A Mathematician's Lament

A Mathematician's Lament

A good problem is something you don’t know how to solve. That’s what makes it a good puzzle, and a good opportunity. A good problem does not just sit there in isolation, but serves as a springboard to other interesting questions. -Paul Lockhart

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

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).

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