Falling Toast: Butter side up or down?

[Gfactor]

Toast dropping science:

http://www.thiel.edu/academics/physics/projects/toast/default.htm

Toast dropping experiment:

http://www.cockeyed.com/science/toast/toast1.html

[Billdo]

For those of you interested in the details of the toast/cat interaction, there was a fun discussion of it in an earlier Comments on Cecil’s Columns thread written in response to Cecil’s 1996 report on cats landing on their feet when falling.

[Kat]

@Chronos

One possibility would be a distortion of the ground so as to envelop the toast-cat assembly as it reaches the surface. Another explanation would be that the cat makes contact with the floor with its paws, and immediately proceeds to roll over onto its back, rubbing the buttered toast against the rug.

Nonsense. What happens is that the strap/string/adhesive/whatever fails, the cat and toast part ways halfway down, and both land separately, cat on feet and toast on butter.

[Pythian_Habenero]

@Chronos

It violates the first premise, since if the cat never lands, it does not land on its feet. And it also violates the second premise, since if the toast never lands, it does not land butter-side down.

Your logic fails right here. If we follow this, then every second in which no toast is in the act of landing butter-side down violates the second rule, and every second in which no cat is landing on its feet violates the first. The assumed part of the sentence is “Whenever toast lands on the ground, it lands butter-side down; whenever a cat lands on the ground, it lands on its feet.” If the cat/toast never lands, it never violates the rule. If your toast happens to blow out the window on its way to the floor and be carried into orbit by successive freak gusts of wind, it is not violating the butter-side-down principle because it is not landing. (Whether or not it’s violating common sense is another question entirely.) If you catch toast or cat on the way to the floor, it never landed, and thus cannot violate the principle. Similarly, therefore, if the cat/toast apparatus remains in the air indefinitely, it does not violate either principle unless and until it lands on the wrong side.

[Mathochist]

Slight side note: Murphy’s Law properly says, “If there are two or more ways to do something, and one of those ways can result in a catastrophe, then someone will do it.” This was the statement by Murphy when an army engineer managed to plug in all 12 plugs on a machine upside-down.[1] This is why all the plugs on the back of your computer can only plug in one way (trapezoid-shaped, “keyed”). The common statement – “Anything that can go wrong, will.” – is properly Finagle’s Law of Dynamic Negatives, or simply Finagle’s Law.[2]

[1] http://catb.org/~esr/jargon/html/M/Murphys-Law.html
[2] http://catb.org/~esr/jargon/html/F/Finagles-Law.html

[octothorpe]

Chronos I think your problem is that you’re looking for rigor when all you need to tackle this problem is a catchy moniker. You just can’t seem to get your head around the ‘cat with a piece of buttered toast strapped to its back’. So, what we need here is a convenient handle. For the sake of argument (which may start another argument) call this cat Feynman’s Cat. Once we have named the beast, the contradiction collapses and causality and Heisenberg’s Uncertainty Principle rule the day. Thus, neither will the cat land on its feet nor the toast land on the buttered-down side until it is observed. Until such time as an observation is made, the cat is in an ever-spinning limbo where the probability of any outcome is even. Of course in a parallel universe a cat spinning with an instantaneous relationship 180° out of phase with your observed cat will be in the same limbo…

Sheesh, i bet you didn’t have this much trouble with Schrödinger’s Cat…

[randshay]

@ignignokt

The Mythbusters team built two machines to drop toast: One dropped the toast from a vertical orientation, the other pushed the toast off the edge of a table.

Pushing the toast off the edge of a table resulted in a statistically-significant portion of the toast landing butter-side down. The Mythbusters team explanation for this: When pushing toast off the edge of the table, the toast does just enough of a flip to land consistently with the buttered side down (as mentioned in Cecil’s reply).

However, the results from dropping the toast from a vertical orientation showed that the toast most often landed butter-side up. The Mythbusters noted that the act of physically buttering the toast causes the toast to “bowl” slightly where the butter knife pressed into one side of the toast. This gives the toast an aerodynamic charactaristic that causes it to most often land with the butter side (the top of the “bowl”) facing up.

At least, that’s how I remember it…

Actually, they did go a bit further with the experiment. Due to the “bowling” effect, they built a machine to butter the toast with pressure equal across the toast surface. The toast still fell butter side up with the greater percentage of induced falls.
Then, to eliminate the table height issue, the machines were taken to the roof of their shop. After several hundred tests, the conclusion was that which side the toast falls on is completely random. In their words, “Myth… Busted”.

[Mathochist]

@Chronos

OK, this one frustrates me no end. It’s patently illogical. We have two premises, here:

1: The cat always lands on its feet.
2: The toast always lands butter-side down.

So how does the cat-toast assembly hovering solve this problem?

Actually, it’s a rehash of the “irresistable force vs. immovable object” poser.

[Chronos]

Your logic fails right here. If we follow this, then every second in which no toast is in the act of landing butter-side down violates the second rule, and every second in which no cat is landing on its feet violates the first. The assumed part of the sentence is “Whenever toast lands on the ground, it lands butter-side down; whenever a cat lands on the ground, it lands on its feet.”

I would disagree. I would argue that the correct formulation is “the toast eventually lands butter-side down”, and “The cat eventually lands on its feet”. There is no violation in the fact that it takes some time for either to reach the ground. There is, however, a violation in the assembly hovering in perpetuity. And if the pair hover not in perpetuity, but merely for some extended but finite time, then all we’ve done is postpone the dilemma, and made its solution no easier in the postponing.

