.That first second is a key.  These first ten notations (a really real Big Ten) are on a scale that heretofore has had no meaning for scholars (or for me), and this Big Ten has never been studied per se by the academic community. I believe it is where we must start.

Observation: Note that it appears that time is being redefined. It looks less like an absolute duration (Newtonian time) and more like a processing time. Perhaps it is a bit more like exascale computing [9] (which would be painfully slow by comparison) than that which is measured and then fades into some whispery thing called the past.As a child we would play games and have to count to ten, 1001, 1002, 1003… each count approximating a second. Dub-Lub. Could we say that these first 144 notations are the initial pulse of the universe? Just that quickly, an exquisitely-deep complexity comes alive. Though we’ll attempt to make sense of each notation, notation by notation, it seems that all those notations, 1-145, or The First Three Seconds, should be taken as a whole. Of course, that title uses the work of Nobel physicist, Steven Weinberg, who wrote The First Three Minutes in 1977. I am sure Weinberg could not have imagined that there are over 150 doublings of the Planck units to get to his pivotal action!.The first year, of course, is a light year, and it is between notations 168 and 169. [10]  The universe is at about the size of our solar system.  Perhaps the first year of one’s own life provides a good analogy. I speculate that we will all know what we have to know within those 169 notations. Thereafter, all the details that follow pick up within the current history of academic research and knowledge.

Notation #1

First we have the Planck scale with Planck Time (and light) built into all the equations. Then, the transcendental, irrational and incommensurable numbers have a thrust that is woven within the thrust of the Planck Charge, which is woven within the thrust within the four forces of nature — gravity, electromagnetism, the strong force, and the weak force. [11] Then, there are the dynamics of all the other non-ending, non-periodic numbers such as pi or Euler’s number. More of these were identified in a posting about numbers [12]..Today’s visualization has notation #1 generating spheres since the first moment of time to this very day, hour, second, nanosecond, attosecond, yoctosecond, right to the infinitesimal interval known as Planck Time. I see this notational sheet actually layering on top of itself as imaged below. Start with Thomas Hales analysis of Kepler’s stacking of cannonballs [13] and it literally forces the emergence of Notation #2 and all subsequent notations. Please note: The processing time for each subsequent layer is 50% slower than prior layer. That could account for dynamics within close-packing of the spheres. Also, as the notations increase so do the circles and spheres from the earlier notation. .What a wild-and-crazy image that is!.To keep track of all the details, I have started a compilation for each notation, [14] Though it is very incomplete, it is a place to park ideas, comments, questions and insights, so I ask you to please be patient, however, your suggestions may prove especially powerful. Please know that you are always welcomed here.

.At one time I was quite focused on the number of vertices. Then with Freeman Dyson’s suggestion [15], we began focusing on the scaling vertices. It begs the question, “Which constructions are the primary building blocks or the seed structures?”

.Because everything starts simply and Euclidean geometry appears to have the deepest intellectual foundation, I initially thought it would be a good place to start. I have a special affection for those five basic solids. Then I read that Euclidean geometry is a subset of projective geometry. That can’t be ignored. So let us start with projective geometry in this second notation and let it extend into every one of the 200 notations going forward.

.Now, that, too, is a special image that cannot be minimized.

.Within the next prime-number notation are the grounds for another dimension of mathematics and here I was once quite sure that Euclidean geometries would come next. Yet, at the Planck scale [16] there is so much going on, it is hard to guess what prioritizes the moment. We know the full complexity of all geometries is about to emerge. So, although we have studied a range of intellectual positions — Langlands, Barrows, Penrose, Rees, Wilczek (and so many others) — in this series of writings, I focus on Langlands. How would this group envision a logical construction path and its modalities?

Theories of Everything.These Langlands programs may actually benefit from the creative-and-adventuresome energies of those focused on defining a theory of everything. Often these people use simple geometries that have become complex. Here, for example, is an image of the Quasicrystalline Spin Network (QSN), what the Quantum Gravity Network [17] scientists consider to be the Planck scale substructure of spacetime. They may be right, however, my guess is that such an object could not manifest any earlier than the fourth notation where we’ve gone from spheres within the first doubling of the Planck scale, to projective geometry with the second doubling, and Euclidean geometry with third. The scaling vertices also become numerous — 8 for the first doubling (Notation #1), 64 for the second doubling (Notation #2), then 512 for the third doubling (Notation #3), 4096 for Notation #4, and 32,768 for Notation #5. To begin such complex constructions as the QSN, we’ll probably need most of the 4096 vertices and a good part of those 32,768 vertices within the fifth notation.

Where our first notation is primarily spheres orienting themselves to each other and the second notation is the beginning of projective geometry, I believe most of the third notation will be that tetrahedral generation pictured within that dynamic image of the stacked cannonballs. Within the tetrahedron is an octahedron. Within the octahedron are four hexagonal plates around the centerpoint, a half-sized octahedron in each of the six corners and a tetrahedron in each of the eight faces. I believe complexity begins here with this basic, basic structure. [18]

With all the other forces in play, there are many possibilities for bonding, cinching and  grappling things together. So, now we propose a second layer of the fabric of the universe.

Looking up any webpage that discusses Langlands and Euclidean and/or projective geometries opens a door, there are many sites and a lot of reading and thinking to do! It has becomes entirely clear that this will not be an easy assignment.

In a 2006 article by Edward Frenkel, he said, “We hope that in this way representation theory of affine Kac-Moody algebras may one day fulfill the dream of uncovering the mysteries of the geometric Langlands correspondence.” [19] (page 71) I suspect for all but a few among the professional mathematicians, this article will be a difficult read. For me, it is virtually impenetrable.  But, I persevere, “What do affine Kac-Moody algebras look like? In what ways would they inform our understanding of this third notation.” I do not yet know the answer, but maybe you do. Please help!

What we have amounts to the third notation, with or without Langlands programs. This doubling has only 512 vertices to share so one might project that there is a thrust of perfection and the best of projective geometries are combining with the best of all the equations currently in position. We have numbers, geometries and equations all working within the same moment which almost instantly gives us the 4096 scaling vertices within the fourth notation. Let us logically attempt to create a range of possible interactions. All of them are possible, probable and doable at some point. Nothing here is static. Everything is pushing toward efficiency, elegance and beauty.

The fourth notation is a simple doubling of the third notation. There may also be another kind of higher-order doubling of the second notation.Projective and Euclidean geometries are striking out on their own yet there are only have 4096 vertices to share. With so many more possibilities for combinations of numbers, geometries and functions, the Langlands-Frenkel dream of a unity of mathematics is happening. What do we call it? Is it legitmately included within the Langlands programs at this point?  It is difficult to know and surely we are anxious to hear from someone from among the Langlands experts to help us integrate what we have here with their work that started back in 1967.The fifth notation, another prime, will open yet another possibility for a mathematical system to emerge. There will be 32,768 vertices with which to develop an integrated mathematical system. Within the sixth notation there will 262,144 vertices and within the seventh — it’s a prime — a new system could emerge and there will be 2,097,152 vertices with which to work.

1. We now need to begin working with a Langland’s person to help guide our thinking. If you have some suggestions, you know what to do!
2. I will continue my research.
3. Together we can get this done.