As a formal study, SUSY began to build momentum in the early 1970’s with the work of Julius Wess and Bruno Zumino. We have written to Sylvester Gates, the first PhD granted at MIT for SUSY studies (1977). He is part of our first generation of scholars who engaged SUSY.
To continue to ask questions about SUSY, a list of scholars (with highly cited articles within the past few years) will be compiled here. For example, we are now reviewing the work of Jonathan Bagger of IAS, JHU, and APS.
From Wikipedia: “The observed hierarchy between the electroweak scale and the Planck scale must be achieved with extraordinary fine tuning. This problem is known as the hierarchy problem.”
There is no other theory that has 67 base-2 notations from the Planck scale to the electroweak scale. There is no hierarchy problem if one starts with IPS at Notation-0. even today, it might be argued that infinity, pi (π) and spheres (IPS) has nothing to do with supersymmetries. But, of course, within our model, IPS is the source of all symmetries
The James Webb Space Telescope (JWST) is finding so many new galaxies, people are again asking, How is it possible? Are there too many galaxies and not enough time? Should we redefine time? Possibly there’s a better way to interpret the redshift data.  Perhaps we are unwittingly double-counting (or more). Is our understanding of galaxy formation too incomplete? What if this universe is fundamentally exponential? Could base-2 notation be a key to it all? 
Time redefined. A dynamic equation that makes numbering possible
Einstein and others tell us that time is not absolute. It’s finite. Not to be confused with a second or some part of it, time is also dynamic. Time is an equation; it makes numbering possible. And as a result, it makes measurement possible. Seconds-minutes-hours-days are all human conventions. Simple equations make time, i.e. one infinitesimal sphere per unit of infinitesimal dimensionless constants and it all manifests as space-time. Time is the result of equations that render Planck units. Yet these current numbers are still just placeholders. NIST and the ISO could adjust those values. Even the 1874 calculations by Stoney could be used to help determine a new set of values based on current data.
Base-2 applied to the symbolic Planck units goes from the first possible moment of the universe to the current time in just 202 highly-integrated, richly-mathematical notations. It is no longer spaceship earth; it’s spaceship universe. We are intimately one; and, we create space-time as we go.
Imperfection — discontinuity, asymmetry and dissonance — comes.
Again, the domain encapsulated by the first groups of notations would be perfectly filled and smooth (no gaps) until there is a formation of the five tetrahedral and five octahedral gaps. A speculation is that due to compression (densities), these geometries would be encapsulated and not become systemic. We know, however, that at some point there comes a notation with encapsulated gaps that becomes systemic, giving rise to quantum fluctuations. And then, those fluctuations begin to reach down into the prior on-going notations (we’re beginning to learn how all notations are always active).
Concepts that could help open historic worldviews that confine us:
Simple mathematics. Looking at those 202 base-2 notations from the Planck base units to the current time, the first 64 notations are below thresholds of measurement and are the subject of the nine studies cited just above.
Finite-and-infinite. This Janus-faced relation has been controversial throughout time. Let’s define it as the quantitative-qualitative in light of those three faces of pi and in light of the first 64 notations. Historic and personal issues regarding infinity are placed on hold.
The nature of sleep cycles. Within sentient and thinking things, there is a constant process by which linear time is recompiled within exponential time and the current moment of the universe. Notation-202, the Now, is always on the edge of the current expansion, could appear to be a time asymmetry but is forever being recompiled within the whole as everything that sleeps does within an infinite cradle of continuity-symmetry-harmony.
Conclusions A hypostatic geometry, hypostatic physics, and hypostatic science
Of course, the word, hypostasis, is loaded with a prehistory that is not ignored, but could be. If today, right now, is the only time that is really real, it seems that we could engage the word as given within its meaning of “that which stands under” or perhaps “the foundations of the foundations.” It is about giving those first 64 notations a special name and definition. It’s a pre-physics that is still physics. It’s a most seminal geometry of nodes, lines and faces that are always dynamic, interactive, testing, defining, creating… and so much more. Scholars have spent their lifetime feeling, contexting, and writing about the subject. They each know a face of that mathematics. They have the textures and refinements. So, let us turn to them and ask, “Can you tell us more? Can you all work together? Might those five bullet-points just above help?”
 James Webb Space Telescope (JWST) follows the work history of the Hubble Space Telescope. In 2016 Prof. Dr. Christopher Conselice defended a two-trillion galaxy estimate from his analysis of the Hubble data. He believed that number was consistent with big bang cosmology as understood by Stephen Hawking and his followers. Other respectable astrophysicists like Mario Livio (Space Telescope Science Institute, Baltimore) have not disputed the Conselice estimate but hold to a more conservative number between 100 and 200 billion. Notwithstanding, the JWST will continue to put pressure on that count and on the adequacies of classic big bang theories. Also, it will be anyone’s guess what is behind all the blindspots between us and the rest of the universe. The New General Catalogue of Nebulae and Clusters of Stars and other deep sky objects will become the largest document in the universe!
