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Math Help - Experts still argue about this one....

  1. #1
    Member Chokfull's Avatar
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    Arrow Experts still argue about this one....

    An angel comes down to you with two arks, ark A and ark B. You may choose to take either ark A or both arks A and B.

    Ark A has either the Mona Lisa, worth millions of dollars, or a worthless spider, and ark B has a goblet worth 1000.

    The obvious choice would be to take both, right? But here's where it gets difficult:

    40 days ago, the angels made a prediction about what you would choose. If they thought you would take both, the put the spider in ark A. if they thought you would just take ark A they put the Mona Lisa in it. Remember that they are almost certainly right.

    I see two ways to look at this:

    (1) You take both; what they predicted 40 days ago barely makes an impact on your choice now, why waste the $1000 cup?

    (2) Taking both would only get you the Mona Lisa under the assumption that the angels were wrong, so that is obviously the wrong choice; the angles are almost certainly right, in which case taking ark A would get you the Mona Lisa.

    Which would you take?
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by Chokfull View Post
    An angel comes down to you with two arks, ark A and ark B. You may choose to take either ark A or both arks A and B.

    Ark A has either the Mona Lisa, worth millions of dollars, or a worthless spider, and ark B has a goblet worth 1000.

    The obvious choice would be to take both, right? But here's where it gets difficult:

    40 days ago, the angels made a prediction about what you would choose. If they thought you would take both, the put the spider in ark A. if they thought you would just take ark A they put the Mona Lisa in it. Remember that they are almost certainly right.

    I see two ways to look at this:

    (1) You take both; what they predicted 40 days ago barely makes an impact on your choice now, why waste the $1000 cup?

    (2) Taking both would only get you the Mona Lisa under the assumption that the angels were wrong, so that is obviously the wrong choice; the angles are almost certainly right, in which case taking ark A would get you the Mona Lisa.

    Which would you take?
    I assume the argument is over whether angels exist or not. Because there is a well-known solution from Game Theory.
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  3. #3
    Member Chokfull's Avatar
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    What solution is that?
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  4. #4
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Chokfull View Post
    An angel comes down to you with two arks, ark A and ark B. You may choose to take either ark A or both arks A and B.

    Ark A has either the Mona Lisa, worth millions of dollars, or a worthless spider, and ark B has a goblet worth 1000.

    The obvious choice would be to take both, right? But here's where it gets difficult:

    40 days ago, the angels made a prediction about what you would choose. If they thought you would take both, the put the spider in ark A. if they thought you would just take ark A they put the Mona Lisa in it. Remember that they are almost certainly right.

    I see two ways to look at this:

    (1) You take both; what they predicted 40 days ago barely makes an impact on your choice now, why waste the $1000 cup?

    (2) Taking both would only get you the Mona Lisa under the assumption that the angels were wrong, so that is obviously the wrong choice; the angles are almost certainly right, in which case taking ark A would get you the Mona Lisa.

    Which would you take?
    "almost certainly".....what exactly does that mean?

    I think mr fantastic might be referring to the St. Petersburg paradox. If we have a probability that the angels are right (or two probabilities, one for false positive and one for false negative), then we can calculate expected value, but the St. Petersburg paradox highlights why a reasonable person might not decide based just on expected value.
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  5. #5
    Super Member Deadstar's Avatar
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    If anyone knew you had the Mona Lisa you'd be hounded by french secret service. Question is therefore loaded.

    I would choose both, hope for the spider, then auction of the arks since they came from an angel after all.
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  6. #6
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Deadstar View Post
    If anyone knew you had the Mona Lisa you'd be hounded by french secret service. Question is therefore loaded.

    I would choose both, hope for the spider, then auction of the arks since they came from an angel after all.
    Maybe the ark would contain not only the Mona Lisa but a certificate of title as well.
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  7. #7
    MHF Contributor Also sprach Zarathustra's Avatar
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    I love to take risks...

    I go for the ark A!
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by Chokfull View Post
    An angel comes down to you with two arks, ark A and ark B. You may choose to take either ark A or both arks A and B.

