# 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

###

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## 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.

-BEC

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.

# Richardson, Louise Mary

`Second email: July 18, 2020`
Dear Ms. Louise Richardson:
Yes, God only knows when we touch another,
and how we learn, and how things change.
My “Louise Mary Richardson” page is here:
It is my note to you from Oct 31, 2017 and

inspired to visit online the history and story of Mary Aikenhead.
What a very special foundation upon which to see our universe.

I wish you well.

Warmly,
Bruce
`First email: Tue, Oct 31, 2017 at 3:49 PM`

Reference:  Forward for Oxford University Press

Dear Prof. Dr. Vice Chancellor Louise Mary Richardson:

Sometimes even Tacitus is wrong. [1] Some age-old “truths” actually hold us back. Two powerful obfuscations came out of the other great British university, particularly from two of their Lucasian Professors, Newton with his absolute space-and-time [2] and Hawking with his infinitely-hot big bang. [3]

Now, I have been reading What Terrorists Want: Understanding the Enemy. And, yes, we have been too slow to create counter narratives to the ideologues of terrorism. I would add that we have also been too slow to challenge conventional paradigms, especially when we find ourselves within circular arguments.

Now, we share a few common experiences. As a kid we would visit Aunt Nellie who worked in the Radcliffe Admissions office. My dad had been a sheet metal worker in the Harvard HVAC group and helped to keep the Mark I and II cooled down in the basement of the Cruft Lab on Oxford Street. While in high school I joined the SDS at Harvard before it was thrown off campus in 1964. By 1969 I was organizing national amendments to end the war in Vietnam with full-page ads in the New York Times and Wall Street Journal, and congressional conferences in Washington, D.C. on global priorities. There wasn’t anything we wouldn’t do.

But something fundamentally was missing.  My driving force was to understand scientific breakthroughs, creativity, and innovation. By 1971 I was onto the EPR paradox [4] and quickly found John Bell [5] at CERN labs. It became obvious that there was something very wrong with our notion of space and time, but we couldn’t break through Newton’s commonsense logic. Hawking was so hooked, the big bang seemed like the only logical choice among cosmological models. It wasn’t. [6] Then, after 100 years of being in an academic closet, the Planck units were re-discovered (2001). Then, in 2011, the first mathematically-integrated chart of the universe was made using the Planck units. Using base-2 from the first moment of physical time to the current time, there were only 202 notations.

That changes everything. Space-and-time are contained. And, now something more fundamental must emerge. Oxford should be on the forefront of understanding what that is. If I were able to assemble an Oxford team, among them would be Harvey BrownArd LouisAlister McGrath, Jirina StoneRichard Swinburne, Roger Trigg, Keith Ward, I.A. Walmsley… and you.

May I follow-up this introduction?

Thank you.

Most sincerely,

Bruce
****************
Bruce Camber
http://81018.com
Austin, Texas

[1]  We seem to settle in with concepts that actually become age-old truths, but these concepts are ultimately flawed. Of course, by and large Tacitus is right:  ‘Truth is confirmed by inspection and delay; falsehood by haste and uncertainty.’ You use the quote within the section, “Challenges” within the  Vice-Chancellor’s Oration 2017
[2] There are comments about the debate between Leibniz and Clarke (Sir Isaac Newton) throughout the website, http://81010.com.  For now, you might particularly engage the second point of this page: https://81018.com/pursuit
[3] There are pages and copies of emails to Stephen Hawking about his Big Bang theory. Ostensibly the argument focuses on the texture of the first fraction of a second of the universe and whether there is “…an infinitely small, infinitely hot, infinitely dense point…”
[4] EPR Paradox, also known as the Einstein-Podolosky-Rosen thought experiment of 1935 opens the question about non-locality and quantum entanglement.
[5] Bell’s Inequality opens the discussion to the widest community within physics and these discussions lead to the conclusions of Nima Arkani-Hamed and Max Tegmark to stop using the concepts of space-time and infinity.
[6] All cosmological models are being called into question.

______________________

# Concepts For A Simple Model Of The Universe

## 1. These 202 base-2 notations easily encapsulate the universe.

Multiply by 2. Start with the smallest units of measurement, the Planck Time and Planck Length, multiply each by 2, then the result by 2, and continue right up to the largest possible measurements, the Age of the Universe and the Observable Universe. Though both are still constantly expanding, your result will quickly be a totally, mathematically-integrated model of the universe that includes everything, everywhere, for all time in just 202 notations.

