Sacred Geometry Transcendentals: the Transformative Principles
Sacred Geometry derives from the primal act of the Division of Unity
∆ represent the transformative principles.
The ancient wisdom tells us that both number and alphabet, that is both mathematics and language sprang from geometry.
Division of Unity: Pi/∏
From undifferentiated Unity (circle) creation occurs through an internal division of unity, the primal act, since there is nothing outside, God creates within itself, the finite reality (the diameter of the circle). In duality 92) the possibility of existence, then form. (3) and multiplicity. The diameter is related to the Circumference by π, irrational…God is never quite resolved in finite terms.
The relationship between the diameter and circumference of the circle represented the teaching of the inner and the outer…the soul and the body…the idea and manifestation.
Tai Chi: divides unity such that each half is the whole as the circumference of the whole=the perimeter of the halves.
The diameter then equals the circumference. thus there is no separation from Unity and in the limit of expression differentiation merges into Unity
Guage Theory: creation arises from the breaking of symmetry.
Unity represented by circle, square, triangle, pentagram/double square. The division of these yields:
π, √2, √3, √5 and ø defines the basic symmetries in nature
√2, √3, √5=Triad of Transformative Principles.
These are all that is needed to define all the forms in nature.
If the form/manifestation is knowable-rational, the diagonal or the root is the irrational, the unknowable.
Where whole numbers, integers represent states of being, qualities in existence, symbolize creative principles or Laws: the sacred roots symbolize process…the dynamic.
The principles of 1) multiplicity/generation- 2)formation-and 3) transformation/re-generation.
Transcendental Numbers: the “irrationals” numbers or √ roots are incommensurate: cannot be resolved into whole numbers…go on infinitely.
π does not repeat-has all patterns of numbers
Pythagoras called the incommensurable numbers “un-utterable”, the “alogon”, the “formless” because they represented the creative power of expansion which itself was un-utterable. Pythagoreans were sworn to secrecy not to reveal the existence of the alogon.
∆ the transcendentals, irrational numbers define the relationship of the finite (material) to the infinite (spirit) or to the Absolute through a discontinuity. The paradox is resolved in geometry ie pattern.
The relationship of number or existence to Unity
Lao Tze: “To seek the root is to return to Source”.
Roots represent the essence of number.
“The root contains within it the method or idea of the progressive transmutation of the self created substance that is matter into its own knowable spirit-image.” R. Lawlor
Sacred Geometry Roots: Proportion & Means
Geometrical Means: the transcendentals are the means terms in certain geometrical progressions.
Root 2, √2 mediates the Octave: 1:2: 1:√2:: √2:2 hence is the generative function.
√5 also mediates the octave as the squares: (√5)2=(1)2+(2)2 hence relating man/life to source and to the “becoming”, reality as the embodiment of Source.
“The root contains in it the method or idea of the progressive transmutation of the self created substance that is matter into its own knowable spirit-image.” Lawlor
Egyptians: proportional thinking vs modern equation thinking. One was the center and mean of all numbers,..no zero or minus #’s
Proportion: geometric means establish the relationship between principles represented by numbers & Unity. Thus mean between:
1 & 2 (Unity & Duality or Being & Becoming)=√2…generation or multiplicity.
1 & 3 (Unity & Form-manifestation) =√3...Formation.
1 & 5 (Unity & Life)=√5…Regeneration
1 &4 (Unity & Matter)=2…Duality
∆ Duality is mean, the relationship between Unity and Manifestation
The path-return to Source from physicallity is the process of resolving dualities through successive forms/incarnations to formlessness.
Process of reconciliation, of the finite to the universal creates the spiral path…the path through matter.
Universe…even all cosmic realities can be symbolized by number. patterns of numbers , becoming mandalas thus patterns of reality.
√’s represent pathways between realties:
• the function of proportion.
• the mathematical statement of the principle of mediation.
• the Law of Correspondence: As above, so below.
Proportion provides the connection
In a proportional statement the √’s are the means relating the extremes. a/b::b/c where b=mean
Three types of Proportion statements
Geometric proportion has three terms, a Trinity.
In Greek called “Logos”: meaning a continuous proportion
The mean term relates the extremes ∆ Christ principle of mediation.
a:b::b:c solving this….ac=b2 thus Unity is a Square in matter where the circle is Unity on spiritual plane.
To create in matter one must differentiate Unity, the square…from this comes multiplicity ∆ √2, the diagonal or division of the square represents the power of generation.
The diameter of the square inscribed within the circle…matter within spirit , is the same as the diameter of the circle. Thus the division of Unity is the same.