- Edwin A. Abbott's "Flatland" is on-line in various places, including

here:

http://nedwww.ipac.caltech.edu/level5/Abbott/Abbott_contents.html

--- In sacredlandscapelist@y..., "J Vincent Beall" <vincent@d...>

wrote:> Well, our physical space-time is 4-dimensional, but time does not

constitue

> a whole dimension in the physical model, as I understand it. It is

like a

> half dimension because objects in our space-time don't seem to have

chain of

> extension into negative time. Time in our universe seems only to be

> positive.

>

> There is a book called Flatland that demostrates the intuitive

> logic that proposes the properties of dimesions higher than three.

It is

> assumed that all unfolding of dimension always adheres consistently

to the

> same set of rules. So, we need only consider the the unfolding of a

simple

> form like a tetrahedron from zero to three dimensions in order to be

explained to

> confident of the rules which apply to unfoldment to four-dimensions.

>

> This contemplation of unfolding a tetrahedron from 0 to 4-D was

> me as Einstein's puzzle, but that might be just to make it a bit

more

> interesting. :)

consideration of

>

> Mathematical dimensions are static and have no metaphysical

> "substance" to complicate them. Physical space however depends in

its being

> on the mystery of "substance" even thought it is completely ignored

in

> scientific study, since all explanations of 'what the "substances"

of our

> experience are' would "turtle all the way down", so to speak.

not know

>

> It might be said that we can know that we are substance, but we can

> what that substance is. In otherwords there is a duality between

description

> and being. We are beings and not the descriptions.

>

> Vincent - In message <gLPSEKA$eE58EwE9@...>, Neil Fernandez

<neil@...> writes>In message <000e01c1fd2a$166cfe20$d9acb882@mtl2>, mswaney

[...]

><mswaney@...> writes

>I think a good handle on how space-time theory treats time differently

I forgot to add that with the fourth Euclidean dimension (calling the

>from the spatial dimensions (I'm not saying this is the 'correct' way!)

>is given by the formulae for distance. If the spatial dimensions are

>called x,y,z, and the temporal dimension is called t, then

>

>-distance (1D) from 0 to x is x

>-distance (2D) from (0,0) to (x,y) is sqrt(x^2 + y^2)

>-distance (3D) from (0,0,0) to (x,y,z) is sqrt (x^2+y^2+z^2)

>-distance (4D) from (0,0,0,0,) to (x,y,z,t) is sqrt(x^2+y^2+z^2-(ct)^2)

>where c is the velocity of light in a vacuum. The "-" is not a typo! :-)

fourth dimension w), distance from (0,0,0,0) to (x,y,z,w) is

sqrt(x^2+y^2+z^2+w^2), which follows on logically/intuitively from the

distance formulae for the first three.

Neil

--

Neil Fernandez