George Gabriel Stokes was a bushy-sideburned Irish physicist and mathematician who for half of the 19th century was the University of Cambridge’s Lucasian Professor of Mathematics, a position held at other times by Isaac Newton and Stephen Hawking. A theorem Stokes formulated is taught to math and physics students today.
Besides genius, Stokes and Maxwell shared something else in common: A fascination with holding cats upside-down and dropping them.
“He was much interested,” Stokes’ daughter later wrote of her father, “in cat-turning, a word invented to describe the way in which a cat manages to fall upon her feet if you hold her by the four feet and drop her, back downwards, close to the floor.” In 1870, Maxwell wrote in a letter to his wife that upon visiting his alma mater, Trinity College, he’d learned there was a legend that he used to toss cats from school windows to watch them acrobatically land on their padded paws: “I had to explain that the proper method was to let the cat drop on a table or bed from about two inches, and that even then the cat lights on her feet.”
Were they sadists? No, said Greg Gbur, a physics professor at the University of North Carolina Charlotte who has blogged about what is now known as the cat-righting reflex: “They were ahead of the curve.”
That’s because while this feat of kitty gymnastics is a useful instinct for animals that climb trees, it’s also a physics conundrum — one that has occupied photographers, scientists and even NASA over the many decades since Stokes and Maxwell dropped felines. (Yes: Cats are even more mystifying than we knew.)
The issue is that the cat flip appears to violate the law of conservation of angular momentum, which says that when one thing rotates, something else rotates with equal and opposite angular momentum in another direction. Put more simply, Gbur said, when you push on the pedals of your bike and make its wheels rotate, the wheels push the surface of the Earth below with an equal force in the opposite direction (though the planet is way too heavy to actually move). But the cat is dropped with nothing to push off of — with no angular momentum to start with — and rotates all the same.
Tuck and turn, kitty!
For a long time, Gbur said, the belief was that the cat must have been pushing off its dropper’s hands. That changed with the advent of high-speed photography in the late 19th century, which early on was used to answer questions about animal motions — like whether all four feet of a galloping horse are ever off the ground at once (they are, which Gbur said means pre-19th-century “paintings of horses can often look very odd to the modern eye, because people were just guessing at the motion.”)
Etienne Jules Marey, a French scientist and engineer, applied high-speed photography to cat dropping. He presented his sequence of 32 shots of a cat in midair at the Paris Academy of Sciences in 1894, and Nature published them the same year. The accompanying article, titled “Photographs of a Tumbling Cat,” said that the images had “excited considerable interest,” though it wryly noted that the cat’s “expression of offended dignity … indicates a want of interest in scientific investigation.” Marey said his now-iconic photos showed the cat first tucked in its forelegs while stretching out its back legs, then switched them, which allows it to use the inertia of its own mass to flip.
Gbur said Marey called this “the tuck and turn” method, and it’s illustrated by what figure skaters do: They pull their arms in to spin faster. When a plummeting kitty pulls in its forelegs, its upper body spins faster than the lower part counter-rotates. Then it switches them, slowing the front part of its body so it becomes the fulcrum for the flipping back part.
Bend and twist!
In 1935, the Dutch physiologists G.G.J. Rademaker and J.W.G. Ter Braak came up with a mathematical drawing of a falling cat, which introduced the idea that the cat’s bent waist — as seen in the high-speed photos — was important. Their drawing basically made the case that the front and back parts of the cat are two soda can-like cylinders that rotate on two axes in opposite directions, resulting in a net angular momentum of zero, a move Gbur calls the “bend and twist strategy.”
The math behind this cylinder idea was nailed down in the 1960s, when Stanford University engineer Thomas R. Kane tackled it, coming up with equations that could predict the amount of turning a cat could do with all this bending, tucking and twisting.
And that led to cats’ improbable contribution to the heady space race of 1960s America.
NASA turned to Kane for help figuring out how astronauts could turn themselves around in zero-gravity, which a 1967 San Francisco Examiner article said they did at the time with “gas jets” whose gas ran out. They gave a $60,000 research grant to Kane, who used math to make computer drawings of the moves that gymnasts then acted out on a trampoline. “As for the cat, he does it without any mathematics at all,” the Examiner article said. “He is therefore ineligible for a NASA grant.”
Life magazine featured photos of Kane’s falling cats and trampolining gymnasts in “spacemen” costumes in a 1968 issue. A year later, Kane and a colleague published what remains the definitive examination of the topic: A paper titled “A Dynamical Explanation of the Falling Cat Phenomenon” — which probably brought the first and only cat photos to the pages of the International Journal of Solids and Structures.
Thank you, cats, for your ongoing contributions to science
Falling felines have continued to mesmerize corners of academia and the Internet. A University of California-Santa Cruz mathematician built on Kane and Scher’s work in the 1990s. In 1998, an Italian researcher dropped a cat named Esther 600 times — yes, 600 — to determine that she could fall on her feet when dropped from 2 to 6 feet, but not from 1 foot (Esther failed 100 attempts at that height. Ouch.) Last year, researchers published a study on how cat-righting might be applied to robotics.
“It turns out that it’s an example of a very deep phenomenon in physics that’s usually referred to as a geometric phase, and that connects to optics, quantum mechanics, geophysics,” said Gbur, who occasionally lectures on the topic. “There’s a lot of depth that you can learn about just from that cat behavior.”
You read it here: Cats can teach us physics. Deep physics.
Gbur said the exact mechanics of the cat flip are still being debated, and he thinks that is because there’s not one answer, which is frustrating to scientists.
“Probably the cat uses multiple different strategies to turn over,” Gbur said. “Physics prefers and tends to look for the simplest possible explanation for a phenomenon, whereas evolution — if I anthropomorphize it — is always looking for the most efficient. Living creatures are doing whatever works best, which may not be the simplest option.”
Gbur, for the record, said he is just a student of cat-dropping, not a dropper. “Not all cats are necessarily very good at it,” Gbur said. “Stick to the videos.”