Enkhbat, Rentsen

Rentsen Enkhbat

Director of the Institute Mathematics
National University of Mongolia
Ulaanbaatar  (Time Zone #6  between 112°30′E   to 97°30’E longitude)

Google Scholar
Publications     More…
Taylor & Francis: On Optimization
World Scientific; Optimization and Optimal Control

We will initiate a Wikipedia page for Prof. Dr. Rentsen Enkhbat.

First email: Sunday, 19 August 2018

Dear Prof. Dr. Rentsen Enkhbat:

I am not a professional mathematician, but I have studied a little throughout my 71 years. I am not a professional physicist, but I have worked with some of the finest since about 1970. My work and websites have been a search for meaning and value and simplicity.

In 2011 in a New Orleans high school geometry class, we were exploring the tetrahedron by dividing the edges by 2, connecting the new vertices, and discovery the half-sized tetrahedrons in each of the four corners and an octahedron in the middle. Doing the same with the octahedron, we discovered the six half-sized octahedron in each corner and the eight tetrahedron in each of the faces, all sharing a common center point surrounded by four hexagonal plates that could tile the universe.

Using Zeno’s paradox, we went deeper inside. Within about 45 steps we were in the range of the CERN-scale of measurements. Within another 67 steps, we were within the Planck scale. We then multiplied our original 2.5 inch tetrahedron including both its internal octahedron and tessellating octahedrons; and within 90 doublings of the Planck Length, we were out to the size of the universe. With Planck Time, we were out to the age of the universe.

Frank Wilczek (MIT) personally encourage our work in 2013. Freeman Dyson (IAS) advised us.

By 2014, we had included the four Planck base units. By 2016, our 34-pages of charts were placed side by side so the numbers could be horizontally scrolled. Throughout this period, we were asking, “How can these 64 doublings below the CERN-scale measurements be used? Is the domain of mathematics and logic only?”

The exponential nature of base-2 is being studied and Euler’s equations and “everything Euler” is being examined and studied. We have a long way to go, so I seek experts to guide our thinking.

Would you consider thinking about the 64 doublings between the Planck scale and the CERN scale of measurements? Could the foundations of applied mathematics emerge from the Planck scale, building progressively with each doubling? Might we consider the primes along the way opportunities for unique expansions of equations?

With your extensive work within optimization, with your institute, and with your extended work on things like the Dinkelbach algorithm, would you consult with us?

Our work is here: http://81018.com

Thank you.

Most sincerely,

Bruce Camber

PS. Our interests are in nonlinear programming,

Trnka, Jaroslav

Jaroslav Trnka
Center for ​Quantum Mathematics And Physics
Department of Physics, University of California, Davis, One Shields Avenue,  Davis, CA 95616 USA

Twitter (not active)

First email: 4 August 2018

RE: Key pages haves a few broken links: https://en.wikipedia.org/wiki/Amplituhedron

Dear Prof. Dr. Jaroslav Trnka:

Many call for a fundamental re-thinking
of space, time, infinity, first principles…
“But don’t step on my favorite theory or
the special relics of our history.”

Why not see the universe as one big Planck scale
whereby various doubling functions kick in and
push the base units up to the current size of the universe,
the current age of the universe,
the current mass of the universe,
and the current charge of the universe?


On Monday, I’ll be at SLAC; are you in the area this summer?
Thank you.


PS.  I’ll try to fix the broken links on those two pages
references above. Also, I will start a Wikipedia page for you
primarily based on your current pages at QMAP and Davis.

PPS.  Everybody knows “…expanding exponentially in every direction,
from an infinitely small, infinitely hot, infinitely dense point,
creating a cosmos filled with energy and matter. 

(quoting Stephen Hawking) is problematic.

