Is there a problem in assuming the universe has a boundary?

Tim13

Hmm. I apologize. I am not sure I understand your point. However I think your point may only add to mine in that the balloon analogy is potentially misleading. Obviously a real balloon is a 3D object and so if it was intended to be a 2D analogy for the universe then I did misunderstand "completely". But please tell me if I understand you correctly - do you posit that a 2D surface could never have any "boundaries"?

Plus, isn't the real universe still 3D even if it is a little flat? Hence the potential confusion when the original topic was about the real 3D universe and whether there is a problem with assuming it has a boundary?

Number Nine

No, he stated that the surface of the balloon which is two dimensional surface, has no boundary, which is true. The expansion of the surface of the ballon provides the analogy for the expansion of space. The surface of the ballon happens to be embedded in three dimensional space, but it doesn't have to be. Space is not embedded in anything.

Tim13

That is probably what he meant. Yet if he believes that space is relatively flat but not strictly 2D (perhaps Euclidian and 3D) then it only adds more evidence that the balloon analogy is potentially misleading for numerous reasons.

Plus, my question was a little more nuanced. I was asking if he posits that a 2D surface could never have any boudaries. I wasn't limiting my question to only 2D surfaces which happen to be balloons because it is possible that he was making a general statement about 2D surfaces. And the last time I looked out my window the obsevable universe isn't shaped like a balloon.

phinds

I take it you did not read the exposition at the link I gave you.

Tim13

I confess that I only skimmed it and didn't fully understand the exposition at the link you gave. I just now went back and reread it. It does a much better job of explaining the potential confusion created by the analogy than what I was attempting to convey. I initially misunderstand the analogy too for some of the reasons stated in the article. Thanks.

phinds

Glad it was helpful. Several of the members here helped me put it together for exactly this purpose.

Tim13

I apologize that I didn't read it more thoroughly earlier. I would have saved myself and others from unnecessary key strokes. Is there a collection of such expositions for different topics on this website?

Mark M

This article is frequently recommended, it was written in Scientific American:

http://www.mso.anu.edu.au/~charley/p...DavisSciAm.pdf

Note that the first page is blank, scroll down.

And two very good FAQs that you may find helpful are these:

http://www.astro.ucla.edu/~wright/cosmology_faq.html
http://preposterousuniverse.com/writ...rimer/faq.html

PeterJ

Then you have to sit in a room and and speculate on the meaning of what the telescope has revealed. I really cannot get this idea that thinking is useless compared with experiment.

I'm afraid I can't remember the discussion. I could not comment much on it anyway. I just took his proposal to mean that physics allows for the possibility that he is right. It intrigued me that for Smolin extension is a mystical illusion while for mystcism it is a scientific one.

This seems unfair on Leibnitz. He wasn't bad at mathematics. But the language of maths has as much trouble with fundamentals as any other language. His point was simply that if there is a fundamental, non-dependent or original phenomenon, then our reason concludes it cannot be extended. If it is extended, then the universe breaks the laws of thought and is paradoxical. He does not claim to know which it is. There is a connection with Russell's paradox so it is not an entirely non-mathematical point. As I see it, he is saying that the original phenomenon cannot be manifest for the same reason that the set-of-all-sets cannot be manifest in naive set-theory. Logic and reality would be in total accord.

I don't thing we need any experiments to form a view about this. It seems to be significant that the idea of a boundary to the universe gives rise to contradictions and does not compute.