4:23 PM on December 14, 2005

For those intersted in the flashing of fireflies: here is the general idea:

1. A firefly flashes its light at a certain rate.
2. Another sees its flash and flashes at its own rate.
3. The first one sees the response and responds by slowing down or speeding up to match the response.
4. The second one sees this response and so on and so forth.

Eventually the fireflies will be phase locked if the inital conditions (i.e the difference in frequencies) is within a certain range. Here is a powerpoint I found that may explain things in more detail.
ok the ppt is a bit flaky but skip to the firefly slides and it might help a bit.

Here is a link to some videos showing nonlinear effects.
posted by ozomatli at 4:26 PM on December 14, 2005

Chaotic systems are not just sensitive to initial conditions, they are sensitive to everything. It isn't surprising that very weak disturbances - below the threshold of human detection - could cause an effect over time.

It is a little more surprising that two lasers will synchronize on apparently random waveforms. One might speculate that the waveform isn't actually random at all, it just includes frequency components that are beyond our ability to measure (two weak, two fast...), giving the appearance of randomness.

I'm not at all sure about the applications to cryptography. A similar laser would synch to the chaos just as well as the transmitter/receiver pair, so isn't it just security by obscurity?
posted by Chuckles at 4:29 PM on December 14, 2005

Actually, from the first link, there was a fairly precise set of starting conditions that had to be met before he saw the anti-synchronization. "Because Huygens intended his clocks to go on board a ship, where the rolling motion might easily topple them, he had placed two 100-pound weights inside their case to keep them stable. This put the weight ratio in the range for antisynchronization to arise. "If the situation hadn't been exactly right, Huygens wouldn't have seen what he saw," Wiesenfeld says."

But still, fascinating stuff. I'd definitely like to see more posts of this nature.

very true fenriq, i should have been more precise in my language, what I meant was that the initial relative phase difference was irrelevant (or starting angles from vertical if you like). My initial conditons were a single phase parameter.
posted by ozomatli at 4:31 PM on December 14, 2005

For those intersted in the flashing of fireflies: here is the general idea:

As a demonstration of how good brains are at massive synchronization, I had a math professor that told the whole room to start clapping, then to start clapping in unison.

It's really easy to do, but when you think about the math involved it seems like it really shouldn't be.
posted by flaterik at 4:33 PM on December 14, 2005

Chaotic systems are not just sensitive to initial conditions, they are sensitive to everything. It isn't surprising that very weak disturbances - below the threshold of human detection - could cause an effect over time.

I would be careful, when I define a chaotic system it is closed to outside "forces". Once I start the clock, these is nothing left but a determined path for the particle to go in phase space. I however cannot know this path because I do not the exact initial conditions on the system. A chaotic system is exponentially sensitive to changes in the initial condtions.
posted by ozomatli at 4:35 PM on December 14, 2005

Okay, I shouldn't say "everything", but the concentration on initial conditions isn't really important. A chaotic system is as sensitive to disturbances as it is to uncertainty in the initial conditions. That isn't everything, maybe everything that would normally be a part of the model of the dynamic system though...
posted by Chuckles at 4:44 PM on December 14, 2005

Last but not least before I swamp my own post here is a pretty good primer to some of the ideas behind nonlinear dynamics and chaos: pdf
posted by ozomatli at 4:44 PM on December 14, 2005

Okay, I shouldn't say "everything", but the concentration on initial conditions isn't really important. A chaotic system is as sensitive to disturbances as it is to uncertainty in the initial conditions. That isn't everything, maybe everything that would normally be a part of the model of the dynamic system though...

I can see your point I think we are just talking past each other. Whatever you would call a disturbance at say t=t_d I would just reset the system and have the location in phase space of the particle at t=t_d (say x=x_d) become my new initial condition at start at t=0. There is nothing unique about what time step you are starting at since each path is determined.
posted by ozomatli at 4:48 PM on December 14, 2005

Well, my second comment was actually just a correction. it does look a lot like a response to you though :P (chaotic synchronization?)

I understand what your saying, I even considered structuring my response in a way that is similar to that perspective... I didn't because I didn't want to add an assumption (or even address the notion) of time invariance when it isn't required.

Also, in general, the disturbance should be a continuous input to the system over time, not just a discrete event.
posted by Chuckles at 5:04 PM on December 14, 2005

Dios - I haven't heard of that, but it's possible, as Huygens' name is one that cmomonly gets mispronounced in very specific ways depending on your country of origin.
posted by kyrademon at 5:18 PM on December 14, 2005

not everybody is as positive about the uses of this phenomenon for encryption
posted by Dr. Twist at 5:26 PM on December 14, 2005

AWESOME post. For anyone interested in this topic, I recommend Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life by Steven Strogatz
posted by anomie at 3:38 PM PST on December 14 [!]

