Could someone elaborate on this aphorism?

Kyriakos

Kyriakos

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"The cosmos* is a sphere, the exact center of which is everywhere, and its circumference does not exist".

It is an aphorism uttered by a number of people, mostly remaining the same, throughout history. From Parmenides, to Plato, To Pascal and before him others.

*Sometimes instead of cosmos, it is written: God.

I was aware that some ancient greek thinkers and schools of thought supported the idea that the sphere is the most perfect form (possibly because every point of its exterior has an equal distance from its center) and thus it is divine. But i do not really understand that quote. Why does it have no circumference?
 
well once you "impose" a circumference you make one point the center of the circle... in an infinite Universe ... all points are the center
with an infinite God ... like wise

and take this with a grain of salt
 
Yes, however does a shape having no center (and this meaning that the center is at every position of space) still count as a sphere? Would it perhaps be an older way to say "the 4-dimensional object which to us seems like an infinite sphere"?

Edit: i found this supposed presentation of a hyper-sphere. I am not sure if it is at all valid, but it is merely a sphere which decreases and increases in size to infinity. However even if it has some merit, obviously this is just a 3d presentation of the elusive 4d object. Still seems a bit ominous to think about (i recall Pascal's "the horrible sphere" quote) :)

4dmat09.gif
 
"The cosmos* is a sphere, the exact center of which is everywhere, and its circumference does not exist".
Click to expand...

apparently it dose still count as a sphere ....


re your edit... it still has a center and a circumference... i think that the saying is not exactly trying to express a geometry or mathematical principle ...
one only has to look at Platonic solids to see that is handled in a different way

http://en.wikipedia.org/wiki/Platonic_solid

All other combinatorial information about these solids, such as total number of vertices (V), edges (E), and faces (F), can be determined from p and q. Since any edge joins two vertices and has two adjacent faces we must have:

The other relationship between these values is given by Euler's formula:

This nontrivial fact can be proved in a great variety of ways (in algebraic topology it follows from the fact that the Euler characteristic of the sphere is 2). Together these three relationships completely determine V, E, and F:

Note that swapping p and q interchanges F and V while leaving E unchanged (for a geometric interpretation of this fact, see the section on dual polyhedra below).
Click to expand...

not really what the saying is about... tho many gods (myself included... have used this ...with dodechedrons and icoshaedrons to smite some wayward hero down)
 
First of all, it doesn't make sense to my scientifically-minded self that a sphere doesn't have a circumference. However, in a philosophical sense, I'm reminded of a song in the "Lost Horizon" musical: "The world is a circle without a beginning, and nobody knows where it really ends..."

To measure the circumference, you have to decide where the beginning is. And perfect things don't have beginnings, because that implies that there was something before that was imperfect.

The ancient scientists and philosophers may have believed in things such as perfect solids, and this notion kept on until we started learning by actual observation in the Renaissance. The Universe (Cosmos, if you prefer that term) is clearly not perfect. But that's what makes it so fascinating!
 
Spheres without circumference and having themselves as center?
What's the definition of sphere?
Still, if you take one point in an 'infinite' sphere, all points on the circumference are just as far away of it - infinitely far away. THat holds true for every point on that sphere.
 
As I understand it, the observable universe is more or less spherical with boundaries defined by the distance light has traveled in the ~13.8 billion years since the beginning of time*. The actual universe is of unknown size but certainly larger than this. It could be just barely larger, it could be a billion times the diameter; we will never know because light has not had enough time to reach our position.

*Its radius is larger than 13.8 billion light years because everything distant has been receding away from us at an accelerating pace, so a light source whose light took 13 billion years to get here has been moving away from us in the meanwhile, leaving it farther away (~40 billion light years, IIRC) in present-day distance.
 
As I understand it, the observable universe is more or less spherical with boundaries defined by the distance light has traveled in the ~13.8 billion years since the beginning of time*. The actual universe is of unknown size but certainly larger than this. It could be just barely larger, it could be a billion times the diameter; we will never know because light has not had enough time to reach our position.
Click to expand...

I think the OP isn't referring to the universe, but to the universe and all what 'surrounds' it.
I don't think the OP is
 
actually the 'universe' is in the shape of a saddle.
I cant quote the math, so dont ask
 
What the hell is the "universe" expanding into?!
 
Kyriakos said:
"The cosmos* is a sphere, the exact center of which is everywhere, and its circumference does not exist".
Click to expand...

The center and circumference do not exist because the cosmos is not a sphere - it doesn't have a boundary.

This guy's just throwing in the word sphere in there in an attempt to create a witty zen-like paradox so that he can appear wittier and cooler. In that sense the aphorism he uses could be viewed as being effective, but in every other sense it is likely a complete failure.
 
Valka D'Ur said:
Source? I've heard this, but was under the impression that it's a theory, not (yet) proven for a fact.
Click to expand...

The problem is that you need to understand the math being used, to understand why.
I am not that good with math. It has to do with time/space expansion
 
It has to do with the amount of mass/energy in the Universe and the speed at which its expanding. From what I vaguely understand there are 3 possibilities, and based on what we think is contained in the Universe and how fast its expanding, the shape of the Universe "must" be a saddle - meaning we're all on a horse.
 
Chiteng said:
The problem is that you need to understand the math being used, to understand why.
I am not that good with math. It has to do with time/space expansion
Click to expand...
I asked for a source, not math. There are people here who can explain the math part.
 
I see you haven't been here very long, so I'm going to explain one of the customs of this forum: When you make a claim that is obviously not based on your own firsthand observations or knowledge, it is entirely fair for other posters to ask you for a link to where you read/heard this claim. It's up to YOU to provide that link. Saying "google it" or the equivalent isn't good enough.

You made the claim. Now back it up.
 
So actually no one knows.
 
Sort of. Observations have shown it to be "flat" (i.e. Euclidean geometry works) to within experimental error, not counting spacetime distortions caused by massive objects. But it might not truly be completely flat.
 
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