Right now I'm just going to post all this information together in one post and take time to review and sort/organize it to see if there maybe something linking them together. My imagination is somewhat bubbling with all these concepts/ideas in proximity.
I. Abstract Constants
"What is the measure of the faery ring? What is the pace of its dance?"
1.618.. = 1+ sqrt(5)/2 = (a(phi) + a = harmonic relationship between co-planar/intra-dimensional measures. "Holographic" or 'living' number in that it acts as a scalar 'lense' providing a holographic projection of a measure. Geometrically, one can generate 'golden volumes' by using phi to measure a line from a square/rectangular body and turn that line perpendicular to the plane of the perpendicular segments. A square generates one height, a rectangle two (which is architecturally interesting, more later). While phi/pi are both present in the Great Pyramid, phi is a predominant measure, creating the approx 52 degree slopes which, as per the LoO material, "collect power" (create a spatial focus).
3.1415.. = C/d = A/r2 = A harmonic relationship between area and perimeter. Equidistance, volume, and angularity are interesting notions within this lense.
Granted i'm approaching these concepts with an architectural bias and the naivete of someone who isn't very fascile with math, but perhaps there is a useful relationship with pi-measured intervals (architectural space) and phi-measured elements (architectural elements). Visually I see this as a measuring of foreground (phi) elements to a background element (pi). Pi seems to inherently be related to volume (time/space, space/time), measured geometrically as it cuts into a 2d 'world' (planar) while phi seems to bear a more directly relationship to limited dimensions (planes). In nature, euclidian planes are virtual, with scale determining the perception of a 'surface'. Our planet is a (mostly) equidistant-volume whose mass determines a perpendicular s/t attracting force, gravity.
9.81 m/s^2 : a = fm1/r2 = (G*m1*m2/r2)/m1[G = 6.67300 × 10-11 m3 kg-1 s-2] = this creates a stratification of densities within a planetary body. This body is in motion and in motion in relationship to bodies and patterns at many many interrelating scales. Rotation is a predominant characteristic of this motion. Rotation is pi related. Subtle trans-planar motion is oblique (ie, wind shear or tectonic sub-duction). G is perpendicular to the center/circumference of the planet, since it is a field condition. If it is a s/t condition which causes material densities to layer dense-to-expansive, then the reciprocal is a t/s condition which causes spiritual material densities to layer expansive-to-dense along the same "lines of force". I see this as creating a "potentiated distance" in that the body and its place on the planet is kept in 'distanced tension' from the soul and its place, hence our tendency to project idealistic 'heavens' "out there" and 'over us'.
The number of wholeness or completion. Expounded upon in many analyses of mythology by Jung, Campbell etc. Also, 4 relates pi and phi: 4/sqrt(phi) = approx pi.
E)RS' Inter-Regional Ratio
[I am the least aquainted with this number, especially architecturally. But in the post linked above it is used to translate between s/t and t/s with dreams, which is a fascinating application.)
156.444 - With this I want to link this image and its related webpage. Link. While it contains a large amount of information in an incredibly droll format it is similar to this post in that its a collection of information related to measure and motion (with all the trappings of excessively newagey speculation, yadda yadda). The reciprocal relationships in the linked graphic are interesting: the siting of the virtual pyramid to the built pyramid. The solidity of the capstone in relationship to the SPACE of the chamber. The scale of pyramid to chamber to capstone.
II) Other Abstract Constants
A) e, i - to copy/paste Gopi's response in the thread linked at the start:
I'm still working on digesting this.Gopi wrote:]"You need to be careful in using that value for the inter-regional ratio throughout, as it is valid only for three dimensional atomic structures, and not for subatomic particles.
The exponential 'e', imaginary 'i', 'pi' and 'phi' are unique numbers, which describe certain inherent geometric relationships.
'e' is the correspondence between the recursive nature of turn of the time region expressed in space/time region.
'i' and 'pi' together give the correspondence between orientations in space/time region and time region.
The linkage of space/time region and time region has to be local in both space AND time, hence it has to be a real number.
That is phi, which is the simplest number that can be defined by a recursion. If you divide a segment into two parts, the ratio of the whole to the bigger segment is the same as the bigger segment to the smaller. Hence you get a number that is alive.
III) The Faery Ring
The trance-drumming of the shaman is interesting to consider. It creates a periodic rhythm which allows a person synch up in a wholistic (or musical) fashion. Dancing requires that the body, mind and spirit be in accord for the dance to be authentic.
If a group of 6 people form a circle, finger tip to finger tip, and all are 6' tall (and so 6' tip to tip') -how would pi, phi, and the gravity relate? A correlating image I see is the rotation of a cliche-ufo, or any rotating body (vortex, lenticular galaxy, dervishes, etc). Whats interesting to me is that these are images of very different events, scale wise.
My interest in this information is its application: the great pyramid, as per the LoO material, was a tool for meeting the self - the application was healing, understanding, encountering, evolving. I'm curious as to how all these things can be intentionally used in the s/t waking world to facilitate trans-regional "health". For example, using the Inter-regional ration to translate between an hour-of-the-body vs an hour-of-the-soul, we might be able to assess what one hour of waking healing work might mean in the reciprocal soul-realm.
I'm curious to eventually understand how this applies to built things in the world - their measures, materialities and the motions they engage in.