1. few things that you people who program these wonderful hyperdimensional snapshots, sequences & even raytraycers are left with, to code 4 dimensions into 2d plane of representation, are, usually, some color-coding and a bit of renaissance perspective.
noticing the illustrations in Geometry & Imagination by Hilbert/Cohen-Voss, the diminishing thickness of lines in perspective is used skilfully to evoke experience of depth (3d).
could someone implement this (pat, quickfur or others skilled in programming...) ? this would let another code-spectrum to be interpenetrate with those currently used, which would allow easier 'mind-plementation' on user's part.
2. (the following is partly spaced out).
the space from which we project is the deeper intent of our projection-making - i.e. we try to acquire a different than usual intuition of n-space by understanding operations and structures within questioned space.
however, that (mind)space which is our major habitual tendency (for our spatial intuition) the cartesian 3-space which is thus almost-hard wired to E3-structuring (& therefore inhibits mostly the acquiring of another in-tuition for space), is the space which is used for almost all the projections I've seen up to this day (perhaps apart from few, like for ex. burbanks', which use a wide FOV projection, however, in flat conditions (zero curvature)). this state of affairs contradicts its own goals, (unique novelty cannot ) and should be corrected.
if you look at the actual visual field in its wholeness, our vision is actually curved the closer to infinity (=farther from frontal focus) it gets (border of vision is horizon defined by eye-holes in our flesh). also the retina is curved surface. open-landscape dwellers tend to mentally curve straight parallel lines, contrary to habitual tendency of urban humans, who have in general tendency to straigten/flatten up slightly curved parallels into straight lines. already leonardo explicitly stated and sketched on curvature of visual space. however, the flat version of perspective prevailed along with flat rationalism and re-wrote experiential, curved space of vision, into rationalized abstraction of E3.
thus, abstraction took value over experience-as-such. such a reduced (non-integral) mode of mind, similar to thinking (not so many ceturies ago) that world is flat, until it was found that it is (at least locally) multiply connected. then Einstein, forcing the cosmological constant into his equations with (maybe unconscious) intention to keep the old flat-mind consesus/habit alive, forced the curvature (=roundness, feminine) out of focus. in the same way, Vision was forced into seeing, even though the seer has been banned from his own seeing by this very act. our souls were hidden to us by ourselves in the night. but Vision - experience-as-such, is naturally multiply-connected, round and ever-returning, not simple, flat and fixed. Turner, Constable, Escher, Flocon&Barre, Termes and recently many others, have shown the many possibilities in which the visual reduction can be released back into its original curved space of silence.
and so i think it would be appropriate to let the old habit go, and form a new one. here is a sequence of perspectival templates, all different from currently used.
a. the first simple? step1 would be to move the projections into simply curved, half-spherical perspective. good exemple is for exemple 180degreeFOV fisheye-lens camera, or exlorations of concave/convex mirrors, glass-spheres... this means unifying the horizon(real line) into a 'circle'(real projective line). expanding into, and embracing from, the shining limit.
b. then step2 would be making it panoramatic - i.e. 2 half-spheres of vision into one whole sphere of vision. front & back of visual space connected as if rotating the viewer 2pi around the vertical (or world around the viewer). two fisheye-views / 2 circles-borders, lines at infinity, touching at single point (left or right). merge the neighbouring halves of 2 infinity-borders, from zenith through point of contact to nadir, and rearrange, similarily to grid transformations of d'Arcy Thompson) into a unity (circle) again.
c. step3 - integrating verticality. we get a 3torus (i think. ?) (or is it a glome?), where each perspective-frame in vertical circular sequence is one complete RP3 (E3+RP2)?. 2 RP3 with their infinity-boundaries. the point of view is from (any?) one point-hole, taken out of RP2. thus an unfolded klein from 2 mobius-strips joined along their boundaries, is left as the patch of fabric, from which this planar representation of whole sphere of vision is woven. this is quaternion-level, as each quaternion on unit sphere corresponds to one viewpoint(or viewing axis, if considered as vector), opposites not identified.
step4 - diagonal yoga: seems to correspond to octonion imaginary space.
diagonals finally get identified. this seems to be abandonment of (<3)'point-of-view' for (>3)'space-of-view'.
step 5 - ??? i run out of languague-skills. is this the lost of operation properties, the running out of 4 boolean-logic values ? the sequence might be considered to end at step, 4 from this perspective. beyond would lie infinite recursivity, from another perspective.
i think i read a comment from wendy in some thread in these forums, where she says that in a certain sense, 4-space (or point?) corresponds to 2d, 5d corresponds somehow to segments and 6d is like 'physical 3-point' ? sorry, if it's not exact quote, but it clearly indicates in some experiential sense, that experiencing 4d is 3d-1d(depth i guess?), 5d: horizontal is lost (thus just 'verticality' is left), and 6d-point of view is like all the views from all the points in 'infinity' (RP3 ?) on one 3-d point ?
i made prolly perspectival grids for one view for each of these levels-of-attunement. coordinate templates, they might need some correction from someone mathematically skilled and imaginatively gifted, but i believe them to be fundamentally true... i don't have math skills, just my imagination. i believe these could really help in imagining projections of multidimensional objects as more complex and more 'mentaly-digestable' gestalts/flows. i can give sketches and references if anyone really interested.