What Would Happen If You Strapped Buttered Toast to the Back of a Cat?

Can you find the solution to this paradoxical situation?
Trevor English

Everyone knows that cats always land on their feet, and buttered toast always lands buttered side down. These are common truths we hold to be self-evident. There's a problem though, a paradox that arises when you combine these two adages together into one simple experiment.

What would happen if you attached a piece of buttered toast, butter side up, to the back of a cat and then dropped that cat from a tall height? Would the cat ever land? Would the cat just spin indefinitely? Would one of the original truths break?

This is known as the buttered cat paradox.

Solving the buttered cat paradox

If we engage in some thought experiments on the subject, we can start to develop a hypothesis of what might happen. As the cat falls toward the ground, the cat will try to spin to have its feet facing downward. The toast, on the other hand, will want to flip to hit buttered side down as well. Many researchers believe that as the two objects, the cat and toast fall, they will slow down and start to rotate, eventually reaching a steady state of hovering a very short distance above the ground while both the cat's feet and the buttered toast try to land in their respective ways. Doing so would create an anti-gravity device.

The paradox in pop culture

This hypothesis and the paradox itself have been presented in a slew of media. In May 1992, the Usenet Oracle included the question in Digest #441. In 2005, the idea of a perpetual motion machine using this concept was explored in the graphical web strip called "Bunny."

The idea even appeared on the British TV show QI, where hosts discussed the idea in great detail. For years now, this paradox has remained unanswered.

Solving the paradox with theoretical physics

If we broach the subject from an engineering and physics perspective, we can gain some insight and possibly break down the original paradoxical nature of the proposition.

Examining both the cat and the toast as capable of exerting a rotational force upon themselves to always land in their respective orientations, we can see how they might interact. The rotational force of each would be respective to their mass, with the cat obviously containing more. Assuming these forces are working against each other, with the cat's larger mass, we can assume that the net force on the body would be in the direction of the cat's force vector.

Physics jargon out of the way, the cat would most definitely win out in this battle in landing on its feet. As long as the toast continued to be strapped to the cat's back after the cat landed on its feet, the toast would continue exerting a rotational force on the back of the cat. Our feline friend would likely be able to overcome this relatively small force through the friction created from its paws on the ground.

Finally, through some simple mathematics and physics, we've found the answer to one of the most famous paradoxes in history! That said, this is just one approach that could certainly be proven wrong. What other ways can you prove or disprove the paradox, and ultimately, what do you think would happen? 

P.S. If it wasn't apparent in the article, the buttered cat paradox is a joke.

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