Why Space is 3 Dimensional
Don4AI
Of late many have pondered the possibility that space has higher
dimensionality (hyperspace). These ideas stem from Gauss et al, but have
found a formal representation in the Riemann theorems of the 1800s.
Unfortunately, since a space must not only account for independence among
the dimensional variables but rotational dynamics as well, it was found
that spaces of 4 or higher dimension of orthogonal coordinates, which must
also account for objects with rotational dynamics, contiguously transforms
into higher dimensionality. The result is a contradiction resulting in all
momentum and energy being pushed into infinite dimensions. (The proof is
not hard and is included below.)
The conclusion is space MUST be 3 dimensional since only with 3 dimensions
can coordinate independence and rotation be reconciled.
Feedback will be cheerfully accepted.
Don.
Proof: Let space consist of N independent dimensions denoted by X(i).
Where the X(i) are orthogonal to each other. Also let the rotational
directions be representable by X(i)X(j), where i =/= j.
Now, the total # of rotational representations is 1/2*N(N-1) > N if N>=4.
If X(p)X(q) represents some dimension, X(k), and all dimensions have been
represented, and if s and t are a pair of subscripts not yet used to
represent dimensions, then X(s)X(t) represents either nothing or the same
dimension as X(p)X(q). But it CANNOT represent the same dimension as
X(p)X(q) since this implies the planes PQ and ST are parallel or
antiparallel to each other. Or that X(s) or X(t) is the same as either X(p)
or X(q) which is a contradiction.
But X(s)X(t) CANNOT be nothing either since this means the plane ST cannot
represent rotations. Thus N can only be 3 or less. However, if N is less
than 3 then there is no way to represent rotations and thus space is unphysical.
Don4AI
Chuck
Maybe your three dimensional maths is too restricting?
Im sure that for mathmaticians to explain Eintein's general theory of
relativity, they had to invent some sort of multi-dimensional maths. Could
this be your problem?
CAlgea
On 04 Oct 97 pr...@unix.ccsnet.com (George Hammond)
responded to
article <19970927154...@ladder02.news.aol.com>,
don...@aol.com (Don4AI) wrote:
>>
>>The conclusion is space MUST be 3 dimensional since only with
>>3 dimensions can coordinate independence and rotation be
>> reconciled.
>>
>>Feedback will be cheerfully accepted.
>
>>Don.
>
>I tend to agree with your observation that R=1/2(N(N-1)) and only
> for N=3 can you have R=N; hence this is why space is 3
>dimensional. The human body must have as many degrees of freedom
>as the space it lives in to survive and we would look and feel
> pretty funny if N was NOT three
> George Hammond
In general I agree with George but consider this.
How many dimensions does a Mobius strip have?
How many dimensions does a Klein bottle have?
Looks are deceiving and it may be that there is no dimensions or
only one dimension. "Imagination is more important than knowledge"
so keep an open mind.
_
Charles W. Algea
An amateur philosopher with Alternative Views at
http://members.aol.com/calgea/index.htm
George Hammond
Dries van Oosten
I'am not saying that there are more than 3 spacial dimension, but I really
can't see why the human body should have as many degrees of freedom as the
space it lives in. Do you have any basis for that statement?
And another thing, could anyone repeat the stuff about coordinate
inpendence and rotation and the implications that has on space. I missed
the original post.
Dries van Oosten
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share the same views and hardly ever argue. Eat
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Rick
If anyone out there has had any first hand experiences of 4-dimensional
space, I'd love to hear about it. For a few seconds, while reading
Flatlands in high school, I saw in 4D & knew I was in it (no, no drugs were
involved...). I've not been able to come to such a full understanding of
space & (consequently?) never experienced this again.
To try to describe the experience would be folly; if anyone wishes to
debate the point w/ me I would first encourage them to read Flatlands & try
to appreciate our all too common limitations of perception.
That's all for now..........
Rick
Jim Akerlund
> don...@aol.com (Don4AI) wrote:
> >>
> >>The conclusion is space MUST be 3 dimensional since only with
> >>3 dimensions can coordinate independence and rotation be
> >> reconciled.
> >>
> >>Feedback will be cheerfully accepted.
> >
> >>Don.
