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Math Help - A possible new paradox puzzle?

  1. #16
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    Quote Originally Posted by wonderboy1953 View Post
    How can Wilmer claim there's no line in this universe? Wouldn't he first have to know what a line is in the first place to deny it? (btw the concept of a line is taught in schools, straight or otherwise. I can picture Wilmer struggling in class while the teacher is going over lines in geometry).

    In regards to me, no double standard as I'm going by this universe which still leads to a paradox. In regards to what undefined is proposing, it'll work in another universe and here I stand.
    There is nothing to suggest that Wilmer would struggle to understand the concept of a line. It's a matter of there not being any way to prove a line exists in this universe or perceive it with our senses. The same goes for point and plane.

    Going back to your original question, maybe you'll like this response better. Suppose we have a line segment we want to measure. So obviously then, this line segment is observable in some sense, even though it's "one dimensional". So we can have a see-through ruler that looks like the line segment but is longer (and is also "one dimensional"). It's for example a very thin glass rod with regular markings (the color of the markings differs from the color of the segment). We place the ruler on top of the line segment and look through it to see how long the line segment is. We never have to use more than one dimension.
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  2. #17
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    Quote Originally Posted by undefined View Post
    There is nothing to suggest that Wilmer would struggle to understand the concept of a line. It's a matter of there not being any way to prove a line exists in this universe or perceive it with our senses. The same goes for point and plane.

    Going back to your original question, maybe you'll like this response better. Suppose we have a line segment we want to measure. So obviously then, this line segment is observable in some sense, even though it's "one dimensional". So we can have a see-through ruler that looks like the line segment but is longer (and is also "one dimensional"). It's for example a very thin glass rod with regular markings (the color of the markings differs from the color of the segment). We place the ruler on top of the line segment and look through it to see how long the line segment is. We never have to use more than one dimension.
    "There is nothing to suggest that Wilmer would struggle to understand the concept of a line." Once he brings up a line, then he must implicitly understand it, otherwise he doesn't know what he's talking about.

    "So we can have a see-through ruler that looks like the line segment but is longer (and is also "one dimensional"). It's for example a very thin glass rod with regular markings (the color of the markings differs from the color of the segment). We place the ruler on top of the line segment and look through it to see how long the line segment is. We never have to use more than one dimension." How would this "see-through ruler" have been made in the first place? (I do think of everything).
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  3. #18
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    Quote Originally Posted by wonderboy1953 View Post
    Once he brings up a line, then he must implicitly understand it, otherwise he doesn't know what he's talking about.
    There is a difference between understanding something and claiming it does not exist *in this universe*. For example I think it's easy enough to understand what a centaur is, but not many people would claim they exist in the universe.

    Quote Originally Posted by wonderboy1953 View Post
    How would this "see-through ruler" have been made in the first place? (I do think of everything).
    How do we make the line segment in the first place???????
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  4. #19
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    "How do we make the line segment in the first place???????" Exactly my point (with the see-through ruler).

    As far as lines go, why is that concept taught in school (which doesn't seem to affect many people?)

    To add, Wilmer sounds like a Kronecker (except that, at least, Kronecker was willing to accept the concept of a number).
    Last edited by wonderboy1953; September 10th 2010 at 10:10 AM. Reason: addition
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  5. #20
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    Quote Originally Posted by wonderboy1953 View Post
    "How do we make the line segment in the first place???????" Exactly my point (with the see-through ruler).
    My point is, we make the ruler in the same way we make the line segment. If we can't make the line segment, then what is it exactly you're trying to measure?

    Quote Originally Posted by wonderboy1953 View Post
    As far as lines go, why is that concept taught in school (which doesn't seem to affect many people?)
    It's taught because as you say it's a useful and powerful concept. Doesn't mean it exists physically. Is there a point to your question?

    Quote Originally Posted by wonderboy1953 View Post
    To add, Wilmer sounds like a Kronecker (except that, at least, Kronecker was willing to accept the concept of a number).
    My understanding is that there's a general consensus among mathematicians and scientists and also non-science/math people that lines are an abstraction (also, an idealization) and do not physically exist.

    For the physical universe we need to think about things like Planck's constant.
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  6. #21
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    "My point is, we make the ruler in the same way we make the line segment. If we can't make the line segment, then what is it exactly you're trying to measure?" The straight line (do you understand it? would you like a definition?)

    "It's taught because as you say it's a useful and powerful concept. Doesn't mean it exists physically. Is there a point to your question?" If the schools recognize it in their instruction, then what's Wilmer's problem? (because the line itself is undefined doesn't mean it can't exist in our universe. Conceiving of it can make it exist in a mathematical universe).
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  7. #22
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    Quote Originally Posted by wonderboy1953 View Post
    "My point is, we make the ruler in the same way we make the line segment. If we can't make the line segment, then what is it exactly you're trying to measure?" The straight line (do you understand it? would you like a definition?)

    "It's taught because as you say it's a useful and powerful concept. Doesn't mean it exists physically. Is there a point to your question?" If the schools recognize it in their instruction, then what's Wilmer's problem? (because the line itself is undefined doesn't mean it can't exist in our universe. Conceiving of it can make it exist in a mathematical universe).
    Granted the jump from "we cannot prove it exists" do "it does not exist" is not really justified. I would classify it as careless use of speech more than anything else.

    As for the straight line, yes, I'm afraid you'll have to define what it is you want to measure. Because obviously the way I understood it is not the way you intended.
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  8. #23
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    Quote Originally Posted by undefined View Post
    Granted the jump from "we cannot prove it exists" do "it does not exist" is not really justified. I would classify it as careless use of speech more than anything else.

    As for the straight line, yes, I'm afraid you'll have to define what it is you want to measure. Because obviously the way I understood it is not the way you intended.
    We should have debated this in the philosophy subforum (does anyone else want to join in?)
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  9. #24
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    Quote Originally Posted by wonderboy1953 View Post
    We should have debated this in the philosophy subforum (does anyone else want to join in?)
    Mmm, I don't think this is going very well as philosophical debates go; I believe this is going the way of the threads in that forum that have been closed by moderators.
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  10. #25
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    Quote Originally Posted by wonderboy1953 View Post
    I can picture Wilmer struggling in class while the teacher is going over lines in geometry
    Nope. "A line" is easily "seen" on paper or blackboard or whatever...
    Now YOU show me one in space.
    Slow down some WB...before you become a legend in your own mind
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  11. #26
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    "There ain't no such thing as "a line"."

    Quote Originally Posted by Wilmer View Post
    Nope. "A line" is easily "seen" on paper or blackboard or whatever...
    Now YOU show me one in space.
    Slow down some WB...before you become a legend in your own mind
    Aha! You do know what a line is.
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  12. #27
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    Quote Originally Posted by wonderboy1953 View Post
    "There ain't no such thing as "a line"."
    Aha! You do know what a line is.
    Nooooo I don't: the "teacher" who made that chalk mark told us it was
    a line but he didn't know any better...like, a bit later, the poor soul told
    us it had NO WIDTH, so how can it be anything? Get my drift?
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  13. #28
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    Quote Originally Posted by Wilmer View Post
    Nooooo I don't: the "teacher" who made that chalk mark told us it was
    a line but he didn't know any better...like, a bit later, the poor soul told
    us it had NO WIDTH, so how can it be anything? Get my drift?
    That's why he's the teacher and you're the student.
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