Saul Luizaga schrieb:

>>> Or maybe you leave your 3D body and become a 4D spirit that then will 
>>> incarnate a 4D being and so on...
>>
>> But if so, how could you possible remember and/or integrate the 
>> experience with a 3D mind? Maybe you could remember that *something* 
>> happened, with a gained benefit of a new spiritual perspective...
> 
> Is a possibility, but again, who remembers being a 2D person before this 
> life? maybe is part of the "instinct" of each person, but who knows...

You can't be (and never could have been in any prior life) a "2D 
person": Evidently, there /are/ 3 dimensions (or more), so each "2D" 
being must also be embedded in 3D space, and therefore /be/ a 3D being.

Similarly with 4 (space-like) dimensions: Either we /are/ 4D beings, or 
there is no such thing as a 4th dimension.

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>> It is worth nothing, however, that the time dimension is *not* 
>> identical to the space dimensions (one would hope not!) and distances 
>> are measured differently in time than in space.
> 
> Well, AFAIK there's actually no fundamental reason to apply different 
> "measuring tapes" to time and space: The constant vacuum speed of light 
> can serve as a ruler for both, with the distance of a light second 
> equating a second.
> 
> It just happens that it's still more practical to use meters for 
> space-like dimensions and seconds for time-like dimensions.

When you start measuring "events" which happen at different points in 
space and different points in time, it becomes worth using a "spacetime" 
measurement which simultaneously encodes both.

(Not that I know much about such things...)

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It seems to me people are confusing mathematical formalisms with reality.

4D Euclidian geometry is an interesting mathematical system. 4D 
time-dimension geometry is an interesting mathematical system. 2D Euclid 
is an interesting mathematical system. (Euclid was reputedly so 
fascinated by it that he was speared to death by some random Roman.)

Whether these systems have any baring on the Real World which we inhabit 
is an entirely orthogonal question. ;-)

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clipka wrote:
> Saul Luizaga schrieb:
> 
>>>> Or maybe you leave your 3D body and become a 4D spirit that then 
>>>> will incarnate a 4D being and so on...
>>>
>>> But if so, how could you possible remember and/or integrate the 
>>> experience with a 3D mind? Maybe you could remember that *something* 
>>> happened, with a gained benefit of a new spiritual perspective...
>>
>> Is a possibility, but again, who remembers being a 2D person before 
>> this life? maybe is part of the "instinct" of each person, but who 
>> knows...
> 
> You can't be (and never could have been in any prior life) a "2D 
> person": Evidently, there /are/ 3 dimensions (or more), so each "2D" 
> being must also be embedded in 3D space, and therefore /be/ a 3D being.

You're missing the point: by 2D person we mean you live in a 2D world as 
we live in a 3D world, without being able to experience any other 
dimension. Of course 2D, 3D, 4D, etc are included in a nD universe but 
we're not gonna call everything a nD being or object, we have to call 
the object dimensional feature by how many dimensions that being/object 
is able to experience not by how many dimension that being/object is 
included in.

> Similarly with 4 (space-like) dimensions: Either we /are/ 4D beings, or 
> there is no such thing as a 4th dimension.

read above.

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ANd nobody knows if we were or not 2D beings.

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Invisible wrote:
> These are two seperate, unrelated geometries.
> 
> 4D Euclidian space is interesting because it's a straight extension of 
> 3D Euclidian geometry.

I should read more about this, sounds interesting.

> Somewhat weirder is hyperbolic geometry, where multiple "straight lines" 
> through a single point do not intersect each other [except at that 
> point]. You really need to play with this:
> 
> http://cs.unm.edu/~joel/NonEuclid/NonEuclid.html

I'll check it out.

I've been trying to figure out how to calculate hyperbolic geometry, so 
I may create new "circle limit" Poincare disk tesselations. I figure it 
must be possible to create such a thing with POV-Ray functions, but so 
far all my attempts have been total failures :(

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>> These are two seperate, unrelated geometries.
>>
>> 4D Euclidian space is interesting because it's a straight extension of 
>> 3D Euclidian geometry.
> 
> I should read more about this, sounds interesting.

3D Euclidian space = the place where we (apparently) live.

4D Euclidian space = the place where objects such as the hypercube live.

4D non-Euclidian space = any space with 4 dimensions that *isn't* 4D 
Euclidian space. This includes a system where time is the 4th dimension, 
but also many other kinds of space as well.

>> Somewhat weirder is hyperbolic geometry, where multiple "straight 
>> lines" through a single point do not intersect each other [except at 
>> that point]. You really need to play with this:
>>
>> http://cs.unm.edu/~joel/NonEuclid/NonEuclid.html
> 
> I'll check it out.
> 
> I've been trying to figure out how to calculate hyperbolic geometry, so 
> I may create new "circle limit" Poincare disk tesselations. I figure it 
> must be possible to create such a thing with POV-Ray functions, but so 
> far all my attempts have been total failures :(

I believe you can use ordinary 2D coordinates for hyperbolic space, you 
just need to remap them when plotting them in normal 2D space. 
(Unfortunately, I can't find any formulas for doing this.)

Note that there is more than one way to project hyperbolic space into 

trying to copy Escher's Circle Limit.

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clipka wrote:
> Well, AFAIK there's actually no fundamental reason to apply different 
> "measuring tapes" to time and space: 

It's not measured *quite* the same way... The distance between two events is 
sqrt(x*x+y*y+z*z-t*t) Note the - sign.

-- 
   Darren New, San Diego CA, USA (PST)
   I ordered stamps from Zazzle that read "Place Stamp Here".

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Darren New wrote:
> clipka wrote:
>> Well, AFAIK there's actually no fundamental reason to apply different 
>> "measuring tapes" to time and space: 
> 
> It's not measured *quite* the same way... The distance between two 
> events is sqrt(x*x+y*y+z*z-t*t) Note the - sign.

Hence "non-Euclidian space".

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clipka wrote:
> Kevin Wampler schrieb:
> 
>> It is worth nothing, however, that the time dimension is *not* 
>> identical to the space dimensions (one would hope not!) and distances 
>> are measured differently in time than in space.
> 
> Well, AFAIK there's actually no fundamental reason to apply different 
> "measuring tapes" to time and space: The constant vacuum speed of light 
> can serve as a ruler for both, with the distance of a light second 
> equating a second.
> 
> It just happens that it's still more practical to use meters for 
> space-like dimensions and seconds for time-like dimensions.

I think that this becomes problematic for measuring between points which 
aren't connectible by a lightlike geodesic, but maybe there's some 
clever way around that (although I don't see how).

In any case, I was referring to the fact that under special relativity 
spacetime has a metric that differs from that of a 4D Euclidian space 
along the dimension corresponding to time.  For instance, the length of 
a vector can be negative, which is impossible under a Euclidean metric.

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