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dehammer you are confusing English and mathematics. And I might point out to you that you have already stated, on numerous occassions, that you are good at math ... so why the sudden inability to discuss basic math concepts.

Do you even know what the word "EDGE" means in mathematics? If not please look it up.


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there are two discussions going on, one uses math, the other plain english. the point where the discussion of the edge came it, had nothing to do with math, only english. therefore the mathematical definition of edge is not required for this part of the discussion. please pay attension.


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Like I've said before I'm no mathematician, but according to This Website amoung others "For an undirected graph, an unordered pair of nodes that specify a line joining these two nodes are said to form an edge"

Also per wikipedia : "In graph theory, a graph consists of a set of connections between objects. Each object is a vertex. Each connection, between two vertices, forms an edge, or arc "

So wouldn't a line connecting two vertices on a sphere be considered an edge or arc?

Of course does this mathematical definition of an edge have any meaning in reference to the "edge" of the universe?

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The universe having an edge is all about mathematics. No one seriously believes that if you go in a straight line far enough you will run into a wall that can be tagged with grafitti.


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No, there is no wall (as far as we know), but there is a theory that there is nothing outside of the universe, that space expands to hold the universe. If this theory is correct, there is someplace that there is no space at all. Seems like someone recently told me that there was nothing outside of the material of the big bang, that that was all of existance as space expanded for the big bang. Wonder who told me that. If the universe is actually finite physically, then there is an edge to it. if its infinite, then there is no edge. There is nothing mathematical about that.


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Quote:
Well measuring this purely mathmatical fractal
Oh, OK we are talking theoretically, not real beaches, planets or universes.
Thanks anyway I did kinda get the concept but that clears it up.

Quote:
Sure, as soon a I can learn to walk on air, Ill show you the edge
Why go to all that bother? Just explain where the edge of the surface of a sphere is and I'll be happy. Come up with a half decent answer to this and I'll forgive all your previous misdemeanours.
Hint...remember not to leave the surface.


Eduardo
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D.A.,
"It is, however, possible, to have infinite complexity in finite space."

Elaborate please. While it's not neccessary to
go to fractals to make the point with regard to
the mathematical concepts, (there are an infinite
number of points on a line of any length), doesn't the term 'complexity in finite space` imply that
something other than non-material concepts are
under discussion?.

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Quote:
Originally posted by Eduardo:
[QUOTE] Why go to all that bother? Just explain where the edge of the surface of a sphere is and I'll be happy. Come up with a half decent answer to this and I'll forgive all your previous misdemeanours.
Hint...remember not to leave the surface.
actually from the surface its impossible to find an edge except perhaps in some high level math formula. from inside the sphere, OTOH, the edge is the surface. Since our earth includes the atmosphere, we are inside the greater earth sphere. granted most people only think of the earth's hard material surface as the globe, but this is not the airless moon.

actually the same can be said of the universe if its a physically finite entity. If space only exist where it has expanded the universe to, then there would be an edge where there is nothing beyound. It would be physically impossible to go into this place as there is nothing there to go into. Ive read several sf books that used that as their primise. quite interesting reading, if a little on the farside.


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dehammer wrote:
"but there is a theory that there is nothing outside of the universe"

Your words are correct but I'm not sure you understand what they mean. This is not in any way infer an edge.

Pragmatist asks:
"doesn't the term 'complexity in finite space` imply that something other than non-material concepts are under discussion?."

Not as I was intending it when I wrote what I did. My point was that it is possible to have infinite complexity within a finite universe. Nothing more.


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Quote:
actually from the surface its impossible to find an edge
well done dehammer, you're getting there.

A one dimensional line curved into a circle has no end.
A two dimension plane warped into a sphere has no edge.
A three dimensional volume (or universe) warped into a hypersphere has no edge.

I'm not saying that's how it is, just that it is possible for a universe to be finite in volume and have no edge.


Eduardo
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Da, please explain, if space is expanding and there is no edge, where does it expand into.

ed, the circle may have not end, but from having stood inside of one, i can tell you the circle is the edge.


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Quote:
Originally posted by dehammer:
Da, please explain, if space is expanding and there is no edge, where does it expand into.
Who said it has to expand into anything?

It is expanding in the same way a balloon expands when you blow air into it.

Quote:
Originally posted by dehammer:
ed, the circle may have not end, but from having stood inside of one, i can tell you the circle is the edge.
The circle is the edge of what?

Not the line that's for sure, the circle is the line.


