[FRIAM] mathematicians computer graphic-ians — a little? help please

[Steve Smith]

and why stop at 4 when you can go higher?
https://www.youtube.com/watch?v=tfGf6gHQZQc
>
>>     First,
>>
>>     Just finished reading, _the crest of the peacock_ (ibid
>>     lowercase), by George Gheverghese Joseph. Subtitle is
>>     "non-European roots of mathematics." Wonderful book, highest
>>     recommendation and not just to mathematicians.
>>
>>     My three biggest shames in life: losing my fluency in Japanese
>>     and Arabic; and excepting one course in knot theory at
>>     UW-Madison, stopping my math education at calculus in high
>>     school. I still love reading about math and mathematicians but
>>     wish I understood more.
>>
>>     To the question/help request. Some roots of my problem:
>>
>>     One) I am studying origami and specifically the way you can, in
>>     2-dimensions, draw the pattern of folds that will yield a
>>     specific 3-D figure. And there are 'families' of 2-D patterns
>>     that an origami expert can look at and tell you if the eventual
>>     3-D figure will have 2, 3, or 4 legs. How it is possible to
>>     'see', in your mind, the 3-D in the 2-D?
>>
> I've only dabbled with origami and share your implied questions about
> the way people who work with it a lot seem to be not only able to
> "guess" what a 2d pattern of folds will be in 3d but can "design" in
> 2d to yield 3d shapes.   I suspect a formalization of how they do it
> is closer to group theory than geometry.    As for "how is it
> possible?"   I think that is the fundamental question for all forms of
> "fusing" sensory data of one type into higher level abstractions.  The
> only way I know to acquire such a skill is to practice, practice,
> practice. 
>
> For highD data, that means (for me) working in as high-dimensional of
> a perception space as possible (e.g. stereo + motion parallax with
> other depth cues like texture and saturation and hue.   Manipulating
> the object "directly" with a 3D pointer (spaceball, etc.) or better
> "pinch gloves" or even better, haptic-gloves (looking a bit edward
> scissorhandy).    My best experiences with all of this have been in a
> modestly good VR environment (my preferred being Flatland from UNM,
> named after EA Abbot's Victorian Romance in Many Dimensions (for the
> very reason you are asking about this I'd say)) on an immersive
> workbench (8' diagonal view surface tilted at 20+ degrees with active
> stereography, head and hand tracking, and pinch gloves).  You
> literally "reach out and grab geometry and rotate/drag it around".  
> I'd also recommend "listening" to them, but that can be a little trickier.
>
> Staring at clouds and other phenomena which are 3D ++ (the shape of a
> cloud as observed is roughly an isosurface of temperature, pressure,
> humidity over the three spatial dimensions) as they evolve
> (facilitated by timelapse and best observed as they "squeeze" over
> mountains or "form" over bodies of water.
>
>>
>>     Two) a quick look at several animated hyper-cubes show the
>>     'interior' cube remaining cubical as the hypercube is
>>     manipulated.  Must this always be true, must the six facets of
>>     the 3-D cube remain perfect squares? What degrees of freedom are
>>     allowed the various vertices of the hyper-cube?
>>
> The conventional projections of the Tesseract into 3D are only rotated
> around the yz, xz, xz axes... the additional ones that include the w
> axis do not present as "perfect cubes".   See second :40 and on in
> this video: https://www.youtube.com/watch?v=fjwvMO-n2dY
>
> It might be easier to accept this if you notice that off-axis
> rotations of a cube when projected into 2D yield non-square faces in 2D
>
>>
>>     Three)  can find static hyper— for the five platonic solids, but
>>     not animations. Is it possible to provide something analogous to
>>     the hypercube animation for the other solids?  I think this is a
>>     problem in manifolds as many of you have talked about.
>>
> The mathematical objects you are talking about are called regular
> convex 4-polytopes,  Wikipedia has a good article on the topic:
>
> https://en.wikipedia.org/wiki/Regular_4-polytope
>
>>
>>     Question: If one had a series of very vivid, very convincing,
>>     visions of animated hyper-platonic solids with almost complete
>>     freedom of movement of the various vertices (doesn't really apply
>>     to hypersphere) — how would one go about finding visualizations
>>     that would assist in confirming/denying/making sense of the visions?
>>
> The video above tumbles you through some regular 4 polytopes... I'll
> give everyone else the trigger-warning <trippy man!>
>
> This guy: https://www.youtube.com/watch?v=2s4TqVAbfz4 has added 3D
> printed models frozen in mid-4D tumble to give you (maybe) some added
> intuition.
>
> There are a plethora of commercial HMDs out now that would facilitate
> a great deal more than just staring at your laptop while geometry
> tumbles through 3, 4, nD.  These days I bet you can drop your phone
> into a google-cardboard device ($3 on amazon), load up a copy of
> Mathematica or similar and find a program to let you tumble yourself
> through these experiences.  
>
> I do look forward to your "trip report" and will take you to task if
> *I* start dreaming in hyperspace again!
>
> - Steve
>
>
>
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