William F Pokorny <ano### [at] anonymousorg> wrote:
> On 07/28/2018 09:49 PM, Bald Eagle wrote:
> >...
> > http://math.ucr.edu/home/baez/octonions/integers/integers_1.html
> ...
>
> "... arranged in a pattern like this:"
>
> <cool figure>
>
> "which you should imagine in 8 dimensions."
>
> Five hundred cups of coffee, first thing in the morning on my very best
> thinking day - and that last bit is not going to happen. :-)

lol.   I sometimes think that comments like that are someplace between serious -
because you could believe that someone like him might be able to stare out the
window and build that, or what he thinks is that - in his head,

and a sort of academic joke ---  "the alert reader will be able to recognize
these  integers as being evenly arranged on the surface of the C8
hypersphere...."



Admittedly, I have enough to keep me busy trying to extrapolate 3D-projections
of 4D objects into meaningful mental imaginings
http://www.dimensions-math.org/

But I suppose in some ways I "get it" enough to work with.

https://www.youtube.com/watch?v=zwAD6dRSVyI

I often picture the higher dimensions as arrangements of space that I just can't
see from my viewpoint - or in my timeline.  Imagine a sphere revolving around
the origin along a unit circle.   Looking down the axis of revolution (which is
the eigenvector of that matrix) one sees the circular motion.  Edge-on however,
you'd only see the sphere bobbing up and down in that sine-wave motion.

Moving that sphere along a spiral path (a loxodrome) on a larger sphere, in 2D
you'd see a revolving sphere start at r=0, which expanded out to r=1, and then
shrunk back down to r=0.  "Edge-on" you'd get a slice of that, or if passing the
larger sphere through your plane of perception, the sphere would start
stationary, start bobbing with increasing amplitude, and then settle back down
to rest.
Working back and forth through the familiar spatial dimensions, I can imagine 4D
objects as the whole series of frames in an animation of its projections
onto/into the 3D space I'm observing over "time".  Then I "just" put them all
together in an overlay to get the gist of it.

But I KNOW that there are "places" or "spaces" where I can't sense what is
happening, even though it is.  Like the actual circular motion of the apparently
bobbing sphere.  That "direction" is hidden.  But you COULD imagine it as
another dimension.   A color signifying the scalar value of the x-coordinate, a
numerical readout, a change in the size of the sphere to make it look closer or
farther away, --- but some OTHER metric other than location.

Harder to explain in text are higher dimensions, but after watching Brian Greene
talk with researchers about the fundamental nature of space, thing like
https://nylander.wordpress.com/2008/08/25/cross-section-of-the-quintic-calabi-yau-manifold/
become a bit more tractable.
Any given point in 3D space is a "doorway" to higher dimensions where a particle
may move in ways that we cannot see or experience (currently).  A point particle
might be a stationary node on a vibrating filament in 4D or 5D space,

[or a rotating filament, like a Troposkein Curve  {whose name I had to work to
look up AGAIN} ]

it could be a point on a "sheet" that billows in 7D space, and what wee see in
3D space may only be the frequency of motion on the part of the thing that
aligns with this 3D portion of 8D space-time-(whatever x 4).   Vibrations along
that thing of different amplitudes and frequencies in higher dimensions can sum
at that point in 3D to give an apparent motion based on "forces".

http://news.povray.org/povray.binaries.animations/message/%3Cweb.56dddcec5a67670a5e7df57c0%40news.povray.org%3E/#%3Cweb
.56dddcec5a67670a5e7df57c0%40news.povray.org%3E

Mass / gravity
Charge
Strong force
Weak force

We see their effect - but no one know what they ARE, or why they are, or what
makes them operate.

Bret Victor makes a good point about how programmers often work "blindly"
imagining what WILL happen once the code gets executed.

https://vimeo.com/36579366

So I only see this as a matter of degree.  Think about juggling the 4D vectors
of a POV-Ray animation, or the higher dimensional vectors of nested arrays of 3D
vectors in an animation.  Placements of objects with differing textures and
finishes and performing transforms on them to add or subtract them from a CSG
operation - while keeping track of coincident and near-coincident surfaces.



OK - off to get 2nd coffee.

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