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# By Aristotle, Newton & Hawking!

###### BY BRUCE E. CAMBER MAY-JUNE 2020 – WORKING DRAFT **PREQUEL** EMAIL TWEETS WANTED (HELP!)

**Introduction**. Three thought leaders of our common history were also leaders in their own day. They held their ground when challenged. Throughout the years, their work became sacrosanct. Yet, among all the concepts they each introduced, I believe that they held onto a key conceptual mistake that still blocks us even today.

As a people we long for heroes and leaders; and, these three were ready to accommodate. Headstrong geniuses of their time, once they got into the limelight, they did not easily share it. They were not about encouraging others to discover their own gifts. They were more about imparting their genius to their adoring publics.

But, all three were fundamentally wrong about a foundational concept. They’ve thrown off generations of scholars. They’ve held us all back; and now it’s time to correct their mistakes, forgive them, and get on a path to breakthrough to new levels of insight.

**Aristotle**

**Aristotle** (384–322 BC, Athens)^{1} was wrong about a most-basic geometric fact. Obviously he could not have had perfect tetrahedrons within his toolbox. If he did, he would have known that one *cannot perfectly tile and tessellate the universe with just tetrahedrons*. He thought it was possible.

**There are obvious gaps**. Using the very tightest configuration of just five tetrahedrons sharing a simple edge, a most fundamentally important geometric gap is created. Simple logic tells us that it is a relatively early gap in physicality. Aristotle never saw this 7.35+ degree gap; and to his dying day, he promulgated an error as a truth.

There’s always so much more to learn.

Aristotle had such stature that this error was repeated by scholars for over 1800 years. Even today, not many people know about the gap. That should change. Our children should see it and begin to appreciate it profoundly.

**What is it?** I believe this simple gap is the beginning of the geometry of quantum fluctuations. That’s huge, but there is so much more. First, we know this — it is necessarily created by just five tetrahedrons which also outline a face of the dodecahedron, and define the primary faces of the icosahedron and the Pentakis dodecahedron. Aristotle’s mentor, Plato, defined the five basic solids — the tetrahedron, hexahedron (aka cube), octahedron, dodecahedron and icosahedron.

That gap has everything to do with basic structure. It just may also have everything to do with creativity, individuality, consciousness…

**Enter Jeffrey C. Lagarias & Chuanming Zong**. In 2012 they wrote a most-definitive article about the gap. These two mathematicians provide the background and an introduction to the people in the 1400s who observed and noted Aristotle’s mistake. Then, drawing from the 1926 research of D. J. Struik, they cite Johannes Müller von Königsberg (aka Regiomontanus, 1436–1476) as the first to recognize the error. The first to document it was by Paulus van Middelburg (1445–1534), a professor of astrology in Padua. Even though Aristotle’s error had finally been observed and analyzed, people focused on the fact that it was an 1800-year mistake. They also focused on the concepts within cubic-close packing of tetrahedrons and spheres. Over the years Kepler, Minkowski, Hilbert, and Hales — just to name a few — contributed insights to analyze technical aspects regarding packing densities.

In 2015 Lagarias and Zong were recognized for their work. That is all very interesting, however, we are still looking for the scholars who have asked and answered the question, “What is the net-net effect of that natural gap on our understanding of ourselves and our universe?”

Such questions should never be ignored, so let’s speculate a little.

**Projections about the meaning of it all**. We turn to our outline of the universe — the 202 base-2 notations from the Planck scale to this current time. Yet, we specially consider the uniqueness of the first 67 infinitesimal notations which are mostly below the thresholds of measurement. Notation-67 is the threshold of wave-particle duality. Notation-76 is the current limit of a measurement of a unit of time. If Notation-0 defines a finite-infinite cusp, these 67 notations are a new field for exploration.

