Imagining a Glome

[Nick]

How is it possible to imagine a glome? Imagining a 4-hypercube is (sort of) easy with practice, because you can reconstruct a model of it (two cubes with all verticies connected).

But how would a glome be modeled?

[houserichichi]

Since a sphere is nothing more than a cube with an infinite number of vertices in all directions it would be the exact same extension that you made from 3-cube to 4-cube only with more vertices. Infinitely more, but nonethemore difficult.

[Nick]

When I try to imagine that, I get a sphere.

[houserichichi]

Pat posted this video in this post.

(May need this codec to play)


For the hypercube pretend that each vertex is connected with a set of strings. Move one of the cubes around and watch the strings. Gives you interesting shapes. Pretend the strings can pass through eachother (in 3D). It looks like a hypercube, or the representations, no?

Now picture an infinite number of strings (a surface) connected to an infinite number of vertices between two spheres. Move one sphere around and imagine what the strings would look like if they could pass through eachother. Same idea as the cube with strings, no? Again, this is just a visualization, nothing more.

[thigle]

difference in difficulty (of imagining a hypercube and a glome) amounts to the one between difficulty of imagining a cube and a sphere. (by dimensionalAnalogy :wink: )

actually that model of hypercube where one connects vertices of 2 cubes is analogous to a model of 2d shadow of 3d cube(which gives in parallel projection a hexagon for 'outer shadow' and square for 'inner'(minimal) shadow.). and the hypervolume of the hypercube is between those 8 cubes that seem to interpenetrate in 3-space that one projects into.

as hard to get at it as to get at 3d volume from 2d-shadow of wireframe cube - between the hexagon and square (rhombic-dodeca and cube for hypercube), there are the shadows of all the other possible views(orientations) of the object (cube/hypercube).

as a sphere is a chunk of 3-space ...
a)... bounded by a circle(=1-sphere topologically) that rotates pi/2 around its diameter, into the 3rd dimension. or..,
b)... bounded by a circle A, A=(r,C(xyz)) moving in the direction orthogonal to its plane, through distance of its diameter, while changing its radius from zero through r to zero. the way r grows from 0 to r to 0 is graphed by a halfcircle over a diameter of 2r.

analogically, glome is a chunk of 4-space...
a)... bounded by a 3d sphere that rotates p/2 around its diameter, through the 4th dimension.
b)... bounded by a sphere S, S=(r,C(xyz)) moving in a direction orthogonal to its space, through distance of 2r, while changing its radius from 0 through r to 0. the way r grows from 0 to r to 0 is graphed by a halfcircle over a diameter of 2r.

[thigle]

houserichichi, that stringy model seems to me like a spherinder in case that those 2 spheres just move and don't change orientation by rotation. to get a glome though, one needs not just the 4-space between arbitrarily positioned spheres. the whole issue of projection parameters...

[papernuke]

All I imagine is 9 spheres together ... which is nothing