|
miademus
Jan 16, 2007, 8:42 PM
Post #1 of 72
(2082 views)
Shortcut
Registered: Nov 8, 2005
Posts: 511
|
is it possible that parallel cross, you tihnk so?!?
are you thinking of beyond?
"changed the thread,in some ways so that everyone gets the meaning"
(This post was edited by miademus on Jan 16, 2007, 9:14 PM)
|
|
|
|
|
quadfire
Jan 16, 2007, 8:45 PM
Post #2 of 72
(2073 views)
Shortcut
Registered: Sep 13, 2006
Posts: 203
|
I prefer my lines to be skew
|
|
|
|
|
wjca
Jan 16, 2007, 8:47 PM
Post #3 of 72
(2070 views)
Shortcut
Registered: Jan 27, 2005
Posts: 7545
|
I wish English was your first language or that I at least spoke foreign, then I might know what the fuck you're talking about. And what's up with your glamour shot avitar pic?
|
|
|
|
|
devils_advocate
Jan 16, 2007, 9:01 PM
Post #4 of 72
(2055 views)
Shortcut
Registered: May 18, 2006
Posts: 1823
|
That's Blue Steel.
You have no idea how hard it is being really, really, really, really, really, rediculously good looking.
|
|
|
|
|
miademus
Jan 16, 2007, 9:02 PM
Post #5 of 72
(2051 views)
Shortcut
Registered: Nov 8, 2005
Posts: 511
|
well measuring out what the helli 'm trying to tell ya takes time ,anyway your going to talk shit like always...
damn i tried a whole week but my avatar damn it does not change, i'm freakin. i know that pic is  shit......okey!!i knowww it, i know i know i know!!!
well...ehem...a deep point...
|
|
|
|
|
quadfire
Jan 16, 2007, 9:12 PM
Post #6 of 72
(2042 views)
Shortcut
Registered: Sep 13, 2006
Posts: 203
|
wjca wrote: I wish English was your first language or that I at least spoke foreign, then I might know what the fuck you're talking about. And what's up with your glamour shot avitar pic?
They were all at the bar getting smashed, when one guy started arguing nonsensical philosophy with another about mixing fire with water, crossing parallel lines, tree's falling in the forest, hovering cat/toast combinations, and perpetual motion machines.
is that about right?
edit to add: I still like my lines skew, 3 dimensions are better than 2
(This post was edited by quadfire on Jan 16, 2007, 9:15 PM)
|
|
|
|
|
miademus
Jan 16, 2007, 9:31 PM
Post #7 of 72
(2028 views)
Shortcut
Registered: Nov 8, 2005
Posts: 511
|
wow quad you did very well, couln't explain it better ...
|
|
|
|
|
kriso9tails
Jan 16, 2007, 10:54 PM
Post #9 of 72
(1988 views)
Shortcut
Registered: Jul 1, 2001
Posts: 7772
|
Two parallel lines can cross... just so long as they aren't parallel to each other. Other wise, parallelograms would be hard to draw.
|
|
|
|
|
blondgecko
Moderator
Jan 16, 2007, 11:34 PM
Post #10 of 72
(1971 views)
Shortcut
Registered: Jul 2, 2004
Posts: 7666
|
They can if they're drawn in a closed universe.
|
|
|
|
|
rrrADAM
Jan 17, 2007, 5:32 AM
Post #11 of 72
(1923 views)
Shortcut
Registered: Dec 19, 1999
Posts: 17553
|
They will ALWAYS cross... Draw them on the earth (a sphere) and they will cross, just as the longitudinal lines cross at the poles. Since space IS curved, they will cross in space also.
The Euclidean Geometry we all learned in school is only acurate in a flat space, or on a flat surface, but this is NOT physical reality...
Example:
In Euclidean Geometry, we all learned that the angles of a triangle always equal 180 degrees when added together, but if you draw a triangle on the earth in a large scale (1,000s of miles), and measure the angles, they will NOT equal 180 degrees, but considerable more... In fact, if you do it on a large enough scale, you can do it with 3 90 degree angles. This is because the earth is not flat. In fact, the lines will be curved.
Avoiding this curvature is impossible, since matter curves spacetime.
(This post was edited by rrradam on Jan 17, 2007, 5:37 AM)
|
|
|
|
|
perp
Jan 17, 2007, 9:48 AM
Post #12 of 72
(1903 views)
Shortcut
Registered: Sep 30, 2004
Posts: 83
|
par�al�lel
adj.
1. Being an equal distance apart everywhere: dancers in two parallel rows.
2. Mathematics
a. Of, relating to, or designating two or more straight coplanar lines that do not intersect.
b. Of, relating to, or designating two or more planes that do not intersect.
c. Of, relating to, or designating a line and a plane that do not intersect.
d. Of, relating to, or designating curves or surfaces everywhere equidistant.