**Infinite-finite-and-Hilbert**. Within this model there is a thrust created, a finite-infinite bridge best characterized by functions of continuity, symmetry, and harmony, three most-basic facets of the sphere. Quite contrary to the work and logic of David Hilbert, it would seem that the face of the infinite is within the finite. First, there are simple perfections where everything fits with no gaps. Although as simple as possible, granted, it becomes complex rather quickly.

**What works survives**. Every possible geometric combination that works provides form, function, structure, and then substance, relations, and networks of relations. What works best, survives. The universe, the penultimate opportunist, is creating something big that requires solid foundations. Perhaps somewhere around Notation-50, our universe begins to experiment with those five tetrahedrons with its built-in gap. Out of an abundance of shapes and configurations, the five tetrahedral structure is surrounded by* perfectly* manifesting forms and structures. Within a moment, that gap comes alive. Perhaps as early as Notation-50, the gap becomes a structural system, and then becomes a *systemic fluctuation*. Just a guess, the first expression of these systemic fluctuations just might be considered a primitive consciousness. By Notation-67, when it can be measured and “observed”, it will be defined as a *quantum fluctuation*.

**Notation-50 and systemic fluctuations**. Here we could postulate the beginning of identity, individuality, creativity, undecidability and unpredictability — a transmogrification from the perfect to the imperfect and indeterminant. Here may well be the birth of life as we experience it firsthand. The perfect is still there, yet it is now beginning to be masked with color, charge, flavors, sounds, and an assortment of other patinas.

A simple mistake by a legendary man has been hiding one of the most substantial mysteries of our time. It is time to absorb it and begin to absorb the new realities that it has been hiding.

We’ll always have a lot to learn.

**Newton**

**Issac Newton** (1642 – 1726, Cambridge, England)^{2} was wrong about a philosophical orientation adopted by the world as its commonsense perception of space and time yet that opinion does not integrate with tested formulas by Max Planck and Albert Einstein. Newton was bold to proclaim that space and time are *absolute*, the very fabric of our essential reality.

It certainly feels true. When you look up into the clear night sky, it goes on forever. Doesn’t it? And, the answer is, “No, it only does as far as the current expansion.”

In 1687 Isaac Newton finished his landmark, three-volume book, *Philosophiae Naturalis Principia Mathematica*. Better known as just *the Principia*, it helped to firm up the foundations for what we now know as the scientific method. Though glimpsed by science and mathematics (1) dating back to Babylonian astronomy (c. 1830 BCE) and the Egyptian medical schools (c. 1600 BCE), and then (2) seriously enhanced by Aristotle and the logic within his treatise, *The Organon*, and then (3) energized with the work of Copernicus, Johannes Kepler, and Galileo, one can say with some confidence that science as we know it today consistently grew out of Newton’s *Principia*.

Yet, within this landmark writing came his most important contribution to the disinformation of the world’s culture: absolute space and time. These absolutes will not begin to recede as a footnote in our intellectual history until a better orientation is adopted by most people. That is a problem because, to date, alternatives have been non-intuitive. Leibniz came close in 1716 within his indirect dialogues with Newton through Samuel Clarke — Leibniz said space and time are relational, derivative and finite. So we ask, “If not the container for all that is, what is?”

For many that question is about one’s belief in God.

We try not to engage in “God Talk” on this website. One’s personal belief systems are largely a factor of family systems. Our attention is focused on universal systems and their constants.

**Enter Max Ernst Ludwig Planck** (1858 – 1947, Kiel, Berlin)^{3} In 1899 Max Planck developed the equations to render base unit numbers of length, time, and mass that were defined by universal physical constants. Although largely ignored throughout his lifetime, this may well be his most important work. One of the earliest analyses of that work began in 2001 by Frank Wilczek. It was published in *Physics Today* in three parts. Titled, *Climbing Mt. Planck I, II, and III*; a key calculation was overlooked.

Too simple for most, Planck had tied Planck Length and Planck Time together: Planck Time is equal to Planck Length divided by the speed of light. Of course, his little formula for Planck Time, can readily be re-written; the speed of light is equal to Planck Length divided by Planck Time.

**That formula works!** It worked in 1899. Using Planck’s numbers, the value is 299,792,422 meters per second. Without fanfare or celebrations, Max Planck had defined the speed of light using the mathematics of his equations a full 73 years before the National Institutes for Standards and Technology (NIST) accepted a slightly closer estimate, 299,792,456.2 meters per second defined in 1972 by K.M. Evenson and his group within the National Bureau of Standards in Boulder, Colorado.

**Planck’s numbers are real; they work with real laboratory measurements**. To date, the academy virtually ignores them. Applying base-2 creates a natural progression of those numbers and the first 67 notations have only been marginally explored. Here is an even more logical way to study the earliest universe where space and time are clearly derivative. The question is, “…derivative of what? …light?”

In 1905, Max Planck advised a young Albert Einstein as he began to tie mass and energy together. Yet, at no time has the academy started with Einstein’s sacred formulation, e=mc^{2}, the very first step of the Planck scale.

**So, what comes first?** If we look into the finite-infinite relation from the point of view of the sphere, well-removed from particles and waves, we begin to see what just might be facets of light that could well be more fundamental than space and time. Finally, Newton’s absolutes did not seem quite so absolute.

A simple door with simple logic opens a new path to explore. Another “hiding in plain sight” story, we have been looking at this door since 1899. We seem to have a difficult time opening that door and walking down that extraordinary path on the other side. It follows continuity, symmetry and harmony and puts our unique time within this dimensionality into a whole new light.

Newton was the second Lucasian Professor and Hawking was the 17th.

**Hawking**

**Stephen William Hawking** (1942-2018, Oxford, Cambridge)^{4} captured the world’s imagination. He was a superstar. Everybody knew his name. In 1973 a young Stephen Hawking and George F. R. Ellis co-authored *The Large Scale Structure of Space-Time* at the University of Cambridge in England. Yes, although looking at the large-scale structure, Hawking and Ellis made a mistake at the get-go:

“The subject of this book is the structure of space-time on lengthscales from 10

^{-13}cm, the radius of an elementary particle, up to 10^{28}cm, the radius of the universe.”

They missed the real foundations. They missed the core structures. They missed all the really cool stuff from 10^{-13} cm down to and including the Planck Length at 10^{-33 }cm. Within our base-2 outline of the universe, that range is from Notations 73-to-75 down to Notation-0.

By 1980 the big bang theory was clearly on the ascendancy. By 1988 with the publication of his book, *A Brief History Of Time*, especially with its rapid rise to multi-millions of books sold, Hawking was also on the ascendancy as the primary spokesperson for big bang cosmology.

In 2016, he rhetorically asked his basic question:

“

Where did the universe come from?”He immediately continues:

“The answer, as most people can tell you, is the big bang. Everything in existence, expanding exponentially in every direction, from an infinitely small,infinitely hot, infinitely dense point, creating a cosmos filled with energy and matter. But what does that really mean and where did it all begin?” -from the PBS-TV series, “Genius” aired in May 2016. (My emphases)

**He was**** wrong**. But, until he died on March 14, 2018, the big bang seemed to be the best answer even though it was fraught with problems and open questions.

When it comes to theories and mathematics, simple is better than complex.

For most of Hawking’s life, Max Planck’s numbers were considered by the leading scholars of this world to be a curiosity. Dirac had his very-large numbers. Planck had his very-small numbers. Dirac’s were too big to matter and Planck’s were too small to be significant. Again, it wasn’t until 2001 that Wilczek introduced the world to the meaning and value of Planck’s numbers. Slowly, the academy began to test those waters; yet, it was much too late for Hawking to enter. His 1973 co-author, G.F.R. Ellis, on the other hand, was open to explore the failures and deeper problems within the concept of an unfathomably hot beginning.

**It doesn’t work**, and it’s a conundrum. The big bang theory has been backed up with the humor of a twelve-year television series (2007-to-2019) that is now in endless re-runs. Yet, ever so much more daunting is the mythopoetics of Hawking’s life.

