Quote:
Originally Posted by r6r6r
"appear to be 2D creatures having an illusion of 3D" is how that should have been stated. Sorry.r6
|
Hawking made it clear--- in his book "Brief History of Time" ---how we cannot be 2D creatures, using his 2D silouhette / plane diagram of dog with tube going through.
However, there is another perspective / viewpoint that does not divide the 2D plane in half, as hawking did.
Take the mininimal 2D cross section triangle(
| ) adn turn it sideways so we see face / opening--- texticonic example
/\ -- as the eternal NOW.
Place a vertex / dot in the center of that triangle with a lines from vertex / dot. One to each of triangles three corners. We have created a subdivision of 2D triangle into three subtriangles, but we also have created a birds-eye-view of ftetra(4)hedron.
We can also see this 2D subidivided triangle as a tetra(4)hedron, that is half-way between being inside-out and outside out i.e. the one of the vertexes is on trajectory to go through its diametrically opposing face / opening and when it is a the half-way point / position we have a 2D subidivided triangle.
So, in this sense / perspective we see how 3D can become or appear to become 2D or vice versa. Also from this perspective we can see the face / opening of triangle as both the open beginning of tube and the open end of a tube opening.
I say tube in the sense that over snapshots of time--- |||||| ---we can say we have a 3D tube.
But before getting to far ahead of ourselves, just think of the central vertex oscillating between forward and obverse positions i.e. the vertexial-dot / node goes from one side of triangle plane thorugh openging to the other side, and then back and forth.
In so doing we create two or more scenarios;
1) a 2D triangle plane that is warped i.e. some aspect of the 2D plane is no longer in the same plane as its corners ex a piece of plywood will warp become curved and twisted at more extremmes.
In the above we considering aspects of cone but more specifically a Euclidean cone because were not actually invoking a curve with a Euclidean triangle.
A tetrahedron is the minimal cone i.e. if we increase the number of lines from center dot and the number of corners that those lines connect to were increasing the frequency of that 2D plane and increase frequency gives the
appearence of curvature.
http://www.rwgrayprojects.com/synerg...igs/f1020.html
This is also true of polyhedra becoming geodesic domes ex the disney epcot center is a 16 frequency geodesic dome ergo the higher the frequency the more spherical a geodesic will appear, provided the proper angles are applied.
I've strayed off my primary 2D triangular opening > 3D tube concerns but the other stuff is intimately related. Just get into more complexity.
The inside-outing tetrahedron can also be viewed statically as a triangular based di-pyramid--- <> or <|> ---i.e. to face / opening bonded tetrahedra or as two positions of the singularly warped Euclidean 2D plane.
One last important note, there is one polyhedron that shares the intimately the 60 degree coordination of a triangle and that is the cubo(6)-octa(8)hedron and the spherical cubo-octahedron's external surface area is exactly equal to the foru cross-sectional planes--- see tetrahedrons four 60 oriented planes ---that
defines the cubo-octahedron.
http://www.rwgrayprojects.com/synerg...s/plate31.html
r6