## 3D geometry

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• Folks, Glad to read so many messages from people like me. Otherwise, I would have no outlet for these strange obsessions of mine. I especially liked the
Message 1 of 6 , May 14 7:18 AM
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Folks,

Glad to read so many messages from people like me. Otherwise, I would have
no outlet for these strange obsessions of mine. I especially liked the
Hermes & Mercury stuff, though I haven't had time to digest it yet, my life
is a poverty of "Have To" and "Don't Have Time". Whine, Snivel, Whimper.

Anyway, as for the multi-dimensional quandary, from a mathematical point of
view, dimensions above 3 are no problem. I encourage anyone to experiment
with multi-dimensional magic squares, cubes, tessaracts, and 5th 6th etc,
dimensional hypercubes. After you do this, you can see pretty easily that
time is not an ordinary dimension. All these magic tessaratcs and higher
dimensional hypercubes exist in the same way as do magic squares and cubes -
presumably no problem in visualization - well the cubes are kinda hard to
see all at once - they are usually written down in two-dimensional sections.

In any case, a 4 dimensional magic hypercube is just like an extended magic
cube which is just like an extended magic square. And so, mathematically -
our most trustworthy sense - "extra" spatial dimensions are not anything too
weird at all.

However, there is a big difference between spatial dimensions and the
temporal dimension. That's why we can't measure time in inches. A four
(spatial) dimension cube - or hypercube - will not have the same properties
as a three (spatial) dimension cube that also has a temporal dimension.

But now for some real fun boys and girls, why do we think that there is only
1 temporal dimension - the "one" we call time?

It is easy enough to work with as many spatial dimensions as are needed to
solve the problem at hand. The preferred number for physicists to explain
the universe is 11. We just make them up as we go along, and it works
pretty well. But what makes the temporal dimension so unique? If there are
so many spatial dimensions, then why not as many temporal dimensions as we
want?

Mark

----- Original Message -----
From: "johnberger_x" <magician@...>
To: <sacredlandscapelist@yahoogroups.com>
Sent: Monday, May 13, 2002 9:54 PM
Subject: [sl] Re: 3D geometry

> --- In sacredlandscapelist@y..., "J Vincent Beall" <vincent@d...>
> wrote:
> > What do you think that the author of the manual means by visualize
> the
> > hypercube? It doesn't seem to me that this is very straightforward.
>
> Here's someone who thinks they have it down:
>
> http://dogfeathers.com/java/hyprcube.html
>
> Forgive me if this is obtuse or naive, or if I am missing something
> very important in this concept, but the whole concept of the
> hypercube seems inherently flawed to me.
>
> One site I looked at contained the following statement: "Imagine a
> person who lives in 4 spatial dimensions, watching a hypercube
> rotate." Well, I live in four (plus) spatial dimensions. The fourth
> dimension is simply an additional axis, not a wholly independent
> realm of space and time.
>
> So if you accept that the fourth dimension is time, then wouldn't
> a "hypercube" simply be a cube that exists for a fixed duration which
> is the temporal equivalent of the length of its physical 3-D sides?
>
> So all you have to do is can figure out a way to measure time in
> inches, and you can make a hypercube, a four-dimensional cube.
>
> Alternatively you could program a computer environment in which the
> time and space units can be more easily converted back and forth from
> each other, a much easier proposition, especially since you don't
> have to account for relativity.
>
> It just wouldn't be extremely entertaining, I suspect. It would just
> be an animation of a 3-D cube that exists for a certain duration,
> then ceases to exist.
>
> --John B.
> http://www.chaosdancer.com
>
>
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>
• ... experiment ... 6th etc, ... easily that ... I m not sure I see that. Time is a measurable axis on which we move. It s pretty much a dimension, like any
Message 2 of 6 , May 16 9:41 AM
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--- In sacredlandscapelist@y..., "mswaney" <mswaney@e...> wrote:
> view, dimensions above 3 are no problem. I encourage anyone to
experiment
> with multi-dimensional magic squares, cubes, tessaracts, and 5th
6th etc,
> dimensional hypercubes. After you do this, you can see pretty
easily that
> time is not an ordinary dimension.

I'm not sure I see that. Time is a measurable axis on which we move.
It's pretty much a dimension, like any other dimension. What's
interesting and unique are 1) how we perceive time, and 2) the ways
we move through time.

> However, there is a big difference between spatial dimensions and
the
> temporal dimension. That's why we can't measure time in inches.

On what do you base that statement? Why isn't time spatial? I am not
currently able to measure it in inches because I don't know how to
hold my tape measure. I think if you could figure that out, you could
not only measure time in inches, but it would be more accurate and
more relativistically sound than measuring in minutes.

> pretty well. But what makes the temporal dimension so unique? If
there are
> so many spatial dimensions, then why not as many temporal
dimensions as we want?

There could well be. My own theory is that some of our higher mental
and spiritual functions (as we perceive them) occur and can be
represented as higher-dimensional functions. After all, if knowledge
or creativity or imagination is quantifiable, it should be able to be
modeled mathematically.

You can argue that some or all of this already models into the 4-D
neurochemical structure of our brains, but it seems to me that
there's an abstraction to some of these qualities that wants to be
recognized and may not boil down to a simple chemical formulation.

-j
• more power to you in your quest. the only comment i would make is that the use of the platonic solids and any symbolism connected with them is linked to
Message 3 of 6 , May 20 10:32 PM
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more power to you in your quest.

the only comment i would make is that
the use of the platonic solids
and any symbolism connected with them
is linked to various movements and historical periods.

for some folks the issue is not so much about
various other kinds of polygons and their potential
mystical implications as it is about historical detective work.

for instance, trying to understand how of some of the neoplatonist
medieval and renaissance scholars, churchmen and builders
structure of the cosmos thru their work.
--or how neoplatonist ideas influenced the art deco and streamline
design movents of the 1920's and '30's.

if that is also interesting to you, you may find good reading
in Mike Bispham's essay on Platonic Atomism in the
Cathedrals in the essay section of the Sacred Landscape website.
B.

At 05:15 PM 5/13/02 +0000, you wrote:
>I'm looking to go deeper into the the study of symmetry rather than
>limiting myself to what is already considered "sacred geometry".
> I know the Platonic Solids and the Archimedean Solids
>are talked aboutin sacred geometry books. But there is so much more
>to the study polyhedra. Actually the study of Polytopes would cover
>polyhedra which are 3-d polytopes, and 2-d polgons, star polygons,
>and into higher dimensions, like that of a 4-d polychoron.
>These are things that you must be willing to let go of "sacred
>geometry" to start to understand.
> To me all ideas take form and can be descibed numericaly,
>and geometricaly. It's all part of the same, it's all Sacred
>Space.
>
>
>
>
>
>
>Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>
>
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