The only difference between the quiet expansion and the big bang
theory is the first picosecond which defines the first three epoch
rather strangely. Yes, in the big bang theory, the Planck Epoch,
the Grand Unification Epoch, and the Inflationary Epoch are
exceedingly short. Yet, within our base-2/Planck scale model,
that process involves as many as forty doublings before the
Electroweak processes begin, and as many as another 60 to 100
additional doublings before the Quark-then-Hadron processes begin.
And, within this model, we are still within the first second of the
unfolding universe. That is a lot of space for pure mathematics
and geometries. -BEC

Faust, Drew Gilpin

Drew Gilpin Faust
Harvard University
Cambridge, MA 02138

Autobiographical article

Most recent email: 28 July 2018

“Drew Gilpin Faust was the president of Harvard University when I sent an email introduction about this project. Followed by many people around the world as a foremost historian and for her leadership of Harvard, her insights into this model or framework for the universe would be highly regarded because this model necessarily reinterprets the very nature of history — here it is totally dynamic and a key to our unfolding.” https://81018.com/attitudes/#AST

Dear Prof. Dr. Drew Gilpin Faust:

Congratulations on a brilliant career;
may it become ever more brilliant.

We are all entering a new phase of our life.
My wife, Hattie Bryant, has written a book about it,
I’ll Have It My Way: Taking Control of End-of-life Decisions.
Once we have made those decisions, we can live a bit more freely.

Please forgive me, but I have taken great latitudes and
I invite you to pull up the reins as tight as you desire.

On my homepage today, there is a link to an email that was sent to you
last year. It is slightly updated in its current iteration on the web today.
I suspect you never saw it given the volumes you received and continue
to receive.

Here are the three URLs as references:

It is obvious that I am pushing the boundaries in many ways.
However, at the same time I do not want to be impolite. Harvard
has been a most-important place in my life. I studied with Arthur
McGill (1975, HDS) and informally with Arthur Loeb (as a member
of his Philomorphs). Also, I have enjoyed the company
of so many including Hillary Putnam, WVO Quine and
so many others. I will want to respect your wishes.

Thank you.

Most sincerely,

First email: March 9, 2017

Drew Gilpin FaustProf. Dr. Drew Gilpin Faust
President of Harvard University
Lincoln Professor of History
Harvard University
Cambridge, MA  02138

Dear President Faust:

Congratulations on all that you are doing… an amazing career.  I just read your address for the 2013 Harvard Campaign to seize the future.  Yet to seize the future, we need to understand much more deeply the derivative nature of space and time and the currency of history.

Today’s hyper-connected world brought me to Harvard through an online article (2009) wherein you and Wayne Carbone were widely quoted regarding sustainability and composting (two issues that I often feel in my aching muscles).  That opened the door to read your address, To Seize an Impatient Future  (Sept. 2013).  I am confident by the way you shape concepts that as an historian you have experienced the relative nature of time… how a moment in the past comes so alive, it is the now.

Back in 1970, I was quite active with Arthur Loeb in his casual group called the Philomorphs. We met in the attic of Sever Hall where geometrics of every kind were in process of being constructed. Bucky Fuller was our hero and a reverential associate.  We were attempting  “…to reimagine how we teach and learn”  (your words).  We were attempting to spark a real revolution in pedagogy by trying to under the foundations of being, knowing, and envisioning. What is space? How does it create time? Unfortunately, all of our learning theories de facto adopt Newton’s commonsense worldview whereby everything is contained within space and time.

Worldviews hold us all back; we needed an integrated, highly-order, and evolving UniverseView. In 2011, we unwittingly backed into one within a high school math project studying nested geometries. With a few months, we discovered the work of Kees Boeke, a Dutch high school teacher. In 1957 he wrote A Cosmic View: The Universe in 40 Jumps. It was UniverseView-lite, a first step. Though he did not start small small enough or go large enough, it was brilliant for his day. Physicist Arthur Compton wrote an introduction. Today, it is an IMAX presentation at the Smithsonian.

Boeke used base-10 exponential notation. We used base-2 which is 3.333 times more granular and it encapsulates natural biological and chemical processes. It is also quite manageable. From the Planck Length to the edges of the known universe (using the Hubble’s 2012 measurements) gave us a range. Then, by using the highly-informed estimates of the age of the universe, starting at Planck Time, we confirmed that there are just over 200 notations. I created such a chart for our high school geometry classes. I was hoping to find it on the web and at that time assumed it was out there somewhere.

It wasn’t. And, that is an academic oversight with huge implications. The first 65 notations from the Planck Length/ Planck Time provide a place for Alfred North Whitehead’s pointfree geometries (mereotopology), as well as finite-infinite studies, brain-mind studies, combinatorics, Langlands programs, computer automaton, and all those disciplines that have never had a place on the grid. Here, at last, we find the heart of self-replicating systems.

