Seminars at Quantum Future School, still have those?
- Thread starter Cyre2067
- Start date
Hint6:
The very same "polar opposite" THING, but from another perspective:
or, view the same, in black and white, with huge resolution (as created from numbers by Mathematica): here
Hint7: This THING, in the space where it lives, has 600 vertices, 1200 edges, 720 pentagrams, and 120 dodecahedrons (though not all are seen in this projection, as some of them coincide).
The very same "polar opposite" THING, but from another perspective:
or, view the same, in black and white, with huge resolution (as created from numbers by Mathematica): here
Hint7: This THING, in the space where it lives, has 600 vertices, 1200 edges, 720 pentagrams, and 120 dodecahedrons (though not all are seen in this projection, as some of them coincide).
John G
The Living Force
Given "polar opposite", not 3D, and the 353535 interpenetrating triangle clue, plus the general look of it, I'm tempted to think something like the two 7-dim 56 vertices polytopes that E8 adds to E7. There however seems to be many more vertices than that so you may be forming the full 240 vertices of the E8 polytope with your 120 vertices 600-cells (that I know you have worked on). I need to try to count the vertices. Oops I see from your post, it has 600 vertices, WOW!... oh yeah after further review there's a 600 vertices 120-cell dual.... the 120-cell and 600-cell are both 4-dim which means the idea of forming the 240 vertices of the 8-dim E8 polytope from two 4-dim 120 vertices 600-cells seems somewhat illegal but Tony Smith does it with the following description:
Here is another way to see the 240 E8 root vectors: Recall that the dual polytope to the 600-vertex 120-cell (4-dim hyper-dodecahedron) is the 120-vertex 600-cell (4-dim hyper-icosahedron) which can be made from vertices and Golden Ratio points on the edges of a 4-dim 24-cell and that if the rational points of the 4-dim space are taken to be a 4-dim subspace spanned by {1,i,j,k} in the 8-dim octonion space with basis {1,i,j,k,E,I,J,K} and the irrational Golden Ratio PHI = ((1 + sqrt(5)) / 2) points are taken to be a 4-dim subspace spanned by {E,I,J,K} then the 120 vertices of the 600-cell generate an E8 lattice in the 8-dim octonionic space.
Here is another way to see the 240 E8 root vectors: Recall that the dual polytope to the 600-vertex 120-cell (4-dim hyper-dodecahedron) is the 120-vertex 600-cell (4-dim hyper-icosahedron) which can be made from vertices and Golden Ratio points on the edges of a 4-dim 24-cell and that if the rational points of the 4-dim space are taken to be a 4-dim subspace spanned by {1,i,j,k} in the 8-dim octonion space with basis {1,i,j,k,E,I,J,K} and the irrational Golden Ratio PHI = ((1 + sqrt(5)) / 2) points are taken to be a 4-dim subspace spanned by {E,I,J,K} then the 120 vertices of the 600-cell generate an E8 lattice in the 8-dim octonionic space.
....Has its "polar opposite". Is this image of the "polar" 'combined' with the original image?? I've looked at this this "polar" image for some time now looking for some patterns and shapes. One interesting shape I have managed to see thus far is the polygon in the center that is a heptagram...ark said:
Could this "polar" have something to do with the following?
July 11, 1998 F****, Ark, Laura, TR and JR
[...]
A: Realm border is when the reality shifts for
all.
Q: (A) Yes, but why is this reality shift related
to magnetic field disturbance? What is the
connection?
A: Your physiology and etheric orientation are
both tied into the magnetic state of your
environment.
Q: (L) Okay, you said before that the magnetic
field is going to reverse...
A: Magnetic poles reverse.
Q: (L) Okay, what is the magnetic field going
to do. It is going to change in some way. Is it
going to increase, decrease... is this to a
degree - something other than direction -
amplification? (T) Will anything change in the
strength of the field?
A: Let us illustrate. Now: Earth. [A circle is
drawn with radiating spikes all around fairly
close to the surface.] Earth after: [A circle is
drawn with double radiating spikes with those
in Polar Regions considerably longer than the
others.]
Q: (T) So, it is the same, except it is larger?
A: Close.
Q: (T) Are you indicating that the magnetic
field will be stronger?
A: Broader and larger.
Q: (L) What is the cross in the middle?
A: Geodirectional grid reference. You
incorrectly added circle on side. Lines of
magnetic field alignment should be shown as
longer at poles. "Crosshairs" in illustration
are for directional reference only.
Q: (T) Does this mean it will be stronger
also?
A: Larger and broader.
Q: (A) People work near strong magnets much
stronger than the Earth's magnetic field, yet
nothing happens to them that we can see.
A: Not true. Body chemistry is altered. Is not
long term or permanent exposure.
[...]
Hmm, could this image possibly be Earth in 4D?!? Hmm.......
July 11, 1998 F****, Ark, Laura, TR and JR
[...]
A: Realm border is when the reality shifts for
all.
Q: (A) Yes, but why is this reality shift related
to magnetic field disturbance? What is the
connection?
A: Your physiology and etheric orientation are
both tied into the magnetic state of your
environment.
Q: (L) Okay, you said before that the magnetic
field is going to reverse...
A: Magnetic poles reverse.
Q: (L) Okay, what is the magnetic field going
to do. It is going to change in some way. Is it
going to increase, decrease... is this to a
degree - something other than direction -
amplification? (T) Will anything change in the
strength of the field?