 Our understanding of the redshift (color, distance, frequency, light, time and wavelength) just might be challenged. We will start a pointed study of the redshift as currently understood.
 Counting within base-2. As noted in the prior homepage, just one sphere doubled, then doubled again and again, 64 times or 264 (our Notation-64) would amount to over 18,446 trillion infinitesimal spheres. At one second (as noted in just the prior paragraph of that homepage) is 539 tredecillion spheres per second. We have just scratched the surface in our quest to learn about exponential notation and all the possible counting schemas. The possibility of trillions of galaxies with quadrillions more planets has begun to peep into our spheres of plausibility.
Possibly more to come…
References & Resources As these references are studied, key references and resources will be added within this website.
Longing for the Harmonies, Frank Wilczek and Betsy Devine, W. W. Norton, 1988 Editor’s note: More true today than at any time, Frank and Betsy’s dedication quote to Amity and Mira, sets the tenor of this book, “…awaken our understanding and longing for the harmonies” (which comes directly from Kepler).
There is so much insecure arrogance in our world. One would think with all that we don’t know and all we learn every day about the depth and breadth of what we don’t know, well, wouldn’t you think we’d become a little more reflective and introspective.
Abstract. A model of the universe is introduced, based on simple logic, mathematics, and geometries, created by parsing the universe into 202 base-2 notations.* It starts with Planck Length and Planck Time and goes to today’s size and age of the universe. Those Planck’s units are placeholders, symbolically the very first units of everything, everywhere for all time. Our hypothesis about the look and feel of the first moment that defines space and time, posits the sphere and pi to be the most logical. Qualities and quantities are manifest. The qualities appear infinite and perfect and are represented by continuity, symmetry and harmony, the primary three qualities of spherical geometries. Through cubic-close packing of equal spheres, tetrahedrons and octahedrons are rendered, perfectly filing space; it’s a smooth beginning with no gaps. At a point in time five tetrahedrons share a center point to create a gap and fluctuations emerge. Five octahedrons create the same gap, and together they create many kinds of gaps, and the probable beginnings of quantum physics. This a very different, simple model that needs the courtesy of a critical review. Here, too, is a most-comprehensive STEM tool that lays out the first second (Notation-143), the first millennium (Notation-179), and the first billion years (Notation-199). Notation-202 is 10.9816 billion years in duration; less than 2.83 billion years has manifest. This simple model absorbs big bang cosmology.† After discussions (with charts and other graphics), our savants from our sixth-grade classes began to grasp it, so your comments and questions are always welcomed. Thank you. -BEC
Key words: Time, space, mathematical models, geometric models, pi, spheres, tetrahedrons, cubic-close packing, octahedrons, perfection, imperfection, continuity, symmetry, harmony, 202 base-2 notations, integrated UniverseView, Frank Wilczek, Carl Hogan, Joanne Baker, Nature Magazine, time, space-time, Max Planck Institute…
Consider a simple concept of time.
What do we believe about time? In a limited survey, a commonsense belief is that time goes on forever. In this model time is finite. Most people have an intuition about a second. Possibly it is the most-used, shortest duration of time. There are 60 seconds in a minute, 60 minutes in an hour (3600 seconds), 24 hours in a day (86,400 seconds), and 365 days per year (31,536,000 seconds). Factor in Leap Year with its 366 days, we’re up to 31,556,952 seconds. Multiply that by 10 billion years for 31,556,952,000,000,000 seconds. Factor in 13.82 for a generous estimate for the billions of years, and that would give us 436,117,076,640,000,000 seconds. That’s from the very start of the universe to this day with some room for error. For Isaac Newton time goes on forever. Again, within this simple model, time is finite. The universe is somewhere around 436 quadrillion seconds from the very first moment of time to this day, right now.1
Consider everything, everywhere, for all time.
The story of our first new idea that we uncovered has been told and retold many times. It is the story of the 202 base-2 notations from the Planck base units up to Now. We came up with a simple chart for length — https://81018.com/big-board/ — and lived with it for several years. Then we added Planck Time, and a year later we added Planck Charge and Planck Mass. It.was difficult to follow the numbers on each line so in 2016 a horizontally-scrolled chart emerged — https://81018.com/chart/ — and then a website so we all could access it at anytime.
That new chart literally came alive. We had observed how each notation was building on the prior notations. There was a causal efficacy; the geometries, pi, dimensionless constants, and cubic-close packing were tying each notation together. At some point it became apparent that all notations had to be active all the time. That was a steep learning curve. We had to ask ourselves, “If that’s true, then what is time?” We started at the Planck base units and assumed Planck Time is the smallest unit and the first unit. That work in 2017 was part of a NASA Space App exploration at their facility in Huntsville.2
We thought we had emerged with our own homegrown STEM tool and began sharing it with other schools. It came with our rough outline of the universe in 202 base-2 notations. We had slowly started learning a bit more cosmology and theoretical physics; Frank Wilczek’s books were helping to guide us and there were people like Freeman Dyson who tried to keep us on the straight and narrow.
