If Langlands Programs are a possible Standard Model of Mathematics…

We’ll have to learn the Langlands Programs.

by Bruce Camber  Working, first draft.  Revisions in process (all articles on this site are subject to revision at any time). This is the most recent article and usually it will be the roughest. Your comments are encouraged.

Austin, Texas:  I believe the Langlands programs can help us to understand the first 60 or so notations. Yet, these programs (and conjectures) are difficult for non-mathematicians. In three working drafts, I barely scratched its surface. The first article, Langlands I, is a call for analysis and simplicity. The second article, Langlands II,  a search inside simplicity, looks for natural starting points to begin to define a possible fabric of the universe. The references to Langslands are shallow. And, in the third article, Langlands III, I made some preliminary guesses about the nature of the first four notations. The one Langlands quote from Edward Frenkel is all but gratuitous.

To date, the Langlands writings have been of very little help.

References. With no less than four ArXiv articles about Langlands program open on my desktop,  I have been wondering if both Galois theory and abstract algebra can somehow be reduced to more simple concepts if each had more simple starting points.

Search.  I thought, “What was the first moment in time? Is it best described by the Planck base units?  What is the beginning? If we can agree on that, we can start building.”

I opened several searches of the Langlands’ literature. The only discussions on the web for “Langlands programs” + “Big bang theory”  are within this website and other closely-related websites.  So, although I suspect most of the folks within the Langlands group believe the big bang theory is the best description of our earliest universe (and, of course, I do not),  “infinitely hot and infinitely dense” are not among the Langlands programs  conceptual frameworks.  “Langlands program” + infinity  gives us ” infinite dimensional representations of Lie groups” but no discussion about the infinite qua infinite and the finite qua finite.

In another search I tried “Langlands program” + “Planck units” because it is important to know how Planck Time and Planck Length relate to the Langlands programs.  Langlands + pi  and Langlands + circles and Langlands + spheres are all being explored. And finally, I searched for Langlands + Euler’s equation.  There is an entire section of Langlands’ Euler Products but we have just begun that investigation.

The Push Back. Various mathematicians in the literature say it will take a few years to understand the basics, especially if by working through the conjectures on one’s own schedule. I call my schedule, Langlands Programs for Dummies. My weakness with Galois theory and abstract algebra is significant. Yet, there are people like Edward Frenkel who try to write simply and clearly. But Frenkel is an exception. There appears to be within our global culture a natural instinct to keep most plebeians outside one’s discipline. Perhaps scholars, in disbelief that they get to do what they love to do, believe it is better to be a bit aloof and to keep people guessing. In mathematics they can continue working with their numbers and concepts without too much interruption.  However, life is too important for that attitude especially when the questions addressed by these mathematicians are fundamental to knowing who we are, where we came from, and where we are going.

Moving on. So, after a very quick review, let us pick up with the fifth notation in our hunt for concepts that can empower insights about the structure of the universe.  I will continue to keep an open ear and heart for inspiration from Langlands, but for now, I’ll continue with simple logic and the simple equations and structures that have been defined to date.  Yes,  although it behooves all of us to somehow simplify the Langlands Programs, it should not slow us down.  We have at least 67 notations to create out of nothing!   A review of Notations 1-4  Notation #5

Here are a few of the pages preceding this page:

  1. November 23, 2017:  A never-ending blanket of the smallest possible spheres grappled-and-cinched by basic charge, light (space-time), mass, and special numbers.
  2. November 18: Number generation, the perfections of circles-and-spheres, formulas, and the nature of forms
  3. November 15:  Before we can understand the complex, we need to understand the simple things. An introduction to our study of the Langlands programs.
  4. November 12:  Seven reasons to look more deeply at our chart (at the top). It is still a  largely-unexplored  model of the Universe
  5. November 9:  Over 1000 Simple Calculations Chart A Highly-Integrated Universe
  6. November 8: We live in an exponential universe.

“Behind it all is an idea so simple, so beautiful, that when we grasp it — in a decade, a century, or a millennium –
we will all say to each other, how could it have been otherwise?” -John Wheeler, physicist, 1986, Princeton 

Chart1-24 24 of the 202 notations that chart the universe using base-2: A mathematical matrix and system for cosmology, ontology, physics and more

Homepages: Langlands I, II, III Prior |1|2|3|4| 5| 6| 7| 8|9|10|11|12|13|14|15|16|17|18|19|20|Original