I know my question is rather ambiguous... but pls do share ur knowledge

When it is an illusion?

Otherwise, they dont.

well, if you define two parallel lines to be two lines that never meet, then they can never meet, by definition.

On the surface of a sphere. But if two lines on the surface of a sphere ca nbe called parallel, is debatable.

Hans

At some schools the following definition of pararel lines used to be given:

</i>Paralel lines meet at infinity.</i>

This is a formulation based on the teachings of Wittgenstein (Tractatus..) where he proposed logical operators (and, or, not, if etc) not to be the part of the picture of the world which the language provides. Eg. a sign warning not to smoke contains a picture of a (smoking) cigarette crossed with a red line. The red line ( in the meaning of "not") is not a part of the picture of the cigaret.

The sentence <i>Paralel lines meet at infinity.</i> states that <i>the lines will never meet </I> without using the logical operator not/never (infinity cannot be reached).

Originally posted by MRC_Hans
On the surface of a sphere. But if two lines on the surface of a sphere ca nbe called parallel, is debatable.

Hans

Sure they can, have a look at this image of a sphere with 2 parallel red lines!

Only kidding!

In generalised geometry, surfaces can have zero, positive or negative curvature. Parallel lines never meet on surfaces whose curvature is everywhere negative or zero. On surfaces with positive curvature, parallel lines always eventually meet.

When you take two parallel laser beams and project them into a black hole. The beams will meet at the centre.
As space compresses the lines whilst remaining parallel come closer together.

I know I said I wouldn't write to the physics board but I couldn't resist..
:D

Originally posted by Quantum Quack
When you take two parallel laser beams and project them into a black hole. The beams will meet at the centre.
As space compresses the lines whilst remaining parallel come closer together.

I know I said I wouldn't write to the physics board but I couldn't resist..
:D

I dont know if anyone is exactly sure what happens in a black hole... but I think that as soon as they pass the even horizon, the beams are no longer parallel, because they are being effected by the gravity....

His original question, however, did not state that the lines had to be starting at the same destionation, so you could find a black hole with zero rotational velocity, and fire them from opposite sides... not at each other, but slightly parallel, and they would enter the black hole parallel.... but like I said, who knows what happens with in the hole?

Also, lines are supposed to go to inifinity in both directions, lines (in this discussion I believe) are a purely mathmatical concept that have no.. representations in the real world.

*lasers are comprised of photons, which are affected by gravity.

I would suggest that even when the parallel beams of light come together at the black hole centre they are still parallel.
As the gravity and space compresses the lines remain parallel however they are closer together ( relativistically) closer but still the same distance apart.

Any one want to have a little fun with this?

One of the starting points for the general theory of relativity is to ask the question: what do we mean when we say two lines are parallel? If you answer this question properly, you will eventually discover Riemannian geometry.

For example, consider a sphere, such as the Earth (approximately). Are lines of longitude parallel? (They meet at the poles...) What about lines of lattitude? Which kinds of lines on the Earth are parallel, exactly?

I would suggest that even when the parallel beams of light come together at the black hole centre they are still parallel.
As the gravity and space compresses the lines remain parallel however they are closer together ( relativistically) closer but still the same distance apart.

Any one want to have a little fun with this?

But being "the same distance apart" is a very poor definition of parallel.

I think that the only way for 2 parallel lines to meet, is for the space between them to be compressed.

Why should 2 parallel lines meet if they are on a sphere? eg: going around the equator at a fixed distance to each other?

Originally posted by tablariddim
I think that the only way for 2 parallel lines to meet, is for the space between them to be compressed.

Why should 2 parallel lines meet if they are on a sphere? eg: going around the equator at a fixed distance to each other? You either have to screw with your notion of "line" or "parallel" to address the issue in curved space. Lines are only on a sphere at most two points (one, if they are tangent, two if they pierce through the sphere). Curves can be on a sphere, but what does it mean for two curves to be parallel. Then, you could define geodesics on the sphere (a specific kind of curve), but the infinite continuations of any two distinct geodesics on a sphere will meet.

Something to think about: In spherical geometry, lines of lattitude (except for the equator) are not "straight" lines (technical term <i>geodesics</i>), but lines of longitude are. The reason is that a straight line ought to be the shortest distance between any two points it connects. Lines of longitude do the job, but lines of lattitude do not. An aircraft flying between two cities at the same lattitude on the Earth does not follow a line of lattitude if it wants to get from one city to the other in the shortest amount of time (i.e. by the shortest route).

Definitions are required here if we are dealing with curved space e.g. a shere.

1) A line is not is a particular type of curve. A line is a conveniant ideal in flat space but not in curved. In Euclidean space, a line should be defined as one whose gradient is constant at all points on the line, i.e. it is a straight line. A curve is simply a smooth and continuous function in R(3)(Or what ever you define it to be)

2) In curved space, I think a line should be referred to as a geodesic. These geodesics are curves whose curvature everywhere is zero. Lines of latitude are not geodesics and so as James suggested I think that these should not be regarded as isomorphic to straight lines in flat space.