P3D Re: Missing dimension (part 2)

[Larry Berlin <lberlin@xxxxxxxxx>]

>Date: Sun, 4 Apr 1999
>From: roberts@xxxxxxxxxxxxxxxxx (John W Roberts)
>...........................
>>****  Since both eye's observe the same Y information (if set side by side
>>in the face) it is not the Y dimension that is added. 
>
>It is "added" to the case 1 (two-dimensional world) scenario, to make the
>three-dimensional world scenario (even though the Y dimension is not
>"actively" involved in human stereo perception).

****  Wrong. It's there in the 2D scenario just as much as in 3D. It is very
actively involved in *human stereo perception.* Just try misaligning your
stereo images before viewing and see how active it is!!! You could say it's
an *active constant*. Without it being there AND being a constant, you won't
get stereo that you could enjoy. Without it you can't easily define 2D!



>.................
>>So we postulate that the 4th dimension is beyond our direct understanding.
>
>That's not necessarily an incurable condition. Medical diagnosticians can
>sometimes view time-sequential 2-D slices of a 3-D view to build up a mental
>3-D model. It may (or may not) be possible for a human to learn to build
>up a 4-dimensional model, and to build up that model by viewing
>time-sequential 3-D slices of that 4-D view. That would be machine-aided
>perception rather than direct human perception, but it would at least
>involve understanding and perceiving a 4th dimension in a fashion.

****  As I proposed in a message previous to this one.


>
>>Assuming the 4th is literally
>>another axis behaving more or less like the familiar X Y and Z axes. What if
>>it's nothing like that at all? It's effect might be observable on the other
>>dimensions like we observe Z within changes of X. 
>
>This appears to be a definition issue.
>A "dimension" could be anything - color, temperature, taste, electric charge,
>etc. But if we're talking about spatial perception, I think it's sort of
>assumed that the dimensions described will all be spatial dimensions.

****  Yes it is a definition issue. The truth is we don't know what it would
look like in a 4D world. Maybe it would manifest as differential coloration
due to spectoscopic properties, or something else. The point is that to
model it, we have to specify something as representative. Even in the
familiar 3D, we don't find ordinary objects connected to physical
manifestations of the three axes! We can place rulers next to objects, or
glue them on, but we don't think of a cup without rulers as being any less
dimensional as one with attached rulers.

If we attempt to model a cup in a 4D world, where do we glue the extra
rulers? How are we to know it's a 4D cup instead of a 3D one? If 3D is a
mere projection out of a 4D realm, how do we set up the model for what it's
like inside 4D (where we can see manifestations of each dimension)?

>
>In the technical field of scientific visualization, many more than three
>dimensions are often depicted in a single image. A newspaper weather map
>is a classic example. But the extra dimensions shown are not intended to
>represent *spatial* dimensions.

*****  That's a good example, and one which we can use to at a minimum to
attempt to represent other spatial dimensions. After all, the weather map is
a 2D representation of a phenomenon that is 3D physically and has all those
other properties too, like wind speed, temperature, pressure, altitude,
gradients of various sorts, etc.

I have yet to see any representation of a 4D hyperspace object that is
anywhere near as comprehensive as a weather map.

Even the rotating stereoscopic hypercube I provided the URL to leaves a lot
to be desired in terms of understanding hypercubes.

>
>>An alternate scenario arises. A 4D creature could have three or four eyes
>>arranged with non-linearity. ......................
>
>Interesting - perhaps instead of 2 eyes (each N-1 dimensional perception),
>it takes 2^(N-2) eyes (each N-1 D) to properly perceive in N dimensions.
>So the 4-D critter might have four 3-D eyes (arranged, for example in
>a tetrahedron in X,Y,Z) to properly perceive in the W direction.
>


Except that the tetrahedron has to exist in an XYZW environment...
complicating the example a bit since the tetrahedron may not be a
tetrahedron anymore.

This implies that a 5D creature might require 8 eyes, each of which are
capable of 4D perception...

The fact that this model seems to extend towards a steep gradient of growing
complexity that far outstrips the additional number of dimensions means it
is perhaps an unlikely scenario.

You pointed out that even in our 3D world, the ideal 3D view might involve
multitudes of eyes in all possible locations. Yet our two eyes satisfy the
minimum requirement of observing in a given instant, a 3D perception.
Therefore it's unlikely that higher dimensions would require more than some
minimum number of eyes and not necessarily complexify their internal
structures with other dimensional perceptions. 

The problem is to define just what is supposed to be observed and what order
of sensory mechanism can do the observing.

For all we really know, two eyes, each with a 2D perceptive ability might be
all that's required for 4D or 5D too. Maybe having 4 eyes arranged in a
tetrahedron, each with a 2D retina is sufficient all the way up to 42
dimensions at which point something else happens. Maybe that fourth spatial
dimension would be felt (heard, smelled, ...) rather than seen? 

Interesting paradoxes!

Larry Berlin

Email: lberlin@xxxxxxxxx
http://3dzine.simplenet.com/


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