2 types of 2D

[darthbadass]

This website uses a "vertical" plane as the 2nd dimension, but I prefer a "horizontal" plane. I think if there was such a universe it would be exist like that: you'd see a top-down cross section, not a left-right cross section. That way a soldier could actually retreat from battle .But I really can't say which way of thinking is "right".

[Keiji]

The problem is they aren't "walking on a table top" in a horizontal plane. Suppose there was nothing but air around them - how would they move?

[Nick]

iNVERTED, could you explain what you mean?

I always thought (but was too afraid to post it) that if you rotate the 2d world around three dimensionally, you could have a tabletop 2d world without gravity... then I thought that if you rotate the 3d world around four dimensionally, you could have a 3d world without gravity. Y/n?

[Keiji]

The problem with that is that gravity isn't only on the y axis.

Gravity attracts small objects to big ones. So, us (small objects) stick to the earth (big object). We call the axis of gravity y by convention. However, if we were to look at the north pole, gravity would be going south, and if we were to look at the equator, gravity would go horizontally.

Similarly, in a 2D world, if you have a planet with a bionian on it, he will be attracted to the planet. Doesn't matter if the 2D world is vertical or horizontal in relation to us.

And if there was no gravity, it would be as if he was in space. Then he would need rocket boosters to move.

However, it would certainly be possible to have a 2D space in which the laws of physics were different so that the concept of gravity didn't exist.

[Nick]

Yes, but we are attracted to bigger objects because they bend spacetime. The bending of spacetime could be attributed to higher dimensional gravity (though some scientists disagree with this). So, if a 2d world relied on 3d gravity, then I would be right, right?

[Keiji]

If a 2D world was connected to a 3D world enough to use its gravity, then yes, the direction of gravity would indeed be dependent on the orientation. However, if this was the case, a 2D being wouldn't be able to move as it is locked into its own dimension and cannot touch anything "below" it.

[jinydu]

Yes, but we are attracted to bigger objects because they bend spacetime. The bending of spacetime could be attributed to higher dimensional gravity (though some scientists disagree with this). So, if a 2d world relied on 3d gravity, then I would be right, right?

I think you are thinking of General Relativity. Actually, when spacetime "bends" in General Relativity, what that really means is that the formula for the inner product (and hence the formula for spacetime distance) changes from what it would be in "flat" spacetime. All of this can be done without reference to a higher-dimensional spacetime.

To (over)simplify things, let's consider space only. We know that in ordinary 3D Euclidean space, the distance from the origin to a point (x, y, z) is:

Distance = √(x² + y² + z²)

What General Relativity says is that in the presence of mass/energy, this distance formula must be modified. However, the modified formula still involves only x, y and z, with no 4th spatial variable. Thus, space is "bent", but without any reference to a higher-dimensional space that it bends into.

Admittedly, that explanation is rather oversimplified, since it talks about just space instead of spacetime. But I hope you get the idea.

[houserichichi]

Yes, but we are attracted to bigger objects because they bend spacetime.

We are attracted to more massive objects, not necessarily bigger. Black holes are pretty small as are neutron stars but they are so dense and massive that their gravity sucks us right in.

Admittedly, that explanation is rather oversimplified, since it talks about just space instead of spacetime.

Still keeping it simple but moving a step ahead, the metric in differential notation (it's usually written as a tensor in the form of a 4x4 matrix) is just

d(tau)^2 = - (dt)^2 + (dx)^2 + (dy)^2 + (dz)^2

or switch all the signs around on the right: (- + + +) or (+ - - -). Not a huge mental leap by any stretch of the imagination.

[papernuke]

to me the left-right way is right, because if they were up-down then, they wouldnt have anywhere to go to and would just be surrounded with air

[Nick]

to me the left-right way is right, because if they were up-down then, they wouldnt have anywhere to go to and would just be surrounded with air

I have no idea what you're talking about. Why wouldn't they have anywhere to go?

[Keiji]

Locked, because we have a different topic for this.

http://tetraspace.alkaline.org/forum/vi ... .php?t=555