Though I have learned from select Harvard professors over the years, today’s tools provide instant access, virtual meetings of the mind, with the best of your best. Yet, the big impact waiting to be manifest is when the world finally moves from limited worldviews to an integrated UniverseView.

Might we further discuss how we all re-envision education?

Most sincerely,
Bruce Camber


PS.  I just love this statement:
May Harvard be as wise as it is smart,as restless as it is proud,as bold as it is thoughtful,as new as it is old,as good as it is great.”

By the way, my first time at Harvard was as a baby; my father worked for Harvard. He was a sheet metal worker who installed the cooling vents for the Mark I. My grandparents were the grounds and custodial care folks for Episcopal Theological School at that time.

Lenat, Doug


Knowledge is “…contextualized logical axioms (in the formal language, CycL) based on extensions to first-order predicate calculus, and then use that enormous ontology, inference engine…” -DBL

Dear Doug,

I now have open on my desktop your PhD dissertation, the summary about you within Wikipedia, and some of your current work. My work within AI and quantum computing is introductory at best, yet to learn quickly I try to find the best teachers, but then ask, “What are they missing?”

Now, who am I? Access to my somewhat full-disclosure starts here. I also know full well that my work since 2011 is idiosyncratic bordering on crackpottery. I have been looking for somebody to dismember the logic — people seem so afraid to engage — and perhaps that person is you.

We all grew up with Euclid’s Axioms where space is homogeneous, isotropic and unbounded. Newton and Hawking adopted the logic. Yet, if we adopt the dimensionless constants like pi, boundaries are introduced with the Planck base units and our most-current time (the Now).

Using that same line of thought, should (or could) algorithms also be contained by that application of base-2?

Most sincerely,

This homepage is called a “how-to” page…

HOMEPAGESJUST PRIOR|1|2|3 |4|5|6|PI|8|9|10|11|12|13|14|15|16|17|187|19|20|21|22|23|24|25|ORIGINAL

Sphere to tetrahedron-octahedron couplet
Planckspheres, cubic-close packing, emergence†

The Emergence of the Universe

By Bruce Camber_  _*Inspiration for this page_ _And, Another Version of this homepage

This website is a study of a model of the universe based on an application of base-2 exponentiation (multiplying by 2 or doublings) that eventually encapsulates-and-relates everything, everywhere, for all time in just 202 notations. This model of the universe starts with Planck Length and Planck Time, the smallest possible measurements, and goes to the largest. It starts with the very first moment in time and goes to this very moment in time.

There has never been a mathematical model of the universe quite like it.

To get an intuitive sense of this model is difficult. Four sacred cows of science need to be reexamined; these are best summarized as continuity, symmetry, harmony and the finite-infinite relation. Continuity applies to the nature of time. Symmetries apply to the structure of space, focusing here particularly on the very small-scale. Harmony is a focus on the dynamics of perfection and imperfection whereby chaos, indeterminacy, creativity, free will and fluctuations all emerge. And, all three are the face of the finite-infinite relation. [1]

The dynamic image at the top of this article opens this analysis. The first sphere is the first instant of space and time with a very specific mass and charge. These numbers were all calculated by Max Planck in 1899 and have been studied in earnest since 2001 when Frank Wilczek wrote a three-part series, “Scaling Mt. Planck” for Physics Today. [2]  When he received his Nobel prize in 2004, these three articles took on the patina of authority.

The next step for scholarship was obvious, but everybody seems to be ignoring it.

The first moment of time is derivative, finite and discrete. Newton’s absolute space and time are sidelined to introduce a new scale of the universe that begins with Planck Length and Planck Time. The focus of that image, including the ellipsis (36 displayed), is the first emergence.” [3]

Seemingly out of nothing – no space, no time – it all starts with just one sphere, defined by the Planck base units and many dimensionless constants, that is followed by another sphere, then another and another…. For now, we’ll call these spheres, planckspheres. If these spheres could be observed — obviously much-much-too-fast-and-too-small to measure — perhaps this process might be described as a line or a string coming out of nowhere, literally defining space and time as it emerges. This is the beginning of time, and this first moment is still emerging, today, at this moment…. It is still creating space/time and the dynamics that are mass/energy (or charge). It is assumed that all four Planck units are inextricably interwoven throughout the 202 doublings [4] (or notations) that bring us to this very moment within this day.

