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Demonstration
So, what would happen if we stick a slice of toast with butter to a cat's back and we throw it to the air? The cat, by law, will land on its feet, but the toast, (by law too) will land on the butter's side. Against this problem of physics laws, the nature chooses the best (and laziest, I think) way of taking a solution: the cat may just not fall.
Advanced computer model depicting the physics of a cat-toast device.
The cat with the toast, once it's free in the air, will float at its cat-toast equilibrium point, where butter repulsion forces and cat forces are in balance. This point can be adjusted by removing some butter from the toast, adding it, or cutting some hairs (or legs) from the cat. In theory, this will cause the cat to remain stationary, however, in reality, due to varied nature of gravity and the non-uniform profile of Earth, the cat will simply spin around its center of gravity at ever-increasing speed.
In fact, most civilized species in the universe already use this principle in order to build their UFO's. Thus, the buzzing that you can hear when you see an UFO is actually the purr from the cats.
Physics
The diagram at right shows that FBT is the force exerted by the butter so that it falls down, and FC are the forces the cat's feet exert so that it doesn't break its ass when falling. The following equation:

Such that Θ = π + 3μ√2 gives us that when:

The cat defies gravity.
Propulsion
"Duhn-duh-duh-DUH-DUH! Duhn-duh-duh-DUH-DUH!"
In order for the equilibriated cat to escape its inertia one must attach a propulsion device. The necessary item consists of cellotape (and if possible some object such as a bottle top); when the cellotape is attached to the cat's tail, the cat feels compelled to escape the anomaly caused by the disruption in tail dynamics. Thus the cat engages in accelerated motion in a direction diametric of the cellotape.
Theoretically if one attached, further, a piece of string to the tail disruptor one may have a suitable steering mechanism, however this theory has not been tested --- and some well positioned, suspended, tuna would probably suffice.
It has further been suggested that if one were to wrap the cat with rolls of insulated copper wire and rig the landing site with magnets, the cat and toast could become a rotating generator. Of course, these effects only last as long as the cat lives. Once the cat dies, the toast wins. The life of the cat could theoretically be extended by enclosing the landing site in a box containing a source of radiation, and closing said box once the cat is safely inside — thanks to the law of quantum possibilities, the cat is simultaneously both dead and alive. If the box is never opened, the quantum state of the cat being alive continues to cause the cat and toast to spin, thus generating electricity for all eternity.
And its formula:
Alternative Uses
A well known alternative use for the floating cat-toast combination is as the basis for a high speed hover train.
For the purposes of this explanation, the combination of 1 cat and 1 piece of buttered toast (as shown in the above drawing) will be refered to as a "floater".
While the cat-toast combination is floating in mid-air it can be utilised in the following ways:
A number of 'floater's' can be tied together to form a sort of floating raft. If a carpet (preferably of eastern design) is spread out over them, we have just made a so-called 'magic flying carpet'.
If more 'floater's' are used a larger mass such as a box-car can be placed on top forming one part of a hover train. A number of these can be linked together depending on the size of train required. The train will be able to travel at high speeds and there are no friction forces to overcome.
This property of rotating cats has also been utilised by addicts of kitten huffing to add a second hit to the huffing experience. By strapping buttered toast to the kittens they huff, the huffer begins to hover and rotate, this is known as hover-huffing and is only for the seriously serious huffer as it results in a truly disorienting experience (DO NOT DO THIS WITH THE ORANGE ONES).
Oscar Wilde's Cat-Toast Device
Textbook diagram of antigravitory cat theory
Proposed inverse of device
Some quantum mechanics have suggested that an inverse of the Cat-Toast device would be possible. The inverse would consist of a piece of buttered toast glued butter-side-up to the stomach of a cat. The cat would attempt to land on its legs but the non-buttered side of the toast would prevent it. Likewise, the buttered side of the toast would want to land, but the cat's back would be unable to hit the ground. However, while this would seemingly have the same effect as a regular Cat-Toast device, it would actually have a quite different effect where the cat and toast would be crushed into singularity. This would occur because unlike a traditional Cat-Toast device where the cat and toast repel opposite each other, the inverse Cat-Toast device has the cat and toast repel towards each other. This squeezes the cat and toast into an infinitely small piece of matter, much like a black hole. The cat, however, would soon escape due to its nine lives (which are replenished during such quantum discrepancies) and the toast would get burned anyway from the massive amounts of heat released during the compression process.
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