
MindTrap
Disembodiedvoice
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Re: Mathematical Explanation... [Re: GazzBut]
#1840108  08/22/03 06:49 PM (19 years, 5 months ago) 


Quote:
GazzBut said: You go to a hotel with infinite rooms and ask for a room but the receptionist tells you all the rooms are full (infinite amount of guests!) how can you get a room in the hotel??
Brute force?

Diploid
Cuban
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Posts: 19,274
Loc: Rabbit Hole

Re: Mathematical Explanation... [Re: Deiymiyan]
#1840966  08/22/03 11:07 PM (19 years, 5 months ago) 


Given a = b:
a^2 = ab
a^2 + a^2 = a^2 + ab
2a^2 = a^2 + ab
2a^2  2ab = a^2 + ab  2ab
2a^2  2ab = a^2 ab
2(a^2 ab) = 1(a^2  ab)
2 = 1
QED LOL!!
 Republican Values: 1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.
4) We need a smaller, lessintrusive government.

lucid
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Re: Mathematical Explanation... [Re: GazzBut]
#1840985  08/22/03 11:13 PM (19 years, 5 months ago) 


NComplete Problems and the Combinatorial Explosion... Good Stuff...let me know if u have a solution, I'll give ya 5 bucks fer it
 "nomind unthinks nothought..."

lucid
Jack's AlteredConsciousness
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Re: Mathematical Explanation... [Re: lucid]
#1841014  08/22/03 11:19 PM (19 years, 5 months ago) 


^^ Look up "The traveling Sales Person Problem" and the entire class of NComplete problems...
 "nomind unthinks nothought..."

Xibalba
Stranger
Registered: 05/14/00
Posts: 2,114

Re: Mathematical Explanation... [Re: Diploid]
#1841128  08/22/03 11:58 PM (19 years, 5 months ago) 


Edited by Xibalba (09/30/05 09:15 AM)

Deiymiyan
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Re: Mathematical Explanation... [Re: Deiymiyan]
#1841252  08/23/03 12:48 AM (19 years, 5 months ago) 


Wonderful contributions from everyone!
Anyone want to talk some more on the subject...?
The String theory sounds intriguing... I've read that it appears to have a "dead end" .. Seems to lap with Supergravity which may be a system in which the String is housed.
Any thoughts? I'd like to look into that a little more if anyone has a reasonable grasp on the subject matter.
 Dei Gratia de integro,
Veni Vidi Vici:
In Nomine Domini..

kaiowas
lest we baguette
Registered: 07/14/03
Posts: 5,501
Loc: oz

Re: Mathematical Explanation... [Re: Diploid]
#1841321  08/23/03 01:19 AM (19 years, 5 months ago) 


Quote:
Diploid said: Given a = b:
a^2 = ab
a^2 + a^2 = a^2 + ab
2a^2 = a^2 + ab
2a^2  2ab = a^2 + ab  2ab
2a^2  2ab = a^2 ab
2(a^2 ab) = 1(a^2  ab)
2 = 1
QED LOL!!
sure 2=1 but since a^2ab is 0, then 2=1 doesn't matter, because you have to account for 0, and not DIVIDE by it.
 Annnnnnd I had a light saber and my friend was there and I said "you look like an indian" and he said "you look like satan" and he found a stick and a rock and he named the rock ooga booga and he named the stick Stick and we both thought that was pretty funny. We got eaten alive by mosquitos but didn't notice til the next day. I stepped on some glass while wading in the swamp and cut my foot open, didn't bother me til the next day either....yeah it was a good time, ended the night by buying some liquor for minors and drinking nips and going to he diner and eating chicken fingers, and then I went home and went to bed.

Phobos
Registered: 10/15/00
Posts: 435

Re: Mathematical Explanation... [Re: kaiowas]
#1841499  08/23/03 02:06 AM (19 years, 5 months ago) 


Without much thought, I'd have to say there's way no way to get into the hotel. The statement that the rooms are "full", whether the rooms are infinite or not still stands. The hotel is FULL.. would this understanding be correct? Any arguments?

Xibalba
Stranger
Registered: 05/14/00
Posts: 2,114

Re: Mathematical Explanation... [Re: Phobos]
#1842792  08/23/03 12:09 PM (19 years, 5 months ago) 


Edited by Xibalba (09/30/05 09:14 AM)

Phobos
Registered: 10/15/00
Posts: 435

Re: Mathematical Explanation... [Re: Xibalba]
#1842796  08/23/03 12:11 PM (19 years, 5 months ago) 


They would HAVE to be infinitely polite, considering an infinite amount of people would have to move their belongings into the next room, when you could have just went down the road to the Holiday Inn that was vacant.

fireworks_god
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Re: Mathematical Explanation... [Re: Phobos]
#1842870  08/23/03 04:09 PM (19 years, 5 months ago) 


Or you could just go to the last door and move in, instead of having everyone else move, you yourself could be infinitely polite.... hehe
Infinity doesn't make sense to us, does it? Nope. If there are infinite rooms and infinite people in those rooms, where does the room for you come from? I have no fucking clue... Peace.
 If I should die this very moment
I wouldn't fear
For I've never known completeness
Like being here
Wrapped in the warmth of you
Loving every breath of you

