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As faith began to make way for reason during the Enlightenment, humans began to deduce the relationships between certain mathematical patterns in nature. Of course a certain aesthetic appreciation for symmetry and proportion had existed for millennia; witness the extraordinary precision with which the later Pyramids, Stonehenge, and much of Classical Architecture was erected for example. The Platonic school of philosophy had a strong intuitive grasp of the idea that geometry underlay the structure of nature, although it relied too heavily on theory and not enough on actual measurement.
The Savants and Cabals of the Enlightenment choose their symbolism with some subtlety.
The profession of Arianism, (Christ as a non-divine but merely enlightened human), or outright Atheism, could get you into a lot of fatal trouble in those days. Thus they adopted a sort of compromise position and replaced the mad capricious Deity of the bible with the Architect of the Universe, an altogether more reasonable sort of creature whose works lay amenable to rational understanding. Out of this idea Freemasonry evolved to promote the ideas of the Enlightenment under various degrees of secrecy, and obfuscation, depending upon circumstances. Originally it had strong anti monarchist and anti-clerical (particularly anti-Catholic) currents, but these have ameliorated with time. It has become rather superfluous since science gained the ascendancy in the westernised world, and has since descended into mere clubbishness, and sometimes petty corruption.
Interestingly, soon after the Enlightenment had started, Geometry became superseded by Algebra. Now Algebra simply consists of Geometry without the diagrams and it gives you the freedom to do Geometry in as many âdimensionsâ as you want. The ancient Egyptians appear to have understood Pythagorasâ theorem to the extent that they could construct a right angle by tightening a rope knotted to make a 5x4x3 triangle. However it took the Greeks to work out that the square on the hypotenuse equals the square on the other two sides for ANY right angled triangle.
Astonishingly, Isaac Newton, one of the greatest figures in the Enlightenment, worked out planetary motion entirely by geometry, using painstakingly collected measurements and gruesomely complicated looking diagrams before distilling it all down to elegant algebraic form as F = Gm1m2/r^2. Despite the algebraic notation this remains, like all algebraic equations, an essentially geometric relationship.
Now when the modern mind looks at many of the architectural and symbolic marvels of ancient cultures it discerns, within at least some of it, the encoding of geometrical relationships to many of the phenomena in the natural world. Some ancient structures exhibit alignment with celestial events, some exhibit proportions such as the so called Golden Mean which reflect geometric relationships which occur naturally in biological forms or in shapes such as the pentagram or in spirals.
Perhaps we should not get too excited about such secret or sacred relationships and let our apophenia run away with itself. After all, it seems that as well as tool making apes and talking social apes, we have also made an evolutionary career for ourselves as pattern recognising apes.
However, letâs run with the concept of sacred geometry for a while and see where it leads, for the occult so often holds the door open to the sciences of the future.
A really sacred geometry should show us the proportions and relationships inherent in the entire macrocosm and microcosm, real secret of the universe stuff.
Can such a thing exist?
I suspect that it does, and that we already have a fair proportion of it, although we seldom recognise it as such. Most of it appears as algebra rather than the more easily visualised geometry; however the algebra reflects the basically geometric structure of reality.
Earlier attempts to distil from the microcosm and the macrocosm a sacred geometry such as exhibited by the cabalistic Tree of Life or the musings of Ramon Lull, (author of the original Liber Chaos!), suffer from a lack of good observational data and from contamination with theological nostrums.
The accurate macrocosmic stuff begins with Newton and becomes magnificently expanded by Einstein.
Einstein worked out the basic geometric relationships between space and time, and between mass and energy, and presented the answer as what he called Special Relativity. Such fundamental things basically exist as geometric relationships between one phenomenon and another.
He then went further and developed General Relativity to include the effects of acceleration and gravity. General Relativity describes the macrocosm in exclusively geometric terms: -
Space/time curvature = Mass/energy density
Thus what we perceive as matter actually consists of a curvature in space and time, and what we perceive as gravity actually consist of the effect of that curvature on matter.
Whilst we can draw out the diagrams to represent the Special Relativity algebra as geometry on paper, we would need multidimensional paper to do this with General Relativity, so we usually have to leave it as algebra.
Now in contradistinction to many other rebel physicists, I don't think Einstein got it wrong, I think he got it very very right. However I think more will eventually come to expand upon his insights, in particular I suspect that: -
6D Space/time curvature(s) = 6D Charge/spin densities
Now when Einstein intuited and calculated the geometry of space/time and gravitation we had only an embryonic understanding of particle physics, the microcosm, and he could not include it into a grand unified theory, although he strove mightily to do so.
The particle physics theory of the microcosm has since taken off in a quite different direction to the geometric model of the macrocosm. Particle physics theory depends on the idea of 'Quanta', (minimum sized indivisible bits of reality), hence quantum physics, in which the fundamental building blocks of reality occur as dimensionless points with a probabilistic wavelike distribution in space and time; hence they cannot have a properly geometric description. Although the quantum theory gave predictions that modelled observations, Einstein considered that it still contained a profound metaphysical flaw.
I suspect that a fully geometric model of quantum physics requires 6 dimensions, three of space and three of time, rather than the three of space and the one of time that both relativistic and quantum theories currently employ.
At the time of writing, General Relativity still provides our best official understanding of gravity which defines the large scale structure of the universe, but Quantum Physics provides the official descriptions of the other 3 forces in nature, the electromagnetic, the weak nuclear and the strong nuclear forces. Nevertheless the quantum descriptions seem to imply some very strange and paradoxical metaphysical ideas and the accompanying Standard Model of particle physics still seems largely phenomenological because it fails to provide much in the way of a mechanistic description and it contains many seemingly arbitrary constants. The description of the strong nuclear force remains particularly messy. The standard model conspicuously fails to explain the existence of 3 generations of each type of fundamental fermion particle, quark, electron, and neutrino.
Yet having described three of the four fundamental forces, if only imperfectly, with quantum physics, physicists have attempted to bring gravity into the same fold to create a Grand Unified Theory of all four, and the search for a theory of Quantum Gravity has dominated the agenda of a generation of fundamental physicists.
A quantum theory of gravity would imply that Einstein got it wrong in describing gravity as curvature in spacetime geometry and would instead describe gravitational fields as mediated by the exchange of virtual graviton particles, whilst gravitational waves would arise from the exchange of real gravitons. Nobody incidentally, has ever captured a virtual particle; theorists merely hypothesise their existence to explain field effects.
The search for a theory of quantum gravity has failed to bear fruit, and all the particles implied by various versions of it, gravitons, the supersymmetry particles, and the Higg's particles, have all failed to appear in experiments so far.
Rather than try to quantize gravity, I suggest that we should try to geometricate the quanta. In a 'Quantum Geometry' virtual particles would not exist, all apparent fields would arise from various spacetime curvatures subtended by real particles. Various papers on this site attempt to show that quantum geometry can exist in a spacetime having six dimensions, three of space and three of time. I suspect that we need to investigate the geometry of time more fully to get to a fully unified grand 'theory of everything'.