Buttered Cat Paradox

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Actaeus
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Buttered Cat Paradox

Postby Actaeus » Mon Nov 10, 2008 2:10 am UTC

So, most of you know of the buttered cat paradox.
You probably haven't considered any applications, and we don't have a thread for this. Unbelievable.
At my blog I have a post about a hovercraft possibility, but y'all probably have better ideas.
So, what should be done with a hovering buttered cat?
(sorry if this looks like blagspam, it isn't. I'm thinking that no matter how this thread goes, it should be pretty hilarious)

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Re: Buttered Cat Paradox

Postby Katrina » Mon Nov 10, 2008 2:24 am UTC

Given that cats have a nonfatal terminal velocity of 60mph, then there are four questions:

1) Is the cat above a height where it could reach 60mph?
2) If a cat that is going >60mph is also buttered, will the counter-force actually propel the cat upwards to a potentially gravity breaking velocity?
3) Is the bread hot, and subject to cooling, and does the temperature of the butter effect repulsion?
4) Are you certain that it is butter, and not a substitute masquerading as butter?

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Re: Buttered Cat Paradox

Postby Klotz » Mon Nov 10, 2008 2:36 am UTC

Clearly the cat lands on its feet then rolls over on its back, smearing the butter on the floor.

CT symmetry* is still conserved without violating conservation of energy.

*cat-toast

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Re: Buttered Cat Paradox

Postby BlackSails » Mon Nov 10, 2008 3:36 am UTC

What happens is the toast quantum mechanically tunnels through the cat, so the cat lands feet first, and the bread goes through the cat to land buttered side down.

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Re: Buttered Cat Paradox

Postby qbg » Mon Nov 10, 2008 3:58 am UTC

Klotz wrote:Clearly the cat lands on its feet then rolls over on its back, smearing the butter on the floor.

CT symmetry* is still conserved without violating conservation of energy.

*cat-toast

But as soon as the cat touches the ground, the toast takes over and continues to accelerate downwards and rotates. The centrifugal/centripetal force on the cat will cause cat disintegration if the cat is dropped from a non-trivial height.

Poor kitty.

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Vieto
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Re: Buttered Cat Paradox

Postby Vieto » Mon Nov 10, 2008 5:56 am UTC

but, due to quantum immortality:

from the cat's point of view, the cat can never die.

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Re: Buttered Cat Paradox

Postby mrbaggins » Mon Nov 10, 2008 6:57 am UTC

Put it in a box, such that it is simultaneously landing feet first and butter first, but we can't be sure til we open it.
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Re: Buttered Cat Paradox

Postby Xaldibik » Mon Nov 10, 2008 7:06 am UTC

Meteorswarm wrote:Wouldn't a simpler hovercraft be simply a piece of toast, buttered on neither side? If it has no buttered side, it cannot land, correct?


No, it is said that buttered toast always lands buttered side down. Now consider buttering both sides, or taping two pieces of buttered toast together buttered side out on both sides, or more interesting, buttered side in.

As to the buttered cat, what would increasing speed due to its gravity affect? Its mass would stay the same, but surely wind would create a vortex sucking things in, much like a tornado. Has anyone considered the affects of this? What would happen? Would the mass eventually grow enough to have a gravity pull strong enough to pull the earth towards the buttered cat, causing the illusion of landing?

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Re: Buttered Cat Paradox

Postby evilbeanfiend » Mon Nov 10, 2008 7:56 am UTC

http://preview.tinyurl.com/6pdeyo

thus the initial premise is incorrect by using science and there is no paradox
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Re: Buttered Cat Paradox

Postby Actaeus » Mon Nov 10, 2008 12:05 pm UTC

Well, you would have to drop the hovercraft from over 1' then to get it started.
mrbaggins wrote:Put it in a box, such that it is simultaneously landing feet first and butter first, but we can't be sure til we open it.
Buttered Shroedinger's Cat? hmmm...could we make a quantum hovercraft, though?

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Re: Buttered Cat Paradox

Postby mrbaggins » Mon Nov 10, 2008 12:12 pm UTC

I think we would have to somehow catch the Schroedingers buttered cat in free fall... Else it would land before the box was sealed.

Or we could box it and then throw it up in the air.
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Re: Buttered Cat Paradox

Postby Actaeus » Mon Nov 10, 2008 12:14 pm UTC

But when we opened the box, the collapsing wavefunction would cause violation of the cat and/or butter laws!

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Re: Buttered Cat Paradox

Postby Beacons! » Mon Nov 10, 2008 3:37 pm UTC

Xaldibik wrote:No, it is said that buttered toast always lands buttered side down. Now consider buttering both sides, or taping two pieces of buttered toast together buttered side out on both sides, or more interesting, buttered side in.


