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Question on The Dichotomy Paradox

  1. Oct 24, 2011 #1
    Okay, I didn't really know where to post this, but whenever I hear about this paradox it is in a conversation relating to physics. Anyway, for those that don't know the paradox, it states that to get to point 'B', one must get halfway there before they can be all the way there. And to get halfway there, they must get halfway to halfway there (1/4) and so on. In saying this, it is rendered impossible to get to your destination. I am asking why. The distance you are at acts much like an asymptote, getting closer and closer to 0, while never reaching it. If it never reaches 0, then shouldn't there always be a distance to travel, no matter how far you break down 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128 and so on? If there is always a distance to move, than it is possible to begin moving, correct? The paradox assumes that movement is impossible because the pattern continues infinitely, meaning there is no beginning distance for the smallest halfway point to begin, which is true, but the smallest is not needed because an object can simply begin moving, speedily making it's way to 1/4 the distance, and then to 1/2, and finally to point B from point A. Just a thought I had, and wanted to share it with others to see if I was right or wrong.
  2. jcsd
  3. Oct 24, 2011 #2
  4. Oct 25, 2011 #3
    I know. I meant how is it true?
  5. Oct 25, 2011 #4


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    Staff: Mentor

    It isn't true. (assuming you mean how is it a real paradox) It's basically just a product of an underdeveloped understanding of math (at best!).
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