Diffusing the big bang will not be easy, but diffuse it we must.

**The logic and simplicity of the 202 notations**. Going from the Planck units to the current expansion appears to have the most simple mathematics of any construct of the universe offered to date. It has a natural inflation. It starts superconductingly cold and naturally heats up and becomes superconductingly hot just in time to absorb the epochs of big bang cosmology.

The problem with our so-called *Quiet Expansion* is that its concept of space-and-time is non-intuitive. There is some light on this path. Others have been talking about the *Now* as well.

**The Now**. In this model, there is no past and no future, only *the Now* for the entire universe. All of the 202 time periods are still active and everything, everywhere for all time is related to everything, everywhere for all time. It is all constantly encoding and re-encoding the universe.

Every thought-word-and-deed affects the look and feel of the universe.

And, because there are multiple paths throughout the 202 active notations (categories, clusters, containers, domains, doublings, groups, jumps, layers, periods, sets, steps…), in this model, it is not only a *small world after all*, it is also a small and intimate universe.

## Conclusion

Currently there is no way around the naïveté within this three-point charge against three of the foremost scholars of our entire history. I expect each point will be hammered, yet it is only by such hammering can it all be shaped into real possibilities. Thanks. – BEC

__________

Three sections follow: (1) Footnotes & Endnotes, (2) References, Reflections & Resources, and (3)_Miscellaneous Notes including emails and tweets.

**Footnotes & Endnotes**

**Navigation**: Please click only on the section number to return go back. This page is a working document and editing continues on the *Footnotes & Endnotes*, as well as the *References & Resources* and the *Miscellaneous Notes* and it will all actively continue to be edited and updated for the next several months. Thank you. – BEC

**[1] Aristotle (384–322 BC, Athens)**.

*“Be a free thinker and don’t accept everything you hear as truth.Be critical and evaluate what you believe in.”*

**1a**.** **Jeffrey C. Lagarias &** **Chuanming Zong, *Mysteries in Packing Regular Tetrahedra *(**PDF**), American Mathematical Society (AMS), December 2012 In 2015 Lagarias and Zong were awarded the 2015 AMS Levi L. Conant Prize at the Joint Mathematics Meetings. And, there is even more…

**1b**. Dirk J. Struik. If you do not have time to read the “*Mysteries in Packing*…”, you should know that Lagarias and Zong credit Struik, a Dutch-American and MIT mathematics professor, for reopening these discussions that broke the 1800+ year impasse. The primary reference: D. J. Struik, *Het Probleem ‘De impletione loci’* (Dutch), Nieuw Archief voor Wiskunde, Series 2, 15 (**1926**), no. 3, 121–137

**1c**. The geometric gap of 7.3561031+ degrees was first encountered within our work in July 2013 in the process of prioritizing numbers to answer the question, “What are the key numbers to create this universe?” This geometric gap was judged to be the fourth most important after (1) pi, (2) Kepler’s Conjecture, and (3) 0-and-1.

**1d**. Continuity, symmetry and harmony. Pi has to come into being in some manner. The spheres of the Kepler conjecture have to originate somehow.

To answer the question, “Why is there something rather than nothing?” we assume that something is more fundamental than space and time, matter and energy. Here is our attempt to define the concepts that create a finite-infinite relation that gives rise to homogeneity-isotropy. Within this emerging model, the infinite is the qualitative; the finite is the quantitative. Instead of retiring the concept of infinity (Tegmark, 2012), in this model, it is the centerfold but with very specific definitions.

**1e**. From systemic to quantum fluctuations. Because so many concepts are being introduced, these comments will become future postings and homepages within this site. In March 2020, I wrote up an overview of some of these concepts (**PDF**) to get some feedback from the FQXi people. Here are the key claims.

Recognizing how idiosyncratic it is to associate the geometric gap with fluctuations, it is certainly a greater stretch to differentiate types of fluctuations. Yet, that study has begun and eventually we’ll be showing a video of what we call “squishy geometries” and the rather unusual motions created by tetrahedrons.

