Theos-Talk Archives (January 2005 Message tt01073)

Following up the previous e-mail on this subject: (See below)

(You'll need the latest version of Internet Explorer (5+) or Netscape (4.7+) 
browsers, with Java activated (in "Preferences") to handle some of the below 
web sites and animated demonstrations.)

---------------------------------------------------------------------

Dear Cass, and other friends interested in further 3-D imagination or 
visualization training.

After playing with the Tesseract at:
http://www.cut-the-knot.org/Curriculum/Geometry/Tesseract.shtml ...
Click on the "Explanation" link below the interactively animated diagram, and 
go on to see how Fractals work -- which adds some more fun... 

After you see how the 2-D triangular "Sierpinski gasket" fractalizes, compare 
it to the 3-D UNIOMNIFORM fractalization at:
http://users.aol.com/leonmaurer/UNIOMNIFORMexploded.gif
(Hint: Each triangular face of the diamond shape fractalizes into a 
Sierpinski gasket.)

See if you can imagine the 3-D UNIOMNIFORM fractalizing by starting with the 
largest Diamond shape and replicating it, one inside the other -- similar to 
the way the Sierpinski gasket fractalizes.
(Hint: Note that the simple diamond shape [octahedron] inscribed in a sphere 
has three axes.) This is analogous with the way the spherical fields 
fractalize inwardly (shown in cross section of only one of three perpendicular 
zero-point spin axes) at:
http://users.aol.com/uniwldarts/uniworld.artisans.guild/chakrafield.html

Then, imagine how the Tesseract can be fractalized similarly, by replication 
of one cube INSIDE the other, like the spherical (chakrafields) fractalize 
into bubbles within bubbles, within bubbles, etc.

Incidentally, this training enables the mind to break its limitation of 
materialistic thinking (i.e., seeing everything, superficially, as being solid 
matter only) and allows us to comprehend how the Universe (and every being in it) 
can exist on multiple planes of consciousness or separate fractal hyperspace 
fields (of descending frequency-energy orders) that are "coadunate but not 
consubstantial" (i.e., of varying substantiality and energy, enfolded within the 
same space) and invisible to each other. Yet, each field is capable of 
containing an infinite variety of holographic forms (encoded on the surface of 
the field as vibrational interference patterns) that could seem like the only 
reality to the awareness (centered in the zero-points) on that plane (state of 
consciousness). 

When fully realized, this ideation can subjectively prove (to ourselves) that 
each of us exists as a series of transcendent fields of consciousness 
enfolded within the overall "aura" (Atma, or analogous fractal of the universal 
spiritual field) surrounding the human body. See:
http://users.aol.com/leonmaurer/Chakrafielddiag-fig.col.jpg

In a nutshell; The purpose of meditation practice (with and without a seed -- 
beginning with visualizations such as the above) as taught in the yoga 
aphorisms of Patanjali -- is to transcend the ordinary sensory impressions that 
modify the mental thoughts related to the lower physically oriented self awareness 
or lowest state of ordinary consciousness... And, ultimately, to realize the 
unity of the "self" with all zero-points of awareness on all planes of reality 
up to the universal Self on the highest spiritual plane. 

According to Patanjali, experiencing that altered state of consciousness on 
the plane of Atma or spirit, and through the practice of achieving it, 
comprehending the nature of the willful control of the forces on each plane and the 
recognition of the "ultimate division of time" -- is the final awakening to a 
realization of one's true self, or the condition of "enlightenment." 

Hopefully, some of us already have, and with sufficient "self devised and 
self determined study and practice," most of the rest if us (including me :-) 
might reach that condition someday.

Best Wishes,

Lenny 

In a message dated 01/28/05 6:56:28 PM, LeonMaurer@aol.com writes:

Dear Cass,

Your daughter has the trick. All we have to do is make a mental rotation of 
the 2-D image in our mind's eye and then look at it from any angle we want to 
-- including from the back side. People with great mechanical aptitude or 
artistic talent do this automatically. Anyone who tries this and practices 
until 
they can easily draw any object from the same 3-D angle they see it in their 
mind, will be born with that "talent" in their next life. It's not much 
different from learning to ride a bicycle -- which the brain-body doesn't 
forget 
(at least during this lifetime). However, the mind, especially its higher 
aspects of intuitive memory, never forgets. Although, to be an adept artist 
in 
a new body, it will take practice in training the new brain to improve the 
skill 
and teach it how to coordinate the eye with the hand so the action becomes 
automatic. Incidentally, the same process works with sound and skilled 
musicianship. 

