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  1. #21
    Perry Way's Avatar
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    Quote Originally Posted by nick mulder View Post
    Hang on - 'the first ooops' and what exactly is over ?
    Well not a small oops but a big oops, like turning the lights on after opening all the packages of photographic paper, but now that sounds kind of dumb after all these smart theorists have contributed their pieces.
    I love the wilderness and I love my trail cameras, all Fuji's! :) GA645, GW690 III, and the X100 which I think is the best trail camera ever invented (to date).

  2. #22
    Perry Way's Avatar
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    Quote Originally Posted by Dan Henderson View Post
    Actually, I think you regressed, not digressed.
    You're probably right, but I hope you also knew I was just clowning. Those who know me in real life know that my vocabulary is mighty rich and colorful, I just don't like to wear it as my outer layer of clothing.
    I love the wilderness and I love my trail cameras, all Fuji's! :) GA645, GW690 III, and the X100 which I think is the best trail camera ever invented (to date).

  3. #23
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    I think it is very interesting that Perry first began formulating these thoughts about photography and infinity on May 25, which is universal Towel Day, in honor of Douglas Adams, author of the Hitchhiker's Guide to the Galaxy. Adams's characters traveled around the Universe in the Heart of Gold, a spaceship powered by the infinite improbability drive. Read the Guide, and you'll become a believer in what an infinite number of monkeys can do. Anyway, assuming Perry is not aware of Towel Day, what were the chances that he'd come up with this infinity question on that very day?

  4. #24

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    (on whether pi contains all finite substrings)

    Quote Originally Posted by Q.G. View Post
    Yes, we do.
    It doesn't.
    Cool. Do you know where I can find a sketch of the proof?

    We *do* know that as n increases, the probability of finding a given substring in the first n digits approaches 1, right?---which I think means that the finite substrings of pi are dense in the space of all finite strings of digits.

    -NT
    Nathan Tenny
    San Diego, CA, USA

    The lady of the house has to be a pretty swell sort of person to put up with the annoyance of a photographer.
    -The Little Technical Library, _Developing, Printing, And Enlarging_

  5. #25

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    Quote Originally Posted by ntenny View Post
    (on whether pi contains all finite substrings)



    Cool. Do you know where I can find a sketch of the proof?

    We *do* know that as n increases, the probability of finding a given substring in the first n digits approaches 1, right?---which I think means that the finite substrings of pi are dense in the space of all finite strings of digits.

    -NT
    Have you read Shakespeare?

  6. #26
    Leighgion's Avatar
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    The Infinite Monkey should be a superhero.

  7. #27

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    Quote Originally Posted by Q.G. View Post
    Have you read Shakespeare?
    Wasn't that Shakespeare's theorem that ntenny was quoting?

  8. #28

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    Quote Originally Posted by Q.G. View Post
    Have you read Shakespeare?
    I'm not sure what you're saying here. Is your point just that _Hamlet_ isn't written in digits, and therefore the decimal expansion of pi doesn't "contain" it in a literal sense?

    (Which of course is true, but there are plenty of ways to represent text numerically, and I think most of us are talking through that relationship transparently.)

    -NT
    Nathan Tenny
    San Diego, CA, USA

    The lady of the house has to be a pretty swell sort of person to put up with the annoyance of a photographer.
    -The Little Technical Library, _Developing, Printing, And Enlarging_

  9. #29

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    Quote Originally Posted by ntenny View Post
    I'm not sure what you're saying here. Is your point just that _Hamlet_ isn't written in digits, and therefore the decimal expansion of pi doesn't "contain" it in a literal sense?

    (Which of course is true, but there are plenty of ways to represent text numerically, and I think most of us are talking through that relationship transparently.)

    -NT
    If so, the opening words of Hamlet are right there, right after the decimal point. And next to that. And in the first place it is combined with the second place, all in one. And ...

    And not just in Pi.
    Also in you social security number. The zip code of your local library. The ... [etc. The possibilities are infinite].

    So given an infinity, is it there?
    Of course not. Infinity does not exist.

  10. #30
    Perry Way's Avatar
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    Quote Originally Posted by Q.G. View Post
    So given an infinity, is it there? Of course not. Infinity does not exist.
    BINGO! That's the answer I was waiting for!
    I love the wilderness and I love my trail cameras, all Fuji's! :) GA645, GW690 III, and the X100 which I think is the best trail camera ever invented (to date).

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