1. 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.  2.

3. 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.  4. 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.   5. 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.  6. 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.  7. Originally Posted by Guitarist 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   8. 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 ?  9. 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.  10. 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.  Bookmarks
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