BTW, such visualization practice also teaches us to recognize that the 
consciousness or spirit is separate from what it sees or experiences, and is 
one of the most important aspects of meditation practice that leads to self 
realization or enlightenment. (Vide, Patanjali's Yoga Aphorisms.) The trick 
there is to advance visualization to such a state that one can see beyond 3-D 
into the higher fractal dimensions -- such as symbolically pictured in my 
chakrafield diagrams:
http://users.aol.com/uniwldarts/uniworld.artisans.guild/chakrafield.html
http://users.aol.com/leonmaurer/invlutionflddiagnotate.gif 
http://users.aol.com/leonmaurer/BuddhaBabyGordianKnot.gif
http://users.aol.com/leonmaurer/TaiChiFldDiag-figure-2.gif
http://users.aol.com/leonmaurer/Chakrafielddiag-fig.col.jpg

You might also be interested in seeing how the fractal spherical geometry 
and the fractal regular polygon (octahedron) geometry interrelate -- by 
meditating on these 3-D images:
http://users.aol.com/leonmaurer/UNIOMNIFORMexploded.gif

Best wishes,

Leon

In a message dated 01/24/05 10:08:08 PM, silva_cass@yahoo.com writes:

>
>Dear Leon
>Had fun with the Tesseract 4, and notice that it reduces to two dimensions.
> My daughter draws in 3D, when I asked her how she did it, she says she
>sees everything from above or outside of the image, as if looking down
>on it.
>Cass
>
>leonmaurer@aol.com wrote:
>
>
>In a message dated 01/19/05 7:03:22 AM, silva_cass@yahoo.com writes:
>Subject: IS IMAGINATION THREE DIMENSIONAL?
>
>>That is my question.
>>Cass
>
>Depends on what you are capable of imagining -- based on how well developed
>is your power of imagination. 
>
>I could imagine in 3D and color since I was a young child. It started me
>drawing in 3D and perfect perspective (that amazed my family and teachers)
>before I was 7 years old. Most of the students I met, when I studied art in 
my
>teens at a special school for talented children, also had that capability. 
Some 
>of us could even draw in 3D from our imagination and even with our eyes
>closed or not looking at the paper. (In fact, that was one of the tests for 
>entry into that school.) Such a skill came so naturally to me, that I 
couldn't
>imagine that anyone else couldn't do it -- until I tried teaching such
>drawing ability to all my untalented neighborhood friends. :-) 
>
>I still believe it can be trained, however ... Since, in later years, I was 
>successful in teaching others to visualize and rotate 3-D images -- 
>and even look at them from behind and also from the inside out. 
>Incidentally, one of my brothers had a similar talent (and he became 
>a well known comic book illustrator, and later, an animation and film 
>production designer)... Although, none of my children showed that same 
>early talent. Incidentally, my intuitive understanding of how we see and 
>imagine in 3D depth, helped me invent 3D Comic books in the early 50's. 
>See: http://www.ray3dzone.com/LM.html 
>
>So, perhaps, for those born with it, it's a talent that was developed in
>a previous life. (And, therefore, could be trained in this life.) I know 
that 
>after some years of meditation and visualization practice, I am able to 
imagine 
>forms in 4 and even 5 dimensions. For example, I can see a 4D hypercube
>or tesseract, and even a 5D hyper-tesseract in my minds eye... But, I can't
>describe such images -- except, possibly, as a 2-D or 3-D line drawing... 
Vide,
>my chakrafield diagrams -- which symbolically, represents an imaginary cross-
>section of a 7 or more dimensional sphere. Also, look at how a 4D tesseract 
is 
>drawn in 2D and animated in 3D at:
>http://www.cut-the-knot.org/Curriculum/Geometry/Tesseract.shtml
>
>Enjoy your imaginings,
>
>Leon...