You can't have 2 pieces of toast in the paradox due to Lord Sandwich's uncertainy law.
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Re: Buttered Cat Paradox

Postby Jebobek » Mon Nov 10, 2008 3:45 pm UTC

If the butter is not too melted and soaked into the toast, I would think that the rotational speed would increase until the butter is launched off of the toast, and the cat lands on its feet. I'd like to think of it as a magnet that loses its power on one side, where the other side is stronger and is attracted to the floor.
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Re: Buttered Cat Paradox

Postby meat.paste » Mon Nov 10, 2008 6:29 pm UTC

We could harness the rotational power of a Cat-Toast gyro to power turbines. Once a CT system has begun to spin, the centrifugal force will cause the butter to begin to move toward the surface of the toast, which would increase the moment arm of the butter based torque on the system, which will accelerate the rotation even further. Care must be taken to keep the rotation below the point where the butter will fly out of the toast, of course. The attachment of a suitable rotor into the cat will aid in transferring power to the generator as well as keeping the CT system from rotating too quickly.

Naturally, if you wanted to destroy a city, you could set up rotating CT bombs that would continue to spin until a critical velocity was reached. At that point the CT system would disintegrate taking whole city blocks with it. This would require the development of military grade butter that will not depart from the toast prematurely.
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Re: Buttered Cat Paradox

Postby oxoiron » Mon Nov 10, 2008 8:19 pm UTC

Mmmm....military grade butter.
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Re: Buttered Cat Paradox

Postby Jebobek » Mon Nov 10, 2008 8:26 pm UTC

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Re: Buttered Cat Paradox

Postby wst » Mon Nov 10, 2008 8:28 pm UTC

How about desk toys? Nothing more awesome than a fuzzy blob screaming "MROOOOOOOOOOOOWWWWW!!!!! HISS" while you're doing your homework.
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Re: Buttered Cat Paradox

Postby Jebobek » Mon Nov 10, 2008 8:38 pm UTC

wst wrote:How about desk toys? Nothing more awesome than a fuzzy blob screaming "MROOOOOOOOOOOOWWWWW!!!!! HISS" while you're doing your homework.
Oh my freaking God... That is the funniest mental image I've ever had.
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Re: Buttered Cat Paradox

Postby sgt york » Mon Nov 10, 2008 9:19 pm UTC

Contrary to popular belief, this isn't really a problem in the real world. As the distance (x) of the c-t pair to the ground decreases, the rotational velocity increases as the c-t pair rapidly flips between the two allowable states. If the c-t pair was a geometric point, this would not be a concern; however, it is a complicated surface. Points far from the center of rotation experience linear accelerations and velocities (v). As x=>0, v=>c, and time dilation takes care of the rest. But even this is not the case. This assumes perfect vaccuum, perfectly rigid attachment of the toast to the cat, and infinite structural integrity of both cat and toast.

In a physics textbook world, this could solve the energy crisis. In the real world, it just makes a big mess.

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Re: Buttered Cat Paradox

Postby Firnagzen » Tue Nov 11, 2008 11:22 am UTC

mrbaggins wrote:I think we would have to somehow catch the Schroedingers buttered cat in free fall... Else it would land before the box was sealed.

Or we could box it and then throw it up in the air.


Bigger box.

Hey, even greater idea! Place a C-T complex between two interconnected spatial wormholes, preferably of the non-gravitational kind, such as may be achieved using the Aperture Science Handheld Portal Device, and allow gravity to take over.
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Re: Buttered Cat Paradox

Postby Hydralisk » Tue Nov 11, 2008 1:55 pm UTC

You guys have never watched Mythbusters have you?

Buttered toast does not always fall butter side down, in fact it's the same as unbuttered/double buttered toast - it's about 50-50 chance.

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Re: Buttered Cat Paradox

Postby Cynical Idealist » Tue Nov 11, 2008 2:11 pm UTC

Katrina wrote:4) Are you certain that it is butter, and not a substitute masquerading as butter?

Well, I can't believe it *isn't* butter!

I am so, so sorry


Hydralisk wrote:You guys have never watched Mythbusters have you?

Buttered toast does not always fall butter side down, in fact it's the same as unbuttered/double buttered toast - it's about 50-50 chance.

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(from page 2)
knight2417 wrote:Cats don't always land on their feet. They have quick reflexes that help with that, but its possible for them to land on they backs. Also if the cat lands on its feet the toast has not technically landed, therefore the toast is not landing butter side down.