> >
> >I tend to agree with your observation that R=1/2(N(N-1)) and only
> > for N=3 can you have R=N; hence this is why space is 3
> >dimensional. The human body must have as many degrees of freedom
> >as the space it lives in to survive and we would look and feel
> > pretty funny if N was NOT three
> > George Hammond
>
>
> How many dimensions does a Mobius strip have?
> How many dimensions does a Klein bottle have?
You seem to have Sides and Dimensions mixed up here. Both the Mobius
strip and the Klien bottle exist in 3 dimensions. The weird thing about
them is that both objects only have one side.
>
> Looks are deceiving and it may be that there is no dimensions or
> only one dimension. "Imagination is more important than knowledge"
> so keep an open mind.
>
> _
> Charles W. Algea
> An amateur philosopher with Alternative Views at
> http://members.aol.com/calgea/index.htm
Thought for the day:
The Nuclear bomb was created before Supersonic flight.
Jim Akerlund
kiLLmYdog
I dont know all that cool math stuff about n and r and x. i know x, but
it just landed me an f. either way, from a philisophical standpoint, if
your equations prove 3 dimensions as the limit, and you are worried
about rotation, why isnt it acceptible to believe that in 4 dimensions,
you can rotate as well with much more impressive equations. Its a
simple concept im sure when you take a flat triangle and lay it on a
sphere. the triangles properties change as you add a dimension making
euclidian geometry kinda silly in trying to define the perimiter, angles
etc etc.. even know we still use 2 dimensional equations, its only
viable in the 2 dimensional perspective. add a dimension, the third,
which you are sure exists, and you change the formulas. someone has an
equation to rotate us in the 4th and hasnt memorized it yet, so they are
failing geometry too. and the teacher put him in a corner with a dunce
cap...whats that damn hat look like? must be cool. who knows...
kisses..
Marco Krijgsman
Space is 3D because we live in it ! It is easy to think of an universe with 7
spacial dimensions and 1 time dimension. This would also mean that, for
instance, the gravitation force decays to a 1/64th for every doubled distance.
This would not allow stable atoms to be formed, molecules and therefor no life
can be formed... hmm at least not life formed out of atoms and molecules.
If 'space' was a two-dimensional place. The gravitational pull would decay
equal with distance. Two-dimensional atoms can be formed but life, as we know
it, is certainly impossible.. how would it feed ?
Hawking refers to this as the antropical principle (I hope I spelled correctly).
Why space is 3D is like asking, is life possible ? Well we're here, and living !
Perhaps, in other universes, 7D creatures are debating if a 3D universe with
only 1 time dimension is possible. The complexity of their world would require
enormous intelligence to survive only.
---------------------------------------
Marco Krijgsman
du...@worldaccess.nl
Smart1234
>>
>>The conclusion is space MUST be 3 dimensional since only with 3 dimensions
>>can coordinate independence and rotation be reconciled.
>>
>>Feedback will be cheerfully accepted.
>>
>>Don.
>>
>>I tend to agree with your observation that R=1/2(N(N-1)) and only for
>N=3 can you have R=N; hence this is why space is 3 dimensional. The human
>body must have as many degrees of freedom as the space it lives in to
>survive and we would look and feel pretty funny if N was NOT three
>George Hammond
>
>
Space isn't necessarily 3 dimensions in my theories. I even show a partial
4th dimensional view at my home page. Basically it shows how convergence, and
divergence, can meet in curved space in a composite partial view.
If interested :
http://members.aol.com/smart1234
JeffTB123
>From: du...@worldaccess.nl (Marco Krijgsman)
>Date: Thu, Oct 9, 1997 2:38 PM
>If 'space' was a two-dimensional place. The gravitational pull would >decay
>equal with distance. Two-dimensional atoms can be formed but life, as >we know
>it, is certainly impossible.. how would it feed ?
>Hawking refers to this as the antropical principle (I hope I spelled
>correctly).
>Why space is 3D is like asking, is life possible ? Well we're here, and
>living !
I've always been surprised that Hawking hasn't been ridiculed more for his
circular reasoning on this subject. To me it sounds like he's saying:
"things are the way they are because that's the way they are." And this is
SCIENCE?!!
I'm not sure what hawking called it, but in other sciences it's called
anthopomorhisism (sp?). It's like projecting human qualities onto a car
("She's a beauty") which is fine as long as you remember that it's all in your
head and that the outside world is not necessarily limited by our minds'
conceptions of it.