That the first second wasn’t until Notation-143 was quite surprising. We surmised, “This chart is mostly about the first second of the universe after that very first instant when it all began. This model is mostly about the infinitesimal.” One of the many ah-ha moments was when we asked, “Isn’t that the first second of the universe even as it unfolds today?” It was a puzzling question to ask. We began to see that the universe is almost fully symmetric. It appeared to have a dynamic, causal, working relation back to Notation-0 and up to Notation-201. I thought, “That puts a lot of pressure on Notation-202, especially the current time. All the peculiarities of time symmetries and asymmetries have to be within Notation-202.”
Plus, there were so many other questions. Where does gravity come in? How does inflation work here? What about quantum indeterminacy and fluctuations? Is it a quanta of energy or a dynamic relation? What are blackholes and dark energy-and-matter?
We knew we had a long way to go before we could truly tackle those well-known unknowns. At that point, we were trying to figure out the geometries and numbers for those first few notations. We were being pushed to study pi and infinity more closely.
Reconsidering the nature of pi and infinity
The concept of Infinity has been a problem for the world. Self-assured people have come up with special concepts and stories about the very nature of infinity. Told for many generations, those stories have become a key part of a family’s traditions. Not only are these the stories of Mom-and-Dad, but from the generations; “This must be the truth. Absolutely so.” That kind of assurance can become arrogance; and when it does, it becomes a problem. It is often difficult to discuss new ideas and concepts if there is limited or no openness. So I asked myself, “Is there a way to respect those stories but have mathematical and scientific concepts that everyone might embrace and about which these should not offend, even if an atheist?”
Our attention increasingly focused on pi.,,
We concluded that it had been undervalued and under-analyzed among our scholars. It provides a pivot point between the finite and infinite. It is a natural connection. It is a key part of so many basic equations that describe fundamental things and nobody was talking about those keys or essence as a starting point. The more I learned about Hilbert, Gödel, and infinity, it seemed a simple redefinition was in order. They didn’t have those early notations to challenge them. Let pi provide the simple bifurcation whereby the infinite is qualitative with its continuity/order, symmetry/relations, and harmony/dynamics. And, the finite is the quantitative. It’s measurable. The more time we spent with pi, the more challenging and exhilarating it became. The most speculative jump we made was to consider that a natural inflation could be assumed at a rate of one infinitesimal sphere per infinitesimal unit of time and space. Using the Planck numbers that calculated out at 539 tredecillion spheres per second. Using Stoney’s numbers renders 4609 tredecillion spheres per second. The nature of that inflation, explored in an earlier homepage about thrust, is slowly being expanded and pi is leading the way.
Consider these the foundations of our foundations.
The first 64 notations are currently below possibilities for physical measurements. Might these be considered the foundations of the foundations? If primordial spheres manifest at the Planck scale and there are 64 base-2 doublings before anything can be measured, isn’t that a new domain, a major amount of space? Just one sphere doubled 64 times would amount to over 18,446,744,073,709,551,616 infinitesimal spheres. It may be too small for arrogance but perfect for Langlands, string-and-M theory, SUSY, hypothetical particles… and so much more.
And finally, consider simple complexity.
On the cusp of the finite-infinite relation. It looks simple, but there is nothing simple about a sphere. Her numbers go on forever, always changing and always the same. Those symmetries appear simple, but are the expression of those endless numbers. Attractors and repellers are seemingly in the fiber of its being. The Fourier Transform and dimensionless constants are quite literally everywhere. One might say that the sphere is a bundle of nerves, infinitesimal but profoundly alive. Here is the continuity-order, symmetry-relations, and harmony-dynamics within the perfections of the infinite unfolding within everything quantitative. The perfectly perfect is hypostatic. Simple configurations of five tetrahedrons or five octahedrons come together and become a gateway for fluctuations, imperfection, and creativity.
The new is opened. A deeper complexity is defined. And, there is so much more to learn, do and explore. Thank you.
We especially welcome your comments and insights. Thanks again.
A key part of this chart is between notations 64-and-67 where quantum fluctuations become dominant. There comes a place when the composition of measuring devices and the people using them interfere with the measurement. As we go smaller, it becomes increasingly difficult. There will be three zones: 1).Not measurable, 2).Transitional area, and 3).Measurable. The area that is not measurable has had major studies some of which are noted here.
Note: The tetrahedrons and octahedrons used in these models have an actual place along the Notations 0-202. The length of the side is about 2.5 inches with is between Notations 111-and-112 (1.65 to 3.3 inches). The models are representational, not literal and become structural within Notation-1 and are infinitesimally present within Notation-202.
Emails To scholars around the world, their writings help clarify issues and inspire us.