[Chomez]

An example of home testing regarding the subject can be found here at http://www.cockeyed.com/science/toast/toast1.html, if anyone’s interested.

[masheene_comcast.net]

@Chronos

OK, this one frustrates me no end. It’s patently illogical. We have two premises, here:

1: The cat always lands on its feet.
2: The toast always lands butter-side down.

So how does the cat-toast assembly hovering solve this problem? It violates the first premise, since if the cat never lands, it does not land on its feet. And it also violates the second premise, since if the toast never lands, it does not land butter-side down. Not only does this not solve the dilemma, it makes it worse! We need a scenario in which both the cat and the butter do, in fact, reach the ground, and with their appropriate surfaces. One possibility would be a distortion of the ground so as to envelop the toast-cat assembly as it reaches the surface. Another explanation would be that the cat makes contact with the floor with its paws, and immediately proceeds to roll over onto its back, rubbing the buttered toast against the rug.

I think your logic is flawed in the assumption that “a cat always lands on its feet” is the equivalent of “if a cat is airborne, it will land on its feet”. This is not true. Just because the cat or toast has not landed on its feet yet does not prove the first part of the conditional statement false. It would be like saying “if it’s raining outside, then my head will get wet.” You cant say that it’s not raining just because my head is not wet (yet).

[Amok]

@Fear Itself

In this column, When toast falls, what’s more likely: Buttered side up or buttered side down?, both the OP and Cecil refer to the “van is always at the corner” effect. I get the selective memory meaning, but why a van, and why at the corner? Is this a well known or widely reported instance of selective memory?

I don’t know if it is, but the phrase “the van is always at the corner” was used by a respondent to Cecil’s 1994 column on streetlamps going out:

Dear Cecil:

This is an example of what we in our lab call “the van is always at the corner” because one only notices the van when it is indeed parked at the corner, not the times when it is gone. How many lamps does one walk under that don’t go out? You just notice those that do. --Josh Telser, Chicago

That may be where the person who wrote in about buttered toast got it from.

[Pythian_Habenero]

@Chronos

I would disagree. I would argue that the correct formulation is “the toast eventually lands butter-side down”, and “The cat eventually lands on its feet”. There is no violation in the fact that it takes some time for either to reach the ground. There is, however, a violation in the assembly hovering in perpetuity. And if the pair hover not in perpetuity, but merely for some extended but finite time, then all we’ve done is postpone the dilemma, and made its solution no easier in the postponing.

Do you believe that the rule is violated if the toast or cat is caught before hitting the ground?

[JeffB]

I’m disappointed that Cecil didn’t mention that Matthews won an Ig Nobel Prize in Physics in 1996 for his work.

[Muffin]

@octothorpe

Once we have named the beast, the contradiction collapses and causality and Heisenberg’s Uncertainty Principle rule the day. Thus, neither will the cat land on its feet nor the toast land on the buttered-down side until it is observed. Until such time as an observation is made, the cat is in an ever-spinning limbo where the probability of any outcome is even. Of course in a parallel universe a cat spinning with an instantaneous relationship 180° out of phase with your observed cat will be in the same limbo…

When we open the box to look in, I don’t know if we will find a live cat, a dead cat, a cat facing up, or a cat facing down, but regardless of the spin of the spin, I expect we’d find a lot of cat barf.

[tracer]

@Chronos

If one is to find flaw in Matthews’ work, I would put it rather on the claims of universality. It may well be that there are practical limitations on the size of “people”, and therefore of countertops, due to the fundamental constants of nature. But there are no such limitations on the size of toast. A significantly smaller piece of toast (say, a cracker-like thing) would make multiple complete roations before hitting the floor from a standard, cosmically-dictated countertop. The perversity is then our own, in insisting on eating toast of such an awkward size, rather than cracker-sized, or some intermediate size optimized to land butter-up.

There’s another factor: Matthews’ work only applies in Earth gravity.

In lighter gravity (e.g. on Mars), bipeds could afford to be taller without the risk of bashing their brains out when they fall. This would mean greater table heights. But in lower gravity, objects fall more slowly, not more quickly. So, not only would the table top be higher off the ground for a Martian bipedal buttered-toast-eater, his toast would accelerate downward more slowly, both of which factors enable it to complete more revolutions before hitting the ground.

[akinney]

Simple physics would indicate that the if the butter was on one side of the toast then the buttered side of the toast would be minutely heavier than the other side. Thereby causing the toast to fall on the buttered side when it flipped in mid air due to its weight.

[tracer]

@Muffin

When we open the box to look in, I don’t know if we will find a live cat, a dead cat, a cat facing up, or a cat facing down, but regardless of the spin of the spin, I expect we’d find a lot of cat barf.

I say we hook the Spinning Cat-Toast Ensemble to a drive shaft of some sort. Voila! A cat-toast motor. It consumes no fuel beyond 3 square meals of cat food per day, and can generate enough torque to propel anything (because the pair must remain spinning at all times – no measly 18-wheeler’s drive train is going to slow it down).

[DSWojo]

you buttered the WRONG side… LOL… old joke

Doug

[Muffin]

@tracer

I say we hook the Spinning Cat-Toast Ensemble to a drive shaft of some sort. Voila! A cat-toast motor. It consumes no fuel beyond 3 square meals of cat food per day, and can generate enough torque to propel anything (because the pair must remain spinning at all times – no measly 18-wheeler’s drive train is going to slow it down).

I think you might have hit on a solution for the SDMB’s hampster problem.