Just one more time: Most scientists and scholars now believe that Planck Length and Planck Time are the very smallest possible measurements. If you double them, then double them over and over again, in just 202 doublings, you will have reached the size of our Universe and you will have gone from the beginning of time to this present moment in time.  It sounds impossible, but the math is the math.

•  Rather special. Though simple logic, simple math, it’s still just a model. As a challenge, take this model as a given, to explore in what ways it could be an outline for the initial structures of the universe. Also, if simple logic and math do not work from the Planck Scale to the CERN scale to the Large Scale Universe, then logic and math should not work anywhere. Continuity is continuity. Order is order.

Eventually we added Planck Charge and Planck Mass to our doublings and continued to study how the numbers and the inherent logic worked together.  We have been exploring this model since December 2011 and have discovered that it seems quite sustainable! No scientists or scholars have seriously challenged it. Of course, it is idiosyncratic and it does raise rather unusual questions. Notwithstanding, the universe within just 202 doublings (clusters, containers, domains, layers, notations, sets and/or steps), so far, actually does seem to cohere 1 (Footnotes/endnotes at bottom).

•  Sweet. By the 31st notation, Planck Mass has increased to 103 pounds. That may be an ideal weight for some, yet in this notation, space and time are still so small that science has always considered these values meaningless.  We do not. Though an entirely novel concept, we take it as a given that there was a time when the universe was just 103 pounds. Though necessarily defined by point free vertices, it already has more active ratios than our imaginations can grasp (1.23794×1027). It exceeded one million vertices by the eighth notation, one billion at the 11th, and one trillion at the 15th, and a quintillion vertices at the 17th notation.  To follow that quiet expansion, look at line 9 in the chart below.  More

## 2. This Quiet Expansion is a Natural Inflation. Here’s a sampling.

•  In this model each notation is more than just a simple doubling. The next notation doubles in size and doubles in content and each notation it would appear is currently defining our universe. As we live with the model, grasping the first notation as the start of the universe and the current notation as our current moment in time, all the notations come alive as a process that gradually builds upon itself, every notation changing and growing because of the others. To think about this very different sense of space-time, I did a sampling of six of the notations somewhat evenly spaced across the 202 notations. Of course, these Planck scale doublings are all predictive numbers. Within these six notations that were sampled, each demonstrates a natural inflation that is a quiet expansion.  A sampling  Prime numbers...2

•  Being natural is good. If one were to wonder about the basis for bifurcation theory, chemical bonding, cellular development, and isotropy-and-homogeneity, we may have found a new opening to explore. Then, if one were ask about the source of this thrust, again I think we may have found another good opening to explore.

The alternative is not pretty, elegant, or logical. Any one of the many theories that use the big bang logic of infinitely dense and infinitely hot are incomplete, unnatural, and riddled with questions. Worse yet, the big bang philosophy and psychology have trashed our culture with a de facto nihilism and dystopia.  It is bad physics. It is bad mathematics. And, it’s bad psychology.

•  Sweet.  (1) The quiet expansion continues its doublings until finally at the 67th the folks at the CERN labs (Geneva) are able to pick up something and our core sciences start to evolve.  (2) Truly sweet is that this natural inflation approximates all the cosmological epochs that were defined by big bang theorists; however, in this model there is no bang.     (3) The 67 notations provides more than enough “room” for every possible system of mathematics to be applied. Remember the 64 doublings within the Checkerboard story!  More  And more...

## 3. Light has variable speeds and many faces.

•  Planck Length divided by Planck Time equals the speed of light. And, as you might anticipate, with every doubling, that approximation of the speed of light naturally continues. See line 10 within the horizontally-scrolled chart. More

•  That is very special. Light, Time and Length are being redefined by each other and by Charge and Mass.3

Please take note that between the 143rd and 144th notation, the universe is finally one second old and Planck Length has grown to the size defined by the distance that light travels within that second.

It is simple math and simple logic yet it re-engages us to expand and begin to understand a rather extended spectrum of light, of course, well beyond the visible spectrum and well beyond where it has been defined to date.

This work has given new meaning to an old song (1977), “You light up my life.” The very final refrain goes something like this: “It can’t be wrong when it feels so right…” More

•  Sweet.  Here is the first time light, defined by another very simple mathematical formula, can be found within a simple mathematical progression. The formula from Planck predates Einstein’s!  More

## 4. Space-time is long overdue for a facelift.

•  The Gnarls and Knots of Space-and-Time. Definitively cast in stone in 1686 when Newton released his blockbuster, Principia, time-and-space took on an absolute frame of reference and this view became our commonsense worldview.  It became a realism (and naturalism) whereby our external reality is assumed to exist as it is given and experienced. Both concepts — space-and-time — have been problematic and now some really smart scholars want to throw them both out; we believe it would be better to redefine them in light of our model with its 202 notations. Here, the universe begins within the Planck Scale. Our challenge is to figure out how the universe evolved within those initial notations, and then how it continued to the 202nd notation and to this very second within our expanding universe.

