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 April 8th, 2014, 12:21 PM #1 Senior Member   Joined: May 2013 Posts: 109 Thanks: 0 False axiom Hi guys. Haven´t been here for a long time, but glad to come back. As usual i have a problem. let me say: "from any given point in the space we can map any other point in that space". Is this true? Let´s assume Earth (hardly a mathematical point), can we reach any point of the universe by drawing straight lines? I doubt it. Cheers.
 April 8th, 2014, 04:14 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Pedro, if we could, would it bring down the price of groceries?
 April 8th, 2014, 05:34 PM #3 Math Team   Joined: Apr 2012 Posts: 1,579 Thanks: 22 I take it that this is a question about what sort of geometry accurately characterizes the actual universe as best we understand it? Obviously, in Euclidean geometry, you can get from any point to any other point in a straight line.
April 8th, 2014, 05:36 PM   #4
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Quote:
 Originally Posted by johnr Obviously, in Euclidean geometry, you can get from any point to any other point in a straight line.
Indeed, this statement is true in universal geometry (Euclidean, hyperbolic, elliptic). Perhaps clarification is in order?

 April 8th, 2014, 05:43 PM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra What sort of straight line are we talking about? (And does it matter?) In reality, with space being curved to varying degrees everywhere, it's rather difficult to work out what a straight line actually is. It probably even changes depending on the speed you are travelling because your own mass will warp the space around it. Added to that, all the mas in the universe is moving, so the curvature of space is constantly changing. I suppose that over long distances, the place you'd end up would be chaotic with respect to the initial trajectory, but it is still presumably piecewise continuous, which suggests to me that it's plausible that everywhere is accessible via a straight line. Unless there are parts of the universe that are travelling away from us quickly enough that we can never catch them up.
April 8th, 2014, 07:44 PM   #6
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 Originally Posted by v8archie Unless there are parts of the universe that are travelling away from us quickly enough that we can never catch them up.
The Minkowski cone, yes. That would certainly be a novel interpretation of "straight line"!

 April 8th, 2014, 09:39 PM #7 Senior Member   Joined: May 2013 Posts: 109 Thanks: 0 The point is: when you introduce the coordinate time, everything changes. You need time to draw a line: is the original destination still in the same place? Cheers.
 April 9th, 2014, 11:36 AM #8 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 A line is imaginary, is it not? Has no size, thickness et al... So how d'heck ya gonna draw it?
 April 9th, 2014, 03:17 PM #9 Senior Member   Joined: May 2013 Posts: 109 Thanks: 0 with an imaginary pen.
 April 9th, 2014, 05:42 PM #10 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms At the point that you introduce a physical pen you introduce error. How do you decide if a line crosses a point even if it's not moving? With mathematically perfect lines it's easy enough but approximations make it hard.

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