**Systemic fluctuations.** Those two words in May 2020 only had 569 references within a Google search. These fluctuations, admittedly a guess, originate with the five tetrahedral structure fully engulfed by perfected systems. With the emergence of particle physics between Notation-64 to Notation-67, they become part of the look-and-feel that define all physical systems. It is a stretch, for sure, however, we will continue to pursue it further.

*So, yes, there will always be more. Go to our References & Resources section.*

**[2]** **Issac Newton** (1642 – 1726, Cambridge, England).

“*No great discovery was ever made without a bold guess*.”

**2a**. Tested formulas by Max Planck and Albert Einstein defrock Newton’s absolute time and space pageantry. Follow all four values from Notation 1 to Notation 202, our universe is naturally exponential. Space and time are derivative and finite.**2b**. Very fabric of our essential reality. A new aether (ether) emerges. Described often in these pages, the subject has initially addressed (2017) as the fabric of the universe.**2c**. Of course, Aristotle’s influence on the way we think runs deep. Newton credits Aristotle’s work, *The Organon*, within his *Principia*. Yet, we should ask which comes first, basic logic, or the continuity-symmetry-harmony, the heart of the structure of the universe.**2d**. Leibniz challenged Newton in 1715 and 1716. In his lifetime, Leibniz advocated for a relational view of the universe and it perhaps is the best foundation for an alternative approach.

**[3] Max Ernst Ludwig Planck** (1858 – 1947, Kiel, Berlin)

“*All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind.This mind is the matrix of all matter.*“

**3a**. A key calculation has been overlooked. The math is simple. The results dramatic.**3b**. **Ken M. Evenson** *et al* (1972), “Speed of Light from Direct Frequency and Wavelength Measurements of the Methane-Stabilized Laser“, *Physical Review Letters*, **29** (19): 1346–49. Bibcode: 1972 PhRvL..29.1346E, doi:10.1103/PhysRevLett.29.1346). *Quantum Electronics Division, National Bureau of Standards, Boulder, Colorado 80302*)**3c**. More fundamental than space and time. Simple logic redefines the finite-infinite relation and the nature of light, and the nature of space and time.**3d**. Continuity, symmetry and harmony are three facets of both the finite and infinite. It is the baseline of this model of the universe. Here it seems all are universals that are, in the same instant, dimensionless, dimensionful, and dimensional.

[4] **Stephen Hawking** (1942-2018, Oxford, Cambridge)

“*The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge*.”

**4a**. * The Large Scale Structure of Space-Time *is a classic; however, it is not easy reading because it is laden with formulas (PDF).

**4b**.

*: Hawking reviews the history, but does not rule out absolute time. He is after all, the 17*

**A Brief History Of Time**^{th}Lucasian professor, following in the footsteps of Sir Isaac Newton, the second Lucasian professor. Although scholars from around the world were calling for a re-evaluation of its growing status, there was increasingly less room for discussion. Its devotees accepted it as fact, not theory, and Hawking championed that big bang right to his dying day.

*More…*

**4c**. **George F. R. Ellis**, Hawking’s 1973 co-author, had begun to recognize the deeper problems with conclusions from those early years of explorations at University of Cambridge. In 2012 in his collaboration with Roy Maartens and Malcolm MacCallum, (*Relativistic Cosmology*** [PDF]**, Cambridge University Press), the big bang model is clearly under close scrutiny and every assumption is on the table: inflation, singularities, the most-recent measurements of the Hubble spacecraft of the cosmic background radiation, fine-tuning…. he is open to explore virtually every issue; yet with close to 50 years of analysis, he can not be absurd to himself. In February 2020, with colleague, A.A. Coley, the topic is, *Theoretical Cosmology ***(PDF)**, virtually all the same issues are reviewed.

