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 Forum index » Archive » Archive: General » ARG: Sable & Shuck
Hilbert's Hotel
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bailey
Kilroy

Joined: 17 Jan 2005
Posts: 2
Location: New Orleans, LA USA

 		Hilbert's Hotel
it didn't do much for me, but this page might put something together for someone else...

http://www.anselm.edu/homepage/dbanach/infin.htm

I apologize in advance if someone already found this.

PostPosted: Wed Jan 19, 2005 3:26 pm
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Misfitt
Boot


Joined: 12 Jan 2005
Posts: 39
Location: Miami, FL

 		trans-what? what-finite? what-what?
If we have to figure out or understand the theory of TRANSFINITE NUMBERS to solve this. . .I'm in a lot of trouble.

PostPosted: Wed Jan 19, 2005 6:21 pm
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bailey
Kilroy

Joined: 17 Jan 2005
Posts: 2
Location: New Orleans, LA USA

 		i don't think we have to figure them out. i was kinda grasping at straws and googling to see what i could come up with. before i found that page, i had no clue hilbert's hotel was anything other than something the pm's came up with. when i saw it, i just thought about the math connection. i'm not nearly smart enough to get all of that.

PostPosted: Wed Jan 19, 2005 7:56 pm
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Meak
Decorated

Joined: 07 Jan 2005
Posts: 230
Quote:
THE ALEFS

The famous mathematician David Hilbert used to illustrate his popular lectures with stories about a hotel with infinitely many rooms.8 This mythical hotel, usually called Hilbert's Hotel, is supposed to have omega rooms: Room 0, Room 1, Room 2,... , Room n, and so on. As in the last section, it is convenient to start counting with 0.

To fix the ideas, I have drawn a picture of Hilbert's Hotel in Figure 45. In order to fit it on the page, I have assumed that each floor is equipped with a science-fictional space condenser, a device that makes each succeeding story two-thirds as high as the one before. The shrinking field also affects the guests. Thus, although the ceilings on Floor 3 are only two or three feet high, the space condenser on that story shrinks the guests to one or two feet), and they are perfectly comfortable. 1 will leave it as an exercise for the reader to check that if the first floor is ten feet high, and each successive floor is two- thirds as high as the one before, then the total height of the hotel's stories is thirty feet.

One of the most paradoxical things about Hilbert's Hotel is that even after it fills up, more and more people can be squeezed in, without making anyone share a room! Say, for instance, that guests have arrived, and every room is occupied with a guest n in each Room n. Now, say that one more guest arrives: Guest . How to fit him in?

Easy! We put Guest in Room 0, which is emptied by moving Guest 0 to Room 1, which is emptied by moving Guest I to Room 2, which is emptied by . . .

Fine! But what if there had been an infinite number of new guests? Even such a procession of + guests could be lodged in Hilbert's Hotel.


--------------------------------------------

Um.... I have no idea what that means... but it is so exactly like the description of Hilberts we get at Pathway Travel, it makes you wonder how much further mathematics we need to know in order to solve this ARG!

What I find most interesting is the reference to w squared. This kind of fits with the note left in the guest book about room 441 being a perfect square! I dunno, clutching at straws maybe?

It also explains about ALEF, and it's somewhat infinite properties, which also comes up on the Sable and Shuck site.

I really hope the PM's aren't sitting back watching us struggle with this.....

[/quote]

PostPosted: Wed Jan 19, 2005 8:24 pm
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tinneke9
Veteran

Joined: 04 Jan 2005
Posts: 82
Location: Belgium

 		by the way i can't see what math has to do with stella,

i mean i'm pretty good at maths, but this?... Confused
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PostPosted: Thu Jan 20, 2005 9:52 am
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