That is not quite true. While the portion of the universe that we can see does indeed make a sphere (with a radius of c*t[sub]age of universe[/sub]), the global geometry of the universe is somewhat unknown. We know that space and time are geometrically connected, so the shape of the universe is intrinsically 4-dimensional, but what type of 4D object is still debated.Since the church seems to go by classical hellenistic philosophy does the church believe what Plato said about the universe being in the shape of a dodecahedron? The consensus among modern physicists is that it’s round or spherical.
How in the world did Plato come to that conclusion through reason?Since the church seems to go by classical hellenistic philosophy does the church believe what Plato said about the universe being in the shape of a dodecahedron? The consensus among modern physicists is that it’s round or spherical.
I’m not thoroughly sure of Plato’s geometic solids. He said either the universe was in the shape of a dodecahedron or was created by one.How in the world did Plato come to that conclusion through reason?
Kinda both I think.Is this a philosophical question or a scientific one?
The Church doesn’t decide scientific questions.Kinda both I think.
Actually, it has.The Church doesn’t decide scientific questions.
If the universe is a 4D sphere, then it has no edge, and if one traveled in a straight line, one would simply circumnavigate it and come back to the starting point.I think the universe is round like the Earth, and if one were able to travel all the way to its edge, and “poke one’s head through,” like on those old woodcuts, he’d poke his head into the bottom of the ocean of the “Heavenly Earth.” This makes sense of Genesis where it says the heavens are like a dome, a firmament, and that they separate waters above from waters below. Perhaps, also, our Earth is hollow and has a universe inside of it with a “Hell Earth” at its center. This makes sense of the idea of “astral planes.” Astral means stars, and the astral below the Earth would be the universe within the Earth, the “Hell” universe.
The whole thing could be like an onion. This makes sense of Jacob’s vision of the ladder with angels “ascending and descending” on the ladder. The rungs of the ladder are different worlds, contained all within one another like the layers of an onion, so that after our time here on this “Middle Earth” is finished, we will either get a whole lot bigger (heaven) or a whole lot smaller (hell).
Yes I have a lot of time on my hands to think.
I will try my best…Would anyone like to explain the Poincare conjecture about the 3-sphere and its relevance to the shape of the universe?
My only stipulation is that any such explanation be intelligible to a wider audience than just professional mathematicians. The “wiki” explanation unfortunately fails this test.
I remember the church had something to do with Galileo’s imprisonment for this idea that the earth wasn’t at the center of the universe.Actually, it has.
Peace,
Ed
Not quite, but don’t want to mess up the thread.I remember the church had something to do with Galileo’s imprisonment for this idea that the earth wasn’t at the center of the universe.
I think you may be confusing yourself, as well as others who read this. An n-sphere is the surface of an n+1-dimensional manifold (sometimes called an n-ball).Not quite, but don’t want to mess up the thread.
The reason it is a 1 sphere = circle has 1 dimension: a line wrapped around and meeting itself. If you want a 2 dimension circle, we call it a disk.
2 sphere = sphere because we are looking at the surface. If you want a 3 dimensional sphere, we call it a ball.
3 sphere = universe in that we are looking at the surface, ie where we live, 3-d space. We live on the ‘surface’ of the 3 sphere. It is warped into a 4th dimension.
Of course, if you want to use modern physics, we are not looking at space, but space-time so the universe 4d, and the sphere is a 4 sphere in 5 dimensions.
Remember the sphere started out with a 0 diameter at the BIG bang!!!
More accurately, the surface of a disk-a 2d ball. The circle is 1 dimensional.I think you may be confusing yourself, as well as others who read this. An n-sphere is the surface of an n+1-dimensional manifold (sometimes called an n-ball).
A 1-sphere is the surface of a circle (a 2D object) and requires only the angle theta to define a unique point on this surface (well, unique within the range 0 to tau).
I don’t see any difference between what you said, and what I said. But I’ll grant that what you said is also accurate.A 2-sphere is the surface of a ball (a 3D object) and requires the angles theta and phi to define a unique point on the surface.
Our universe (a 4D object) is a 3-sphere because we live on the surface of time and require the positions x, y & z (or, continuing the spherical trend, r, theta & phi) to define a unique point.
I do not think that a solid disk has an n-ball or n-sphere designation. A circle is a 2D object, it requires radial and an angular (or, if you prefer Cartesian, x & y) coordinates; the topology, however, requires only the surface of the object.More accurately, the surface of a disk-a 2d ball. The circle is 1 dimensional.
For starters, you said that we live in a 4D world which means a 5-sphere. This is false. You also said that our 3D world is “warped into a 4th dimension.” This is also false, we live in a 4D world.I don’t see any difference between what you said, and what I said. But I’ll grant that what you said is also accurate.
From en.wikipedia.org/wiki/Ball_(mathematicsI do not think that a solid disk has an n-ball or n-sphere designation. A circle is a 2D object, it requires radial and an angular (or, if you prefer Cartesian, x & y) coordinates; the topology, however, requires only the surface of the object.
As to the dimension of a circle, from mathworld.wolfram.com/Dimension.htmlIn mathematics, a ball is the space inside a sphere. These concepts are defined not only in three-dimensional Euclidean space but also for lower and higher dimensions, and for metric spaces in general. A ball in the Euclidean plane, for example, is the same thing as a disk, the area bounded by a circle.
To see how lower and higher dimensions relate to each other, take any geometric object (like a point, line, circle, plane, etc.), and “drag” it in an opposing direction (drag a point to trace out a line, a line to trace out a box, a circle to trace out a cylinder, a disk to a solid cylinder, etc.). The result is an object which is qualitatively “larger” than the previous object, “qualitative” in the sense that, regardless of how you drag the original object, you always trace out an object of the same “qualitative size.” The point could be made into a straight line, a circle, a helix, or some other curve, but all of these objects are qualitatively of the same dimension. The notion of dimension was invented for the purpose of measuring this “qualitative” topological property.
If you are familiar with the general theory of gravity, gravity is an effect of the warping of a 3D space into a 4th dimension. If you look at the world dynamically, you get a space-time of 4 dimensions, warped into a 5th dimension to produce gravity.For starters, you said that we live in a 4D world which means a 5-sphere. This is false. You also said that our 3D world is “warped into a 4th dimension.” This is also false, we live in a 4D world.