I took the most comfort from an article in 2017, *Physics on the Edge*, where he names all the key players and essentially shows how confoundingly muddled it all is. Our 2017 academy of scholars do not have clear answers.

**References, reflections & resources**

**Please note**: The primary links into this section are from the *Endnotes & Footnotes* from where there is the word, *More… *Links back to that *More*… are from the [Numbers].

**[1] ****Aristotle**. Our work began in a high school geometry class. We knew it required a tetrahedron and octahedron to tile and tessellate the universe. In 2011 we walked with Zeno deeper and deeper inside each object and learned a lot. You should know that our shapes were all perfectly made according to Plato’s specifications.

Yes, in 1998 we manufactured our own tetrahedrons and octahedrons!

It was hard to believe that neither Aristotle nor 1800 years of scholars (at least 90 generations) did not have their own perfect tetrahedrons in their toolbox. We wondered if geometry had slid from importance or was Aristotle beyond criticism?

The icosahedrons and Pentakis dodecahedrons use the five-tetrahedral configuration; they have gaps, and we dubbed it “squishy” or quantum geometry. By 2011, now with many years of visceral experience, and within our new chart of the infinitesimal scales, we thought that such a pervasive gap had to be significant.

We began thinking of quantum fluctuations and then systemic fluctuations.

[**1a**] **Jeffrey C. Lagarias **& **Chuanming Zong**. In 2011, just about the time we were beginning to explore the infinitesimal universe, Lagarias and Zong had begun writing the best little introduction that I’ve found to this geometric gap. It is a relatively short article (**PDF**) for the American Mathematical Society (AMS), December 2012. We appreciate that the AMS has made it readily available.

Also see: Lagarias, Clay Fellow Senior Talk, “Packing Space with Regular Tetrahedra“ and Chuanming **Zong**, *Can You Pave the Plane Nicely with Identical Tiles*, 2018

The people of China and the USA — not the governments, but the people — must find common ground. One would think that mathematics and the sciences would give us an abundance of places with which to build ties that are greater than politics. Articles like this encourage us. As important as their personal relation is, these two are also building relations between the University of Michigan and Tianjin Center for Applied Mathematics (TCAM). Zong was initially at Peking National University. I believe that the work of Lagarias and Zong actually changes the quality of life for everyone and for everything within this universe.

So, it is incumbent on all of us to begin to understand this gap (See #19), the first in the universe. It just might teach us all to become more patient with each other, especially with our superficial historic differences.

[1b] Personal. For me, Aristotle was always secondary to Plato. I am still in my earliest stages of plowing beyond a perfunctory understanding of Aristotle. Just from this encounter, I am fascinated with him. It appears for some of the Aristotelian crowd, his understanding of the tetrahedron is a bit of an embarrassment. Substantial studies do not touch it. My interest was so piqued, I started simple — with the Wikipedia overview — and then went on to other authors who came up in specific searches. I empathize with the less well-known authors, people like Ric Machuga, a professor at a junior college (Butte College, Oroville, CA). His book, *Life, the Universe, and Everything: An Aristotelian Philosophy for a Scientific Age,* was published in 2011.

[1c] **Zeno, Aristotle, Planck and Infinite Divisibility**. I remember well the puzzled look of our students, when in 2011 I said, “Zeno has bumped into a limit called the Planck Length. We cannot *divide-by-2* forever.” Planck gave the universe boundaries and logical conditions for those boundaries. Not entirely satisfied with that perception, a Russian by the name of Sergey Fedosin has taken another step: *Infinite Hierarchical Nesting of Matter. *I always immediately look to see what their starting points are. Within that document, they do not discuss the Planck base units and so they miss the possibility of defining the domain from the Planck units to the particle physics in a highly textured manner.

**More References, reflections & resources:[2] Issac Newton** did not have the advantage of Leonhard Euler‘s exponentiation. He created the concept after Newton had died. Of all possible manners of notations, base-2, is the most simple, yet it still lacks proper respect. The chessboard stories are told but under-appreciated.

