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Rick Re: [GTh] Re: The Scientific method

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  • kurt31416
    Hi Bob, By random, I mean how close to algorithmically random the statistical sample is. Algortihmically random being random with the lucky rolls removed, what
    Message 1 of 20 , May 2, 2010
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      Hi Bob,

      By random, I mean how close to algorithmically random the statistical sample is. Algortihmically random being random with the lucky rolls removed, what you approach if you roll the dice a lot.

      In this case, we could use sophisticated techniques like fuzzy k clustering or whatever to test the randomness of Thomas, but I'm not so sure the results would be as strong. Lots of arbitrary choices, and far from intuitively clear you've accomplished anything.

      But, given the number of possibilities, (number of sayings or partial sayings in Thomas), and number of instances, (number of Mark sayings or partial sayings), you can calculate the probability the largest gap (those 32 between 66 and 69) would happen if you rolled dice.

      In other words, what is the probability that 32 saying gap would happen by random chance, and it's less than 1 in 100.

      -------

      As for it being Poppycock, I'll turn the other cheek, even though I don't think Jesus ever said it, and it comes to us from Paul, through the Didache.

      I looked pretty hard, because I had a hard time getting a handle on it, and it sure seemed to be something someone would have done before. I did find a site with a "Mister Statistics" where people would ask obscure statistics questions and he would answer them. He came up with a solution, but it was wrong, which one of the posters pointed out, to his embarrassment, so he said he'd get back with the answer, but never did. So, it's relatively obscure, at least.

      But it's there, and it's hard pure math, and anyone comfortable with math can point out any error, certainly after my clarifying it, and determine if it's poppycock. Who knows, perhaps their literature search and/or knowledge of statistics will find a case of someone else doing it before. Hard for me to say about that, but I'm pretty certain the math is correct. For what it's worth, it wouldn't be the first time I solved a logic puzzle others seemed to find difficult.

      -

      Flipping a coin doesn't work logically, Bob, because the probability of a saying being a Mark saying in Thomas isn't 50/50. And, as Mark sayings are used up in your dice rolling, the odds change, depending on the luck of the dice in the first part. It's a more difficult puzzle than it first appears.

      The bottom line, Bob, is that less than 1 out of 100 cases, with that many Mark sayings out of 114, if random, will have a gap of 32 or more. Mathematical fact. Easy money at Las Vegas if they will bet against it.

      And no, from what I've seen, Biblical scholarship is rather weak on the math. Still waiting for one person to even be able to follow the relatively simple math/logic I presented. Granted I probably did a poor job of explaining it, but I'm here to answer questions. It's a universal system for testing randomness, not just Mark in Thomas.

      I hope that addressed all your points, if I missed one, let me know.

      Rick Van Vliet
    • Bob Schacht
      ... This is not a dice roll problem. By your framing, this would be a die with only two faces, and that makes it a coin toss. [snip] ... Most statistics can
      Message 2 of 20 , May 3, 2010
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        At 04:33 PM 5/2/2010, kurt31416 wrote:
         

        Hi Bob,

        By random, I mean how close to algorithmically random the statistical sample is. Algortihmically random being random with the lucky rolls removed, what you approach if you roll the dice a lot.

        This is not a dice roll problem. By your framing, this would be a die with only two faces, and that makes it a coin toss.

        [snip]

        ...Flipping a coin doesn't work logically, Bob, because the probability of a saying being a Mark saying in Thomas isn't 50/50.

        Most statistics can handle this, using appropriate probabilities for each category (parallel/not parallel)

        And, as Mark sayings are used up in your dice rolling, the odds change, depending on the luck of the dice in the first part. It's a more difficult puzzle than it first appears.

        Here you make a good point, but wind up hoist on your own petard. This is the reason your dice analogy won't work, but it is a good point against my coin toss analogy. At the risk of provoking our list moderator's complaint against technicalities, this is covered in statistics by "sampling without replacement." But I shall eschew further discussion of the statistical details.

        I hope that addressed all your points, if I missed one, let me know.

        Richard Hubbard raised a series of excellent questions for you to ponder, regarding definition of terms.

        Bob Schacht
      • kurt31416
        Hi Bob, Well, if the equation says 99% of the time, if random, there wouldn t be a sequence that long, I ll bet on it. Sayings, sub sayings, sentences, words,
        Message 3 of 20 , May 3, 2010
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          Hi Bob,

          Well, if the equation says 99% of the time, if random, there wouldn't be a sequence that long, I'll bet on it.

          Sayings, sub sayings, sentences, words, or individual characters.

          And since the probability of a Mark (or anything in general) isn't 50/50, I just don't see your point about preferring a coin toss vs. dice. A fair dice/coin produces statistically random numbers, and if you roll/flip them a lot, it approaches maximum algorithmic randomness/maximum entropy/maximum complexity/largest compressed file size.

          Richard Van Vliet
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