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zhisheng



Joined: 06 Apr 2010
Posts: 10

PostPosted: Sun Apr 11, 2010 2:58 pm    Post subject: Reply with quote

Yep, transposing the truth here amounts to taking just the right point of view, wherein the primal nature of the problem stands out and the the irrelevant recedes to the background.

Anyway here is how each line through the plane determines its own unique symmetry relative to pairs of points on a circle. I have drawn a circle and a line L below. The lines in the figures of this post have nothing to do with the line of the previous post.

Note that each pair of points A and B on a circle determines exactly one line of its own, and this line crosses the line L at exactly one point, which I shall label as L(A,B). Another pair of points X and Y on the circle determines its own line, and another point L(X,Y) on the Line L. I will say that two pairs of points on the circle are symmetric relative to the line L if they points they determine on the line L coincide.

Thus, in the figure below, the pair A and B is not symmetric (relative to L)to the pair X and Y because L(A,B) is not L(X,Y), but the pair A and B is symmetric with the pair C and D because L(A,B)=L(C,D).



Note that if you have any pair of points A and B on the circle, and a third point C, there is exactly one line through L(A,B) and C. This line cuts through the circle at exactly one point: we shall denote that point by
[A,R,B]

Thus the pair A and B is symmetric with the pair R and [A,R,B].



Recall tha the major arithmetic operations, like addition and multiplication tend each to have a "neutral" point. For addition, that neutral point is 0: 0+p always equals p. For multiplication, the neutral point is 1, 1 times p always equals p. In other words, a neutral point appearing in an operation does not change the identity of the other point appearing with it. For this reason, a neutral point is often called an identity point.

Once a symmetry is given, choice of a neutral point for it is more or less arbitrary. We will choose a neutral point for our symmetry relative to L by picking a point E at random (see below). Having chosen a neutral point, we can now precisely describe the operation. But first we must give it a name: say #. We don't use + or x because these already have a specific meaning. We define then, for any two points P and Q on the circle,
P#Q=[P,E,Q].

Thus P#Q is the point such that the pair P and Q is symmetric with the pair E and P#Q.



It is important that we keep in mind that the operation # depends both on the line L and the neutral element E, and that if these are changed, then the operation changes too.

In the next posts I will illustrate with some specific examples.
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zhisheng



Joined: 06 Apr 2010
Posts: 10

PostPosted: Sun Apr 11, 2010 4:30 pm    Post subject: Addition Reply with quote

For this example I will take for L the vertical line which is tangent to the left side of the circle, and for E the point on the circle horizontally to right of the tangent point.

I have taken two points P and Q more or less at random and shown what their resultant P#Q is.



Now put theoriginal projective line into the picture, and adjust notation so that things mesh. We shall here write + for # and 0 for E:



So, in the figure above, we have taken two numbers P and Q on the number line at random (actually so the action fits on the screen). We want to add the two together.

So we project them back to the circle and get the orange points on the circle P and Q.

The neutral point for addition is 0, and projecting it back to the circle leaves it fixed.

Now we take P#Q where # is the operation relative to the line L and the point E=0. We write # here as +. Using the method described above, we get P+Q. Now we project P+Q back to the number line and get the sum P+Q.


Last edited by zhisheng on Sun Apr 11, 2010 10:08 pm; edited 2 times in total
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zhisheng



Joined: 06 Apr 2010
Posts: 10

PostPosted: Sun Apr 11, 2010 5:42 pm    Post subject: Multiplication Reply with quote

For the second example I will take for L the line cutting horizontally through the center of the circle, and for E the point on the very top of the circle. Here the line L cuts through the circle at two points, and so neither of these points can appear in the operation #.



As before, we shall bring in the number line and adjust notation. We shall write x for # and write 1 for E:



So, in the figure above, we have taken two numbers P and Q on the number line at random (actually so the action fits on the screen). We want to multiply the two together.

So we project them back to the circle and get the orange points on the circle P and Q.

The neutral point for multiplication is 1, and projecting it back to the circle brings it to 1.