See above.
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Re: Buttered Cat Paradox

Postby Mr_Rose » Tue Nov 11, 2008 2:23 pm UTC

Hydralisk wrote:You guys have never watched Mythbusters have you?

Buttered toast does not always fall butter side down, in fact it's the same as unbuttered/double buttered toast - it's about 50-50 chance.

The Mythbusters test was flawed in that it did not simulate the commonest revolving toast freefall situation, and simply dropped the toast. If they had done it properly, with a slice of toast placed butter-side-up on an average table then slid the toast off, their results would have been rather different.
Essentially they fell fro the classic experimenter's gaffe of making the test "fair" rather than simulating the observed conditions.

But also, Cynical up there clearly has you pegged.

Besides that though, all of you have utterly utterly failed to account for the fact that a cat with a piece of toast strapped to it will think it's trapped in a tunnel due to the guard hairs in its coat being deformed and, as such, will not rotate at all. We must learn how to deign around this before we can develop a functional C-T complex generator.
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Re: Buttered Cat Paradox

Postby wst » Tue Nov 11, 2008 6:56 pm UTC

I thought some people figured out that the odds of toast landing BSiD was the result of the speed of rotation of toast, and probabiliy, with over a 50% chance of BSiD. Then they figured out it'd land the right way up if you wore stilts. (This was with a plate though)
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Re: Buttered Cat Paradox

Postby Jebobek » Tue Nov 11, 2008 7:14 pm UTC

Mr_Rose wrote:Besides that though, all of you have utterly utterly failed to account for the fact that a cat with a piece of toast strapped to it will think it's trapped in a tunnel due to the guard hairs in its coat being deformed and, as such, will not rotate at all. We must learn how to deign around this before we can develop a functional C-T complex generator.
We could superglue toothpicks to a cat's body so that they're all sticking up, and then attach the toast to the toothpicks with some more superglue. Then the guard hairs are less deformed.
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Re: Buttered Cat Paradox

Postby Beacons! » Wed Nov 12, 2008 11:10 am UTC

Jebobek wrote:
Mr_Rose wrote:Besides that though, all of you have utterly utterly failed to account for the fact that a cat with a piece of toast strapped to it will think it's trapped in a tunnel due to the guard hairs in its coat being deformed and, as such, will not rotate at all. We must learn how to deign around this before we can develop a functional C-T complex generator.
We could superglue toothpicks to a cat's body so that they're all sticking up, and then attach the toast to the toothpicks with some more superglue. Then the guard hairs are less deformed.


Alternatively, we could just superglue some cats together.

You know, just to see what would happen.
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Re: Buttered Cat Paradox

Postby jaap » Wed Nov 12, 2008 12:46 pm UTC

Beacons! wrote:
Jebobek wrote:Alternatively, we could just superglue some cats together.

You know, just to see what would happen.


Before you break out the glue I think you first need to find out if they're left or right-handed (footed?) so that you know which way round to attach them. I guess the advantage of toast is that it's adextrous.

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Re: Buttered Cat Paradox

Postby Jebobek » Wed Nov 12, 2008 2:12 pm UTC

Beacons! wrote:
Jebobek wrote:
Mr_Rose wrote:Besides that though, all of you have utterly utterly failed to account for the fact that a cat with a piece of toast strapped to it will think it's trapped in a tunnel due to the guard hairs in its coat being deformed and, as such, will not rotate at all. We must learn how to deign around this before we can develop a functional C-T complex generator.
We could superglue toothpicks to a cat's body so that they're all sticking up, and then attach the toast to the toothpicks with some more superglue. Then the guard hairs are less deformed.


Alternatively, we could just superglue some cats together.

You know, just to see what would happen.
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Re: Buttered Cat Paradox

Postby thoughtfully » Wed Nov 12, 2008 3:07 pm UTC

Hydralisk wrote:You guys have never watched Mythbusters have you?

Before Mythbusters the buttered toast thing was debunked on Newton's Apple, back in the 80's. PBS trumps commercial TV again. As you might imagine from considering the aerodynamics, the side of the toast that ends up on top depends on the height it is dropped from, and therefore how many revolutions it undergoes. It just so happens that for most toast, dropping it from approximately counter height corresponds to a net rotation of close to 180 degrees.
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Re: Buttered Cat Paradox

Postby Klotz » Wed Nov 12, 2008 7:10 pm UTC

You all might want to check out this paper.
http://www.iop.org/EJ/article/0143-0807 ... 950405.pdf

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Re: Buttered Cat Paradox

Postby viscusanima » Fri Nov 14, 2008 6:42 am UTC

What about using the cat/toast combination, combined with an axle, to power a boat/car/vehicular equivalent? You stick it on the back, and the force generated by the incredibly fast spinning of the cat and toast propels the vehicle forward.

