Zeno's paradox in cake (dichotomy and taking the last bit)

[Fat Guy]

I was at some friends' house over the weekend and they served a cake for dessert. About 7/8 of the cake was served and eaten immediately by the assembled guests. The remaining 1/8 sat there of a bit until somebody took 1/2 of it, leaving 1/16 of the cake. Another person took half of that, leaving 1/32 of the cake. Then someone took half of that, leaving 1/64.

I realized that what I was seeing in action was one of Zeno's paradoxes, specifically the dichotomy paradox. If people keep taking half of what's left, finishing the cake will require an infinite number of steps and is therefore impossible.

This seems to happen a lot. Refrigerators around the world are filled with milk cartons with one sip left. Platters with one slice of meat remaining. People don't want to take the last bit, so they take half of it.

Is this some sort of act of perceived politeness, this never willing to finish anything? Me, I'd rather someone take the last piece so I don't have to throw it out and can put the serving vessel in the dishwasher.

By the way I ate the remaining 1/64 of the cake, demonstrating once again that Zeno is wrong. But if my friends ran the world, he'd be right.

[Tri2Cook]

Is this some sort of act of perceived politeness, this never willing to finish anything?

I think that's exactly what it's supposed to be. Nobody wants to be the person sitting there eating the last bit while everybody else watches, wishing they had taken it. The comedian Jerry Clower told a story of how they were taught as children that it was never, ever ok to take the last piece of chicken or biscuit from the plate. One night he was at his uncle's house for dinner and everybody was sitting around the table looking longingly at the last piece of chicken when a gust of wind blew out the lamp. His uncle screamed in pain and when his aunt got the lamp lit there were 5 forks sticking in the back of his uncle's hand. I've always thought that pretty much sums up the situation. Everybody wants to take it but doesn't want the spotlight on them when they do. Personally, I'm with you. If you want it, take it. If someone else wanted it... you snooze, you lose.

Edited September 28, 2009 by Tri2Cook (log)

[JAZ]

There's a way to maintain some politeness and still get rid of the last piece of whatever it is, but it requires a partner, or at least someone whose behavior you can count on. When there's a small piece of cake or the last cookie left and the host asks if anyone wants it, you say, "I'll split it with someone." Then the piece can be eaten, but no one has to eat the last piece alone.

[Anna N]

There's a way to maintain some politeness and still get rid of the last piece of whatever it is, but it requires a partner, or at least someone whose behavior you can count on. When there's a small piece of cake or the last cookie left and the host asks if anyone wants it, you say, "I'll split it with someone." Then the piece can be eaten, but no one has to eat the last piece alone.

Yep. That's the way we handle it with family and friends.

[Simon_S]

I dunno, I quite enjoy this game. Even when dining alone, my wife and I regularly play it, occasionally getting down to a mere crumb before one or other of us has to take the last "piece" and thereby run a gauntlet of scorn, derision and taunts of selfishness. We wouldn't have it any other way!

[Aloha Steve]

Do any of you folks live with a Teenager?

The current drink of choice in our home is Crystal Light Fruit Punch. By default I am tasked with keeping the watch so we never, ever run out. When I go to fill my glass, if there is a 1/2 inch left in the pitcher, I KNOW it was the Hormone Kid. Even though the rule is, if you take the last of it, you must make a new pitcher. He NEVER takes the last therefore never has to spend the 2 minutes opening the little tubs, pouring them in the pitcher, adding water and stir.

Is it being polite ? HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA

Its called The Teenage Creed, "I have therefore everyone else can $%@%% off."

Edited September 28, 2009 by Aloha Steve (log)

[haresfur]

I was at some friends' house over the weekend and they served a cake for dessert. About 7/8 of the cake was served and eaten immediately by the assembled guests. The remaining 1/8 sat there of a bit until somebody took 1/2 of it, leaving 1/16 of the cake. Another person took half of that, leaving 1/32 of the cake. Then someone took half of that, leaving 1/64.

With 3 children, my father developed a superb eye for dividing a pie in fifths. Your friend needs to work on sevenths.

[heidih]

This extends to empty containers themselves being left in place. We had an extra freezer in the laundry room that was filled with stock, bones, and kid snacks. I can not tell you how many times I reached in to get something and thought a box I moved seemed unusually light. Yup- empty boxes. Even though they had free rein of the freezer they were embarassed to be the one throwing the box out? In the pantry it was the same deal. Out of a big bag of mixed chips, one lone bag would sit for weeks. A bag of jerky would be in there with literally a scrap so small the dog would have laughed at it.

[Chris Amirault]

With 3 children, my father developed a superb eye for dividing a pie in fifths. Your friend needs to work on sevenths.

I read this and thought: does Zeno's paradox apply to pie? I don't think so. There's something about the slab turning into a slice turning into a piece turning into a crumb that doesn't happen with the more deliberately cut and structured pie, I think.

[haresfur]

With 3 children, my father developed a superb eye for dividing a pie in fifths. Your friend needs to work on sevenths.

I read this and thought: does Zeno's paradox apply to pie? I don't think so. There's something about the slab turning into a slice turning into a piece turning into a crumb that doesn't happen with the more deliberately cut and structured pie, I think.

True, pie is more, "Excuse me, I'll just clean this up for you." But the prevention is the same. Except for the selfish people who throw off the slice count because they are on a diet, too full, or whatever.

[Landru]

This definitely happens in office cultures. A box of donuts or bagels appear in the breakroom or kitchen. Soon thereafter there is a box of cut in half bagels and donuts. Then those bagels/donuts get cut into quarters (by the same people who did the original halving) and so on.

Not being one of those halvers, I don't know the philosophy of it, but my suspicion is that it would be *too much* to take a whole one, therefore "I'll leave half". Of course, subsequent people don't want somebody's half donut, so they cut a new one...and so on. Of course, I also suspect that the halvers end up eating the whole donut/bagel over time.

Me-I just brazenly take a whole one and don't shilly-shally about it.

[JAZ]

That's why when I buy pastries donuts or bagels for a crowd, I always buy the "miniature" ones -- not so small, actually, but small enough that people don't seem reluctant to take a whole one.

[BeeZee]

I attended a "christening" for a new office this week, a new venture my husband is part of.

I had to smile a little, remembering this post, when the question was posed if anyone wanted the last of the champagne...

And then the partner's wife asked me if I'd split it with her, and we did.