if i would devise a fictional scifi story based on my lucid dream:

let the lujcid dream communications of aliens. a language of aliens. how to decipher that?

ok starting with sphere, it represents uniformity. of no information content, of lowest entropy in alphabet of aliens which is mathematical. i mean topoilogical wise sphere is the shape that has lowest information.  and upper direction and below direction shape might be two reverse information contents. or some information having 4d structure that turned out looking like that in 3d. 

what kind of 4d surface would looked like that 3d surface.

lets continue resume topology study awhile sometimes.

for sure a uniform surface would had created the sphere. a uniform surface in 4d. or any higher dimension either. 

 

coming to elliptical movement:  if it were to be an algebra of rotations/transformations ending in a eccentricity having circle in other words ellipse. that might mathematically mean entire thi8s system: 

a shaoe of 3d surfaces moving in a transformations/rotations --> the movement it self: is 2d. the shapes are 3d.  if all were from  a higher dimension, if we went to devise some fregean logic in such language: 

the 2d movement of elliptical surface would might had meant: 

applying a higher order function to a shape set. like transformation of an information with a higher order function. what if aliens languages were mathematical.  (in this scifi story i create from a lucid dream i mean)

(i paused mathematics study awhile. i woould continue that sometimes. )

like for instance taking some morphism approach,  functional wise what would that elliptic path would had meant? 

 

it might meant metaphor concept int heir language.

since elliptical movement algebra is not exactly same as topologocial geometry's topology spaces functions. 

so it might be metaphor concept of aliens, when a topological structure is binded to another algebra form of 2d elliptical movement. 

so initial hello of aliens might had been:  starting with metaphor concept.  since we humanity is not like them, they might wanted to assure a metaphor concept or show its necessary to communicate in first hello of aliens.

 

ok i liked this scifi story i created :) 

 

ok i should learn more maths cause i hadnt learnt commutative algebra yet any. i paused studying topology whilst. but thinking of what kind of 4d surface might had created the surface i described of spehere and such lower and upper structuring. if it were to  be a higher dimensional structure actually trying to fit to 3d dimensions. or being perceived in 3d dimensions.

i think commutative algebra might be needed if ever aliens and humans communicate. to create morphisms in communication/shared topics. in this scifi story i  create from recent last week's lucid dream i mean.