Rhizoid
carbon unit
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Posts: 1,739
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Re: Mathematical Explanation... [Re: fireworks_god]
#1842896  08/23/03 04:58 PM (19 years, 5 months ago) 


It's called "Hilbert's Hotel", and the Wikipedia article about this hotel mentions an even crazier story:
No cigars may be brought into the hotel. Yet each of the guests (all rooms had guests at the time) got a cigar while in the hotel. How is this? The guest in Room 1 got a cigar from the guest in Room 2. The guest in Room 2 had previously received two cigars from the guest in Room 3. The guest in Room 3 had previously received three cigars from the guest in Room 4, etc. Each guest kept one cigar and passed the remainder to the guest in the nextlowernumbered room.

Deiymiyan
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Re: Mathematical Explanation... [Re: Rhizoid]
#1843022  08/23/03 06:38 PM (19 years, 5 months ago) 


I sure hope that the infinite1 numbered guest brought with them their "heavyduty infinity bag" to carry the infinate number of cigars with them.
 Dei Gratia de integro,
Veni Vidi Vici:
In Nomine Domini..

Rhizoid
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Re: Mathematical Explanation... [Re: Deiymiyan]
#1845020  08/24/03 04:19 PM (19 years, 5 months ago) 


I don't know anything about the math of String Theory except that it combines the math of Quantum Field Theory with the math of curved spacetime. But any quantum theory of gravity would have to connect with those two types of math in some way.
One interesting aspect of mathematical explanations is whether the fundamental objects described are discrete or continuous. For example, a gas or a liquid is always treated as a continuous quantity in equations that describe the macroscopic mechanics of gasses and liquids, but on a microscopic level we know that they are actually a discrete number of atoms or molecules. Then on a subatomic level we find quantum fields, which are continuous quantities. Then on the still smaller Planck level, we will likely see some sort of discrete structure again, although we don't yet know what is the correct theory at that scale.
I used to believe that our most precise models should be discrete because the real information content of any theory must be finite. But then I realized that this presumes that information is quantized, which I'm not so sure about any more.

Deiymiyan
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Re: Mathematical Explanation... [Re: Rhizoid]
#1845099  08/24/03 06:19 PM (19 years, 5 months ago) 


"One interesting aspect of mathematical explanations is whether the fundamental objects described are discrete or continuous. For example, a gas or a liquid is always treated as a continuous quantity in equations that describe the macroscopic mechanics of gasses and liquids, but on a microscopic level we know that they are actually a discrete number of atoms or molecules. Then on a subatomic level we find quantum fields, which are continuous quantities. Then on the still smaller Planck level, we will likely see some sort of discrete structure again..." 
You know how there is duality in the ParticleWave theorum...
That might mean that there is also a duality in this case as well... "The DiscreteContinuous Theorum"... Where the relativity of each independent part is proportionnal to the scaling factor...
 Dei Gratia de integro,
Veni Vidi Vici:
In Nomine Domini..

Diploid
Cuban
Registered: 01/10/03
Posts: 19,274
Loc: Rabbit Hole

Re: Mathematical Explanation... [Re: Rhizoid]
#1845307  08/24/03 08:57 PM (19 years, 5 months ago) 


Quote:
this presumes that information is quantized, which I'm not so sure about any more.
In Information Theory it is treated as quantized and that seems to be intuitively correct.
Diploid
 Republican Values: 1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.
4) We need a smaller, lessintrusive government.

Rhizoid
carbon unit
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Posts: 1,739
Loc: Europe
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Re: Mathematical Explanation... [Re: Diploid]
#1845572  08/24/03 11:14 PM (19 years, 5 months ago) 


Yeah, a classical signal transmits discrete bits of information, and we're used to think about information as 1's and 0's. But information theory also has the concept of "mutual information" which is defined as the reduction of the Shannon entropy after some new piece of knowledge has been acquired. This entropy reduction does not have to take integer values, it can be a fractional number of bits. But it may still come in discrete levels if the probabilities of the possible states are quantized... which might be the case if information is quantized. Eh.

Xibalba
Stranger
Registered: 05/14/00
Posts: 2,114

Re: Mathematical Explanation... [Re: Rhizoid]
#1845638  08/24/03 11:42 PM (19 years, 5 months ago) 


Edited by Xibalba (09/30/05 09:11 AM)

Rhizoid
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Re: Mathematical Explanation... [Re: Xibalba]
#1845828  08/25/03 01:08 AM (19 years, 5 months ago) 


Both are named after David Hilbert. But there is no other connection between Hilbert's Hotel and Hilbert spaces, except if you count the fact that some Hilbert spaces have an infinite number of dimensions.

GazzBut
Refraction
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Re: Mathematical Explanation... [Re: Xibalba]
#1847708  08/25/03 04:27 PM (19 years, 5 months ago) 


Good work Xibalba!!
 Always Smi2le

