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Geek Culture / The cat/buttered toast paradox EXPLAINED!

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TheComet
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Posted: 10th Apr 2012 17:06
Let us begin with a simple analysis.

1) Buttered bread must fall butter side down.
2) A cat always lands on its feet.

So what happens when a piece of buttered bread is attached to the back of the cat?

Acording to Newtons third law, a force acting upon an object will
exert an equal but opposite force on the adjacent object. The cat exerts a force C on the toast, which in mathematical notation is Ft = -C =( Mass of cat ) * g.

Acording to Murphys law of probability, any event in a constant time frame is said to happen to the inverse of the most preferable. In this case, we have only two possible cases, P(T = toast) lands buttered side up, or Ti=1-P(T) (Inverse probability of toast) landing downwward.

But From our previous mention of Murphy's Law, we can clealy see that P(T)= 0( or 0% of it happening ) and P(T) = 1 ( or 100% of it happening ).

Thus this is an equilibrium problem as there are two forces acting in two different directions, namely T and C. If The Air resistance is taken into consideration, and we have that C = T then if the toast is placed only slightly to the side of the center of gravity of the cat then we have a non-equilibral condition. So this then implies a rotational tourqe ( call it t for short ). t can be calculated by applying the tangental force aplied multiplied by the cross product of the radius r of the cat to the toast. So

t = Cos(theta) * r * ( Aplied force )

This applied force is quite weak as it's only reliant on air
resistance. But this then presents us with another problem. We have a conflict of laws of physics and philosophy ( ie. Murphy vs Newton )

Einstein in his thesis on general relativity however shows that
Newton's third law does not always apply to objects nearing the speed of light. So the only conclusion we can draw is that the cat with toast strapped to its back will rotate at near light speed. However, the closer one gets to the center of the cat the faster the cat will have to spin. So the cat will not only spin, but be completely mangled in the process by the fact that it's insides spin faster than it's skin and outer flesh.

The law that cat's land on their feet is also going to play a part
in this discussion. We realised the two forces C and T will
simultaniously act apon one another, causing the cat and the toast to either shoot upwards indefinitely, increasing in speed as gravity decreases the further one is away from earth, hover above the ground, or plummet downwards. The latter seems the most feesable, with a difference however that it will not stop. The immence rotations of the cat and toast will generate enormous amounts of heat as it comes into contact with the ground through friction and tunnel downwards, eventually reaching the
center of the earth. By that time the cat's legs will have been eroded away, the butter will be off the toast and thus the laws which we first used do not apply any more. So the cat will stop spinning somewhere in the earth's crust.

Can we use this as a source of energy?

Scientists all over the world have tried their best to contain the unstable reaction of cat and buttered toast, but were unable to design anything usable.

A group of scientists from the CABT lab (cat and buttered toast) were able to create a genetically enhanced toast with cat legs. However, as soon as the butter reached critical mass, it spun out of control and destroyed the lab.

Experiments show that suspending the cat and buttered toast in a chamber full of water causes the cat to catch on fire, fueled by the hydrogen and oxygen from the split water molecules, and then explode.

We have yet to find a solution to this problem.

TheComet

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SpyDaniel
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Posted: 10th Apr 2012 18:43
I've dropped toast in he past and it has landed butter side up, NOT down
Fallout
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Posted: 10th Apr 2012 19:46
Quote: "I've dropped toast in he past and it has landed butter side up, NOT down "


And I often throw cats out the window and watch them land limp legs up.

Seppuku Arts
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Posted: 10th Apr 2012 20:34
If you push cats out of a tall building did you know they're more likely to survive than if you pushed them of say...a 3 storey building? Because once they hit terminal velocity they're able to slow down their fall in a similar fashion to a flying squirrel?


I watch too much QI...


SpyDaniel
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Posted: 10th Apr 2012 21:01
Quote: "And I often throw cats out the window and watch them land limp legs up."

