Thread: "Visualizing Space from Ana/ Kata."

--------------040406090808040903010702
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 7bit

So it sounds like no, you don't feel any real 4D visualization ability.
I can't even see how the first 24-Cell section is a cube, let alone
guess the next shape, but again I don't think sections are a good test.
I barely feel that I can visualize the 2D sections of a cube!

On 11/29/2015 10:58 AM, andreyastrelin@yahoo.com [4D_Cubing] wrote:
>
>
> Hello Melinda,
> I think that sometimes I'm very close to the visualization of 4D
> objects and scenes. It may be either in form of orthogonal projections
> of scenes on 3D space (with details of 4D surface as internal
> structures of 3D bodies), or (in the case of 4D convex polyhedra) in
> form of our familiar stereographic projections of the surface (as
> division of space to set of 3D polyhedra).
> But it needs some training. Just now I tried to solve easy problem -
> what are 3D sections of 24-cell by spaces orthogonal to the longest
> diagonal segment? When you start from the vertex they are cubes, but
> when you cross next level of vertices, what you get? I think that I
> know the answer, but it was more like calculation than a vision.
> Andrey


--------------040406090808040903010702
Content-Type: text/html; charset=utf-8
Content-Transfer-Encoding: quoted-printable



">


So it sounds like no, you don't feel any real 4D visualization
ability. I can't even see how the first 24-Cell section is a cube,
let alone guess the next shape, but again I don't think sections are
a good test. I barely feel that I can visualize the 2D sections of a
cube!

Hello Melinda,

=C2=A0 I think that sometimes I'm very close to the visualizatio=
n
of 4D objects and scenes. It may be either in form of orthogonal
projections of scenes on 3D space (with details of 4D surface
as=C2=A0internal structures of 3D bodies), or (in the case of 4D
convex polyhedra) in form of our familiar stereographic
projections of the surface (as division of space to set of 3D
polyhedra).

=C2=A0 But it needs some training. Just now I tried to solve eas=
y
problem - what are 3D sections of 24-cell by spaces orthogonal
to the longest diagonal segment? When you start from the vertex
they are cubes, but when you cross=C2=A0next level of vertices, wha=
t
you get? I think that I know the answer, but it was more like
calculation than a vision.

=C2=A0 Andrey

--001a113413c0527ff90525c3886a
Content-Type: text/plain; charset=UTF-8

If we want to imagine how a 4D being might "see" shapes intuitively, it
might be more analogous to the awareness we have of our entire 3D body,
where we can "feel" a 3D volume all at once. Their visual system would be
converting some 3D grid of sensations into a mental model of what they are
observing.

We see the 3D world by projecting it onto a 2D array of nerve endings, the
retina. By analogy, a 4D being might see the 4D world by projecting onto a
3D volume of nerve endings -- some sort of 3D retina. So I was thinking,
what do we have that might be analogous to this 3D bundle of nerve endings?

One possible answer is: our entire bodies. Of course, we are not a giant
retina, but just imagine for a moment that all the nerve endings in your
body which are constantly sending you messages about how your arms and legs
are feeling, what your stomach is doing, etc., imagine they are all
actually sensing colour (instead of temperature, pain, or whatever they
sense normally).

Melinda's example of a blind person feeling a model car is very close -- if
a hologram of this model car was superimposed/projected inside your belly
for example, and all the nerve endings in your belly could "feel" / see the
hologram, then you would be instantly aware of the entire volume of the
model car, the inside, the outside, all the parts in the engine, etc.

If the model car was very far away in 4D, it would be projected very small
inside your body in 3D, and difficult to sense the details. If the model
car was very close in 4D, it would be projected large in 3D, some of it
might escape your field of view. It's not exactly correct to say you would
see it "from every angle" -- there is still a viewing angle, it's just an
angle from some 4D direction. It's more like us looking at a 2D drawing of
a car, we'd see the insides of the car, but not "from every angle" just
from "above" in some 3D orientation.

Anyway, maybe this will provoke some thought experiments along these lines.
: )

--001a113413c0527ff90525c3886a
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable