Symmetries within the first 67 notations actually create space.

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Symmetry defines our universe.*

by Bruce E. Camber  Most recent update: July 2020 Also see: Continuity Harmony Infinity

We say, “Symmetry begets relations which beget geometries which beget space.”

  1. Consider the perfect symmetry of a circle. Go inside the circle, find the lattice, (top left image) and follow it until it becomes a simple tetrahedron. Discover the octahedron within it, and then the four hexagonal plates around the centerpoint of the octahedron. These appear to be the simplest possible beginnings of geometry as well as our universe. Yet, within our simple chart of the universe within its 202 doublings from the Planck scale to the Age of the Universe, geometry seems to lose its functional applicability around the molecular level, i.e. the tetrahedral methane molecule (.72 nm or notation 86).

    Of course, just because we can’t measure it per se, doesn’t imply that finer structures are not there.

    Throughout the years, science has developed tools to measure lengths, time, mass and charge at smaller and smaller increments. Our limit on length today seems to be defined by CERN (Geneva) and labs like it. That brings us down into the range of the 67th notation. Given all the continuity equations we know there is something within the 66 smaller notations. Referring back to our base-2 chart at the 66th, our scaling vertices alone number 4.0173451×1059 which gives us enough vertices to construct every possible potential geometry. One could assume that includes the geometries that make up the foundations of universe! In this model each doubling builds progressively and each actively defines our expanding universe!

  2. Begin with the Planck base units. Within the nexus of equations that define these units, might we hypothesize that each equation is a circle that is part of a sphere? Perhaps experts can help us to see how Langlands programs, scalar field theory, or even loop quantum cosmology (LQC) actually define the simplest geometric relations? Of course, we do not have answers and we may never have answers qua answers. Yet, we might hypostatize an answer (more than hypothesizing and less than reifying). Each doubling has time, length, charge and mass, and scaling vertices. Simple geometries necessarily emerge within a natural inflation. Though the possibilities quickly seem endless, we will need to make choices (i.e. line 12 of the chart) being somewhat guided by our initial analysis of just six sets of numbers out of the 202.

  3. Yes, there are many experts to whom we will turn with our questions. Our model is such a stretch it is difficult for most scholars to engage. Yet, we will continue researching and trying to find those who are open enough either to pull us back into the real world or to encourage our explorations. We will delight with any judgment by those with knowledge, insight and wisdom.

  4. Though just dynamic ratios, we believe each notation does unique work to structure our universe. We first began by exploring the workings of just numbers; now we will begin to watch every possible geometric relation within those numbers. Our goal is to get this new paradigm to start shifting the old to discover how every notation is always active.

  5. Symmetry bridges the finite and infinite. Symmetry is infinite and it extends throughout the finite yet is not finite. More

It could be said…

“Science gives space and time too much space-and-time.”

Isaac Newton was the stinker who got us going in this direction. It may have something to do with being the Lucasian Professor at Cambridge University. He became the second person to hold the title. He oversold absolute space and time and had no respect for anyone who didn’t buy into it.

A rather novel story about geometry The deep history of space, time and geometry has been captured by experts like Brown, Davies, DiSalle, Lightman,  and Penroseamong many other scholars. None of these people had ever seen a model of the universe that started at the Planck units and naturally expanded using base-2 notation. We are in search of scholars who would truly considered analyzing this nascent model.  Though ours is a bit more recent and at least six-times more detailed, in 1957 Kees Boeke introduced a similar model using base-10.

Getting our geometry chops up Changing our orientation to space and time is not easy. This site will struggle with it as long as there is a web and air to breathe. Some have asked, “Why haven’t we seen this model until now?

* Symmetry: The second face of the infinite.

Of the many faces of symmetry, we focus on symmetries in mathematics (particularly scale symmetries such as fractals, symmetry groups, symmetric groups  including Galois theory, Lie groups, and more), and symmetries in physics.

The first article in this series is about continuity. The next article focuses on harmony. It is followed by an article about hypostatic structure. Our introduction to it was written in April 2017 called, Hypostatic Way of Learning & Knowing.

For more:

References and Resources

Edmund J. CopelandPeter Millington, and Sergio Sevillano Muñoz, Fifth forces and broken scale symmetries in the Jordan frame, Journal of Cosmology and Astroparticle Physics, February 2022

Types of symmetry: Reflective symmetry, functional symmetry, spherical symmetry, radial symmetry, biradial symmetry, and bilateral symmetry. Also, Translation Symmetry, Rotational Symmetry, Reflection Symmetry and Glide Symmetry. What else?