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Zeno's Paradoxical Chocolate Bar

the breaking and sharing of chocolate according to the rules of Zeno
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Zeno's Paradox (see link) is concerned with the business of an arrow that never reaches its target. (even though it does)

Zeno's Paradoxical Chocolate Bar brings joy to all of those who sit together in discussion of the famous conundrum. It's a simple bar of chocolate that resembles a long arrow once it has been released from its cardboard carton and foil wrapper.

On closer examination, the arrow can be seen to have a set of parallel lines running down the entire length of its shaft. The first one of these is half-way along the arrow. Participants begin the process of eating the arrow by breaking it here. The half with no lines on it is now divided evenly between all of the guests. The remaining half is then broken into two pieces at the next line and again divided evenly.

This process is repeated until the lines are so small that a magnifying glass and a razor blade are required to separate the pieces, and still it continues, because as long as there is half of something, then mathematics tells us that there is another half remaining to be divided again.

Eventually the participants resolve the paradox, the proof of this being that no chocolate remains. All are sworn to secrecy as to the outcome of the puzzle being one of the conditions of purchase required by the makers of the notorious Zeno's Paradoxical Chocolate Bar.

xenzag, Apr 02 2014

Zeno's paradox http://en.wikipedia.../Zeno%27s_paradoxes
see Dichotomy paradox, and Arrow sections [xenzag, Apr 02 2014]

[link]






       Instead of trying to remember how the amount of chocolate approaches a limiting value, and how Zeno's Chocolate Paradox was all about a Greek dislike for infinite processes, I'll just stick to being prosaic, and remark that chocolate is discrete, not continuous. (It's made of discrete, individual not all _that_ divisible atoms, as opposed to some infinitely divisible ... "chocolate ether" -- ??)   

       They'd argue about the quarks or the electron cloud, wouldn't they? Sorry for being wrong like this. Must go. Gotta rush.
skoomphemph, Apr 02 2014
  

       For marketing purposes, be sure that the label promises:   

       "Contains infinite pieces of chocolate!"   

       But, not limitless.
sophocles, Apr 03 2014
  

       Trouble is, you have to eat faster and faster!
pocmloc, Apr 03 2014
  

       //"Contains infinite pieces of chocolate!"//

But that would be a false claim - it would be relatively easy to put an upper limit on the number of molecules of chocolate a given bar contains. Planck's constant can even be used to put an upper limit on the number of any kind of particle in the chocolate bar.
hippo, Apr 03 2014
  

       So Brilliant! Just imagine eating chocolate with a razor blade and discussing Zeno's paradox, really interesting - and making the connection between that oh-so mysterious arrow, and something mundane like a bar of chocolate, what a genius!   

       Hey, I've got a bag of crisps here, imagine if it were Zeno's Bag of crisps? It's a bag of crisps and half of the crisps are whole, and the next quarter are broken in half, and the next 8th of the bag of crisps is broken into quarters, and the next 16th of the bag of crisps is broken into 8ths and it all goes down to tiny tiny crumbs that you have to eat individually and it TAKES AGES! Brilliant.
Zeuxis, Apr 03 2014
  

       [Zeuxis] No, that's Zeno's Diet - the latest miracle fad celebrity-endorsed diet. By eating things in fractions of 1/2, 1/4, 1/8, 1/16, 1/32, etc., you will slow down your consumption, eat less, and lose weight.
hippo, Apr 03 2014
  

       Chocolate bun for [xen] and a 1/2 bun for [hippo]!!
xandram, Apr 03 2014
  

       [hippo] Here, "infinite pieces" is about the least false claim you'll see in marketing lately.   

       And, anyone who'd sue you for false advertising would need to produce tunneling electron microscope pictures to prove you wrong.
sophocles, Apr 03 2014
  

       [hippo], as I intimated earlier, you would speed up your consumption.
pocmloc, Apr 03 2014
  

       I'll just have the chocolat tortoise thank you very much.
zeno, Apr 10 2014
  

       So, it's like taking a bite, then half a bite, then half of half a bite, then etc.   

       So the question is: how do you half-bite something?
Ling, Apr 10 2014
  

       Mightn't it be better to provide a Banach-Tarski Paradox chocolate bar with similar pre-scored infinite divisions? It would certainly be more popular at parties. I suppose the expense of including a Cantor-dust chocolate shaver and an Axiom of Choice in the packaging could prove troublesome.
Hive_Mind, Apr 11 2014
  
      
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