Mortal Monkey on 7/7/2006 at 14:53
Well we can't help you if you won't tell us what your problem is, can we now?
Sap'em on 7/7/2006 at 14:56
head splodes!:confused:
Renegen on 7/7/2006 at 15:13
That finger thing helps up understand how a 2 dimensional world can be wrapped with a 3rd dimension. You can move forward/backwards and up/down as part of the 2 dimensions, and then on the e plane, which is around.
How can we know that a 2 dimensional world wrapped in a 3rd dimension isn't possible when we can't visualise anything other than the 3 dimensional world we live in?
Mortal Monkey on 7/7/2006 at 15:40
If you wrap a universe so that you can travel on the W, Y and e plane like in that picture, the universe was originally 3-dimensional anyway.
But indeed, it is hard to imagine a finite universe. What happens when you hit the end? Is your velocity somehow diverted into the other dimensions? Or do you just cease to exist?
Agent Monkeysee on 7/7/2006 at 15:57
Quote Posted by Mortal Monkey
Well we can't help you if you won't tell us what your problem is, can we now?
DURR INTERNET WIT I was referring to descenterace's and Deep Qantas' posts which didn't shed any light on anything.
You guys are relying way too much on the visual aids in that flash animation. Those were BAD VISUAL AIDS DON'T LISTEN TO THEIR LIES
I'm having trouble understanding what it is you're not getting about this. You seem to understand that a Flatlander Universe that is curved like a toroid or a tube is a 3-dimensional universe, and a two dimensional being traveling along that surface would get back to where it started because its path loops in the 3rd dimension. So... what don't you understand?
Renegen on 7/7/2006 at 16:47
Quote Posted by Mortal Monkey
If you wrap a universe so that you can travel on the W, Y and e plane like in that picture, the universe was originally 3-dimensional anyway.
What? You have a 2D world, up/down, forward/backwards. Then you add the e dimension where you can rotate, yes it adds depth to the 2D world but it's a different world than our 3D one.
Mortal Monkey on 7/7/2006 at 21:01
Well adding a dimension is hardly the same as bending a universe, is it now?
Agent Monkeysee on 7/7/2006 at 21:24
Quote Posted by Mortal Monkey
Well adding a dimension is hardly the same as bending a universe, is it now?
It's exactly the same. What do you think adding a spatial dimension is? It's giving the Universe a topology along that dimension. A curved Universe is one kind of topology.
It's a 2-dimensional surface on a 3-dimensional space. If you have beings that only perceive the 2-dimensional surface, they are ignorant of the 3-dimensional curvature. Nevertheless they move in that 3rd dimension, as is evidenced by the fact that they loop back around on themselves despite, from their perspective, never deviating from a straight line.
Similarly you can have a 3-dimensional surface on a 4-dimensional space. It's more or less the same thing. If you have a Universe in a closed-loop in the 4th dimension, then you would find yourself back at your starting position despite the fact that you traveled in a straight line through 3 dimensions. A 4-dimensional surface on a 5-dimensional space would act similarly. Etc.
What is your main contention here? That you can't perceive the dimensions and thus don't believe they exist? Or that the conception of a curved topology sounds implausible? What?
Pyrian on 8/7/2006 at 01:56
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And even though you could argueably visualize time as a timeline which you could measure, you cannot say that one length in time always equals that length in X, Y or Z.
The fixed speed of light allows you to do exactly that; a light-year is a specific distance
and time. Any string can measure a span of time, and any span of time can measure a string, with c as the translational key. That's one reason why time is considered the fourth dimension.
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However, constructing imaginary dimensions that nobody can measure is something any L. Ron Hubbard could do.
While nobody has successfully measured any of the extra dimensions proposed by string theorists to make their math easier, there's no real theoretical reason why their existence won't eventually be able to be indirectly inferred and even their respective sizes measured. Anything that has consequences is in some way revealed through those consequences.
As an aside, I think "it makes the math easier" is a horrible reason to seriously consider their existence or even call it a "theory" rather than a hypothesis. "String Hypothesis" is IMO a better term for the theory. Honestly, the string theorists I know (okay, that's two, and one of them is a grad student) don't even think it's correct - useful to explore, though.
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My point is, even if you curve that 2-dimensional universe around a 3rd dimension, the volume of the universe is still 0. It's still flat. If the ground you walked on appeared level before, it still does after the universe has been curved. If the road looked to be going straight ahead, it still looks so now. Wether it actually is straight when I draw it here is
irrelevant.
Allow me to repeat - anything that has consequences is in some way revealed through those consequences. A "bent" 1-dimensional universe, as you described earlier, has no consequence within itself as long as it never meets itself (although, if it does, well...). However, in a two-dimensional universe this doesn't work at all, since even the slightest bend causes the pythagorean theorem (for instance) to fail! You can't call that irrelevant, since it's measurable from within.
Agent Monkeysee on 8/7/2006 at 03:47
Quote Posted by Pyrian
As an aside, I think "it makes the math easier" is a horrible reason to seriously consider their existence or even call it a "theory" rather than a hypothesis. "String Hypothesis" is IMO a better term for the theory. Honestly, the string theorists I know (okay, that's two, and one of them is a grad student) don't even think it's correct - useful to explore, though.
Yeah but String Hypothesis sounds stupid.