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Re: Buttered Cat Paradox

Postby meat.paste » Fri Nov 14, 2008 11:46 pm UTC

How about we let the C/BT system rotate freely (That's Cat/Buttered Toast. If you thought it was something else, then :P .) Eventually, they will reach relativistic velocities. If you strapped a thousand of the turbines to a set of large metal hoops, the quantum fluctuations would induce a gravitational singularity and allow faster than light travel, a la the movie Contact.
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Re: Buttered Cat Paradox

Postby Actaeus » Sat Nov 15, 2008 12:49 am UTC

meat.paste wrote:How about we let the C/BT system rotate freely (That's Cat/Buttered Toast. If you thought it was something else, then :P .) Eventually, they will reach relativistic velocities. If you strapped a thousand of the turbines to a set of large metal hoops, the quantum fluctuations would induce a gravitational singularity and allow faster than light travel, a la the movie Contact.

Would time travel resolve the paradox?
If the C-T system obeyed reverse thermodynamics, it could just accelerate away from Earth. Problem solved.

Alternatively: the predicted time of impact is T. You measure the amount of time from every prior instant, and make a logarithmic plot.
Time T is now at [imath]10^{-\infty}[/imath], and thus ceases to exist normally.
You can now observe the entire prior history of the universe, as it lies on the plot, and get arbitrarily close to time T. This log-timeline can therefore contain an infinite, unbounded amount of time, making it a complete timeline which nevertheless conveniently sidesteps the issue.

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Re: Buttered Cat Paradox

Postby qinwamascot » Sat Nov 15, 2008 3:49 am UTC

I'd guess that one of two things will happen. The cat and toast will be spinning so fast that all the butter flies off the toast, or the cat dies from its limbs being ripped off by spinning too fast. The former would probably happen first. After that, it's not an issue anymore. So theoretically we have a paradox, but physically it gets resolved by the fact that unbounded exponential growth will quickly reach a critical point in our system.

if we have an immortal cat and an indestructible piece of buttered toast, we may be in for trouble.
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Re: Buttered Cat Paradox

Postby thoughtfully » Sat Nov 15, 2008 6:03 am UTC

As long as there's a load on the system, the rotation rate can be kept in check. When there's no load, all that's required is some means of separating the cat and the toast until needed.
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Re: Buttered Cat Paradox

Postby v1ND » Sun Feb 01, 2009 6:21 am UTC

Now suppose we put this cat and toast contraption inside a sealed box. The cat's not dead or alive so do we have...

FLYING UNDEAD ZOMBIE CATS!?!?



(Yes I mutilated Schrodinger's cat brutally in the most literal sense of the term.)

(The cat is now most definitely dead, no more of this superposition of states nonsense)

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Re: Buttered Cat Paradox

Postby RoadieRich » Sun Feb 01, 2009 5:07 pm UTC

Meteorswarm wrote:Wouldn't a simpler hovercraft be simply a piece of toast, buttered on neither side? If it has no buttered side, it cannot land, correct?


I think the law is probably better defined as "toast always land unbuttered-side down"?

Hydralisk wrote:You guys have never watched Mythbusters have you?

Buttered toast does not always fall butter side down, in fact it's the same as unbuttered/double buttered toast - it's about 50-50 chance.
Bah. It's possible to prove, mathematically, that under real, breakfast table conditions, toast will undergo almost exactly one-half rotation after falling off a sensibly designed table. Unless you have funny habits involving buttering plates or tablecloths, that means butter side down.

I'll look up the equations for you if you want.
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Re: Buttered Cat Paradox

Postby Actaeus » Sun Feb 01, 2009 10:57 pm UTC

RoadieRich wrote:I think the law is probably better defined as "toast always land unbuttered-side down"?

...UP.
Unbuttered side up.

Or, more precisely, it will tend to land on the side with more butter (the effects of other toppings have not yet been properly tested).

I believe the general effect is one that disappoints the dropper; hence, the Mythbusters (hoping for an interesting result) got a 50-50 tally, whereas someone planning to eat the toast will inevitably drop it butter-side-down.

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Re: Buttered Cat Paradox

Postby Sockmonkey » Mon Feb 02, 2009 3:33 am UTC

My own experiments have shown that the butter invariably ends up being licked off by the cat before the completion of the experiment.
Putting that aside for the moment what are the chances of the toast and cat achieving a stable equalibrium and landing on their side?


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