[QUOTE=xilman;367539]Ok, so your model also violates the law of the excluded middle.

Curious.[/QUOTE]

No, of course not. For once I can say that you misunderstood.
The Universe is neither open nor closed because it uniquely
is both - it is what is called open-closed. This unique
topological space - a three-sphere Riemann-folded everywhere
through a fourth spatial dimension - satisfies the definitions
of both open and closed spaces, because of the absence of
any border or boundary.

The law of excluded middle is fundamental to logic.

[QUOTE=davar55;367540]The Universe is neither open nor closed because it uniquely
is both - it is what is called open-closed. This unique
topological space - a three-sphere Riemann-folded everywhere
through a fourth spatial dimension - satisfies the definitions
of both open and closed spaces, because of the absence of
any border or boundary.[/QUOTE]

If it was clopen it would be both closed and open, so your statement was not correct.

[QUOTE=davar55;367540]No, of course not. For once I can say that you misunderstood.
The Universe is neither open nor closed because it uniquely
is both - it is what is called open-closed. This unique
topological space - a three-sphere Riemann-folded everywhere
through a fourth spatial dimension - satisfies the definitions
of both open and closed spaces, because of the absence of
any border or boundary.

The law of excluded middle is fundamental to logic.[/QUOTE]

[QUOTE=CRGreathouse;367558]If it was clopen it would be both closed and open, so your statement was not correct.[/QUOTE]

I'm afraid you're missing the logic of my explanation. Being open-
closed means being open AND closed, not just one or the other.
Hence not open. Hence not closed, Just open-closed.

[QUOTE=davar55;367564]I'm afraid you're missing the logic of my explanation. Being open-
closed means being open AND closed, not just one or the other.
Hence not open. Hence not closed, Just open-closed.[/QUOTE]

:huh: :lol:

[QUOTE=CRGreathouse;367582]:huh: :lol:[/QUOTE]

If that's funny, re-check out basic topology.

[QUOTE=davar55;367602]If that's funny, re-check out basic topology.[/QUOTE]

I doubt there are many on this thread who know less about topology than you.

[QUOTE=CRGreathouse;367623]I doubt there are many on this thread who know less about topology than you.[/QUOTE]

You'd be way wrong, of course.

[QUOTE=davar55;367527]... but the Universe as a whole is neither open topologically nor closed topologically, so defining the entropy of the whole Universe "might" allow for its entropy to be constantly increasing without ever changing (see earlier post).[/QUOTE]Let's return to thermodynamics rather than topology.

Your statement above appears contradictory. In particular, "constantly increasing" seems at odds with "without ever changing".

As I understand the English language, "increasing" implies "changing".

Care to go into greater detail to resolve my confusion?

[QUOTE=xilman;367630]Let's return to thermodynamics rather than topology.

Your statement above appears contradictory. In particular, "constantly increasing" seems at odds with "without ever changing".

As I understand the English language, "increasing" implies "changing".

Care to go into greater detail to resolve my confusion?[/QUOTE]

Would you do the decency of examining the whole post you
partially quoted? I believe I said entropy for the whole universe
should be defined as a constant, infinite value. Hence when it
increases, it stays the same.

[QUOTE=davar55;367443]Which topic? Cosmology? The monograph? Entropy explained for
the Universe as a whole as being a constant infinite value hence
not producing any contradictory explanatory value, such that it
can always increase if you like and never produce a thermal
equilibrium? The shape and size of the Universe? The defunct
big bangup theory?

There's a whole universe of things to discuss.[/QUOTE]

Sorry, this was the post where I said that.

[QUOTE=davar55;367564]I'm afraid you're missing the logic of my explanation. Being open-
closed means being open AND closed, not just one or the other.
Hence not open. Hence not closed, Just open-closed.[/QUOTE]

Perhaps the universe is ajar.