In that light, our first principle is that our Universe begins and is sustained by the dynamics that are defined within Planck Length/Planck Time and Planck Mass/PlanckCharge. Given these are inextricably interwoven, one of our challenges is to loosen, then disentangle all the knots.

Be assured, this is not your daddy’s or your mommy’s sense of time. Here it is a rate of encoding and imprinting on a universe that has no past. It has no future. It is only right now. This instant. Everywhere, everything shares this same moment and this same infrastructure. [5] This first notation is always the same, yet it is always unique just like pi. Impenetrable, there is nothing smaller; and these spheres penetrate and sustain all things.

So, another principle is that time is not a measurement of duration but of processing speed.

Here is the operational nexus between the finite and the infinite. Here is the beginning of an integrated, mathematical model of the universe and a quiet expansion with a most-natural inflation. Here is our little universe displaying its deep-seated order; yet very quickly, it begins to reveal how disorder, chaos, uniqueness, and creativity emerge. [6] Those geometries are well-known and the dynamics within each manifestation are now being explored and will be discussed in subsequent homepages.

Doublings. In the second notation the most basic projective geometry begins to emerge and structure begins building on basic structures [7] that creates a logical continuum from the infinitesimally small scale structures right up to the 67th doubling where now things can, in some sense of the word, be measured by accelerators like CERN in Geneva, Switzerland.

One of the key purposes of this site is to chart a map that takes us right down into these assumed infinitesimal structures.

Academics and scholars have not adopted this model. Questions should be asked  first, about the jump or “quantum leap” from the CERN-scale to the Planck scale. 
To date, there appears to be no other attempt to define this exquisitely small space using a simple application of base-2 notation and a profound respect for the Planck base units. In this study Planck temperature is derivative of mass/charge; so to approach the Planck temperature value, it has been reverse ordered. Just for convenience, it is now started just one notation above the 202nd notation. The logic supporting such a positioning is still being formulated.

Can the deep nature of that “quantum leap” be calculated today using just the four Planck base units and doublings? Could the first doubling from Notation 1 to Notation 2 be the foundation for all doublings?  There are many different types and applications of doublings that have already been well-researched and defined. To learn a little about each, on one page within this site, these key types of doubling will be studied and further researched in light of the continuity equations from the first doubling to the 202nd doubling. [8] Hopefully period-doubling bifurcation, cellular division, double field theory and gauge-symmetry for T-duality-and-doubled geometry, and multiscale modeling and simulations will inform us.

What other kinds of doublings should be considered? The 64 doublings from the Planck scale to just under the CERN-scale (at the 67th doubling) have been well-enumerated through the study of geometric expansions, especially as outlined by the Wheat & Chessboard story. It begs the question, “Is there a logical progression by which numbers and geometries progress?” Does every kind of mathematics, geometry and logic build upon each other? [9]

Given recent scholarship within the studies of prime numbers, the question should also be asked, “What is the role of prime numbers in this expansion?” There are 45 prime numbers between notation 1 and 202; there are 19 primes from 1 and 67. Could each notation that is a prime open a path for more complex mathematics? That question is being pursued within the development of the following pages: https://81018.com/1-202 https://81018.com/a0 https://81018.com/a1 https://81018.com/a2

So, even as we study these possibilities, a simple stacking renders our first doubling and an infrastructure for all subsequent doublings. Our centerfold image at the top captures the dynamics of doublings. Cubic-close packing, both face-centered cubic (fcc) and hexagonal close-packed  (hcp), has a rich history beginning in-and-around the 1570s starting with the problem of stacking cannonballs on the deck of a ship. Today there are purely mathematical packing challenges as well as applications of atomic and crystallographic stacking and packing. By starting with planckspheres, this most-simple doubling application becomes discernible as the second,  third, and fourth doublings are assumed. Further, subsequent doublings are assumed right on up to 202nd doubling and the current time.  Yet, something unusual is captured within the 67th doubling, we begin to measure it. That length opens the possibilities of particle physics revealing the potential science of the first 64 steps. It begs the question; is this a logical continuum from the infinitesimally small scale structures up to those being measured by accelerators like CERN?

