Sunday, November 26, 2006

"The Buttered Cat Paradox"

The things you learn from Wikipedia. (no, don't ask me how I got here)

"The buttered cat paradox is a paradox based on the tongue-in-cheek combination of two bits of folk wisdom:

Cats always land on their feet.
Buttered toast always lands buttered side down.

The paradox arises when one considers what would happen if one attached a piece of buttered toast (butter side up) to the back of a cat, then dropped the cat from a height.

Notwithstanding the complaints that would arise from PETA and other animal rights groups if someone actually tried to drop a cat, under that scenario one of the two end results would never occur – if the cat landed on its feet, the toast would land buttered-side-up, but if the toast landed buttered-side-down, the cat would end up landing on its back.

...While the paradox originated as a tongue-in-cheek combination of two bits of folk advice, it ended up creating some interesting thought experiments to analyse what would happen if one assume the two rules here would always occur.

Some people jokingly maintain that the experiment will produce an anti-gravity effect. They propose that as the cat falls towards the ground, it will slow down and start to rotate, eventually reaching a steady state of hovering a short distance from the ground while rotating at high speed as both the buttered side of the toast and the cat’s feet attempt to land on the ground.[1] This, however, would require the energy that keeps them rotating and hovering to come from somewhere, otherwise it would violate the Law of Conservation of Energy. There could be multiple ways the cat and toast achieve this - for one, they could draw heat from the air, or sunlight, and convert it into direct kinetic energy; though this would prove hard to do, it is theoretically possible.

Another response is that the cat will land on its feet, and immediately roll over on its back. This, however, means that the cat's feet were stronger than the toast's buttered side insofar as its attraction to the ground, but once on the ground the buttered toast's attraction overpowered the cat's feet. This would give rise to another question: which is stronger, the cat's movement to land on its feet or the toast's butter-side attraction to the ground? The reverse could also be true – the toast lands first buttered side down, and then the cat rolls onto its feet. (However, both scenarios would require the assumption that the cat did not suffer a major injury upon landing, either in the legs or the back.)

In June 2003, Kimberly Miner won a Student Academy Award for her film Perpetual Motion.[2] Miner based her film on a paper written by a high-school friend that explored the potential implications of the cat and buttered toast idea.[3][4]"


Like I said: don't ask.


Daisy said...


nexy said...

clearly, the cat would land on her feet. the reason is quite simple. the average cat weighs between 7 and 11 pounds, while the average buttered bread slice is a mere few ounces. by the sheer weight differential, the force of the cat's propensity to land on her feet will overpower the force of the bread to land on its buttered side.

additionally, the cat uses her ability to twist herself mid-air as she's plummetting to the ground, so as to orient herself to land on her feet. the bread has only gravity with which to work, and cannot twist itself.

and besides, i love cats, and dislike bread and butter.

R. Mildred said...

Why is that even a paradox? Obviously while a buttered peice of toast will land butterside down, and an unbuttered cat will land feet side down, a buttered cat is neither one nor the other, and thus will not neccesarily follow the classical rules that govern either of the other objects.

But what I find interesting is:

What would occur if a buttered cat came into contact with an unbuttered cat?

Is the attractive force of buttered toast and cat feet in anyway cumulative - so would placing multiple slices of toast along the back of the cat make it more likely that a "butter down" result would occur or indeed whether sowing two cats together and sticking a single slice of acros their two backs make the likelyhood of a "cat down" result increase?

Also, the wiki page ignores the possibilty of using a quantum solution to the paradox, for instance if you were to drop a buttered cat inside a locked box with a device which had a 50/50 chance of killing the cat, the buttered cat would simultaneously exist as alive and feetside down, alive and butter side down, dead and butter side down and finally dead and feet side down.

Then when you open the box, you will not only fix the buttered cat into a particular state, you would also cause it, in what ever state it ended up being in, to produce a look of miffed notchalance that would imply that not only has the buttered cat always been dead/alive/butter side down/feet side down, but that it also meant to fall, and that it didn't have anything to do with that lamp that got mysteriously knocked over and smashed a few days ago, and if you were to ask its opinion on such matters - though it would have no idea why you'd ask it in particular because it is perfectly innocent and also above reproach on such matters - it would venture the opinion that it personally blames those generic immigrants who are always coming over here and causing trouble.

