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The Stick Scenario

  1. Mar 30, 2010 #1
    Basically I thought of this theory and it may exist using different metaphors or what not. But I can't really determine any answer to it, this is pretty much it.

    Let's just say for the purpose of making this scenario easier, we have a time machine that can travel back through time.

    Say there is a person who will accept a stick of a certain length, and you are the one that gives him the stick. Now, let's say you alter the length of the stick and then go back in time and give him the stick, and you keep doing this changing the size of the stick (also, let's say the circumstances in which he receives the stick are the same) until you get to the point where let's say in his mind he accepts 0.5 length, and you give him 0.49999999999999999... length. Would he accept it? As to the human eye it would appear to be the exact same length as the 0.5 he had in mind. Is there a point where you can change the length in very small amounts, unnoticeable to the human eye, in which the receiver of the stick would accept it?

    That's just an idea but what is everyone's thoughts?
     
    Last edited by a moderator: Mar 30, 2010
  2. jcsd
  3. Mar 30, 2010 #2
    the mathematical formulation of quantum mechanics is abstract and its implications are often non-intuitive. the centerpiece of this mathematical system is the wavefunction. The wavefunction is a mathematical function of time and space that can provide information about the position and momentum of a particle, but only as probabilities, as dictated by the constraints imposed by the uncertainty principle.
     
    Last edited by a moderator: Mar 30, 2010
  4. Mar 30, 2010 #3

    BobG

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    The stick is a boring scenario since no one can figure out why the guy wants a stick of a certain length.

    More interesting is to split a sum of money between two people. Person A gets to do the dividing. Person B gets to decide whether the division is acceptable or not. If the division is not acceptable, both people get nothing. There is no second chance for division - it's up to person A to guess at a division to be acceptable to both parties on his first attempt.

    If you analyze it, it's very similar to the stick, since rejecting the stick means no stick. There's either some functional criteria that you haven't given us or we're left to figure out why having no stick would be better than having a 3 foot stick, etc.

    The money scenario provides more information about humans, as well. Logically, person B should accept any non-zero amount since rejecting the proposal would get him less. In practice, a person would rather get nothing than accept an offer they see as grossly unfair.

    For any given person B, you should reach a proposal where there's a 50/50 chance of him accepting it. But this wouldn't be your optimal solution since maximizing the average value person A gets should be the goal of person A. A 50/50 chance means the average value is half of whatever person A proposes. If he could reach a near 100% chance of acceptance for a value that gave him more than half the 50/50 value, the 100% chance offer would be the better offer to give.

    In other words, probability is more interesting if it's optimized to provide the best results.
     
    Last edited: Mar 30, 2010
  5. Mar 30, 2010 #4

    BobG

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    And you're saying the guy couldn't care less about the size of his stick? That the position and momentum of his stick is more important?

    That's a possibility. What's the probability of a male proposing that theory as compared to the probability of a female proposing that theory?
     
    Last edited: Mar 30, 2010
  6. Mar 30, 2010 #5
    position and momentum determine how the person responds to the question thus impacting his answer. the guy cares about the size of the stick, but is unable to make a legitimate decision based on the actual size of the stick at that level.

    i don't see the point of your male/female idea. the probability of that can be quantified, whereas the mans choice cannot.
     
  7. Mar 30, 2010 #6

    Math Is Hard

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    :biggrin: :blushing:

    That theory was not only proposed, but commemorated in song, by Maria Muldaur in 1974.
     
  8. Mar 30, 2010 #7

    BobG

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    She sung it, but it was written by Lois Mann. So chalk one up for the males.
     
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