Using 2a. as the definition of parallel lines it is clear that they can't cross, as they are defined to be two lines that do not intersect (cross).
|
|
|
|
|
bizarrodrinker
Jan 17, 2007, 12:58 PM
Post #13 of 72
(1895 views)
Shortcut
Registered: Dec 20, 2005
Posts: 2316
|
rrradam wrote: They will ALWAYS cross... Draw them on the earth (a sphere) and they will cross, just as the longitudinal lines cross at the poles. Since space IS curved, they will cross in space also. The Euclidean Geometry we all learned in school is only acurate in a flat space, or on a flat surface, but this is NOT physical reality... Example: In Euclidean Geometry, we all learned that the angles of a triangle always equal 180 degrees when added together, but if you draw a triangle on the earth in a large scale (1,000s of miles), and measure the angles, they will NOT equal 180 degrees, but considerable more... In fact, if you do it on a large enough scale, you can do it with 3 90 degree angles. This is because the earth is not flat. In fact, the lines will be curved. Avoiding this curvature is impossible, since matter curves spacetime.
Theoretically speaking, you can't draw a "line" anyway. No matter how small or thin you draw it, and infinite number could be placed on top of it. But I s'ppose it wouldn't make for entertaining converstation.
|
|
|
|
|
wideguy
Jan 17, 2007, 1:01 PM
Post #14 of 72
(1894 views)
Shortcut
Registered: Jan 9, 2003
Posts: 15046
|
sounds more like it's not that parallel line can cross than it is there is no such thing a true parallel lines.
|
|
|
|
|
arrettinator
Jan 17, 2007, 4:19 PM
Post #15 of 72
(1871 views)
Shortcut
Registered: Oct 30, 2002
Posts: 8522
|
In Euclidean geometry parallel lines are two straight lines in the same plane which never intersect. In Hyperbolic Geometry parallel lines curve away from each other, and are called ultraparallels. In Eliptic geometry, all lines intersect, curving toward each other, and there are no parallel lines.
I have a problem with NonEuclidean geometry, with the disregard of Euclidean geometry existing in 3 dimensions. We can't have 3 dimensions with out having 2 dimensions. Even with space being curved, if I draw a straight line through 2 points, it's still straight. If it were curved, it wouldn't be a straight line anymore.
(there is no spoon)
 I'm such a geek.
|
|
|
|
|
ryanb
Jan 17, 2007, 10:26 PM
Post #16 of 72
(1836 views)
Shortcut
Registered: Nov 4, 2004
Posts: 832
|
1) It is some time usefull when thinking about continuity to consider the real plane as including "the point at infinity". Parrallel lines do intersect at this point but you have to ask if it is really a point
2) Most of the estimates I have seen of the curveture of the universe describe it as basically flat because curveture of space is the result of mass/energy and the universe is largely empty.
3) There are however paths taken by light that cross twice due to the curveture of space once at the source and once at the some distant focul point. This is called gravitational lensing. It is debatable if these lines are parrallel or if parrallel even has much meaning in this case.
4) when crossing parrallel lines it is best to use a double fisherman's knot though some still prefer using a single overhand knot (or euro death knot) as it is less likely to snag..
|
|
|
|
|
kachoong
Jan 17, 2007, 10:37 PM
Post #17 of 72
(1828 views)
Shortcut
Registered: Jan 23, 2004
Posts: 15304
|
blondgecko wrote: They can if they're drawn in a closed universe.
So if a train toots along for long enough it will eventually crash? Bugger!
|
|
|
|
|
devils_advocate
Jan 17, 2007, 10:42 PM
Post #18 of 72
(1825 views)
Shortcut
Registered: May 18, 2006
Posts: 1823
|
kachoong wrote: blondgecko wrote: They can if they're drawn in a closed universe. So if a train toots along for long enough it will eventually crash? Bugger!
Did you just use the word toots to describe a train in motion?
|
|
|
|
|
kachoong
Jan 17, 2007, 10:44 PM
Post #19 of 72
(1821 views)
Shortcut
Registered: Jan 23, 2004
Posts: 15304
|
devils_advocate wrote: kachoong wrote: blondgecko wrote: They can if they're drawn in a closed universe. So if a train toots along for long enough it will eventually crash? Bugger! Did you just use the word toots to describe a train in motion?
Yabba dabba doo!
|
|
|
|
|
petsfed
Jan 18, 2007, 4:55 AM
Post #20 of 72
(1790 views)
Shortcut
Registered: Sep 25, 2002
Posts: 8599
|
ryanb wrote: 3) There are however paths taken by light that cross twice due to the curveture of space once at the source and once at the some distant focul point. This is called gravitational lensing. It is debatable if these lines are parrallel or if parrallel even has much meaning in this case.
Well, since a straight line is defined as the path light takes between two points in a vacuum, I'd say we have quite the debacle, eh?
That definition is a natural result of "shortest distance between two points" since relativistic distance dilation makes that rather complicated. Light will always follow the contours of space. Its not that the path of light is bent in cases of gravitational lensing, but rather that space itself is bent in such a way that the light will naturally follow that path, like water down an inhomogeneous surface.
As to the topic at hand, another way to define parallel lines is to consider two lines that are both perpendicular to a plane.
