From: Tony Benjamin Csoka (csoka@itsa.ucsf.edu)
Date: Wed Jan 14 1998 - 14:32:52 MST
It is axiomatic that a mathematical point has no dimensions.
TBC
On 14 Jan
1998, Anders Sandberg wrote:
> CALYK <CALYK@aol.com> writes:
>
> > In a message dated 98-01-14 01:46:49 EST, you write:
> >
> > << danny:
> >
> > > Im wondering, do the 10 dimensions include the 0 dimension, making 11
> > >total? (0-point, 1-line, 2-plane, 3-d etc..)
> >
> > What???! >>
> >
> > what dont you understand?
> >
> > isnt it agreed that 0-point, 1-line, 2-plane, 3-d etc.. ?
>
> Each (metric) space has a certain dimensionality, an intrinsic
> property of how it hangs together. Simply speaking the number of
> dimensions of a space is the number of coordinates you need to
> uniquely determine the position of a point. On a line you just need
> one, in a plane you need two, in 3D you need three and in higher
> dimensional spaces you need more. Higher dimensional spaces can of
> course have lower dimensional spaces as a subset (like a line in the
> plane or a plane inside a 3D space).
>
> Note that "dimensions" often are misused to mean something completely
> different, especially in comic book physics where it seems to mean
> "alternate universe".
>
> There are infinitely many kinds of spaces of a given dimensionality
> (and most are not isomorphic to each other), the big question is which
> of them correspond to our universe.
>
>
> --
> -----------------------------------------------------------------------
> Anders Sandberg Towards Ascension!
> asa@nada.kth.se http://www.nada.kth.se/~asa/
> GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y
>
_______________________________________________________________________________
Tony Benjamin Csoka // Tel: (415) 476 2745 // Fax: (415) 476 9672
_______________________________________________________________________________
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