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Xeno's paradox suggests that there are an infinite number of half distances between two points of measure on a whole. So, if a person devised a plan to walk a mile by only travelling in half distances, that person would never complete the mile. For, he would travel a half mile then rest. Then he would
travel a quarter of a mile, then rest. Then an eighth, then a sixteenth, and so on, ad infinitum.
This is an idea for a candy, similar to the "Everlasting Gobstopper" of Charlie and the Chocolate Factory fame. The candy is simply sugar infused into an absorbant medium, such as a hard piece of delicious sponge so that the candy never looses size.
The only instruction that comes with the candy is that it can only be sucked on in intervals of it loosing half of its sweetness. If it is sucked on in this manner, it will be perpetually sweet.
Inspiration
Elephants-on-a-rope
Neelanden deserves the credit for stumbling on the paradox, but not identifying it. [cuckoointherye, Jan 26 2005]
Xeno's Paradox
http://www.jimloy.com/physics/zeno.htm
And why it isn't really a paradox [Worldgineer, Jan 26 2005]
[link]
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Is that a paradox? Sounds more like an asymptote. |
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Nothing like a sponge soaked in sugar and saliva to illustrate another interesting exponential function: bacteria growth. |
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Mathematically it is an asymptote, philosphically it is a paradox. And I only suggest a sponge in order to maintain a reasonable size. |
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//Mathematically it is an asymptote, philosophically it is a paradox.// Which shows how superior math is to philosophy. (divides himself by infinity and disappears in a philosophical cloud) |
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The paradox is a only paradox philosophically, not practically. The stated "paradox" ignores the presence of physical limitations on the granularity of the movements made by a human being. It would be quite impossible to move reliably only one nanometer in a given direction. |
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Sure, in theory, the sugar would never be gone, provided there was a way to ensure that the sucker knew exactly when half the sweetness had gone. But, even if that could be accomplished through some Wonka magic, the sugar content would at some point fall below the threshold of detectable sweetness or the prescribed sucking time would fall below the threshold of the sucker's time measuring abilities. |
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How'd I do? Am I still on track for taking these things too seriously? |
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Good start, [half]. But you forgot to mention that "travelling", "absorbant", and "looses" are spelled wrong. |
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Yeah you took far more than half the fun out of this idea. I'd say you took just about all of it. The spelling errors can be attributed to my inability to recognize them, and your inability not to do so. So are the errors mine or yours? Mathematically, of course. |
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Yours. Throwing a two negatives on a positive still leaves me with a positive. |
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Yeah, [World], I was going along with the paradox thing for the sake of discussion. I did, however, indicate that it is impossible for it to be a paradox under the conditions in which it was being shown to be a paradox. |
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Eww, now I'm feeling ill. Not sure if it's the calculus flashbacks, the philosophical discussion or a cake overdose that's causing it. |
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In both cases there are two negatives. an inability to recognize has a negative connotation and the negative ability. An inability not to recognize has two nagatives as well. |
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Heh, "nagative". That must be in the pseudodictionary. |
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//inability to recognize// Only one negative there. You're just counting it twice. |
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Inability to recognize : non(ability + recognize) = A negative ability to recognize. Ill do the brackets later. DAMN ORDER OF OPERATIONS!! |
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<throws sand in Wordgineers face and "disappears" in a philosophical cloud> "You haven't seen the last of me, Worldgineer!!!!"</tsiwfadiapc> |
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Hmm... non(ability)(recognize) Damn! |
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(wipes off sand and goes searching for cake) Who's birthday, [half]? |
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Actually, the cake is from yesterday. Some geezer in my office turned 40. |
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You know, it's weird. For some reason, the cake seems to be only half as sweet as it was yesterday. |
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Eeew, you tried eating it again? Oh, that was the other idea. Never mind. |
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I had to drive myself to the nearest insane asylum after reading all the math in the annos. They gave me a nice room with thickly padded white cashmere walls. I'll send you guys the bill later. |
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[cuckoo], + for mentioning Everlasting Gobstoppers and Charlie and the Chocolate Factory. |
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This paradox gets sorted out by quantum theory. To move forward requires an amount of energy. To move forward half as far requires half the energy. At some point of infinitessimally small movement, you need only one quanta of energy to move the distance. Less than that you cannot move. Of course with the candy you will get to the point of having only one molecule of sugar left, which is on a scale way above when we need to invoke quantum theory. Good try [cuckoo]. |
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You don't really need quantum theory to break down this paradox. It's just a trick of perception. I linked to someone else's explanation of this to save myself the effort. |
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