Finally, also remember that over small distances (in comparison to the scale at which the curvature of the universe is actually measurable), euclidean geometry is more than sufficient. Sure, 8 foot long parallel line segments, if drawn across the entire planet, will eventually cross, but over the local area they are parallel enough. This is why we call in-phase, single wavelength, focussed light pulses lasers, despite the fact that they aren't precisely collimated. Over the short term, its parallel enough.
(This post was edited by petsfed on Jan 18, 2007, 4:58 AM)
|
|
|
|
|
rrrADAM
Jan 19, 2007, 12:32 AM
Post #21 of 72
(1735 views)
Shortcut
Registered: Dec 19, 1999
Posts: 17553
|
Actually... If we were able to view a line believed to be straight from 'outside' the universe, we would see it as a curved line....
Even light, think 'line of sight', is believed to be straight, but as evidenced by Einstien Halos and/or the light bent by a star, light does not propogate in entirely straight lines... Instead they follow geodesics, which are the 'quickest'/straightest lines through spacetime. Let me explain...
As observed, light travels the 'quickest' path, which to us is in a straight line, but it is not...
Imagine that you were a lifeguard on a beach, and you are 20 yards from the water, and 100 yards to your right a swimmer is drowning who is 50 yards away from the shore...
As seen from above, the most direct route to him would be in a straight line, but since one can travel faster on the sand than one can in the water, taking the direct route to him would NOT be the quickest... Instead it is a ratio (same as refraction) of sand and water that will allow the 'quickest' time that should be followed, and the result would be a bent line. This is the same as why a straw in water is askew, as the velocity of light in water is much slower than in air.
Just as above, QED aside, light is seen to travel the quickest path, and since spacetime is curved by matter, and the more matter there is the greater (denser) the curve is light has to get through, it must follow these curves, but will take the paths that are the quickest.... Geosedics. This is NOT just hypothetical theory, but is consistant with countless experments that confirm it.
The analogy with reducing 3D space to a 2D topology (a piece of paper) works, but you need to curve the paper to see the 'forest for the trees'.... Think of the surface of a cylinder, as that surface is curved, and 2D. The shortest possible line between two points on it will appear straight if viewed from anywhere on the line, but if viewed from any point outside that line, it will appear curved.
(This post was edited by rrradam on Jan 19, 2007, 12:35 AM)
|
|
|
|
|
slablizard
Jan 19, 2007, 12:36 AM
Post #22 of 72
(1731 views)
Shortcut
Registered: Oct 13, 2003
Posts: 5558
|
rrradam wrote: Actually... If we were able to view a line believed to be straight from 'outside' the universe, we would see it as a curved line.... Even light, think 'line of sight', is believed to be straight, but as evidenced by Einstien Halos and/or the light bent by a star, light does not propogate in entirely straight lines... Instead they follow geodesics, which are the 'quickest'/straightest lines through space time. Let me explain... As observed, light travels the 'quickest' path, which to us is in a straight line, but it is not... Imagine that you were a lifeguard on a beach, and you are 20 yards from the water, and 100 yards to your right a swimmer is drowning who is 50 yards away from the shore... As seen from above, the most direct route to him would be in a straight line, but since one can travel faster on the sand than one can in the water, taking the direct route to him would NOT be the quickest... Instead it is a ratio (same as refraction) of sand and water that will allow the 'quickest' time that should be followed, and the result would be a bent line. This is the same as why a straw in water is askew, as the velocity of light in water is much slower than in air. Just as above, QED aside, light is seen to travel the quickest path, and since spacetime is curved by matter, and the more matter there is the greater (denser) the curve is light has to get through, it must follow these curves, but will take the paths that are the quickest.... Geosedics. This is NOT just hypothetical theory, but is consistant with countless experments that confirm it. The analogy with reducing 3D space to a 2D topology (a piece of paper) works, but you need to curve the paper to see the 'forest for the trees'.... Think of the surface of a cylinder, as that surface is curved, and 2D. The shortest possible line between two points on it will appear straight if viewed from anywhere on the line, but if viewed from any point outside that line, it will appear curved.
Fascinating.
Thanks!
|
|
|
|
|
philbox
Moderator
Jan 19, 2007, 1:25 AM
Post #23 of 72
(1725 views)
Shortcut
Registered: Jun 27, 2002
Posts: 13105
|
Adam, you might explain in laymans terms why speed trumps time in light. Why could it not be possible for time to be the constant rather than speed of light in the equation E=mc2
|
|
|
|
|
thegreytradster
Jan 19, 2007, 1:48 AM
Post #24 of 72
(1720 views)
Shortcut
Registered: Jul 7, 2003
Posts: 2151
|
because time is a variable.
Just as height, length or width are
|
|
|
|
|
big_red
Jan 19, 2007, 2:08 AM
Post #25 of 72
(1717 views)
Shortcut
Registered: Dec 29, 2005
Posts: 109
|
If one were to do two parallel lines....would THEY then become cross?
|
|
|
|
|
|
1