• Joanne Baker, Nature Magazine, August 4, 2022 • Craig J. Hogan, University of Chicago, Enrico Fermi Institute, August 4, 2022 • Jürgen Jost, Max Planck Institute, Leipzig, August 4, 2022M • Sir Peter Knight, Imperial College London, August 2, 2022, at 3:320 PM • Peter Scholze, Max Planck Institute for Mathematic, Bonn, August 1, 2022 at 4:51 PM
IM There will also be many instant messages to thought leaders about these ideas and concepts.
@the_xijinping This very simple model of the universe is based on simple mathematics, geometries and logic — https://81018.com — whereby continuity, symmetry and harmony becomes the basis for ethics and value — https://81018.com/ethics/ — and rises above politics.
Fascinating. Engaging. At about that time, I had set aside my writing to Joanne Baker of Nature magazine; and now, thinking of your work, you were inspiring me to be bolder.
As I read your abstract, I could hear myself saying, “Check. Right. Right. Right. Check…” So, now I need to dig into the article and also look at all your other work to see just how bold I can be if I were to write to you. Eventually, you’ll know, but for now, maybe we can be friends.
So, I just did a brief survey of your work. First, “Congratulations on all that you have done. You have done quite a sweep of the world and the universe! As a sequel of Symmetries… I think you could begin to answer some of our many unanswered questions.
You begin the dialogue with the reader, “The world works according to two all-encompassing theories…” and you are so right. Our world has done well with those two theories. Our universe, on the other hand, demands that the two come together.
First, let’s push our understanding of time. We are all so infinitely Newtonian when finite seconds do just fine. Here’s is our look at what we called, The Universe Clock. We start at the Planck base units and assume Planck Time is the smallest unit and the first unit. That work in 2017 was part of a NASA Space App exploration at their facility in Huntsville. We thought we had emerged with our own homegrown STEM tool and began sharing it with other high schools. It came with a rough outline of the universe in 202 base-2 notations. We had started learning a little cosmology and theoretical physics; Frank Wilczek’s books were helping to guide us and an old friend, Freeman Dyson, was trying to keep us on the straight and narrow.
Yet, there was something fundamentally wrong with our model. It didn’t cotton with big bang cosmology. It had at least 64 notations before particle physics and CERN’s measuring devices. Our little model was puzzling yet logical. How could we be so far off and out of step?
I decided that pi was our stumbling block. It was tied up inside so many fundamental equations that describe fundamental things and nobody was talking about its essence and as a starting point. The more I learned about Hilbert, Gödel, and infinity, it seemed a simple redefinition was in order. Might pi provide the simple bifurcation whereby the infinite is qualitative that is continuity/order, symmetry/relations, and harmony/dynamics and finite is the always a quantitative expression?
It gave me a slight reprieve so our 202 notations could stand, and time and space could be inadvertently redefined so all notations could become always active. There is so much more that we’ve slowly uncovered, but I have already overstayed a de facto time allocated to emails such as this. So let me say, “Thank you, thank you, thank you for all that you do, and for taking time to write about the Symmetries of the Primordial Sky. I have questions, but on my continued survey of your work, I know you do not have the time. So, let me ask for permission to write again. Thank you.
Symmetries of the Primordial Sky Abstract (PDF): Quantum field theory, which is generally used to describe the origin of large-scale gravitational perturbations during cosmic inflation, has been shown to omit an important physical effect in curved space-time, the nonlocal entanglement among quantized modes from their gravitational effect on causal structure. It is argued here that in a different model of quantum gravity that coherently preserves nonlocal directional and causal relationships, primordial perturbations originate instead from coherent quantum distortions of emergent inflationary horizons; and moreover, that causal constraints account for approximate symmetries of cosmic microwave background correlations measured at large angular separations, which are highly anomalous in the standard picture. Thus, symmetries already apparent in the large-angle CMB pattern may be unique signatures of the emergence of locality and causal structure from quantum gravity.
Questions related to approach to QFT: 1. Does QFT apply to Planck scale physics? 2. Might the profoundly infinitesimal universe (below the measurements of CERN) be perfectly smooth? 3. Might quantum physics be a question of geometry? More to come…
I just started a page about this note. It’s still rough but it’s the only way I can keep track of the work of scholars to whom I write. Our work will strike you as rather odd, but you may have some “first-impressions” and advice for us and that is why I write to you. I’ll be using your work to further develop my thoughts to follow-up this page: https://81018.com/geometries/
Thank you for your time.
PS. I think I remember seeing you at a UC-Davis conference that touched on the EPR that I dropped in on back in 2018. Also, looking at Steve Carlip’s ArXiv publications, it is gratifying to see so many articles where he is the single author. Also, I grew up in the shadows of Harvard. When still in high school in 1964, I joined the Harvard SDS. Later, in 1971, I was with Arthur Loeb and his group called the Philomorphs in the attic of Sever Hall. In 1975 I was over at the Harvard Divinity School with Arthur McGill where we engaged Austin Farrer’s Finite and Infinite.
