A never-ending blanket of the smallest possible spheres grappled-and-cinched by basic charge, light (space-time), mass, and special numbers.

by Bruce CamberFirst draft (revisions to come)  Initiated: November 20, 2017  Updated: January 21, 2018

Austin, Texas:  Since the very first discussions (December 19, 2011) about our chart of the 202 steps from the Planck scale to the Age of the Universe, the focus has been on the Planck Length / Planck Time and Planck Mass / Planck Charge. Each is multiplied by 2, and then each result  multiplied by 2, over and over and over again, 202 times. There are over 1000 numbers that chart a quiet expansion and a map of our universe.

I have been unsure of the first ten notations (outlined on the left and partially displayed within the chart above). The first notation, the Planck Scale [1], is actually designated Notation #0 [2].  To define Notation #1, I turned to scholars from Plato to Langlands and beyond. This would be the first time both the historic and the current the work of scholars would be held up in the light of those 202 doublings.

I am rather sure that none of these scholars has researched and/or studied the doublings from the Planck scale to the Age of the Universe [3]. Notwithstanding, I think this mathematical grid or matrix is the best possible place within which to test concepts and ideas no matter how idiosyncratic. It is a system, matrix or grid that encapsulates everything, everywhere, for all time.  If it works within this scale (matrix, grid, or system), it deserves further scrutiny.

One of my early guesses was that the Langlands’ conjectures and programs will help to define these first groups of notations. Of course, Robert Langlands is a ground-breaking mathematician from the Institute for Advanced Studies in Princeton.

Given that my mathematics is limited, my progress has been slow. The obvious first challenge is to be able to understand Langlands’ work. The second challenge is to begin to grasp how to apply that work (and the work of a large cadre of Langlands programs scholars from around the world). In two prior posts [4] [5], I cracked opened that discussion. In the process of writing up these documents, I have been encouraged to visualize in rather new ways the potential and the initial thrust of the universe [6] just from within the generation of the numbers that define pi and Euler’s equation. [7] Of all non-ending, non-repeating numbers, pi and Euler’s equation give us an immediate visualization of a basic and perfect form.

So as I have said in several posts, I believe all those never-ending numbers by definition should be considered a bridge from the infinite to the finite and continuity, creating order and sequence, and symmetries, creating relations, define them.

• First principles and even more struggles with first principles
• Analysis and speculations:  This is our third posting on a journey to learn from Edward Frenkel and his mentor, colleague and friend, Robert Langlands. [19] So, I will be looking through their writings for their statements about boundary conditions, spheres, pi, “never-ending and never-repeating numbers” to continue to develop this report on the fabric of the universe and notation 1, 2, 3, and 4. – BEC

Every notation may well be a layer of the fabric of the universe.

.It seems that the ever-changing, never-repeating, exquisitely-fine layer of notation 1 lifts up a projective layering where particular geometries begin to define notation 2, and it begins to push out both as a projective geometry and a derivative Euclidean geometry within Notation 3. Then, in much the same way Thomas Hales envisioned Kepler’s cannonballs, these additional basic structures begin to emerge. Yet with only 4096 vertices, there are limits of possibility.

The many factors for this initial push of inflation, especially coupled with Planck charge, makes for a constantly expanding universe. Yet, even as they emerge, each has the potential to be uniquely defined with one or more of the many inherent mathematical definitions within this nexus of transformation. [19] There is more to come and updates for what is already here!

There are many other pages that  use this stacking image: [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], and [12].