The Disappearing Toast Paradox

Eating dinner this evening with M, who is fighting off something. We had two kinds of soup mixed together (living dangerously, mixing two different brands of organic mushroom/vegetable barley) and toast.

He's done, but my toast is still sitting there. I take a bite and go back to my soup. He picks up my toast and takes a bite. Ordinarily I'd scream about this and he'd grin, but we nonchalantly continue trading bites until the toast is progressively shrinking. I take a bite of half of the remaining toast, put it down and wait. Will he get it? He takes a bite of half of the remainder. hehe He gets it. And still we are taking bites, half the piece disappearing with each bite. The remaining toast is ridiculously small, down to scant millimeters, but we are smiling at each other. When it's down to barely a fluff of wheat and a poppy seed, I attempt to bite half of that, and he bursts out laughing. Why? Conceptual joke! *see Zeno's.

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*Zeno's Paradox. Story as told by M and transcribed as fast as I can keep up.

As the story goes, he (Zeno) was eating a piece of bread at the beach one day, and noticed that he was able to take large bites, and he was able to eat half the loaf in a single bite. And then after he was done chewing that, he pondered for a while-- you could say that he chewed the dilemma over in his mind a little bit-- and he said in order to complete the second half of the loaf, I would have to eat half of it. So he took a bite and ate half of the remainder. And then after he finished pondering and chewing that, he said, huh, in order to finish this loaf, I would have to eat half of the remainder. ...okay?

Okay, then he did that and started to to realize he could never completely finish the loaf because he would always have to eat half of the remainder and have half left, and so he'd have to take an infinite number of bites to finish the loaf.

Now, in reality, Zeno didn't know the concept of infinity, so it was really about Achilles and the tortoise, rather than a loaf of bread, but you get the picture. And that's all I'm going to say about that.

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Which leads us to the corollary:
The Disappearing Toast Paradox. If each person bites off half the piece of toast, an infinite number of bites can be taken before one person admits it's just a crumb...

I love it when we get each other's jokes.

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