I may have crossed paths with Steve Carlip more than once! -BEC
Our page about your work — https://81018.com/2022/07/28/strassler/ — is one of over 2000 pages-and-posts. In my daily monitoring of web activity, I’ll often re-visit a post that’s active the prior day which often prompts the question, “I wonder what (he/she) is up to today?” You’re recently part of that group, so today I revisited our page about your work and added a link to your March 21, 2014 article Did The Universe Really Begin With a Singularity?, as well as to your Facebook page. And to be sure that we include your most recent work, W boson mass too high? is linked.
2. Where is Wikipedia’s article about you? You are mentioned in the Cascading article. There’s a link to Igor Klebanov, but none to you.
3. I have asked the ISO to consider the differences between the Planck base units and Stoney’s units. I then add, “It would also be helpful if there were a discussion about the possibilities of what is being manifest at that time. That is, given our understanding of dimensionless constants, could an infinitesimal sphere be defined by those basic units?”
Of course, your explanation of singularity is classic. It’ll be occupying our thought-space for a long time to come.
Second email: September 12, 2022 at 10:09 PM
Dear Dr. Matthew J. Strassler:
Yes, I rediscovered my note to you from June — https://81018.com/strassler/#First — and then the more recent tweets. I thought you might not mind a question regarding your work in 2015 when you wrote about the data captured by the Planck satellite about the CMB. More recently the JWST results appear to show an even smoother earlier start. Some like Avi Loeb suggest that this smoothness may require a new physics.
But, if we apply base-2 to the Planck base units, out of the 202 notations from Planck Time to this day, there are 64 notations that create a huge grid for that infinitesimal area and time. It is below the thresholds of direct measurement and might be be reserved for Langlands, strings, SUSY and a host of others. Might you comment? Thank you.
September 10-11, 2022: Tweets
2:48 PM · Sep 10, 2022. Matt Strassler, a theoretical physicist studying particles and strings, tweeted, “So, the news from #Kharkiv is surprisingly good, but very worrying. This is not retreat, it is collapse. (Izium, already!) #Putin cannot tolerate more humiliation. I fear he will lash out.”
PS. I am going through your work within inspireHEP.
First email: Jun 6, 2022, 4:50 PM
Dear Dr. Matthew J. Strassler:
I am sure you have a graduate student who could rather quickly bring your website, https://profmattstrassler.com/, up to speed. I think it is worth saving.
At the divinity school (Harvard) back in 1977 with Arthur McGill, we focused on the Finite and Infinite relation through a slow reading of Austin Farrer’s book of that title. In trying to consider the fundamental laws of nature, it seems there should be some working assumptions about infinity. In my reading of your work, it is not clear to me what those assumptions might be.
Intransigence becomes hostility. People from every nation and walk of life are not willing to see a broader, more-inclusive context to grasp the meaning-and-value of life. Limited worldviews clash. Temperatures flare and people fight. A better way is an integrative model of the entire universe within which to know ourselves, our world, and a bit more about our universe.
There are three facets of pi, however, that are not finite or quantitative so we assume (hypothesize and/or hypostatize) these facets define the infinite and the qualitative.
Continuity is our first facet of infinity. It is the very nature of order. Within the finite it looks like a string of numbers and feels like time. Pi qualifies; it’s an equation that has never-ending results that are always the same and always changing.
Symmetry is the second facet of infinity. It looks like geometries and is the very nature of a relation. Within the finite it feels like space. Pi qualifies; it’s a symmetry that generates symmetries. It’s an equation that generates equations.
Harmony is the third facet of infinity. It is the very nature of dynamics; and within the finite, it is always cyclical (periodicity) and experienced as space-time moments. Pi’s numbers, geometries, and equations (Fourier transform and others) are here within an eternal dance and there’s a domain of perfection which may be experienced as a moment of perfection.
Ultimately, pi is the face of both sides of every equation, one is qualitative (infinite) and the other is quantitative (finite). Let those natural, dynamic relations be natural. Let all your relations breathe and come alive. Be open and engage the harmony of the universe.
• Are Planck Length and Planck Time real? Among the scholars in this area, they seem to say, “Real enough.” • Are their numbers real? Infinitesimally small, we are prone to say that these are symbolically real and “close enough.” • What manifests first? Pi drives the finite-infinite equations; we consider a size/time invariant sphere that is defined by those Planck base units (numbers). We’ve also used Stoney’s numbers. Both sets of numbers are symbolic placeholders until there is a new consensus among scholars, NIST and ISO.
Our Story. In December 2011, our high school geometry classes unwittingly made a first pass at defining the universe using base-2 notation starting at the Planck base units. We believed the scholars that the Planck units for length and time were the smallest possible units of space and time. Our conjecture was that they would also be the very first units of spacetime.