The seemingly simple progression, ** **264** **yields a large number, 18,446,744,073,709,551,616. If you were turn turn it into pennies, you could easily retire the world’s debt, all nations and all people… I tried to explain it to my sister-in-law.

2^{202} is another story. Notationally, 6.42775218×10^{60} is the raw number. Once there is an amount associated with it, like infinitesimal spheres, it begins to open the imagination.

Newton did not have Planck’s base units. He was arrogantly unsure of himself. This Lucasian Professor (#2) was confident, however, that space and time were absolute. It is profoundly part of our commonsense worldview. Unfortunately, however, I believe it is wrong. Indeed, the approach of Gottfried Leibniz will render a much richer view of our universe.

There are two living Lucasian professors, Michael Green (#18), and Michael Cates (#19). I’ll keep trying to develop a working relation with them, yet prior history tells me that I am not sophisticated enough for these people. https://81018.com/uni/ https://81018.com/lucasian/

There are related postings within the website that need follow-up. Among them is: https://81018.com/ math/

https://81018.com/malaise/

https://81018.com/arrogance/

**More References, reflections & resources:**

**[3] Max Ernst Ludwig Planck** Within the complex of Max Planck institutes around the world, there have been several attempts to open discussions. In this section, we will look at some of those exchanges more closely.

Max Planck Innovation: https://www.max-planck-innovation.com/max-planck-innovation/max-planck-society.html

**More References, reflections & resources:[4] Stephen Hawking**: There are many articles about the problems within big bang cosmology. A few of these papers will be selected and analyzed in light of the 202 notations. Our first emails to Stephen Hawking referenced our very early attempts to interpret our chart of just Planck Length and Planck Time doublings.

• Mauricio Mondragon & Luis Lopeza,, S*pace and time as containers, Space divisibility, and unrepeatability of events*, 2007, 2012

**Miscellaneous** Notes

**DIRK J. SRUIK**: *“ Aristoteles weiß, daß der Raum durch kongruente Würfel voll ausgefüllt werden kann, behauptet aber weiter, daß das auch mit Tetraedern gelinge. Verf. verfolgt diese falsche Behauptung, die auch für die Lehre vom Vakuum eine gewisse Bedeutung hat, durch die Geschichte der Mathematik. Der erste, der die Unrichtigkeit des Satzes nachweist, ist Regiomontanus. Aber Ramus und Snellius folgen wieder dem Aristoteles. Erst mit dem 16. Jahrhundert tritt völlige Klarheit ein (Benedetti, Blancani, Broscius). (V 3.)“*

**TRANSLATION**: “**ARISTOTLE** KNOWS THAT CONGRUENT CUBES CAN FILL THE SPACE COMPLETELY, BUT FURTHER CLAIMS THAT THIS CAN ALSO BE DONE WITH TETRAHEDRA. THE AUTHOR FOLLOWS THIS FALSE ASSERTION, WHICH ALSO HAS A CERTAIN MEANING FOR THE TEACHING OF VACUUM, THROUGH THE HISTORY OF MATHEMATICS. THE FIRST TO PROVE THE INCORRECTNESS OF THE SENTENCE IS REGIOMONTANUS. BUT RAMUS AND SNELLIUS FOLLOW ARISTOTLE AGAIN. IT WAS NOT UNTIL THE 16TH CENTURY THAT COMPLETE CLARITY APPEARED (BENEDETTI, BLANCANI, BROSCIUS). (V 3.)” D. J. STRUIK, Het probleem “de impletione loci”. *(Dutch)* JFM 52.0002.04 Nieuw Archief (2) 15, 121-137 (1926).

