Parallel 2D spaces

[Keiji]

We already know that in 2D, it is impossible for anything complex to happen due to the fact that paths cannot cross over. So, what if there were two linked 2D spaces? Things could freely move from one space to another, and therefore complex things like brains, computers, etc. would be possible.

Not really anything important, just something interesting to think about

[Nick]

If there were two linked 2d worlds, that would create a 3d worlds (even if there are only 2).

[Keiji]

Not necessarily - a realm has an infinite number of positions in three dimensions (even if there were bounds to the realm, the gap between one acceptable position and the next is infinitely small, making the number of positions infinite).

Two linked planes would have an infinite number of positions in two dimensions, but a finite number of positions in the third. Therefore, it is not a 3D space.

[Nick]

Oh, I see.
I thought by "linked" you meant that they were stacked next to each other.

[moonlord]

I think having three linked planes is mandatory. You must be able to have torii. See how many things in our world are torii.

[Keiji]

Why?

[moonlord]

1. Why need torii? Because you'll need pipes most probably.
2. Why need three linked planes? I've just realized you can use the universe 'limit' as border. So you only need two planes.

[Keiji]

1. Why need torii? Because you'll need pipes most probably.
2. Why need three linked planes? I've just realized you can use the universe 'limit' as border. So you only need two planes.

Actually, I just realized (yes, over a year later) that you do need three planes: the two end ones for stuff to actually move in, and the middle one as separation. If your planes wrap in a loop, then you need four planes, because you need two separators.

[moonlord]

Funny indeed. Care to explain the second part? Didn't quite grasp it.... "wrap in a loop"..?

[Keiji]

In other words, if your first plane is not only to the left of your last plane, but simultaneously also to the right, then you need four planes.

[moonlord]

Right. The fourth plane would act like the borders of the first and third planes.

[wendy]

Why do you assume that the two dimensional space is embedded as planes in 3d space? This sort of model has been proposed for 3d as well, but the idea that space is somehow "embedded" as parallel slices of larger space makes me no sense.

Firstly, one supposes that a change might be to only an adjacent dimension. If the universes are arranged as pages of a book, then the only option for change is from page 7 to page 6 or to page 8. The universe is more dynamic than this, and one might suppose hundreds of thousands of dimensions as the embedding space.

High dimensions, such as this is no stranger to physics. The entirity of all of the N particles of a gass is represented by a single point, in 6N dimensions. It's called phase space.

One can understand the rotation of 4d objects by visiting a six-dimensional object, or 5d by visiting a 10 or 11 dimensional one.

One image, that amuses my mind, is based on a notion in 'the secret of the gods', where there are life-forms that range upwards, where, for example people are as ants in the city, and the city has a concious. Since we know in physics, the age of life / heart beat is roughly constant for all things, this goes upwards too: a city that might last for thousands of years, one heartbeat might be a day long, and we are much as a speck of dust in the instant of the eye.

Such can be modeled, so that all things have the same area, by considering that the euclidean plane is really a surface of concentric horospheres, and one's lot, be it city of gnat, is the same size closer or further out from the centre. There is no real centre, one goes inwards to get ever bigger things, and ever outwards to get ever smaller things.

In hyperbolic H4 space, all of these things are still the same size, in space and in time.

W

[papernuke]

What do you mean by two 2d spaces? do you mean as in 2 universes of just like someone's house and someone else's house in the same neighborhood? and what does having two spaces have to do with brains working?
and how would a computer work in 2d? all they would see is a line and how could all the stuff like the processers and adapters etc. fit in it--and still work?

[d.m.falk]

2D=length+width, in other words, more than just a line. Most computers function on 2D circuitry.

d.m.f.