Ooh, I was beaten to the punch.


I was about to post the book that anomie posted, it's a great book that goes through all this cool stuff and more.
posted by Mach5 at 3:43 PM PST on December 14 [!]

Twice!
posted by Foosnark at 6:04 PM on December 14, 2005

"Synchronized chaos" is just another term for "emergent behavior" or "emergent order":

So as it seemed relevant, there will be a speaker at Penn who will give a talk on the biology of the subject:

GRASP Laboratory Seminar
School of Engineering and Applied Science

Julia K. Parrish
School of Aquatic & Fishery Sciences
Department of Biology
University of Washington

"Perception versus Reality: Lessons from Flocks, Schools, Herds, and Swarms"

Friday, April 7, 2006
1:00 p.m.-2:00 p.m.
Wu & Chen Auditorium
101 Levine Hall / 3330 Walnut Street

Animal groups are often cited as a conceptual model for engineered aggregations, just as individual animals are models for many common structures. Thus, the bird becomes the plane, the fish becomes the submarine. But is an ant swarm or a fish school an appropriate model for a distributed intelligence? Have biological systems solved the issues of information acquisition, interpretation, transfer, and storage in novel - and useful - ways? Are there fundamental rules of association within the biological realm, or is inter-individual interaction a species-specific phenomena? This talk will broadly survey what biologists (think they) know about the why's and how's of animal aggregation, focusing principally on fish schools.

Julia K Parrish is an Associate Professor in the School of Aquatic and Fishery Sciences at the University of Washington. For the past 20 years, Julia has studied fish schooling, in an effort to tease apart questions of cost:benefit of group membership, and the epiphenomena of group pattern arising from the decision-actions of individual members. She is the editor of the book Animal Aggregations in Three Dimensions (Cambridge 1997) as well as many articles on fish schooling in the peer-reviewed literature.

For further information, visit www.grasp.upenn.edu or call the GRASP Lab at 215-898-0374.
posted by Rothko at 6:17 PM on December 14, 2005

Oh, and (this is good).
posted by Rothko at 6:18 PM on December 14, 2005

Dios: yes. Apparently Huygens was critical of Newton's theory of gravtity since it went beyond mechanical principles and relied on an unseen force. This is in a chapter of Chomsky's book entitled "language as a natural object" which I presume makes a similar argument about language learning as Newton did about gravity. [cite]
posted by jessamyn at 6:41 PM on December 14, 2005

Good post. Really interesting stuff.
posted by klangklangston at 6:59 PM on December 14, 2005

I guess I just don't buy the theory of chaos, which makes reading things like this pretty unenjoyable.

How could someone sync pendulums completely? I mean so that every single atom in each pendulum had their respective sub atomic particles, and quarks and so on all spinning exactly in unison? Then how do you account for the slight differences in gravity effects between the 2 pendulums? How do you regulate, time and equalise the number of neutrenos that pass through them throughout the exeriment? How about other radiation such as radio? How do you do the same for your measuring equipment? How do you compensate for relativity effects since both pendulums aren't in the same spacetime?

Until someone can flush out all of that and more how could you ever have data to support chaos? It just seems like an ideal, something that tries to describe the effects of what we can't measure.
posted by parallax7d at 7:37 PM on December 14, 2005

dios, you read Chomsky? Not bad for a dyed in the wool conservative. Now if we can just get the MeFites reading Kristol...

[great post by the way ozomatli]
posted by caddis at 7:40 PM on December 14, 2005

I'd like to be the first to point out that this is a great post.

Whuzzat? Oh. Oh well. At any rate, I probably won't be the last. Fascinating stuff, thanks.
posted by soyjoy at 8:24 PM on December 14, 2005

I guess I just don't buy the theory of chaos, which makes reading things like this pretty unenjoyable.

What's not to buy? Not to sound snarky, but I don't think you understand what chaos theory is. Chaos is a mathematicallyt rigorous thing. Look up about strange attractors. You can build your own if you wanted too.

How could someone sync pendulums completely?

This has nothing to do with chaos at all.

I mean so that every single atom in each pendulum had their respective sub atomic particles, and quarks and so on all spinning exactly in unison?

To be honest I have no idea why this would be important. This is all classical mechanics here. Also no one is claiming that.

Then how do you account for the slight differences in gravity effects between the 2 pendulums?

They are so unimportant as to be negligable.