Cruel and funny
Fallout
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Posted: 10th Apr 2012 21:27
Quote: "If you push cats out of a tall building did you know they're more likely to survive than if you pushed them of say...a 3 storey building? Because once they hit terminal velocity they're able to slow down their fall in a similar fashion to a flying squirrel?"


I heard that, but my experiments with dropping them from light aircraft did not support that theory.

29 games
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Posted: 10th Apr 2012 21:40
At the risk of sucking all the fun out of this.

Toast generally lands butter side down because it's dropped from a height that only allows for one half rotation as the toast falls, i.e. pushed from a table top or sliding off a plate that's being carried, so if the toast was butter side up to begin with it would land butter side down.

Apparently, for the toast to go through a full rotation, the toast would have to be small (I think it about 11mm x 11mm) or you'd have to drop a full sized slice from a few metres up (but I can't remember how high).

If you were to flip buttered toast, like a coin, it's essentially a fifty-fifty chance of butter-side up or butter-side down. However, I believe in this instance the ten second rule comes into play and, as we all know, blowing on dropped food is the best way of getting rid of any germs so you may still eat the toast (removing fluff and hair and whatever else is stuck to the butter to suit your tastes / standards of hygiene).

Quote: "I watch too much QI..."


QI has nothing on lectures in dynamics from a bored lecturer.
Travis Gatlin
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Posted: 11th Apr 2012 00:18
Hold on. Ok. The mass of the cat is greater than the toast and the butter combined so the cat will naturally land first... lol

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Dark Java Dude 64
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Posted: 11th Apr 2012 00:40
Exactly! Also, the cat has actual muscles functioning to keep it upright during the fall, whereas the non muscular toast doesnt! The cat would land feet down, BUTTER UP!!!!

Comet, you haven't recommended micro controllers to me on my thread!! How dare you darken my doors in such a manner?

Kezzla
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Posted: 11th Apr 2012 01:07
perform the experiment in space... voila! Perpetual motion!

Sometimes I like to use words out of contents
MrValentine
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Posted: 11th Apr 2012 02:38
one word... VACUUM

WLGfx
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Posted: 11th Apr 2012 02:42
Well any of the extreme experiments on cats being thrown from extreme heights landing on it's feet are a million to one.

But then again scientists say that extreme impossible circumstances can happen one in a million chances. And the wizzards of the unseen university have also calculated that million to one chances occur 9 times out of 10.

(Quoting Pratchett) he he

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Dark Java Dude 64
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Posted: 11th Apr 2012 03:02
?[i][/i]

Seppuku Arts
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Posted: 11th Apr 2012 03:25
Quote: "And the wizzards of the unseen university have also calculated that million to one chances occur 9 times out of 10."


Priceless.


zeroSlave
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Posted: 11th Apr 2012 07:47
Hey now. There is only one wizzard. And he comes with his very own Luggage. Which would be my suggestion for a place to experiment with this cat toast issue.

Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.
Green Gandalf
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Posted: 11th Apr 2012 12:05
I guess it all depends on the cat. One of our cats always lands on his feet, the other always lands on his stomach. That's because he's so huge he has no choice.

The other great mystery is why does buttered toast always fall buttered side down on the only patch of dust and cat fur on the floor?
Benjamin
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Posted: 11th Apr 2012 12:15 Edited at: 11th Apr 2012 12:16
Quote: "The other great mystery is why does buttered toast always fall buttered side down on the only patch of dust and cat fur on the floor?"


We already have the scientific explanation for this.



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SpyDaniel
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Posted: 11th Apr 2012 16:28
What about strapping another cat which is the same mass as the first cat, to the back of the first? Which cat would land feet first?
Green Gandalf
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Posted: 11th Apr 2012 17:01
That would really make the fur fly.
Fallout
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Posted: 11th Apr 2012 18:02
Quote: "What about strapping another cat which is the same mass as the first cat, to the back of the first? Which cat would land feet first?"


I predict a double face plant.

