Some more stuff to discuss

[nestheking]

It is me again

Unfortunately I did not read all of the messages. They are more than 1.000 at the moment. I read maybe half of them.

Here are more stuff to discuss:

1. Let's say Vilma (Fred's wife, she is smarter than Fred) understood everything about 3d world. She can easily imagine the 3rd dimension. So, what can she do? Can she bend a line outside of her 2d world? I can not answer this question as "ABSOLUTELY NO!". I just answer it as "No, because the 2d world does not allow her to do so." Maybe she need to invent something to do this event. Or she needs help from Bob to take her or the end of the line out. Similarly if WE discovered everything about the 4d, we need something to bend our cube.

2. Can UFOs be Emily's tetranails. Because they appear suddenly and vanish suddenly, no radar contact, some weird lights etc. (I have not seen them yet.)

I have more questions but at the moment I want to see your comments. And it is better to discuss one or two topics at the same time. Thanx.

[Geosphere]

1. since we have no clue of 2d physics, who knows?

2. A lot of 'paranorma' may be described away as interdimensionsal. Again - who knows?

[elpenmaster]

vilma can bend the 2d world in a 3d dimension by eating a lot, and thus agglomerating the mass of her and the food into one place, so she would make more gravity because she would have more mass, and the gravity would bend the 2d world into the 3rd dimension

[Geosphere]

I still have to see some proofs on this gravity bending the next dimension thing.

[pat]

I think the attempted point was this. In the presence of a gravitational field, everything warps. Light bends, rather than following straight lines. The appearance of time slows down. The appearance of length shortens. Blah, blah, blah, all that general relativity stuff, blah, blah.

Einstein's relativity hinges on making coordinate systems (via tensors) and describing how warped they are.

Now, one way to visualize these coordinate systems is something like log-log graph paper. The paper is perfectly flat... but things look to be different sizes at different places. The graph paper is extrinsicly flat.

Another way to visualize this is to take a piece of paper and curl one corner up off of the table. Now, project a grid onto the curled paper. Now, plot something on that grid. Things look to be different sizes at different places. The graph paper is extrinsicly curved.

Part of relativity is that we can choose to picture the warping caused by gravity as either squishing up our coordinate system in what is basically a flat universe. Or, we can choose to picture the warping caused by gravity as a curling and pulling of our universe in some direction(s) orthogonal to space-time.

You've seen black holes represented as a sort of smooth funnel in a fabric, right? That's the view where a black hole is curling or pulling our universe in some orthogonal direction. If, instead, you did a contour plot of that fabric viewed from directly above, you'd get concentric circles around the black hole that get closer and closer together the closer you are to the center of the black hole.

So... warping space-time into some other dimension? Maybe. Warping time and space in place? Maybe. It doesn't matter which way you think of it.

[PWrong]

The way I see it, if gravity curves space into another dimension, it's not the kind of dimension we're talking about here. Planespace doesn't curve into the third dimension, and realmspace doesn't bend into tetraspace, it bends it into a completely separate dimension.

We have to find a better way to avoid confusion about this. Every topic seems to end up in an argument about gravity and time. Maybe we should start saying that gravity curves us into the G dimension, and Time can be described as the T dimension. These non-spacial dimensions always exist and are not related to the spacial dimensions in any way.

[pat]

We have to find a better way to avoid confusion about this. Every topic seems to end up in an argument about gravity and time. Maybe we should start saying that gravity curves us into the G dimension, and Time can be described as the T dimension. These non-spacial dimensions always exist and are not related to the spacial dimensions in any way.

Sounds reasonable. The number of dimensions in which we can move and in which things operate is a very different question from the number of dimensions in which our space must be embedded.

This may not be the proper bulletin board for discussing some of the embedding issues. But, maybe. There are parts in Jeffery Weeks's The Shape of Space about what Flatland would be like if it were the surface of a Klein bottle. Weeks does a great job keeping separate the issue of how a Klein bottle would have to sit in 4-D to not intersect itself from the issue of what the Flatland perception of it would be. The Flatland perception could be that it's perfectly flat.

In video games, you can often exit the top of the screen and end up returning at the bottom. You can exit the left side of the screen and end up returning at the right side. This is topologically a torus. But, for all intents and purposes in the video game, it's just plain/plane flat.

[RQ]

Yes, that's why it is a representation.
Anyway, back to the curled up dimension. It would seem that this is the only way to explain how starting from one point you would eventually end up at the same spot.

[elpenmaster]

would the volume of a klein bottle be infinite, zero, or what?