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Odd Couples: How Ice Skaters and Fireflies Tell Us Something About the Language of the Universe

Rob Brown 02 Dec 2012

Dark matter: Credit NASA, ESA and M.J. Jee, 2007.  Hubble image from 2004.

The universe has always possessed the language it needs to conduct its own affairs. I don't think it could be otherwise.

Because my daughter participates in competitive figure skating, my wife and I spend a lot of time at the ice rink. Well, to be accurate and fair, my wife spends a lot of time at the ice rink.

Today is different. The recent Thanksgiving holiday activities disrupted regular free skate schedules, so I volunteered to take my daughter this morning to the special free skate sessions that were offered at the rink. Sitting in the upper bleachers where the air is a little warmer, if only marginally so, I watch the disorder on the ice below. Kids and adults are everywhere, all over the ice working off the sumptuousness of recent holiday dinner and desserts and pent up energy from confinement with their relatives. It's interesting to observe the range of skills present on the ice. As some cling desperately to the walls, others confidently glide and spiral and pirouette with grace. The ice buzzes with activity.

I've observed this scene dozens of times before, but suddenly it takes on an otherworldly appearance to me. Sitting high above on my cold perch, I feel a strange detached sensation, imagining myself as something like a Martian scientist observing the behavior of some recently discovered phenomenon on the blue-green planet out there. The icelings with metal blades attached to two of their appendages hurtle around in a cage paved with ice in utter chaos. But there's something about the chaos that piques my interest. I observe no traffic directing signals, no marked or structured lanes, no apparent communication; yet, each ice-blader seems to adjust its position, speed, and direction to avoid hitting the other ice-bladers. What once appeared as chaos now seems to have a pattern or structure to it. Although I can't seem to predict where any of the ice-bladers will be over time, I seem to be able to predict something that feels oddly important: no collisions will occur in the time window of my observations.* The chaos I observe is not like the random collision-prone molecules in the rarified atmosphere of Mars. Rather, a self-emerging order of collision avoidance becomes apparent. With my dispassionate optical sensors, I can't say I'm observing a social system of cooperation; however, a system of coordinated communication definitely seems to be occurring by which the entities below me dynamically adjust their physical state without centralized guidance or premeditated design (like that we expect to see in pair skating or synchronized swimming).

Smart people have been studying and researching the nature of self-emergent order for quite some time now. Just off the top of my head I think of Benoit Mandelbrot's fractals, Ilya Prigogene's work on dissipative structures, and Friedrich Hayek's speculative work on neural systems. Interest in Hayek's work serendipitously led me to a brief exchange on Twitter recently with Steven Strogatz, the author of Sync: How Order Emerges from Chaos in the Universe. As ironies often unfold in life, I began reading this book on my Kindle as I flew to Washington, DC on the day of our national elections, one of the grandest examples of coordinated communication and activity in the history of our species.

Strogatz begins his book by discussing the curious case of the synchronized blinking of fireflies observed in Malaysia, Thailand, New Guinea, and isolated valleys in the Great Smoky Mountains. As it turns out, the blinking represents a kind of coordinated communication among the fireflies that is surprisingly related to the mathematical concept of coupled oscillators—massive networks of such oscillators.


Synchronized firefly flashes in Elkmont, TN.

The best way to think about coupled oscillators, as Strogatz explains, is first to imagine a single reservoir, like a bathtub, that fills up with water, only to flush when it reaches its maximum capacity. Once it flushes, it begins to refill to repeat the process.

Imagine now a room full of bathtubs, hundreds of them, maybe thousands, all filling and flushing, no two at the same level. So far all we have is a collection of oscillators. None of them are coupled or coordinated. One small modification to the collection, though, changes it to a coordinated system: simply allow that a certain amount of leakage occurs with each flush so that all the surrounding bathtubs absorb some of the water that a tub just releases. The effect is to advance or uplift the fill level of each bathtub to be just a little closer to its trigger level of maximum capacity than it would be otherwise.

Now, for certain amounts and distribution of uplift and the nature of the rate at which the tubs fill (e.g., the rate slows down as the volume increases), the far reaching effect is that over time the tubs will eventually synchronize their filling and flushing. And this behavior, following the abstract mathematical language of coupled oscillators, is apparently what fireflies do when they synchronize their flashing. Weird, huh?