These planckspheres, a key element of the finite-infinite bridge, are defined by pi, the Planck base units, dimensionless constants and simple logic. Every finite-infinite discussion-and-debate should be re-examined. Though tedious,  it must be re-engaged.  There are too many fine scholars who are being torn up and their logic being shredded to not engage every idea that has been posited throughout human history. All of that is within the 202nd notation. The 197th notation takes us up to 343+ million years. Our first 196 notations open a deep study of the earliest cosmological epochs.

Could this model be in line with Neil Turok’s conclusions that the universe is in a perpetual state of starting? So, yes, I believe planckspheres and every form of emergence up to the 67th notation are keys.  https://81018.com/1-202

Many people have asked, Why now?

Of course, the question must also be asked, “Is this model overly simplistic and naive?”  Yet, even if so, could this model of the early universe be closer to the truth than the big bang theory? I believe it is. Thank you. -BEC 



Endnotes and Footnotes:

(in process today, 29 June 2018)

[†]   This dynamic image was first introduced within this website on January 4, 2016 in an article about numbers, “Constructing the Universe from Scratch.” It has now become the center point within this analysis. In that initial article, the question was asked, “Which numbers come first and why? Which numbers are the most important to know and understand?” The image was also used within the following articles: Fabric of the Universe (November 20, 2017, just below point #4), Consider how symmetries within the first 67 notations actually create space (Sept. 17, 2017) and Symmetry: Circles-to-Spheres-to-Triangles-to-Tetrahedrons-to-Octahedrons (September 13, 2017.

[1]  The three faces of the finite-infinite relation extend our earlier discussions about David Hilbert’s understanding of infinity and Max Tegmark’s disdain for the word. Continuity-symmetry-harmony are the mathematical-scientific faces of infinity and each face is captured by the dynamics of pi and the emergence of lattice, tetrahedrons and octahedrons, and eventually complex structure.

[2]  Frank Wilczek wrote his three-part series, “Scaling Mt. Planck” for Physics Today, yet has not acknowledged that Planck base units are the best conceptual orientation to start constructing this universe. As a result of this analysis, we will ask him, “Why not?” To our knowledge, the writings within this website are the first to lift up Max Planck’s base units as the starting point for the universe. We are anxious to discover and understand any articles that analyze their place, power and conceptual richness.

[3]  “The first emergence” is a steady stream of planckspheres being uniquely created just like they were in the very first moment. Every notation has a unique function and every notation is evolving at the same time it continues to do what it has done. Here, perhaps are Neil Turok’s perpetual starts of the universe. Here everything, everywhere is built up and emergent from this fabric of the universe, called an aether and/or dark matter and dark energy, that gives this universe its isotropy and homogeneity.

[4]  The Planck base units and dimensionless constants are inextricably interwoven throughout the 202 doublings (or notations) are based on the “Plancksphere” and that analysis is just beginning. I googled the word, for example, on June 25, 2018 with those quotes and there are just nine results. Using two words, “Planck sphere” with the quotes, there are 320 results. And without the quotes there are just over four million combinations that come close. Such results suggest that this is a new or emergent science.

Within our dynamic image about sphere stacking, the tetrahedral-octahedral architecture begins to emerge. Here, the possibilities for getting things inextricably woven together become staggering. By the tenth doubling there are 134,217,728 scaling vertices with which to work. By the 20th notation it catapults to 1.4411519×1017 — there are no limits to the entanglement of strings and knots and yet-to-be-fathomed geometries to create. By the 64th notation those scaling vertices have jumped up to 6.2771017×1057  and the first particle has yet to emerge!

Unless this simple logic is mistaken, there is altogether too much potential to ignore these possibilities and this orientation any longer.

Also, it should be pointed out that Max Planck’s formula for light — you can see it on line 10 of the horizontally-scorlled chart of 202 notations is a special calculation that needs further study.  The fact that these doublings is a form of base-2 exponentiation suggests that our universe is not linear and just might best be defined by Euler’s identity, considered by many mathematicians and physicists to be the most beautiful of all equations.

