Does anyone know anything about....
Posted 19 January 2003 - 06:14 PM
Posted 19 January 2003 - 08:59 PM
However, if you're looking for ideas involving spatial geometry that will blow your mind, try the Banach Tarski paradox.
Briefly put, a real world solid ball can be decopmosed into a finite number of pieces (4 or 6, depending on how picky you are about including the center point) and reassembled into *two* solid balls of equal volume to the original.
No, I'm not making that up. The math has held up for 80 years.
Needless to say, the 4-6 pieces (defined geometrically) are extremely complex, and this can't realistically be done with objects made of discrete atoms of defined non-infintesmal size, but the consequences of doing it to space are fantastic.
Posted 19 January 2003 - 11:37 PM
In otherwords, try looking at it the other way around. In most geometries, a point is dimensionless, and therefore either two points are identical or they are separated. Though we do sometimes refer to 'contiguous points' in even Euclidean geometry, one basic tenet of the standard grade school geometry is: for any two distinct points, there is some intervening point.
e.g. Name any two numbers, and I can name a number 'between' them. So can you. No mysteries involved.
I am still curious about the specific null space hypothesis you are referring to, but I don't think it's related to this principle.
Posted 26 January 2003 - 09:54 PM
Posted 19 January 2003 - 09:17 AM
Christopher? Uncle Sid? Somebody? Please?????
Posted 19 January 2003 - 07:02 PM
half the distance between 2 points repeatedly and still the 2 points will not touch
hope that helps
Posted 19 January 2003 - 09:44 PM
What I am looking for is an exploitation of the given.
If a point has no dimension then the space between two points has no dimension.
Without dimension the space between any two points is the same no matter the location.
How badly did I butcher that?
In other words; how many angels can dance on the head of a pin?
Posted 20 January 2003 - 12:37 AM
Sounds a lot like Xeno's Paradox, which says the same thing with distances .
Orpheus, that Banach Tarski Paradox sounds wild! You double the volume??
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