Matty H
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Posted: 11th Apr 2012 18:51
I tried it with toast and a dog and got butter side down every time.

MrValentine
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Posted: 11th Apr 2012 18:52
thats because the dog could not help sniffing his... Toast

Wolf
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Posted: 11th Apr 2012 19:59
Quote: "2) A cat always lands on its feet."


My cat fell down the roof and broke its back. Theory disproved.

Creativity is allowing yourself to make mistakes, art is knowing which ones to keep.
MrValentine
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Posted: 11th Apr 2012 20:02
Quote: "My cat fell down the roof and broke its back."


Theory of Cats having 9 lives, still stands...

SpyDaniel
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Posted: 11th Apr 2012 20:09
If a cat has 9 lives, what happens if I sever its spine? Would it respawn somewhere else and continue on? lol xD
Wolf
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Posted: 11th Apr 2012 20:24 Edited at: 11th Apr 2012 20:37
No, he just died... that was sad for the entire family. Mostly me as I grew up with him.

But he was very old, so I guess he already used up his other nine lives

Creativity is allowing yourself to make mistakes, art is knowing which ones to keep.
Benjamin
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Posted: 11th Apr 2012 22:35
Quote: "My cat fell down the roof and broke its back."


I wasn't aware that landing feet-down guaranteed that your back would not break. Sorry for your cat.



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Dark Frager
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Posted: 11th Apr 2012 23:40
After reading all these posts.....


....mind = blown.

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WLGfx
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Posted: 12th Apr 2012 02:31
Definitely feet first always so long as the buttered toast is strapped to the cats under-belly.

Greebo wouldn't stand for it though...

Mental arithmetic? Me? (That's for computers) I can't subtract a fart from a plate of beans!
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nonZero
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Posted: 12th Apr 2012 21:02
Perhaps remove the cat and simply butter both sides of the toast. Technically the toast and eventually the butter will be disintegrated as rotation speed increases...


fig 1.1

Now how do we stop the high-speed rotation? Well, both sides are now "fighting" to land on the floor. 2 sides. 2 floors. So we build a room about 7 foot high and tile the ceiling and floor with unwashed tiles from a public toilet. Now we release our dual-buttered toast in slight favour of the ceiling so as to compensate for natural gravity (some pretesting required). We should now had two perfectly equal forces at work and toast should levitate.


fig 1.2

Next question is, of course, the challenge of finding uses for a room containing a levitation piece of toast...

Matty H
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Posted: 12th Apr 2012 21:28
Quote: "Next question is, of course, the challenge of finding uses for a room containing a levitation piece of toast..."


That's obvious, your hands would be free at breakfast to fasten up your jacket, tie your tie etc. The possibilities are endless.

Scraggle
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Posted: 12th Apr 2012 22:59 Edited at: 12th Apr 2012 23:01
What Paradox?

The buttered toast adage deals with a piece of toast that falls to the ground from a height. In this experiment where the toast is attached to the cat, then the toast is not falling at all, it is already on the surface that it was placed (the cat). Therefore in this example, there is no paradox. The cat will land on its feet and the toast will remain butter side up on the cat much like it would if you placed the toast on a plate.

zeroSlave
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Posted: 12th Apr 2012 23:23
What if you put a piece of buttered toast and a cat in the LHC and fired them at each other?

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Dark Java Dude 64
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Posted: 13th Apr 2012 00:24
Ah there is a good point!

IanM
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Posted: 13th Apr 2012 00:32
I opened this thread hoping for a discussion on Schrödinger's cat, and his less known theory regarding toast being dropped within a closed box - I'm most disappointed, as everyone knows that perpetual motion is impossible, and what self-respecting cat would allow you to glue toast to it's back anyway?

Of course Schrödinger's theories are bunk anyway, because as soon as you hear the dying screech of the cat, or the toast hitting the floor with either a dull thud or a squelch, you know what the state is within the box without having to take a look.