[5]   Everywhere, everything for all time shares this same moment and this same infrastructure. There are many books and articles about the nature of time. Within this study, most have fallen short. Einstein and Planck opened the door to re-analyze Newton’s earlier conceptual frame of absolute space and time, yet nothing more compelling emerged. Newton continues to define our commonsense logic, but should it? If it is established that period-doubling bifurcation, cellular division, double field theory and doubled geometry, and multiscale modeling all share the same common denominator that starts at the Planck base units, absolute space and time can be placed on the historical shelf as a footnote within the imprinting on the sentience of this universe. More work needed…

[6]  Consider disorder, chaos, uniqueness, creativity and fluctuations. The scholarly community is increasingly confused with the terms, infinite, space and time.  David Hilbert’s simple analysis leaves much to be desired. The infinite can be understood as a logical construct where it is the foundation for continuity, symmetry and harmony. These three perfections should all be understood to be a scientific assertion about the nature of order, relations, and dynamics. The various manifestations of fluctuations can be experienced as disorder, chaos, uniqueness, creativity and human will. The geometry for fluctuations begins with the simple pentastar, a clustering of five tetrahedrons. The next base structure, the icosahedron, is a clustering of 20 tetrahedrons. The dynamics of each will be introduced within future homepages.

[7]  Structures begin building on basic structure.   There are two areas where our analysis is focused. The first is on a notation-by-notation analysis but progress is slow because there is so much mathematical logic to be learned. The other is basic geometries, quantum geometries and dynamic geometries.  Here, too, there is so much to learn and, of course, more to come

[8]  There can be strains of continuity within discontinuity. There can be strains of discontinuity within continuity.  The continuity equations from the first doubling to the 202nd doubling come from within a continuity that envelopes our physical universe, so here, too, there is more to come

[9]  There appears to be a rigorous academic study of the logical construction of concepts, geometries, and equations. Mathematics and geometries do build upon each other! These studies will become our studies and as quickly as possible, each will be integrated within our map of the universe. Yes, there is more to come

“In philosophy, systems theory, science, and art, emergence occurs when “the whole is greater than the sum of the parts,” meaning the whole has properties its parts do not have. These properties come about because of interactions among the parts.” -Wikipedia

This page was started on June 21, 2018 in South San Francisco while on our tour of America. On many occasions Hattie and I been challenged to look at the world and ourselves in new ways. Along our route, we’ve spent time engaging with people:

  • At John Hendrick’s retreat, Gateway Canyon Ranch, an hour south of Grand Junction, Colorado, we discovered his CuriosityStream retreat center. That got me thinking.
  • We were in the highly-overpriced Yellowstone Hotel in Wyoming where the National Park Service is attempting to create a Disney-like experience, highly-controlled-and-organized wilderness. That compressed conflict got me thinking.
  • On our drive to Bend, Oregon, I discovered the Simplot Don plant near Pocatello, Idaho and learned about fertilizers and growth and even that challenged my thinking.
  • In Bend, while visiting with friends, I was challenged again to understand why there is such disparity, both political and economic, within our world.
  • On to Portland, the land of inclusivity, two different sets of friends challenged me to see the world through their eyes. There is so much to process and process it we will until each becomes a homepage.

This homepage was simply to clarify the last three homepages:

Thanks again.


The next homepage builds from this page and from those past homes pages linked just above, and from a page written on July 23, 2016 entitled, Chaos-Order, Indeterminant-Determinant.

West, Kanye

Kanye Omari West
Official Website

July 30:2018 @ Noon  Twitter Tweet & Email:

Let’s connect and connect with Katy Perry as well.


Tweet: 30 July 2018 at about 10 AM

I sent this note to @katyperry:
Solipsists rule the world.
And, often their solipsism becomes narcissism.
In time that folds over into a nihilism.
There is now nowhere to go but into a dystopianism.
We’ve got to turn it around. Turn it around”

Editor’s note: This Twitter Tweet did not have the embedded links.

First Tweet: 18 June 2018

An introduction to something to rap about…

@kanyewest You are very smart 
and know there is too much that we don't know.

We're off -- intellectually off, 
emotionally off, and ethically off.

Let's see if there is a better starting point.

Here's a simple model of the entire universe.