We decided to explore. To get down that small, we followed a 4D path inspired by Zeno. We divided the edges of a tetrahedron by 2, and then its internal octahedron and four smaller tetrahedrons, and continued dividing by 2. There were just 112 steps within to the Planck scale. We thought it might feel a bit like Alice’s fall into that rabbit hole as in Lewis Carroll’s Wonderland. But, our walk was highly-ordered, systematic, yet most magical. As we went down deeper and deeper within, it was not at all confusing. Even our shrinking in size each step seemed quite natural.
We rebounded back in the classroom by multiplying the Planck Length by 2. Later we would add Planck Time. And then even later, Planck Mass and Planck Charge. It was extraordinary going from that smallest unit out to the edge of the universe to watch the current expansion, all in just 202 base-2 notations. Yes, from the smallest to the largest sizes and from the first moment of time to 13.81+ billion years later, we had encapsulated everything-everywhere-for-all-time.
Exponentiation. The entire universe, from the smallest possible measurement to the largest in 202 notations, stretches credulity yet it’s 100% mathematical and predictive. All notations are profoundly related and always dynamic. We were so new and naive about it all, we asked questions of the thought leaders of big bang cosmology, Hawking, Ellis, Guth, Steinhardt… and so many others. “What are we doing wrong?” Nobody was willing to guide us, so we placed the time line for the big bang and our big board, side-by -side. We found only a microsecond’s difference with Hawking cosmology. We were beginning to learn about the problems, so when a scholar labeled our model, idiosyncratic, we knew that his judgement was quick and somewhat flippant. There was — and still is — just too much here to consider.
It has taken ten years to begin to understand why change is difficult to engage. First, there is so, so much vested in the Hawking model. It has stood strong for many years. It began building in 1973 when Hawking and Ellis wrote a thesis, The Large Scale Structure of Space-Time. Every new citation, each new book and movie and video, making reference to Hawking’s big bang cosmology, created a muscular defense around Hawking and his model. Yet, that core belief system could not answer a growing number of questions. It had to choose to ignore others. Second, no new model came along. Still, eventually some of our best scholars broke rank and called more stridently for a new paradigm.
We were late to that party and we had no scholarly credentials, yet our emergent model had clear, simple, and compelling mathematics and logic. Nobody argued that.
Those first 64 notations. Although impossibly small, here is a huge infinitesimal domain that is well below the current thresholds of measurement. Unwittingly, all 64 notations, albeit a most-speculative domain, had never been considered. The more we read and studied about the mathematics of Langlands programs, those earliest notations seemed like a natural home. It also seemed like string and M-theory could benefit. Then we began learning about SUSY, and studies like causal set theory (CST), loop quantum gravity (LQG), spectral standard model (SSM), and others. All could benefit. Then came all the hypothetical particles and what we called the Moonshine outliers. They all needed a place to begin working with the two Standard Models. Most naively we raised our hand, “Over here!” Yet, I would guess that we were too simple, too basic, and our grasp so superficial, nobody dared to get too close. We could readily taint their work! I understood… and understand even today.
Consider the obvious. These 64 notations have dimensionality. The conjectured infinitesimal spheres are not “one-dimensional space entities or membranes of higher-dimensional extensions existing in higher-dimensional spaces.” We might say as above, so below, considering that we started with numbers and basic geometries and carry it forward throughout the entire universe.
A new geometry. In May 2022, our simple clear-plastic models opened a new door. We had plenty of images of a five-tetrahedral gap and that work was well-known within small circles of scholars. With various five-tetrahedral models on my desk for several years, one day I asked myself, “Could there be a five-octahedral gap?” In minutes the first models were made; and within the month, we had our first pass at an explanation. A most-challenging composite is a five-tetrahedral gap on the top and bottom with the five octahedral gap in the middle. In June 2022 we began inviting scholars within pure geometry to help interpret where these gaps fit within the larger scholarly models of the universe. My simple thought was that these basic geometries, especially the three with basic gaps — tetrahedrons, octahedrons, and icosahedrons — could be part of the transition from Standard Model of Particle Physics to a new, different, and very-special science of the infinitesimal. The earliest infinitesimal architecture, we conjectured from Notation-0 to Notation-64, would give us that smooth-most-perfect start of the universe and then open a domain, Notations 65-to-67, for quantum fluctuations (our 2017 speculations).
When pressed on the possible application of these gaps, our scholars seem to avoid those discussions. We can avoid it no longer. It is time to engage the gaps and all their implications for mathematics, physics, chemistry and biology (i.e. synapses).
The expanding definition of pi as the actual bridge between the dimensionless constants of the infinite and all finite quantities is a key. Pi and spheres go hand and glove. The first sphere emerges, then one infinitesimal sphere per unit of Planck time. In the first second, we are out to Notation-143 and no less than 539 tredecillion (1042) infinitesimal spheres. In the first year within Notation 169, we would multiply 539 tredecillion by 31,556,952 (seconds per year). Exponential notation has taken over, yet there is a linearity deep within each notation.