Also, those mouse innards it left lying around the house for you to tread on first thing in the morning with bare feet was an installation art piece and how can it really be expected to work under these frightfully bourgeois conditions.


That the quantum solution produces a result not a million miles away from the various colored states of quarks and other subatomic particles found in the theory of quantum chromodynamics might also possibly suggest that matter is, when you get small enough, made up entirely of variously "charged" sub-atomic buttered cats.

belledame222 said...

R Mildred wins.

Sara E Anderson said...

I think we're making some unwarranted assumptions here. Who says that the force of attraction has anything to do with the weight? How could someone possibly dislike buttered toast? I would imagine that magnetic or gravitational forces would be the most appropriate analogy here, but there's really not a lot we can figure out without measuring the relative strength of these attractive forces. It would be difficult to find our control groups - cats without feet, say - as well. All I can say with certainty is that we'll need a lot of funding to finish this important research. Of course, the military applications could be limitless, so we'll have to hit up the Pentagon first. It'll sure be a more useful way to spend our money than the Iraq war, anyway.


Don't you *LOVE* Wikipedia?!?!?!

I'll go on there to look up something like "How old is Barack Obama?", and I'll find myself still on the site (one hour later, mind you) looking up something like "the oldest Maorian hermaphrodite" or something like that.

Whoever came up with the idea for that site is a genius. Really. I mean it. Sheer genius.

Rootietoot said...

my kids tried that a few years kid tried it and the others told him how wrong he was for doing it. He decided the mass of the toast needed to equal the mass of the cat(exclusive of the ductape required to adhere said toast to said cat), if you can picture such. Apparently the toasted cat spun like a gyroscope, inviting speculation as to the source of gravity. I remain sceptical.

Unsane said...

I want some buttered toast -- but not with cat hair in it.

ballgame said...

There is an alternative resolution to this paradox: the cat will land on its feet, licking its chops. Like an electron shifting orbits, though, the toast will be found to have mysteriously changed from a Buttered state to an Unbuttered state during the fall.

rey said...

What r. mildred said.

Plus, with the theory of relativity in mind, I would say that when you have a cat with buttered toast on it's back, you're dropping the cat. The toast is merely a passenger standing still on the larger mass of the cat itself (e.g. people on a moving train are standing still, relative to the train, yadda yadda yadda).

So the cat will land on it's feet. The toast - attached to the cat - was never actually dropped.

rey said...

None of this would matter if we lived in ~OuTeR SpAcE~

Anonymous said...

According to English folk wisdom, when you move house and don't want to lose your cat you butter its feet.
If I had a cat I no longer wanted, which part of it should I butter? Further, should I tape buttered toast to its back as an additional expediting measure,causing it to spin out of the door at approximately, say, knee-hieght?

Vmmer said...

Of course, one must also consider that if they WERE to attach a piece of toast, buttered, to the back of a cat, that it very well might depend on when the butter was placed on the bread/toast. If the bread was buttered then toasted, it might result completely differently than if you toasted the bread, then buttered it.

Personally I would assume that the latter would be correct, as buttered toast landing buttered side down would most likely be the result of Murphy's Law, and is true because of the fact that the butter would need to be cleaned off of the surface. So, would that mean that the property of buttered toast to land face down could actually be the result of a material's mess making properties? This might further lead to the question of whether or not the surface to be cleaned might come into play. Would a white carpet support this capability more than that of ...say a linoleum floor?

However, for the purposes of the argument, I will assume that t must be butter, and it must be placed on after the bread's transformation to toast. Unfortunately, this would result in a major problem. If, as the original article states, that the cat-toast combination were to draw heat energy from the air, then, eventually, the butter may melt and slip off of the toast, causing the mechanism to collapse on it's self and fling the cat in some unspecified direction. To combat this, one might place the cat into a sunless room(henceforth known as the "Cat's Cradle") at absolute zero, or if nothing else, cold. This, again, might hinder the experiment, as the cat would be incapable of absorbing the heat from the atmosphere. said...

Thanks so much for your post, really effective data.