    Ark A has either the Mona Lisa, worth millions of dollars, or a worthless spider, and ark B has a goblet worth 1000.

    The obvious choice would be to take both, right? But here's where it gets difficult:

    40 days ago, the angels made a prediction about what you would choose. If they thought you would take both, the put the spider in ark A. if they thought you would just take ark A they put the Mona Lisa in it. Remember that they are almost certainly right.

    I see two ways to look at this:

    (1) You take both; what they predicted 40 days ago barely makes an impact on your choice now, why waste the $1000 cup?

    (2) Taking both would only get you the Mona Lisa under the assumption that the angels were wrong, so that is obviously the wrong choice; the angles are almost certainly right, in which case taking ark A would get you the Mona Lisa.

    Which would you take?
    Since the theology in which this is set presumes that you have free will, the angels cannot make the prediction for that would imply predestination ... nonsense alert Ooopss.. Calvinist alert!


    CB
    Last edited by CaptainBlack; July 11th 2010 at 12:27 AM. Reason: trying and failing to get php strike-through code to work :(
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  9. #9
    Super Member Deadstar's Avatar
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    \rlap{\vrule height3pt depth-2.5pt  width11em}\text{What's going on in here?}
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  10. #10
    Member Chokfull's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    Since the theology in which this is set presumes that you have free will, the angels cannot make the prediction for that would imply predestination ... nonsense alert Ooopss.. Calvinist alert!


    CB
    This does imply free will, sure, but the angels are "almost certainly right", not "certainly right". If it was a case of predestination, they would be "certainly right", in which case the answer would certainly be to pick ark A.

    Also, I got this from a book called "The Math Book" and they didn't give the probability of the angels being right. I just assumed it was somewhere about 95-99%, but "almost certainly" is all the information the angels give you. I don't think the paradox applies to this anyways. For one thing, there is no fee to play. You just have to meet some overly-generous angels.
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  11. #11
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Chokfull View Post
    I just assumed it was somewhere about 95-99%, but "almost certainly" is all the information the angels give you. I don't think the paradox applies to this anyways. For one thing, there is no fee to play. You just have to meet some overly-generous angels.
    You can disagree with me but I think the paradox loosely applies; suppose you're in a lot of financial trouble such that $1000 would save your life; without the $1000 you would die. Suppose you're happy without millions, you just want to live. So even though the expected value of choosing ark A is very high, since the cost of not winning anything is death, you could be inclined to choose both arks.

    Given the looseness of the connection, I suppose the paradox is probably not what mr fantastic was referring to, though.
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  12. #12
    Grand Panjandrum
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    Quote Originally Posted by Chokfull View Post
    This does imply free will, sure, but the angels are "almost certainly right", not "certainly right". If it was a case of predestination, they would be "certainly right", in which case the answer would certainly be to pick ark A.

    Also, I got this from a book called "The Math Book" and they didn't give the probability of the angels being right. I just assumed it was somewhere about 95-99%, but "almost certainly" is all the information the angels give you. I don't think the paradox applies to this anyways. For one thing, there is no fee to play. You just have to meet some overly-generous angels.
    If I know the probability that they are right this is a trivial decision problem (since I know my utility value for the two outcomes), if I have an idea what "almost certainly" means so that I can assign a prior distribution to them being right, it is again a trivial decision problem. If the problem has an undefined term it is a poorly posed problem and not worth our attention (other than to make fun of it)

    (By the way for the purposes of problems like this there is a technical meaning to "almost surely" which I will assume means the same as "almost certainly", which is in effect with probability 1, which for most purposes is indistinguishable for certainty. Though of course the CIA takes "almost certainly" to mean with probability of about 93+/-6%, but this we will ignore as the CIA is not on the side of the angels)

    So if we know what is mean by "almost certainly" there is no paradox just a common decision problem, the confusion here is in treating "almost certain" as the same as certain.

    CB
    Last edited by CaptainBlack; July 12th 2010 at 12:36 PM.
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