•** Ellis** *et al,* Page 310, Chapter 12 – Structure formation and gravitational lensing

“The basic idea is that quantum fluctuations of the inflaton field behave like one-dimensional quantum harmonic oscillators (with time-varying mass). Zero-point fluctuations of a quantum harmonic oscillator induce a non-zero variance of the oscillator amplitude, ⟨xˆ2⟩ = /2ω. Similarly, the inflaton zero-point fluctuations generate a non- zero variance ⟨δφ2⟩. The fluctuation modes (with co-moving wave number k) are stretched from their original small scale (assumed to be above the Planck scale) by the rapid accelerating expansion of the universe, until their wavelength ak−1 exceeds the Hubble scale (when they are assumed to become classical fluctuations).”

• W. Patrick **Hooper** et al., , 2018, Platonic solids and high genus covers of lattice surfaces

We will be proposing one that has been reached by a few well-grounded scientist/scholars. Unfortunately, it still feels a bit more like science fiction, so we’ll come back to it within our final overview and conclusions.

• Alvaro G. **López**, *On an electrodynamic origin of quantum fluctuations*, ArXiv, 2020**Nonlinear Dynamics, Chaos and Complex Systems Group**, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain (Dated: January 31, 2020)

Here, space and time appear quite derivative. It appears that he was not ready to challenge absolute space and time. He defines a relation that begins with the Planck units. When we apply base-2, we are looking at the natural unfolding. The two formulas mass-energy equivalence and length-time equivalence are bound by light and appear to be bound to each other.

• **Wikipedia**: *A gauge theory is a type of field theory in which the Lagrangian does not change (is invariant) under local transformations from certain Lie groups. … If the symmetry group is non-commutative, then the gauge theory is referred to as non-abelian gauge theory, the usual example being the Yang–Mills theory*

**.**

• Chuanming Zong, *Can You Pave the Plane Nicely with Identical Tiles*, 2018

# An Email to a therapist

You might want to ground your people within a very simple model of the universe. All our current models are too big for most of us and those models tend to cause great anxieties. We call our work, The Big Board – little universe. It mathematically connects everything, everywhere for all time within a functional schema that actually seems to be a much better model for cosmology, physics, and mathematics than the models we currently entertain. The universe can be parsed from the Planck base units (it’s our the start)to this current day within 202 base-2 notations (all simple doublings). Once people understand that we live in an exponential universe, this place we live and have our being becomes quite intimate, comforting and secure, plus we realize that we are an important part of the equation and what we do counts. We make a difference. For more, you might start with today’s homepage: http://81018.com

That’s always recent work.

Please have a glance at the 202 notations, the chart: https://81018.com/chart/ Here is a short-cut: Review these claims:https://81018.com/checklist/; It is simple, simple, simple, so don’t let it appear otherwise.

And, yes, I am always open for questions!

# Tweets

**June 9, 2020**: A few sample tweets**Keeanga-Yamahtta Taylor, Princeton**: @KeeangaYamahtta

You have intuited what science has failed to understand –

There is a profound integration of all things everywhere for all time.

https://81018.com/duped/ is my first analysis of Aristotle’s mistake (geometry), Newton’s mistake (space and time), and Hawking’s mistake (infinitely hot start): https://81018.com/duped/#Now

There will be much more to come.

**Please Note**: I also sent a direct email. -BEC

**Nature Magazine** If you want to make a difference, teach us all something about the scientific foundations that we do not know, i.e. Aristotle’s geometry mistake, Newton’s space-time mistake, and Hawking’s lack of infinity: https://81018.com/duped/ It is all so tightly inter-related and we don’t see it. **Please note**: Shall we re-submit this article to Nature? It was ignored.

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This article was initiated on Wednesday, May 20, 2020.*Duped* became a homepage or top-level post: Wednesday, June 3, 2020.**Last update**: Friday, September 25, 2020**The Prior Homepage**: https://81018.com/alternative/ **The URL for this page**: https://81018.com/duped/

A section on **Aristotle** and geometry: https://81018.com/duped/#Aristotle

A section on **Newton** and absolutes: https://81018.com/duped/#Newton

A section on** Hawking** and “infinitesimally hot” start: https://81018.com/duped/#Hawking**The tagline**: *We reach for the stars, but we’re conceptually blocked…*