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For some reason, I like thinking about paradoxes...

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  • For some reason, I like thinking about paradoxes...

    They're interesting exercises. Like this one:

    https://en.wikipedia.org/wiki/Sorites_paradox

    And an entire list:

    https://en.wikipedia.org/wiki/List_of_paradoxes

    I also like considering things such as Hailstone Numbers and the Collatz Conjecture...

    https://en.wikipedia.org/wiki/Collatz_conjecture

    And other interesting mathematical phenomena. I just wish I were interested in this stuff much earlier in life, rather than when I'm almost 40.

    Yes, I'm weird.
    Skilled programmers aren't cheap. Cheap programmers aren't skilled.

  • #2
    I'm of the opinion that a lot of "paradoxes" simply indicate limits in our way of thinking.

    I actually did some (non-professional) work on the Collatz conjecture some time back. I eventually had to stop; I ran out of interest without coming up with anything new.

    Rosetta Code has a page on the Collatz conjecture (called "Hailstone sequence" there).

    Also:
    Fool me once, shame on you. Fool me twice, you speak with the Fraud department. -- CrazedClerkthe2nd
    OW! Rolled my eyes too hard, saw my brain. -- Seanette
    she seems to top me in crazy, and I'm enough crazy for my family. -- Cooper
    Yes, I am evil. What's your point? -- Jester

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    • #3
      "Which came first, the chicken or the egg?"

      Well obviously, other birds and even dinosaurs and lizards were laying eggs long before there were chickens. So let's re-word this so it's more specific:

      "Which came first, the chicken or the chicken egg?"

      This now hinges on how you define "chicken egg". Is this an egg laid by a chicken, or an egg containing a chicken? If the former, obviously the chicken has to exist first. If the latter, the chicken hatched from an egg laid by a chicken relative that was sufficiently non-chicken to not be considered a chicken. Either way, you have the answer.
      Last edited by TheSHAD0W; 07-23-2016, 10:42 PM.

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      • #4
        One of my favorite game series discusses a few of the paradoxes. The third and final game came out last month and discussed the lottery paradox as such:

        Imagine you're in a rock paper scissors tournament made up of 2^4 players or 16 players. The winner advances onto the next round. What are the odds of winning? 1/16 of course. Now imagine a tournament of 2^100 players. The winner would have to win 100 rounds in a row. The probability of that happening is astronomically low at 1/(2^100). And yet this tournament will have a winner.

        The series has discussed other philosophical ideas such as Ship of Theseus, Prisoner's Dilemma, Schrodinger's Cat, Monty Hall Problem, and probably a few others.
        To right the countless wrongs of our days... We shine this light of true redemption, that this place may become as paradise...Oh, what a wonderful world such would be...

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        • #5
          Quoth Deserted View Post
          I'm of the opinion that a lot of "paradoxes" simply indicate limits in our way of thinking.
          Exactly. For example, the Sorites Paradox is answered by determining what exactly the definition of a "heap" is. Since it's a relative term, it can't really be answered. However, if we go with the famous "unstoppable force + immovable object" paradox, the answer's simple. They'd just pass through each other. Most people don't think about that though because it bends, if not breaks the laws of physics (I suck at science so don't hold me to that). However, both the unstoppable force and immovable object are impossible as well so it's a pointless argument anyway.

          So yeah, most paradoxes are either limits to our thinking, relative, or worded so poorly they don't really have answers (like the chicken and egg one mentioned above).

          Personally, my favorite paradox is the one where if Beethoven goes back in time and gives himself the sheet music to one of his symphonies (that he wouldn't have created on his own otherwise), then that instance of Beethoven goes back in time and does the same, and on and on infinitely, who created the symphony to begin with?
          The fact that jellyfish have survived for 650 million years despite not having brains gives hope to many people.

          You would have to be incredibly dense for the world to revolve around you.

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          • #6
            Quoth Aragarthiel View Post
            Personally, my favorite paradox is the one where if Beethoven goes back in time and gives himself the sheet music to one of his symphonies (that he wouldn't have created on his own otherwise), then that instance of Beethoven goes back in time and does the same, and on and on infinitely, who created the symphony to begin with?
            That's a fun paradox found in many works about time travel. Where did the Terminator''s robotic arm come from? Who taught Link the Song of Storms in Ocarina of Time?
            To right the countless wrongs of our days... We shine this light of true redemption, that this place may become as paradise...Oh, what a wonderful world such would be...

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            • #7
              Now imagine a tournament of 2^100 players. The winner would have to win 100 rounds in a row. The probability of that happening is astronomically low at 1/(2^100). And yet this tournament will have a winner.
              Really, this illustrates the difference between independent and dependent probabilities.

              A lottery is a good example of independent probabilities; there is a uniform chance that any particular set of numbers will be drawn, and no guarantee that any particular drawing will produce a winner (or, indeed, *only one* winner). The numbers are placed into the bowl independently of the entrants' choice of numbers.

              A raffle is a good example of dependent probabilities; when a raffle ticket is sold, the entrant receives half the ticket, and the other half goes into the bowl. This guarantees that for every drawing, there will be exactly one winner - useful if there is a fixed number of discrete prizes, rather than a jackpot which can be divided.

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              • #8
                Quoth TheSHAD0W View Post
                "Which came first, the chicken or the egg?"
                At some point, the Rooster did.
                Skilled programmers aren't cheap. Cheap programmers aren't skilled.

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                • #9
                  Quoth mjr View Post
                  At some point, the Rooster did.
                  Except that a chicken can lay an egg without a rooster's, erm, input.

                  (Sorry - here I go ruining jokes again.)
                  "I look at the stars. It's a clear night and the Milky Way seems so near. That's where I'll be going soon. "We are all star stuff." I suddenly remember Delenn's line from Joe's script. Not a bad prospect. I am not afraid. In the meantime, let me close my eyes and sense the beauty around me. And take that breath under the dark sky full of stars. Breathe in. Breathe out. That's all."
                  -Mira Furlan

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                  • #10
                    Ya'll need to be paradoctored.
                    I am not an a**hole. I am a hemorrhoid. I irritate a**holes!
                    Procrastination: Forward planning to insure there is something to do tomorrow.
                    Derails threads faster than a pocket nuke.

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                    • #11
                      Quoth Ghel View Post
                      Except that a chicken can lay an egg without a rooster's, erm, input.
                      Does that mean eggs are like lesbians - they can get laid with no cock involved?
                      Any fool can piss on the floor. It takes a talented SC to shit on the ceiling.

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