do you posit that a 2D surface could never have any "boundaries"?
Number Nine said: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 balloon provides the analogy for the expansion of space. The surface of the balloon happens to be embedded in three dimensional space, but it doesn't have to be. Space is not embedded in anything.
Tim13 said: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 said:I take it you did not read the exposition at the link I gave you.
Tim13 said: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 said:Glad it was helpful. Several of the members here helped me put it together for exactly this purpose.
Tim13 said: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?
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.twofish-quant said:Lots of things are possible. That's why you have to do observation. You will get nowhere if you just sit in a room and try to speculate about what the universe is like. What you need to do is to ask yourself "if the universe was a doughnut, what would I see?" and then point your telescope to see if you actually see it.
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.I'm interested to understand why he thinks it's wrong.
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.This is the type of "useless word games" that I don't think are useful. The problem is that words are tools that describe things, and the words and concepts we use are those that describe our daily life. The universe can play by very different rules, which makes trying to "figure things out" by "word games" not useful. When you study cosmology, ultimately you have to use the language of math which turns out to be able to describe things that we can't describe in our daily life.