Eduardo
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Quote:
Originally posted by Eduardo:
Who said it has to expand into anything?

It is expanding in the same way a balloon expands when you blow air into it.
The balloon expands into the air surrounding it. There is air inside and there is air outside, the balloon is the edge of it.

Quote:
Originally posted by dehammer:
The circle is the edge of what?

Not the line that's for sure, the circle is the line.
try looking at a circle from the center of that circle. what do you see? a line that seperates you from what is outside of it. If that circle is your home (imagine a two d world) and the circle separates you from empty space, that line is the edge.


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dehammer wrote:
"Da, please explain, if space is expanding and there is no edge, where does it expand into."

The error in your thinking is wholly contained within your question. It IS NOT expanding INTO anything.


What is changing is the space-time metric. The apparent distance between objects that are not gravitationally bound.

Now how dehammer do we measure distances between galaxies? We measure how long it takes light to get from point A to point B.

If the time increases we say the space is larger.

If the speed of light slow down we say the space is larger.

There is no difference between the two statements. Expansion is not expansion in the sense that the public thinks of it when talking about their waistlines. It is an entirely different concept. And one I wish you would make a good faith effort to understand.


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dehammer wrote:
"The balloon expands into the air surrounding it. There is air inside and there is air outside, the balloon is the edge of it."

You just wrote "air outside."

Look up there at your sentence and see it. That is exactly what you wrote.

We are talking about the universe.

There is no outside.
There is no outside.
There is no outside.

Will it help you if I say it a few more times?

There is no outside.
There is no outside.
There is no outside.

Your analogy is meaningless.


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dehammer here's an explanation of what I think Morgan is talking about in reference to the universe not expanding into anything via wikipedia :

"In the analogy, the two dimensions of the balloon do not expand "into" anything since the surface of the balloon admits infinite paths in all directions at all times. There is some possibility for confusion in this analogy since the balloon can be seen by an external observer to be expanding "into" the third dimension (in the radial direction), but this is not a feature of metric expansion, rather it is the result of the arbitrary choice of the balloon which happens to be a manifold embedded in a third dimension. This third dimension is not mathematically necessary for two-dimensional metric expansion to occur, and the ant that is confined to the surface of the balloon has no way of determining whether a third dimension exists or not. It may be useful to visualize a third dimension, but the fact of expansion does not theoretically require such a dimension to exist. This is why the question "what is the universe expanding into?" is poorly phrased. Metric expansion does not have to proceed "into" anything. The universe that we inhabit does expand and distances get larger, but that does not mean that there is a larger space into which it is expanding."

Not sure that I entirely grasp it though, can someone tell me what "surface of the balloon admits infinite paths in all directions at all times" means?

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that is one theory, but there are others, and it is only a theory.


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There are no other theories if you ask 99% of all astrophysicists. I know that because I have one in the family that just finished working at the Gemini Observatories (Cerro Tololo Inter-American Observatory in Chile and WM Keck in Hawaii).

And while I won't compromise her privacy her picture is on page 46
http://www.noao.edu/noao/noaonews/jun06/pdf/86news.pdf#search=%22%22Anne%20Sweet%22%20and%20%22Hawaii%22%20and%20%22observatory%22%22

You care to disagree with her feel free to use a search engine and produce some links that support your belief for this elistist extremist and the rest of those at SAGG that care about science. But do understand that anything I can't answer ... I will send her way ... so please not puff or bluff.


DA Morgan
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dehammer, I shall say this only once...
you might find this hard to believe...but...
I like you... I like that you question things...
but please ... listen... listen to what people say...we are not fighting you ... we are trying to show you the way...


Eduardo
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im just saying that scientist, even want to be scientist should not totally block out the unusual ideas and views simply because they are different.

It is a theory, it is a well accepted theory. it fits all the known data, but there is a lot of data we dont have yet. Why close the idea out just because it does not fit what you expect it to be.

heres an idea, perhaps a little out there. they say the universe is made up mostly of dark matter, yet this dark matter does not clusters of matter like galazies. It is also not drawn to the galaxies like matter is. What if the dark matter is repelled by matter, but gravity. Its own gravity would keep it from forming things like rocks and planets and suns. It would repell and be repelled by matter. If this is true, space is not expanding, galaxies are being push farther away by the dark matter. This would explain why the fartherest galaxies are moving faster since there is dark matter behind them, but little in front. This may be a wild theory, but its there. can you say its not possible?


the more man learns, the more he realises, he really does not know anything.
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