Notices
Results 1 to 9 of 9

Thread: a line

  1. #1 a line 
    Moderator Moderator AlexP's Avatar
    Join Date
    Jul 2006
    Location
    NY
    Posts
    1,838
    i have a two part question, so here's part one. perhaps this is really simple, but i'd like a straight answer on this before i go on.

    When a person draws a straight line on a piece of paper and puts arrows on both ends, it is held true that the line goes on infinitely in both directions, correct? And if so, does it also (theoretically) go off the paper and onto the desk and through the air and through the wall, etc. etc.? Hope you see what I mean.


    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
    Reply With Quote  
     

  2.  
     

  3. #2 Re: a line 
    Guest
    Quote Originally Posted by Chemboy
    i have a two part question, so here's part one. perhaps this is really simple, but i'd like a straight answer on this before i go on.

    When a person draws a straight line on a piece of paper and puts arrows on both ends, it is held true that the line goes on infinitely in both directions, correct? And if so, does it also (theoretically) go off the paper and onto the desk and through the air and through the wall, etc. etc.? Hope you see what I mean.
    In an abstract sense, where the arrows represent a continual line drawn, lets imagine that line continuing for infinity (since the arrows represent that). With this assumption: Yes it's true.

    But that is a very tired-minded guess, so feel free to utterly ignore it.


    Reply With Quote  
     

  4. #3  
    Moderator Moderator AlexP's Avatar
    Join Date
    Jul 2006
    Location
    NY
    Posts
    1,838
    ok, that's what i was thinking. i kind of just wanted to establish that before presenting my real question. oh, and at this point it kind of ceases to be a math question so much (i think) so i understand if it gets moved. really no idea where it would go though. anyways...

    So, you have this line that extends for infinity in both directions. While you follow it along, will you keep going in a circle around the earth, or will you eventually end up increasing in altitude until you're walking into space? I'm thinking the latter, because if the line followed the curve of the earth, it would eventually meet itself and connect. But, if it did this, would it still be infinite? It would have infinite points, being a (rough) circle, but would it be infinitely long? I know things tend to get kind of complicated when dealing with infinity, but I think this is interesting. So ultimately, my question is: curve around the earth, or go into space? I hope that makes sense.
    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
    Reply With Quote  
     

  5. #4  
    Forum Professor river_rat's Avatar
    Join Date
    Jun 2006
    Location
    South Africa
    Posts
    1,517
    This isnt a maths problem really but the answer is quite easy if you accept that laser light travels in a "straight line". So put a laser on top of everest and make sure that it is "tangent" to the earth at that point then its beam will journey off into space, like your theoretical straight line.

    At a deeper level the answer depends on what you mean by straight line, if you only mean locally a straight line then you would pick up the curvature of the earth and walk around it but if you mean globally a straight line in the euclidean sense (so a normal straight line ignoring relativity effects) then you would blast off into space.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
    Reply With Quote  
     

  6. #5  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,620
    Quote Originally Posted by river_rat
    This isnt a maths problem really
    Oh really?
    At a deeper level the answer depends on what you mean by straight line
    Quite. So, let's say a straight line is the shortest path between two points. How do you know what's meant by shortest?

    We need what's called a Variational Principle, which is a really cool result in mathematics, thanks to Euler and Lagrange. But it is mathematics, and it's far from easy, at least to my pea brain!

    Yes, yes, I know, I'm showing off. Ignore me.
    Reply With Quote  
     

  7. #6  
    Forum Professor river_rat's Avatar
    Join Date
    Jun 2006
    Location
    South Africa
    Posts
    1,517
    Quote Originally Posted by Guitarist
    Quote Originally Posted by river_rat
    This isnt a maths problem really
    Oh really?
    By that i mean it is really an experimental physics problem - everything else is prediction and physics. Call it nit picking
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
    Reply With Quote  
     

  8. #7  
    Forum Freshman chrisdlugosz's Avatar
    Join Date
    Dec 2006
    Location
    Buffalo NY
    Posts
    7
    a line forming a circle around earth is no different than you drawing a small circle on your paper. its certainly no longer a ray, but now a curve described by some equation.

    a line or ray will shoot through outer space.

    now i dare to post an even more dastardly question ---
    your infinite line is the X axis on a graph.
    this line has a zero position, infinite positive direction, and infinite negative direction.

    is zero the midpoint ?
    Reply With Quote  
     

  9. #8  
    Moderator Moderator AlexP's Avatar
    Join Date
    Jul 2006
    Location
    NY
    Posts
    1,838
    Quote Originally Posted by chrisdlugosz
    a line forming a circle around earth is no different than you drawing a small circle on your paper. its certainly no longer a ray, but now a curve described by some equation.

    a line or ray will shoot through outer space.

    now i dare to post an even more dastardly question ---
    your infinite line is the X axis on a graph.
    this line has a zero position, infinite positive direction, and infinite negative direction.

    is zero the midpoint ?
    Good question.

    Perhaps zero is the midpoint, and it exists at every single point on the line, and since zero represents "nothing", the line doesn't exist. That kind of makes sense if you think about it. But actually, if you use the midpoint formula, you get the point (0,0), which obviously is the midpoint...but...you can't really plot that, i guess. it'd be like going back to what i said originally about it being at every point. Maybe it can just be wherever you want it to be, or it's relative, or something.
    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
    Reply With Quote  
     

  10. #9  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,620
    Quote Originally Posted by river_rat
    By that i mean it is really an experimental physics problem - everything else is prediction and physics. Call it nit picking
    Nit-pick away! Actually I've never been entirely at home with VPs. Maybe we could talk some about it, as I know you physics guys are dead keen on them.

    And at least we know how to set out the notation on this site now

    Ahh, gwaan.
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •