P3D Re: Missing dimension

[Larry Berlin <lberlin@xxxxxxxxx>]

>Date: Sun, 4 Apr 1999
>From: roberts@xxxxxxxxxxxxxxxxx (John W Roberts)
>...........................
>>Date: Sat, 3 Apr 1999
>>From: Larry Berlin <lberlin@xxxxxxxxx>
>>*****  Problem with this... One dimensional eyes perceive in only one
>>direction. 
>
>Why should that be? Bruce appears to be modeling what human-type vision would
>be like in scenarios of different numbers of spatial dimensions. A human-
>type eye with a 1-dimensional retina would map a large wedge (e.g. 120-180
>degrees) of the two-dimensional plane of the universe, onto a line segment
>(or curve segment).

*****  I was referring not to a direction specifically but to the limit of a
single axis which in my thoughts I called a direction. Side to side as
opposed to up and down. (meaningless in a 2D world anyway)

BTW, he did NOT imply human vision in the other dimensions. He specifically
defined altered situations for each scenario. A 1D retina is one such
altered state.


>
>>If you are to add these two and get traditional 2D then one eye
>>perceives in the X direction and the other eye sees only in the Y dimension.
>>With both eyes he is able to see in 2D. This might be like the optics in a
>>scanner. The resulting view is at a constant distance, ie no relative depth
>>information.
>
>That's nothing like the human-like model of vision that Bruce appears to be
>describing. You seem to be thinking of a model like the compound eyes of an
>insect, except that instead of the directions of view of the component eyes
>extending radially outward from a central point (real insect), you're
>thinking of the directions of view of all the component eyes being parallel
>(so the only difference in views is the lateral displacement), and the
>eye images some tiny fraction of its universe at a 1:1 scale. (And for two
>eyes, the direction of view of the two eyes always being 90 degrees apart.)
>I do not think that is the eye model Bruce had in mind.

****  Bruce wasn't describing the human model. He was starting from the
distorted alternative vision of the book *Flatland*...

Your description above is definitely NOT descriptive of any part of my
thoughts!!! 

I was not in any way thinking of an insect's eyes, nor was I projecting
anything in parallel projection. I was thinking only of the limits and
circumstances imposed by the strange scenario supplied by Bruce,
extrapolated from *Flatland.*. (including 1D retinae...)

The human eye is NOT 1D it is 2D with both X and Y, specifically NOT X and
Z, available from a single eye. It's impossible to describe any of this
without altering in some way our current human vision. 

>
>>............(I said)............The resulting 2D
>>perception is of a plane on it's edge except you may perceive points at
>>different distances on that plane. This would be like stereo 3D without the
>>Y dimension because of the depth information.
>

>I think that's what Bruce had in mind. ............

****  If so, there is the problem of moving from the 2D realm (XZ
limitation) to the 3D realm. True, in a 2D world viewed edge on with two
eyes, one has stereoscopic vision confined to the visible plane which
appears as a line, but that doesn't translate to the 3D world until each eye
has it's own 2D retina and not of the sort using XZ for the 2D component (as
derived in the 2D world specifying a 1D retina...).  

In the other examples the previously accomplished D level was used in the
next world level, giving rise to the discrepancies noted here going from 2
to 3D. That is, XZ + XZ from flatland doesn't provide the same 2D + 2D that
usually equals 3D in a 3D land.

What seems to be overlooked is that Y exists in each of these scenarios. It
remains a constant 0 in 2D. Therefore it's expansion in 3D is more than the
addition of a new Y dimension. It's the definition of size greater than 0 to
the Y dimension, which must have existed before or you wouldn't be able to
define flatland as flat.

Which brings it back to where we started... how does 2D(XY) + 2D(XY) = 3D
instead of 4D? The answer is that Y factors are parallel to the axis of
displacement in observation, in this case the X axis and so they are
constant, identical and are one singular factor instead of separate additive
factors. In reality the formula is (X1, Y) - (X2, Y) = (delta X, Y) = (X, Y,
Z) = 3D. 

A 3D image then is the projection of 3D coordinates onto a 2D plane using
two slightly displaced centers of observation. That's why it works with two
2D eyes powered by a powerful real-time difference engine called the brain.

Larry Berlin

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


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