Now we take P#Q where # is the operation relative to the line L and the point E=1. We write # here as x. Using the method described above, we get PxQ. Now we project PxQ back to the number line and get the product PxQ.
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micpsi



Joined: 11 Feb 2007
Posts: 45

PostPosted: Mon Apr 19, 2010 2:26 pm    Post subject: Reply with quote

Azoth wrote:
firstly, i said super genius cause that guy is obviously very smart, period. second, the golden dawn lifted godnames from older sources.


But they got some of the Godnames in the wrong order, as well as concocting one or two. That's the point. That "super genius" proved that some of their assignments of Godnames to Sephiroth were wrong. This was achieved by correlating the Kabbalistic function of each Sephirah with the way its Godname number characterizes the outer and inner Trees of Life. The Order of the Golden Dawn members had NO real mathematical insight into what they were dealing with and so they made a few errors in their assignments.

When people blindly follow tradition - even modern revisions of a mystical doctrine - it can lead them into error. Only mathematics can show where the error lies.
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zhisheng



Joined: 06 Apr 2010
Posts: 10

PostPosted: Sat Apr 24, 2010 11:20 pm    Post subject: Reply with quote

Quote:
it just may be that the pentagram isn't about Solid (3D) geometries. it's more specifically about resultant proportions in the manifestation of phi.


One of the more interesting 3D manifestations of phi is the pyramid based on a square such that the area of the visible surface equals phi times the area of the base (such as was the Great Pyramid at Giza in its prime).

The epicenter (or center of gravity) of any pyramid is directly above the center of the base, about 1/5 of the distance up towards the apex.

If you build such a pyramid and make it hollow inside, line or paint the inner surface so that it (walls and base alike) reflects light, and then shine light inside (either incandescent light or sunlight), it turns out that there is a concentration of sheng qi at the epicenter.

If one then places a container of water on a stand at the epicenter, or better yet suspends it from above so that the water is at the epicenter, and leaves the water at this position for a certain time (with the light shining), then the water will become suffused with sheng qi.
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Raphael



Joined: 20 Aug 2007
Posts: 1337
Location: SpaceTimeVibration

PostPosted: Thu Oct 21, 2010 9:36 pm    Post subject: Reply with quote

zhisheng wrote:

If you build such a pyramid and make it hollow inside, line or paint the inner surface so that it (walls and base alike) reflects light, and then shine light inside (either incandescent light or sunlight), it turns out that there is a concentration of sheng qi at the epicenter.

If one then places a container of water on a stand at the epicenter, or better yet suspends it from above so that the water is at the epicenter, and leaves the water at this position for a certain time (with the light shining), then the water will become suffused with sheng qi.


We know the Chinese had pyramids too.

But you are implying the Egyptians were into feng shui?
Laughing Laughing

namaste

_________________
KEY 528=Swastika=ancient Spherical Standing Wave Theory
“A theory is more impressive the greater is the simplicity of its premise, the more different are the kinds of things it relates and the more extended its range of applicability…”
-Albert Einstein
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Raphael



Joined: 20 Aug 2007
Posts: 1337
Location: SpaceTimeVibration

PostPosted: Fri Oct 22, 2010 11:56 am    Post subject: Reply with quote

Azoth wrote:
firstly, i said super genius cause that guy is obviously very smart, period. second, the golden dawn lifted godnames from older sources.
as for my query thanks for nothing.
but it is funny i see your post today. i was just reading about the letters M and S. mem as we know. water and Mars? at first i didn't get the connection. but it's pretty neat that you echoed said connection. i won't bother to elaborate.
you misconstrued my tone. there is a lot of speculation out there....


Azoth

hey I see this thread is dated....but the esoteric never is.

what about the M and S?

namaste

_________________
KEY 528=Swastika=ancient Spherical Standing Wave Theory
“A theory is more impressive the greater is the simplicity of its premise, the more different are the kinds of things it relates and the more extended its range of applicability…”
-Albert Einstein
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