Where do we go from here? Mathematicians and physicists are opening pathways to this domain. It is the domain of finite-infinite transformations where there just happens to be a fair amount of activity. From the esoteric to the basics, magazines like Quanta explore the edges of knowledge. New people are introduced everyday. People like Philipp Dumitrescu call into question the very nature of time. Mary Gaillard, a particle theorist at University of California – Berkeley, asks about the very nature of mass. Peter Scholze pushes forward with his perfectoids in Langlands programs. Although those who define infinity in other ways may disagree, it all seems to boil down to the finite-infinite relation. Many mathematicians are attempting to get beyond David Hilbert and Kurt Gödel and the limitations created by their logic that never entertained the first 64 notations and the perfected states within continuity, symmetry and harmony.
Let’s get beyond our worldviews.
Let us look beyond our little worldviews and consider the universe. In the process of exploring our universe, it was gratifying to find that the International Astronomical Union (IAU) and the United Nations promulgating Universe Awareness, a group that got started in 2004 through the initial work of George Kildare Miley, an Irish-Dutch astronomer and professor at Leiden University’s Observatory. Miley was the Director from 1996 to 2003. Once this page has been gone through several edits, I will introduced these folks to this work and references. Already oriented to a view of the universe, the question is, “Will they be open to the 202 base-2 notations that encapsulate this ever-expanding universe?”
So, as you may well imagine, there will be many more scholars to come who will lead us. -BEC
Endnotes & Footnotes These Endnotes are placeholders. I anticipate feedback that will open the discussion. Footnotes may be added. -BEC
Infinite qualities — continuity, symmetry and harmony — shape all finite quantities. All dynamic equations, here is the beginning of spacetime. The keys: Qualitative-Quantitative. Continuity, symmetry and harmony are the qualitative; it follows that real numbers that are generated by dimensionless constants constitute the quantitative. So, students, without fully grasping the most-sophisticated work of Hawking, Hilbert, Gödel and so many others over the decades, can understand the outside parameters defined by 202 base-2 notations, then become increasingly sophisticated as they add more and more textures to it. So, we will tarry on unless, of course, we hit a wall where the feedback is deafening and complete.
Foundations for the mathematics to integrate our Universe We begin with real numbers. These are the best numbers we have today. They could readily be refined, yet the conceptual boundaries defined by base-2 will be little changed. Notwithstanding, we hold that no page within this website is ever finished. Each can be improved.
Emergent Geometries of Quantum Fluctuations When we know there is far more room to expand, we will. Today we have an index of a bit more than a million total words but collectively use less than 170,000 words, and personally limit ourselves to somewhere around 25,000 words. According to Simon Plouffe, there are 215,000,000 dimensionless constants; to grasp that level of subtlety will require new words and new studies. Entirely new fields of study will emerge.
Your doctoral dissertation may not be directly relevant to expand our understanding of pi but given that knots are an important part of the dynamics of geometric unification theory (and I believe pi plays a much more substantial role between the Planck units [such as Planck Length and Planck Time] and particle physics than currently appreciated), it’s an important read.
Surely you are among the geometers, chemists, and physicists who know that five tetrahedrons sharing a common edge create a gap: https://81018.com/gap/ Most do not know that five octahedrons create the same gap; and that stacked, that gap is a beautiful thing to see: https://81018.com/15-2/ *
I have unsuccessfully searched for studies that explore the very nature of it. Could it be associated with quantum fluctuations? Might this be the beginning of a geometry for quantum fluctuations?
Do you have any insights that could help me grasp these realities more profoundly? Thank you.
*PS. Those are models we created and photographed. The face-to-face vertical alignment from tetrahedron-to-octahedron-to-tetrahedron would necessarily create a horizontal alignment much like that pictured. -BEC
Second email: Wednesday, March 16, 9:46 AM
Dear Dr. Julia Collins:
I hope my note below to JPL-NASA is OK with you!
I think a collaboration between you and Marc would be great!
RE: How many decimals do we need? Marc Ryman comments on pi and “How far off would your odometer be if you used the limited version of pi above? It would be off by the size of a molecule.“
Your article about Marc Rayman’s calculation and conclusion is similar to Julia Collins’ more recent article, “Why bother calculating pi to 62.8 trillion digits?” It was in The Conversation, August 2021. It would be great to have Marc and Julia write an article actually showing us all the mathematical steps involved and reflecting on the logic of it all. Or, I could try writing it up with extensive quotes, but I think it’d be better coming from the two. I’ll send Julia a copy of this note.
Thank you for your article. Fascinating. I’ll be quoting you. Is there a better primary source than “The Conversation”? Pi turns the universe on its head by giving us access to facets of infinity: continuity, symmetry and harmony.
Yes, it is too simple. The five octahedral gap is overlooked. I have asked dozens of people now and everyone has been puzzled. All our computer graphics programs appear to ignore it or compensate for it. Even the construction kits like Zometool do not account for it. Isn’t that fascinating?