How do you regulate, time and equalise the number of neutrenos that pass through them throughout the exeriment?

Again without being too snarky I would say the neutrinos have nothing to do with anything anyone is talking about. And IF a neutrino did pass through it owuld do just that PASS through and not effect the system at all. Thats's what it means to pass through. The cross section for neutrino scattering is astoundingly small. You are looking for weak-force scale interactions at a classical level.

How about other radiation such as radio?

Radiation pressure is too small an effect to care about. Plus you used the word "other", but in fact the only radiation you mentioned is radio, unless you think neutrinos are a form of radiation.

How do you do the same for your measuring equipment?

Why ahould I care? All the "effects" you mentioned are miniscule compared to the size of the signal I would be obtaining. This isn't a measurement problem ala quantum mechanics.

How do you compensate for relativity effects since both pendulums aren't in the same spacetime?

You really need to look at the physics involved in the questions you are asking. Unless we are going to be swinging these pendulums at a decent fraction of the speed of light, the relativistic effects are extremely small. Thats why Newton and others were able to so well describe systems like pendulums. This is a CLASSICAL problem.

Until someone can flush out all of that and more how could you ever have data to support chaos? It just seems like an ideal, something that tries to describe the effects of what we can't measure.

I have answered evey question you have. There are tons of data that points toward chaotic behavior. The weather outside is a pretty good one. Again, not to be an ass, but I don't think you know what you are objecting to. You need to actually read the links and the primer I posted. Perhaps an introductory math and physics class as well. Chaotic systems are not controversial anymore and haven;t been for a while. The only thing in contention here, as has been pointed out, is the use of synchronized chaos for encryption. I don't really have th tome or desire to, but synchronized chaos had benn proved mathematically.
posted by ozomatli at 9:28 PM on December 14, 2005

Wow. Nothing is more informative then idiots who know nothing about chaos theory talking about it.

Did I say idiots? Sorry, I meant "idiots" but I'm drunk so I didn't think up a euphamism to mask my conntempt.
posted by delmoi at 9:40 PM on December 14, 2005

I hope thats not directed towards me demoi...
posted by ozomatli at 9:43 PM on December 14, 2005

On reading the article, it is indeed intresting.
posted by delmoi at 9:46 PM on December 14, 2005

More papers: chaos theory, sync & coupled oscillators.
posted by scalefree at 12:31 AM on December 15, 2005

I love Metafilter, for posts and comments like these.

Thank you all.
posted by Samuel Farrow at 1:46 AM on December 15, 2005

Delmoi: like idiots who don't know the difference between "then" and "than"?
posted by Merlin at 4:26 AM on December 15, 2005

ozomatli: You didn't sound snarky, you sounded correct. :) I love when people spend 2 hours thinking about something and thinking they're experts. And until you can prove Fermat's last theorem, I'm not buying the whole "addition" thing.
posted by anomie at 6:37 AM on December 15, 2005

There is an article in the May 1976 Scientific American about synchronized fireflys.

About the same time, I was working with Dick Davidson, a physics lecturer at the U of Wash, on some exhibits at the Pacific Science Center in Seattle. Dick had a friend who was building an "ocean ark" over in Bremerton. It was an old WWII barge that he was fitting out with greenhouses, wind power, etc. to be completely self-contained.

One issue that came up was the small fleet of fishing dorys that would be part of the ark. The problem was how to get a small fleet of boats to identify themselves as a fleet, so they didn't get lost in crowded waters.

Dick came up with a circuit for xenon strobes that used a photo-SCR to reset the oscillators to synch to the fastest one. The result was all the boats would have one of these beacons on their mast and they would all flash in synch. Later that year, the SciAm article came out and we were all pleased as punch.

The same idea was used about ten years later in an attempt to protect gill nets fishing in crowded waters at night. The drunken pleasure boaters would plow right through a net in the dark, despite the light buoys at each end of the net. I was working with a little company called Maritron that was building blinking LED lures for longliners (they were using chemical light sticks). So I suggested reviving Dick's synchonous strobes and putting them along the net floats.

Anybody else have a Dick Davidson story? One of the smartest people I've ever known.
posted by warbaby at 6:41 AM on December 15, 2005

Fermat's last theorem has been proven, anomie.
posted by kyrademon at 9:47 AM on December 15, 2005

Nice post, ozo.

If anyone else doesn't "buy" chaos "theory" you can experiment for yourself here.
posted by plexiwatt at 9:53 AM on December 15, 2005

Now if we can just get the MeFites reading Kristol

oh, we've read him alright.

fantastic post, ozomatli.
posted by 3.2.3 at 11:44 AM on December 15, 2005