helene_t, on Apr 5 2009, 06:22 AM, said:
PassedOut, on Apr 4 2009, 11:46 PM, said:
W.r.t time, do you mean "finite" or do you mean "bounded"? The set of real numbers between zero and one is infinite but bounded. If the real numbers (or some other dense number set) is an accurate model for the timeline, then the set of time points from the big bang to the big crunch is infinite, but bounded.
I may be wrong but I can't see how boundedness could be a feature of time as it "really" is. Suppose your model of the world includes a real variable "time" which runs from -1 to +1, and my model includes a variable "taym" which is defined o.t.b. of your "time" by the equation
taym = ArcTan (time)
Then time is bounded while taym is unbounded, and yet they describe the same physical thing. The laws of nature which involve time will mathematically look different from those involving taym, One could dismiss one of the models because it is too "ugly", i.e. does not have the symmetry properties physicists like, but both models are equally valid and describe the same physics.
W.r.t finite vs infinite, I don't think our brains which can perceive only a finite number of bits can differentiate between infinite and "very large number", but if one believes in a truth "out there" which is independent from our perception, then it could be a meaningful question whether some set in the real world is finite or not. I am not saying it is a meaningful question (someone with more insight in physics might dismiss it), but from a pure philosophical point of view I don't see why it would have to be meaningless.
Yes, I should have said "bounded," but was trying not to change terms within the actual discussion. And the phrase "infinite hotel" was too simple also, but should have referred to the infinite number of rooms in Hilbert's hotel.
When using analogies to make a point, the strength of an analogy depends upon the similarities between the things being compared. Numbers do provide an excellent representation of time, which is why I used numbers to explain why it could never be logically impossible for time to be infinite (unbounded).
However, Jimmy argues (as he must) that numbers do not provide an accurate representation of time. Rather, he claims that time is more like a hotel, which cannot have an unlimited number of rooms. I think that the hotel analogy falls down in many respects, but there you are.
On the other hand, we can't assume that time as it "really" is will always be mapped precisely by our number system at the most extreme moments of the universe.

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