So, what’s next? Can you write about it and get a larger group discussing it?
If it is in any way related to quantum fluctuations — and with my models, there is a nervousness with those models — it’s significant. We can actually make those constructions dance and bounce all around!
Would you like to have a set of models made of the clear plastic that we use? I’d be glad to send a few models to you so you can see-and-experience that “nervousness” to which I am referring. Thanks!
Second email: July 6, 2022, 5:56 PM (Updated: July 15)
Dear Prof. Dr. Salvatore Torquato:
I have not found references online to a five-octahedral gap much like the five-tetrahedral gap that Aristotle missed and, of course, you and John Conway did a major study of it. Have you studied or are you aware of any studies of the five-octahedral gap?
Here is a picture of both gaps together: https://81018.com/15-2/. It is much too simple, but for that reason perhaps it has been overlooked.
PS. We’re making a study of that cluster of fifteen sharing a common centerpoint (with the hexagonals within each octahedron). It would make an interesting gate within circuitry of the infinitesimal. If we introduce the twenty-tetrahedral icosahedron in place of the five-tetrahedral cluster, its complexity and potential functionality increases exponentially. -BEC
Thank you, thank you, thank you for your work (referenced just above).
Back in August 2001 I spent a very pleasant day with John Conway but he did accuse me of being hung up on the relation between the tetrahedron and octahedron. For more I’ll copy in part of the story below. Though I am late to discover your July 5, 2011 paper, I was so glad to discover it today. It adds fuel to the fire and opened the door to your work.
I am so glad to meet you through your writings. I have already inserted references to your work in two articles (referenced below).
After spending a bit more time with your writing, may I call you?
PS. I’ve been working with clear plastic models — made the molds and made thousands of octahedrons and tetrahedrons — to delve into the issues of fragmentation and wholeness. David Bohm’s book by that title, has a prominent place in my library.
Here is what I said about John Conway:
“An earlier history began with the study of perfected states in space time. Sometime in the Spring of 2001, at Princeton with geometer, John Conway, the discussion focused on the work of David Bohm who was a physicist at Birkbeck College, University of London. “What is a point? What is a line? What is a plane vis-a-vis the triangle? What is a tetrahedron?” Bohm’s book, Fragmentation & Wholeness, raised key questions about the nature of structure and thought. It occurred to me that I did not know what was perfectly and most simply enclosed by the tetrahedron. What were its most simple number of internal parts? Of course, John Conway, was amused by my simplicity. We talked about the four tetrahedrons and the octahedron in the center.
“I said, ‘We all should know these things as easily as we know 2 times 2. The kids should be playing with tetrahedrons and octahedrons, not just blocks.’
“What is most simply and perfectly enclosed within the octahedron?” There are six octahedrons in each corner and the eight tetrahedrons within each face. Known by many, it was not in our geometry textbook. Professor Conway asked, “Now, why are you so hung up on the octahedron?” Of course, I was at the beginning of this discovery process, talking to a person who had studied and developed conceptual richness throughout his lifetime. I was taking baby steps, and was still surprised and delighted to find so much within both objects. Also, at that time I had asked thousands of professionals — teachers, including geometry teachers, architects, biologists, and chemists — and no one knew the answer that John Conway so easily articulated. It was not long thereafter that we began discovering communities of people in virtually every academic discipline who easily knew that answer and were shaping new discussions about facets of geometry we never imagined existed.
“Of course, I blamed myself for getting hung up on the two most simple structures… scolding myself, “You’re just too simple and easily get hung up on simple things.”
I have slightly updated the last paragraph of my note from July 7, 2022 at 1:17 PM. It would be good to get something into print about the five-octahedral gap and its compilation with the five-tetrahedral gap on the top and bottom as pictured: https://81018.com/15-2/. Of course, my rather preliminary analysis is from my limited perspective and not appropriate for a professional publication. Also, the significance of the fact that five octahedrons are in perfect alignment with the top and bottom five tetrahedrons all opening to that 7.35610+ degree gap, would be better received coming from a few postdocs. If you have no interest in participating, do you know a postdoc who might? Thank you.
First email: Thursday, July 7 at 2022 1:17 PM
Dear Dr. Boris Lishak:
We have been working with the Platonic geometries in our high school and cannot find any references online to a very simple geometric figure of five octahedrons, all sharing a centerpoint (and three sharing two faces with another octahedron and two sharing only one face). It is a very interesting image when the five-tetrahedrons are added on the top and bottom. That stack has 15 objects sharing the centerpoint. I took the picture below just a few weeks ago but, to date, it appears that there is no scholarship about it.
Have you seen any scholarly analysis of it? If not, it appears from your CV that you have the qualifications and depth of knowledge (Publications and preprints). Would you entertain the idea of being a co-author with a few other postdocs? I have a rough start of it here, yet, of course, you all could easily re-context that work more appropriately. Thank you.