A: Let us illustrate. Now: Earth. [A circle is
drawn with radiating spikes all around fairly
close to the surface.] Earth after: [A circle is
drawn with double radiating spikes with those
in Polar Regions considerably longer than the
others.]
Q: (T) So, it is the same, except it is larger?
A: Close.
Q: (T) Are you indicating that the magnetic
field will be stronger?
A: Broader and larger.
Q: (L) What is the cross in the middle?
A: Geodirectional grid reference. You
incorrectly added circle on side. Lines of
magnetic field alignment should be shown as
longer at poles. "Crosshairs" in illustration
are for directional reference only.
Q: (T) Does this mean it will be stronger
also?
A: Larger and broader.
Q: (A) People work near strong magnets much
stronger than the Earth's magnetic field, yet
nothing happens to them that we can see.
A: Not true. Body chemistry is altered. Is not
long term or permanent exposure.
[...]
Hmm, could this image possibly be Earth in 4D?!? Hmm.......
I won't pretend that I have followed your thoughts on the operations that you have computed, but regardless, you mentioned a lattice, that is, an E8 (?) lattice? Whaetver the E8 is supposed to mean to an illiterate geometrist wanna be like myself, mirth, I don't know at the moment; however, your mention of the lattice reminded me of the following:John G said:
July 10, 1999
[...]
Q: (A) There are infinitely many dimensions
because there are infinitely many slices. Now
we come to densities. There are not infinitely
many densities, there are only seven. Or, are
these seven just for the general public and
there are really infinitely many of them as
well?
A: No.
Q: (A) Good. So, there are seven densities.
Now, how come, there are seven, and not
three or five, or eleven? Does it follow from
some mathematics?
A: What form of mathematical theory best
describes the concept of balance?
Q: (L) Algebra. (A) So, I had the idea that
these seven densities were related to what
Gurdjieff relates to the number of laws that
apply in the various densities; the higher the
density, the fewer the laws that apply, which
means there is more freedom?
A: That is very close. Consciousness is the
key here.
Q: (A) Yes, so my question relates to the
geometric model of gravity and consciousness.
A: Picture an endless octagonal... in three
dimensions.
Q: (A) A lattice, you mean?
A: Okay.
Q: (A) Are these densities related to the
mathematical concept of 'signatures of the
metric?' I would like to model densities with
slices of different geometric properties, in
particular slices with different properties of
the distance.
A: Yes...
[...]
Anyways, enough out me for today.
John G
The Living Force
and the very next line was:
The not understandable stuff comes from Tony Smith not me, there's tons of details I don't understand either and I've spent thousands of hours at Tony's website. E8 is an E-Series (E6, E7, E8) Lie Algebra and the 8 in E8 means the E8 Algebra's root vector polytope lives in 8 dimensions. It's a shape that can tile 8-dim spacetime without any gaps. That could be useful at high energies when curled up space is not curled up but at our normal energies, it's a 4-dim spacetime (for Tony, a 4-dimensional HyperDiamond lattice 4HD made up of one hypercubic checkerboard D4 lattice plus another D4 shifted by a glue vector)... as for octagonal and 3-D that could refer to tiling 3-dim spacetime with D3 cuboctahedra and octahedra, perhaps antigravity-wise useful (Fuller's ideas) for us humans who don't work well with the time dimension. As for signatures of the metric, that's a different use of D3, etc. since you are talking degrees of freedom for spacetime (rotations, boosts, translations, conformal transformations, dilation, etc.). If you think of a 26-dim "macrospace", you could even think of matter and antimatter as macrospace degrees of freedom through something called E6 orbifolding. My guess for one difference between 3rd and 4th density has to do with the availability of the conformal transformations and dilation degrees of freedom (related to complex spacetime vs real spacetime). This is part of Tony's model where Tony references Ark (and Coquereaux).
John G was again right on the target. The THING is 600cell, its "polar opposite" is the 120cell. They are one"dual" one to another. They both are "solid bodies" in 4 dimensions. 600cell has the symbol (so called "Schlafli symbol) {3,3,5} while 120cell has the symbol {5,5,3}. Here is the "standard" projection of the 600cell that you can find on the net:
I like my projection more. But the standard projection reminds me of something. Didn't C's say "Spirograph", when talking about the "comet cluster" (94-10-07)?
I like my projection more. But the standard projection reminds me of something. Didn't C's say "Spirograph", when talking about the "comet cluster" (94-10-07)?
Interesting. I had the exact same thought when you posted it orginally. But then I dismissed that idea somehow because I thought you were taking us along a different pathark said:
Does your paper has something to do with gravity? Is that what inspired you to make this connection? For me it was just a plain association in the grey matter.
Dominique.
ArdVan
Jedi
I woke up this night with the thought why does Ark call these mathematic models "polar opposite". Is this just for fun or does it have a deeper meaning to it? I think I have an idea what a polar opposite may be as Mouravieff describes them, but not that I really understand it.ark said:
Now here this is mathematics. I tried to simplify. What would be a "polar opposite" of for example a 2D-square? I couldn't imagine it. So what would it be for a simple line? A line pointing into the opposite direction? But wouldn't that be more like a anti-line cancelling the given line? What about a line that it perpendicular to the first line?
Well I have no idea? After an hour I had to let go of these thoughts to be able to sleep again.
John G
The Living Force
Here's the definition:
http://en.wikipedia.org/wiki/Dual_polytope
So a square would be the polar opposite of a square (you could think of one square being rotated into a diamond). For a line, I guess it is just the line itself cause the vertices and "faces" are the same thing.