•  It is a very special and rather non-intuitive challenge. There are so many people today who still affirm Newton. They unwittingly do so when one of them looks up into the clear, night skies, observing the panoply of stars, and says, “It goes on forever.” Those wrestling with this new model would say, “We are looking out at our expanding universe. It is still expanding within the 202nd doublings and has been for about 13.82 billion years.”  What happens is that no notation goes away and recedes into a past. Instead, each notation participates in the current definition of the universe and space-and-time, as the fabric of the universe, absorbs every imprint for all time-and-space.

•  Sweet. This new sense of space-time gives it a currency and vibrancy.  The universe has its own clock and as of 2013, the universe was 436 quadrillion, 117 trillion, 076 billion, 640 million  seconds (436,117,076,640,000,000) old.

Let’s turn on the clock.  There are about 31,556,952 seconds per year so at some time we will be adding at least four years of seconds, somewhere over 126 million additional seconds, to bring the total to the current time. A hundred years is just 3.1556 billion seconds. Extend that to 1000 years (31.556 billion seconds), a million years (31.556 trillion seconds), and a billion years (31.556 quadrillon seconds).  Our earth and solar system are approximately 4.5 to 4.6 billion years old.  The estimates for the Milky Way galaxy are about 13.7 billion years (yes, among the original galaxies formed).  Yet, none of it is old; it is all current. All the cosmological epochs are now understood to be ongoing processes of the universe.   More…

## 5. Let us try to rebirth finite-infinite studies.

Science and mathematics have made great use the concept of the infinite; philosophers and theologians have as well.  Yet, over the years we have seen how these disciplines tend not to work very well together, especially those elitists among them, particularly among those religionists and theologians who too frequently don’t work well with anybody except their own.

It is no wonder that a few very bold scholars would like to throw out the concept of infinity. It has an awkward personality. It is too big for most of those yellow academic school buses.

•  We suggest a shakedown. First, let us shake out all the concepts that have anything to do with faith statements — these are too often argumentative, emotional, and sometimes even hostile. Within the quiet expansion model, there are several conceptual assumptions that begin to bind the finite and infinite in special-and-heretofore unexplored ways. These concepts include: continuity-order, symmetry-relations, and harmony-dynamics.  Though an unusual combinations of words, some element of each can be readily understood.

We can do this. The word combinations may be a little gray, but we’ve all used each word at one time or another. Taken together and in this sequence, these words become very rare concepts because each reflects a face of the finite (our beingness, whether it is science, mathematics, psychology, philosophy or religion) and also a face of the infinite.  More   Foundations…   Ethics-and-values…

## 6. Incommensurables, transcendentals and irrational numbers

Numbers. Perfect, unshakeable continuity occurs within numbers that are called incommensurables, transcendentals and the irrational. These numbers are never-ending and never-repeating. Our old friend, yes, a very dear friend of every circle and sphere, is Pi.  Its very close cousin is e, for Euler’s number.  Euler’s equation also defines the universe.  It is the heart of our exponential universe. Also, meet Pi once again.

•  Through our Looking Glass. Most looking glasses are mirrors. This looking glass can also be a magnifying glass. Isn’t it unusual that a number can seemingly go on forever without repeating itself and with no special pattern or repetition?  Doesn’t that define a certain kind of uniqueness?  …diversity?  Within this class of numbers there is a group that is also known as dimensionless constants.  There are quite a lot of them. Yet, in all the discussions about the many scholarly blogs, papers, articles and books, there does not appear to be any discussion about how these numbers must define some aspect of infinity.  Isn’t that an oversight? If we take it as a given within our new definition of infinity, this very special kind of continuity and order can also be understood as uniqueness and diversity. That’s rather special.

Now of all the scholars I know, perhaps Clifford Pickover or John Barrow have started a process of looking at infinity in this simpler way; we’ll be digging further into their scholarship. More…

But, for now, let’s see if we can take it one step further. Let us take as a given that these rather unique numbers (1) originate within the infinite, (2) tell us about the nature of the infinite, and (3) define the transformation between the finite and infinite.

•  That’s different and very sweet.  So, we now have an ordered-chaos and a discontinuous-continuity defining our finite universe.  The next step is to look at the symmetry/relations and harmony/dynamics.

