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Hilbert's Hotel


viridia
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Hi all,

 

On my Facebook I have added one of my friend's fathers, who was our history teacher back at private middle school and also the youth pastor for the adjoining church. He doesn't update his statuses regularly but the ones he does post make me roll my eyes--and he just posted one that both confused me but at the same time, I felt like I understood it and it just didn't make any sense for what he was saying.

 

"Can someone explain Hilbert's Hotel to me- somehow it proves the existence of God but I don't get it."

 

Someone comments, "Hilbert's Hotel has an infinite number of rooms, each one of which is occupied. The hotel is full, and yet it still has vacancies because while infinite number of guests occupy infinite number of rooms, should a new guest show up the guest in room 1 can be moved to 2, 2 to 3, and so on, to accommodate the new guest. It doesn't directly prove the existence of God, but it proves the existence of infinity thus making the existence of God a logical possibility. : )"

 

He responds, "Doesn't it have something to do with non-infinity- ie:there can't be an infinite number of something/anything? But if the hotel keeps adding rooms doesn't that prove infinity? If there can be an infinite number of something than that doesn't help prove the existence ofGod. If there can't be infinite numbers of something then the universe must be limited or finite- thus necessitating a creator- right?"

 

Someone else posts, "No, uncle B it does the exact opposite. It says that while something may appear to be non-vacant, it's actually always vacant.

Another way of putting it is no matter if you double a number (odd or even) it comes out even. So it leaves out all the odd numbers to be vacant for spots. Always making everything infinite."

 

I am...so confused. But then, on the other hand, when I think I understand it...I wonder how that proves the existence of a god, orrr how a hypothetical situation can prove something such as infinity...What? o.o

 

Sorry if I sound a bit uneducated haha. Am I just completely missing something? Do you guys get this? O.o

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Here's how it supposedly connect:

 

Hilbert's Hotel Paradox is the support to why an infinite past cannot exist. (However, there are some problems with the paradox that makes it not quite a proper paradox.)

 

And if infinite past does not exist, then there must have been a beginning to time (and space).

 

And then, based on the Kalam argument, something that begins must have a cause (an unsupported assumption).

 

And since the only cause that can be non-temporal and non-caused itself is God (or so we are to assume), the God must be the first cause to everything.

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...but it proves the existence of infinity...

Hilbert's Hotel doesn't prove shit since it doesn't actually exist. I don't think most people need an imaginary hotel in order to imagine infinity. What a theoretical infinity might have to do with proof of any gods escapes me, however.

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That said, there are infinities that are remarkably inconsequential in real life. Divide 1 by 9 and you get 0.11111111111 (and so on, to infinity). It's an infinitely long number.

 

But who cares? Contrary to what people might conclude instinctively, of course it's not infinitely big - painfully obvious it's not even very large, is it? Clearly less than a humble 0.2 ;)

 

The concept of infinity can easily boggle one's mind but that does not mean that it can shake the foundations of the real world.

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