But it doesn't end there with the flies. A wide range of natural phenomena exhibits similar patterns that are subject to the same abstraction of the coupled oscillator math: cardiac cells, neurons, earthquakes, metronomes, etc. What else? Ice skaters, perhaps? Patterns in war and conflict? A nation that compiles its collective policy goals, propaganda, and prejudices on a given day of the year to elect its leaders?


These metronomes also demonstrate the very real effect of coupled oscillation.

And so, mid-flight between Atlanta and Washington, DC I built a simple model in Analytica to replicate the coupled oscillator to see if I could simulate the synchronized flashing of the Malaysian fireflies. You can see the model here at the Analytica Cloud Player.

Without going into too much detail here, I based the oscillators on the difference equation of the form

Yt = Yt-1 + k*(1-Yt-1)

I also played around with the assumptions to demonstrate most effectively how the oscillators converge on synchronization. What is astounding is the inexorable convergence that occurs with the system characterizations that I found. It may take many cycles to get there, but it always seems to occur. Change the assumptions, and other interesting patterns emerge, such as segregated cohorts of synchronized oscillators, almost as if the oscillators form into tribes or engage in a type of counter point in the luminal language of fireflies. If the saturation constant or uplift values are too small, synchronization never occurs. All we see is a fuzz of up and down based entirely on the random initial conditions of the oscillators. The behavior of each oscillator is simple as well as the language that describes them. And yet, given the right conditions, which aren't immensely implausible, a system of coupled oscillators organizes itself into a surprisingly coordinated arrangement.

∫   ∫   ∫

The universe has always possessed the language it needs to conduct its own affairs. I don't think it could be otherwise. And as a result, today we observe fireflies, cardiac cells and neurons, ice skaters, elections, earthquakes, violent storms, and war. Although each is a concrete example of broader concepts (reproduction, entertainment, the preservation of culture, the dissipation of potential energy, and the intentional thwarting and destruction of foes), none seems to bear any ostensible relationship to the others. And yet they are all related through the simple transaction of information that occurs as the elements of the universe change state, dissipating and absorbing energy in complementary, recursive ways. The complex order and structural arrangements that evolve out of such simple relationships are amazing.

I think there's something else we often take for granted as we explore the universe with our mathematics, and that is the mathematics itself. Of the few examples of the phenomena described above, and there are yet many other examples to consider, a similar math describes them all. Fourteen billion years after its birth, the universe now seems to be reaching beyond the language it uses just to conduct its own affairs. It seems to be developing the language to understand itself, at least here on our little blue-green planet among the local stubs that we call us. And I find that astounding.

And likewise, I'm thankful that I get to enjoy that with the community of people, the us, who have also dedicated their lives to expanding and improving that language. I meant to have this blog post out before Thanksgiving, but a dissipation of energy—a coupling to relatives, dinner, and desserts—conspired to delay my efforts. So although the calendar date has passed us by, to all those in the community of exploration and discovery, I hope you had a Happy Thanksgiving.

*To be honest, collisions do occasionally occur on the ice during free skate sessions, but nowhere near the frequency we would expect among the available opportunities in purely random motion. [back]

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Rob Brown

Robert D. Brown III is the President of Incite! Decision Technologies LLC (, a consultancy supporting senior decision-makers facing complex, high-risk opportunities. These opportunities usually include strategic planning, project selection, planning & risk management, and project portfolio analysis & management. Robert’s twenty-plus-year career has been devoted to providing solutions to clients’ complex problems by employing creative thinking and advanced quantitative business, engineering, and systems analysis. His client experience spans diverse industrial and commercial fields including petroleum & chemicals, energy, utilities, supply chain & logistics, pharmaceuticals, electronics manufacturing, telecommunications, IT, commercial real estate, federal agencies, and education. Through Incite!, Robert delivers analysis, decision support tools and systems, and training in decision-making and risk management with the goal to help his clients measure the value and the risk associated with the important decisions they face in order to make informed trade-offs and choices. He has also been a regular Analytica training resource for Lumina for over a decade. Robert graduated from the Georgia Institute of Technology in 1992 with a Bachelors of Mechanical Engineering.

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