## 7. Continuity-symmetry-harmony create order, relations and dynamics!

•   Pi leads the way. Leading the way out of the infinite is pi. Perfect equal circles, then spheres, then multiple spheres, then stacks of equal and doubled spheres. We are probably within the first ten notations or doublings.  And then, a radius discovers a radius and the first line is created. Then the radii begin discovering radii and lines and dimensionless, point free, vertices are created.  Vertices discover vertices and the first triangles are created. Triangles discover triangles and the first tetrahedron is created. Lines, vertices and triangles discover each other and then the first octahedron is created within the tetrahedron. And, quickly, hexagonal plates are discovered. Triangular plates are discovered.  And diversity begins to move into high gear in a perfectly simple, yet increasingly complex manner. Symmetries abound. Perfection is in the air. But the imperfect and asymmetrical are not far behind.  More…

•   Dynamics.  Euler’s number is somehow holding pi’s hand! The two are working those continuity and symmetry relations and are making a universe one step at a time. More…

•   That is a very special challenge. All shapes and forms and sizes and every manner of symmetry relations are being created. The pulse of energy known as Planck Charge creates a thrust, an energy, a direction, a motion, and soon our little universe is pulsing with activity.  More…

First, called the Planck Scale, it transmogrifies into what some call a Grand Unification.  Here is the first doubling. But for all intents and purposes, it is within a self-discovery mode. Yet, rather quickly (understatement), that self-discovery process organizes and begins what we call the Inflationary Processes right up to and including the 67th notation.  Now declared to be the Electroweak Processes, Planck Charge is huge. Planck Mass is huge. Planck Length has become manageable. Planck Time is still too small to be considered anything other than a placeholder.  More…

•   Sweet.  The rest of the cosmological epochs seem to follow rather naturally in line with the continued expansions (doublings and notations) of these Planck base units. Even Planck Temperature, which was placed at the top of the scale because everything begins simply, is now substantial enough to warm things up and to begin looking like our little universe.  More    And more…

## 8. A Place For Everything, Everywhere, Throughout All Time

•   The first 60 or so notations will never be observed by our machines. These domains are much too small to be picked up by our measuring devices. If there can be no validation by our machines, then we must rely on logic and mathematics. This special domain has a very special word to describe it; it’s call hypostatic. We actually create a real reality when shared by another. It is a really real reality when shared by many.  As more people adopt that structure, we press meaning and purpose into it.  Then we ask, “Is this helpful? Does it seem to describe a real reality for people within our time?”

•   Yes, this is very special challenge for all of us. Because everything, everywhere, for all time must be logically included on this grid — nothing is exempt —  we will hypostatize a place for philosophy, psychology, mathematics, quantum fluctuations, the cosmological constant, religions, the mind, consciousness, sleep, and qualities. More

•   So we have a bit of work to do.  And, we recognize that this work just started in December 2011 and it is still quite naive and young.  The initial goal was to give our high school students a very special chart to integrate Science, Technology, Engineering and Mathematics (also known as a STEM tool).  Today this project is known as the Big Board -little universe.

That was cool. But now, the real work begins. We know we are onto something and have opened a door that is worth exploring. We’ve begun to study some of the older problems within science with such names as inertial frame of reference, point processes, scalar fields and scalar field theory, and path integral formulation. Many of those subjects are listed on line 11 of our horizontally-scrolled chart.

We struggle with it all most everyday so your advice, insight, and help are most welcomed! Thank you.

Footnotes & Endnotes

1 Time: It is good to be reminded that the first second of the universe is between notation 143 and 144. The estimated 500 million years necessary for galaxy formation takes us up in between notations 197 and 198.

2 Number groups:  We will be studying every prime number as a possibility for a new mathematical system. The obvious, primes from 2 to 199 (3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197), prioritize themselves! The challenge will be to logically build the sequence of systems. It is anticipated that the work of Grothendieck and Langlands (IAS) will contain a few keys. More

3  Quantum fluctuations and imperfections.  We believe the geometry of imperfection begins with the pentastar and the pentastar gap.  Though possible within notations 1-to-40, simple logic suggests that these quantum geometries do not manifest until Systems (first column, eight row) begin organizing.  More

PS.  There may be more footnotes inserted in the forthcoming days. If you are observing changes in the post, it is because this post is edited every day. It will change, and undoubtedly grow a little longer.

Special Thanks

Friends from New Orleans came for a visit. Their two images have been in my mind’s eye as I worked on this page. I have been constantly asking myself, “Is there a way to write this up so they understand it?”   -BEC

Welcome

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