SpyDaniel
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Posted: 13th Apr 2012 01:27
What about the toasts thoughts of a cat being glued to it?
nonZero
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Posted: 13th Apr 2012 12:44 Edited at: 13th Apr 2012 12:50
Quote: "...and what self-respecting cat would allow you to glue toast to it's back anyway?"


and...

Quote: "What about the toasts thoughts of a cat being glued to it?"


Which is why I suggested we remove the cat from the equation in the first place

Quote: "...as everyone knows that perpetual motion is impossible..."


...Only in the first, the second and the third (this one) spheres. It is more than possible in the fourth and fifth and there insufficient data on the other spheres due to their high-density magical insulation.

Typical explanation of fifth-sphere physics re: perpetual motion, using 4th-sphere notation:


And that folks, is perpetual motion, aka purpetual motion when spoken of in terms of cats

FYI: Schrödinger's cat was never inside the box. The minute he made the choice to put the cat in the box, reality branched and cloned him, his cat and the world. The real Schrödinger never put his cat in a box. From this we conclude that that moment in time created us all along with all future generations - a fake universe who's existence is merely to allow for the existence of one decision decision made nanoseconds before its creation.

Neuro Fuzzy
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Posted: 13th Apr 2012 13:00
Also, what happens if you place an airplane on a treadmill, but the treadmill moves backwards at exactly the same speed that the wheels are rolling??

Green Gandalf
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Posted: 13th Apr 2012 14:14
Quote: "Also, what happens if you place an airplane on a treadmill, but the treadmill moves backwards at exactly the same speed that the wheels are rolling??"


Sounds like Lee's attempts to keep DBPro free of bugs.
nonZero
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Posted: 13th Apr 2012 15:03
Quote: "Also, what happens if you place an airplane on a treadmill, but the treadmill moves backwards at exactly the same speed that the wheels are rolling??"

You will see a black cat walk by twice. Both times with buttered toast strapped to its back.

bitJericho
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Posted: 13th Apr 2012 16:47
Quote: "Also, what happens if you place an airplane on a treadmill, but the treadmill moves backwards at exactly the same speed that the wheels are rolling??"


The wheels would speed up and disintigrate due to the friction, causing the plane to crash, or if the plane had enough speed to take off, causing the plane to crash on landing...

SpyDaniel
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Posted: 13th Apr 2012 18:39
Myth Busters did the plane on a treadmill myth and confirmed one can take off.
bitJericho
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Posted: 13th Apr 2012 18:58
oh right, see in my head the treadmill was going the wrong way and speeding up the wheels. If we're talking about stopping the wheels, that everything is fine. Just don't cross any wires.

Benjamin
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Posted: 13th Apr 2012 21:02
Quote: "Myth Busters did the plane on a treadmill myth and confirmed one can take off."


Neuro was actually making a parody of the real question. Whether or not the plane would take off doesn't require practical experiments, just logic.



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NIlooc223
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Posted: 14th Apr 2012 05:52
Well said TheComet..

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Ortu
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Posted: 18th May 2012 04:33


zeroSlave
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Posted: 18th May 2012 04:48
That's a pretty clever video. I especially like the part at 0:17.

Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.
Nateholio
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Posted: 18th May 2012 09:09 Edited at: 18th May 2012 09:15
Quote: "Also, what happens if you place an airplane on a treadmill, but the treadmill moves backwards at exactly the same speed that the wheels are rolling?"


The plane takes off. And yes, I have a decade of experience with flying.

Edit: oops, thought I was on page two. Never mind this post.

Just conducted the experiment. The control cat was a nimble young kitty and the test subject was a not-so-nimble portly old kitty. The control landed just fine feet down, while the test crashed face down.

Case closed!

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Indicium
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Posted: 18th May 2012 09:32
Quote: "The plane takes off. And yes, I have a decade of experience with flying."


No it doesn't, they tried it on Mythbusters and the plane didn't move. There's no movement of air across the wings, so why would it?

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