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[Sheb]

It's not so much a line saying "I'm totally taking over this plane" as much as a circle saying the same thing, given that the circle is actually just a one-dimensional set of points (which it is; the single dimension can be measured in radians, even).

Don't you need two coordinate: the radius and an angle?

[10ebbor10]

It's not so much a line saying "I'm totally taking over this plane" as much as a circle saying the same thing, given that the circle is actually just a one-dimensional set of points (which it is; the single dimension can be measured in radians, even).

Don't you need two coordinate: the radius and an angle?

Not if you're only utilizing the surface. You only need to have a radius if you want to describe the volume of the circle. The radius is constant, embedded in the shape of the circleverse, so to speak.

Which is the point we're making here. The Surface of an n-dimensional object is an n-1 dimensional object.

[Sergarr]

It's not so much a line saying "I'm totally taking over this plane" as much as a circle saying the same thing, given that the circle is actually just a one-dimensional set of points (which it is; the single dimension can be measured in radians, even).

Don't you need two coordinate: the radius and an angle?

Unless I'm gravely mistaken, circles have fixed radii.

[Sheb]

Sure, you can describe a point's position on a circle with one coordinate, but the circle itself is bi-dimensional.

[Sergarr]

Sure, you can describe a point's position on a circle with one coordinate, but the circle itself is bi-dimensional.

nope

lrn2topology

[Sheb]

Yeah, you're right.

[Putnam]

Sure, you can describe a point's position on a circle with one coordinate, but the circle itself is bi-dimensional.

To elaborate on Sergarr's statement there: the circle itself is not what we're talking about, it's the surface, which is one-dimensional.

[Reelya]

It seems like a nice point to get back to the cosmology i linked.

Some properties of this proposed space - our visible universe as the 3D surface of a 4D black hole, can be inferred by looking at the lower-dimension equivalents.

e.g. one question in physics (maybe metaphysics even) is "where is the center of the universe". Now, our "everyday" common sense about euclidean spaces says there must be a center and an edge, but look at the lower-order models. You can navigate the circumference of a circle in two directions of it's 1-dimensional axis. Every point is equally the "center". The same for the 2-dimensional surface of a sphere. If it wasn't for the axis of rotation, there wouldn't be any concept of north, south, east, west. There is no true "center".

A 3-dimensional surface of a 4D hypersphere would be the same - a space in which you can move freely in 3-dimensions but there's no middle, and no edge, because it's curved back on itself.

Then there's flatness. As a circle or sphere grow larger, the surface, as seen locally approaches either a straight line or a flat plain. Similarly, a curved space as it grows larger approaches (but never quite reaches) the appearance of a flat euclidean space. i.e. the curvature of the universe is constantly falling to zero as it expands.

[Knit tie]

Reelya, my brain stopped working halfway through.

Then again, I struggle to understand the whole 'everywhere is the centre of the universe' thing. I KNOW about it, but my brain can't believe it.

It's quite simple, really. Our universe is like a surface of a sphere with an extra dimension added, so it is effectively borderless as you can get back to any point by going in any one direction for long enough, as you would do on this very planet by making a trip around the world. Except, again, there's an extra dimension. So there's no real centre of the universe as there are no borders of it to use as referral points.

[kaian-a-coel]

Think of it as the surface of a sphere. Coordinates 0/0 are completely arbitrary.
Earth rotates around an axis, so we have poles and an equator (thus latitude 0 is not arbitrary), but longitude 0 is still arbitrary.

[BurnedToast]

Reelya, my brain stopped working halfway through.

Then again, I struggle to understand the whole 'everywhere is the centre of the universe' thing. I KNOW about it, but my brain can't believe it.

It's quite simple, really. Our universe is like a surface of a sphere with an extra dimension added, so it is effectively borderless as you can get back to any point by going in any one direction for long enough, as you would do on this very planet by making a trip around the world. Except, again, there's an extra dimension. So there's no real centre of the universe as there are no borders of it to use as referral points.

What happens if I go "down".... wouldn't I reach the center eventually?

Or is it just a bad analogy because there is no spoon "down"?

....this comment started as a joke but now I'm really wondering.

[Putnam]

"Down" is a direction in the 4th spatial dimension, so you really can't go "down".

[Gentlefish]

"Down" is a direction in the 4th spatial dimension, so you really can't go "down".

...It's not 3rd dimension? I know 2D has forward, back, left and right. I though 3rd was up, down?

[Eagleon]

I've always liked the Matryoshka universe idea. It wouldn't have to be a star, though, just something on that level that resembles the Big Bang - something about ESA's Planck observatory's observations fitting the big bang predictions better, and I would simply ask them if they've ever seen a four-dimensional star collapse before, and whether they can imagine a universe with laws that just allowed big bang events to happen just whenever. Y'know, like some dude farts and our universe is created. The same one for each fart, because they're all the same, gas diffusion is funky like that in the fourth dimension. Cosmology brawls are fun to start/watch.

[Bauglir]

"Down" is a direction in the 4th spatial dimension, so you really can't go "down".

...It's not 3rd dimension? I know 2D has forward, back, left and right. I though 3rd was up, down?

"Down" in quotes here refers to the down you'd have to travel to reach the center of a 4-dimensional sphere from its surface. Probably we're looking for kata here.