On a cold, rainy day I was perusing the bookshelf in my living room, when a book called Let the Great World Spin caught my eye.
The story centers around a fictional account of Philippe Petit’s very nonfictional August 1974 tightrope walk between the twin towers of the World Trade Center. It was just after 7am on August 7, 1974 when Petit stepped onto a steel cable that he and several friends had spent all night surreptitiously stringing between the towers. For 45 minutes he held lower Manhattan spellbound as he walked, ran, jumped, knelt, and somersaulted across the cable.
The whole book is a masterpiece of storytelling and like any great story, it worked like magic on my senses. I found myself terrified to look down for fear that Manhattan would be splayed out 110 stories beneath me, even though I was safely ensconced on my couch.
Then the PHYSICS alert sounded in my brain. Other than nerves of titanium, what does it take to stay balanced on a tightrope?
As soon as I dove into the PHYSICS though, I hit linguistic gold.
If you’re ever bored, feel free to google English conjugations of funambulate. As it turns out, ‘I had been fumabulating’ is a legitimate sentence. Who knew?
Back to the PHYSICS!
Humans are top heavy creatures. Two thirds of our body mass is concentrated in the top one third of our bodies. Apple, Pear, Surfboard Flat—whatever your body type—you are an inverted pyramid.
On the ground, we stand with our feet apart, broadening the base of our pyramid and providing more stability. A funambulist on a tightrope, however, must balance with one in front of the other, decreasing the base of support and exaggerating her human endowed top heavy nature.
Think of the tightrope wire as an axis and the funambulist as an inverted pyramid-shaped mass trying to remain balanced on said axis. If the center of mass of the pyramid isn’t balanced correctly on the axis, it will be begin to rotate. If that rotation isn’t corrected, gravity (ruiner of all things fun) will cause what I would like to term a funambufail.
The long, weighted poles that funambulists carry help to lower their center of mass. A lower center of mass increases the tightrope walker’s moment of inertia—aka her resistance to rotation. Increased resistance to rotation gives the walker more time to shift her center of mass back to the center of the wire.
Knowing when to readjust one’s center of mass, of course, depends on a performer’s own internal sense of balance. Humans use three different systems, working together in concert, to get sensory information related to balance.
The first is our visual system—that one is pretty self explanatory. If the world looks off-kilter, then it is probably YOU who are off kilter. (Long distances distort our visual sense of balance however, so this is probably the least helpful balance component for tightrope walkers. Hello, vertigo.)
The second system is our trusty vestibular system, which is centered around those fluid-filled cavities in our inner ear. Those cavities give us feedback about movement (up/down, horizontal) and spatial orientation. Getting sea sick or car sick is the result of information from vestibular system conflicting with information from your eyes.
Finally, there is the proprioceptive system— a network of sensors in our joints and muscles that give us information about where our limbs are in relation to each other. Clap your hands behind back. You can’t see your hands, but your brain knows where they are—that’s your proprioceptive system at work.
Visual cues combined with information from the vestibular and proprioceptive systems form a constant feedback loop that gives the funambulist information about where she is in space and where her center of gravity is in relation to the wire.
That little ‘relation to the wire’ bit is what makes funambulating so difficult. Not only is the performer balancing her weight on a very narrow point, the surface she is balancing on sways in response to natural factors, like wind, in addition to responding to her movements. What that means it that a funambulist must constantly make minute adjustments to her center of mass in order to stay balanced.
It’s the kind of feedback loop in which “small errors can be amplified very easily,” according to L. Mahadevan. He’s an applied mathematician at Harvard and recently, he and a few colleagues did some scientific funambulation investigation...because why wouldn’t they?
They created a computer model of a person balancing on a rope while being acted upon by all of the forces, masses, and velocities that a real tightrope walker encounters. Clearly they did this for fun, but also because it was part of a broader investigation of the ways our brains and bodies work together to perform complicated tasks.
Ultimately, Mahadevan and his team figured out two key points. The first was that the rapid fire information about falling being pumped to the brain via the vestibular system is the key component in helping tightrope walkers maintain balance.
The second is a mathematical equation proving what funambulists have known for ages: the easiest rope to balance on has a sway of about three feet at the midpoint. At that point, so say the scientists, the time that it takes the balancer to react is almost exactly the same as the time it takes the rope to oscillate, meaning that funambulists can tune all their balancing senses to the rope rather than trying to integrate sensory information from multiple sources.
If you want a better explanation of funambulation, you’re just going to have to try it yourself.