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So, I just spent some time trying to relax my mind, stretch it, and think about
some of the programming projects I'm dabbling with before writing more code and
another 100 nested, translated functions.
Having dabbled with a bit of math that could be done using quaternions, and
being interested in some of the theories concerning particle physics, gravity,
charge, mass, etc - the following article piqued my interest:
https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/
Which "naturally" led to John Baez's site (there's always so much that leads
there)
http://math.ucr.edu/home/baez/octonions/integers/integers_1.html
http://math.ucr.edu/home/baez/
and that intersected with the spiral/vortex/warp search I was doing to lead to:
https://johncarlosbaez.wordpress.com/2016/10/07/kosterlitz-thouless-transition/
which led me to "phase portraits" of differential equations
https://imgur.com/gallery/icp09
Using, enjoying, and grappling with POV-Ray, it becomes clearer that:
In the absence of a sophisticated modeler, some programming skill is required.
To do many things with programming, it's always easier with math(s), or some
formulas or macros that "do the math".
Working in a high-level uncompiled language makes this slow.
Visualizing the results with a raytracer makes it - slower.
I also came across:
https://www.quantamagazine.org/mathematicians-tame-turbulence-in-flattened-fluids-20180627/
http://www.algorizk.com/windtunnel/overview/
https://itunes.apple.com/us/app/suspension/id488542342?mt=8
The last may be a fun toy that will help process things "in the background".
Lastly, for today, I give you:
The Mistakes I Made As a Beginner Programmer
Learn to identify them, make habits to avoid them
https://edgecoders.com/the-mistakes-i-made-as-a-beginner-programmer-ac8b3e54c312
This was a good read. Being self-taught, I'm glad to see that I do some of
these things already, foresaw and learned ways to to do them myself, and have
begun experimenting with others.
There are also a lot of things in there that I could/should probably look into
learning. Some of the terms and jargon made it hard to follow, but no worries.
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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. :-)
Bill P.
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On 29/07/2018 09:51, William F Pokorny 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."
>
As you do. :-)
> 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. :-)
>
> Bill P.
I could not get past imagining,
http://math.ucr.edu/home/baez/mathematical/(2,3,infinity)_tiling.png
as a RSOCP with the plane translating.
--
Regards
Stephen
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William F Pokorny <ano### [at] anonymous org> 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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"Bald Eagle" <cre### [at] netscapenet> wrote:
>
> 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...."
>
yes, I see it now, it's so SIMPLE!!
[--- brain dissolves into a mass of goo ---]
"the alert reader will quickly grasp that this solves all the remaining problems
of gravity, time, and the structure of the Universe. And a bunch of other
things."
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> "Bald Eagle" <cre### [at] netscapenet> wrote:
>
>>
>> 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...."
>>
>
> yes, I see it now, it's so SIMPLE!!
>
> [--- brain dissolves into a mass of goo ---]
>
> "the alert reader will quickly grasp that this solves all the remaining problems
> of gravity, time, and the structure of the Universe. And a bunch of other
> things."
>
>
>
> ---
> This email has been checked for viruses by AVG.
> https://www.avg.com
>
Hey Fermat! Get a larger margin, ok?
--
/*Francois Labreque*/#local a=x+y;#local b=x+a;#local c=a+b;#macro P(F//
/* flabreque */L)polygon{5,F,F+z,L+z,L,F pigment{rgb 9}}#end union
/* @ */{P(0,a)P(a,b)P(b,c)P(2*a,2*b)P(2*b,b+c)P(b+c,<2,3>)
/* gmail.com */}camera{orthographic location<6,1.25,-6>look_at a }
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