The infinitely-hot start of big bang cosmology is easily absorbed by five most-basic assumptions (and yes, we’d welcome your comments and challenges):
1. Define the very first instant of the universe with Planck’s four base units.1
2. Assume a sphere is the very first manifestation of space-time.2
3. Assume sphere stacking is the next dynamic.3
4. Assume cubic-close packing of equal spheres is the next.4
5. The universe expands very quickly — 1-to-143 (of 202) in a second.5
People are rightfully puzzled by big bang cosmology. Its infinitely-hot, infinitely-dense start for the universe is enigmatic at best. In 2011 while working with high school students, we did some simple calculations that eventually became an alternative model and sharp contrast to big bang cosmology. Ours is a base-2 model that starts with Max Planck’s base units, the ones he calculated back in 1899. With a total of just 202 notations the entire universe is encapsulated and totally interrelated. Too simple and logical for scholars absolutely tied to the big bang, they may want to.engage these 20 concepts, all identified to begin to build a case for our alternative.
The big bang begins with three epochs. Those three epochs represent 143 processes (notations and/or doublings) within our model. Each process is defined by exact numbers for length, time, mass, and charge. Notation-0 is a cold start and a return to Lemaître’s original 1927 theory.* At just one second (the 143rd set of numbers in our model), the quark-gluon plasma has started; nucleosynthesis is quickly on the ascent, and it is all quite smooth and homogeneous:
- Planck Length and Planck Time are so small, there are no less than 64 doublings before any lab will be able to measure anything so small. Planck Length is 10-35 meters. The 64th notation is 2.3×10-15 meters. From the start at Planck Time (5.39×10-44 seconds), the first measurable unit of time is within Notation-84 ( 1.04×10-18 seconds). All the numbers for all 202 notations are found in this horizontally-scrolled chart.
- Those first 64 notations.7 There is ample space-and-time for mathematics to work within these 64 notations of numbers / equations, Witten’s string theory / Langlands programs may come alive within a continuum that includes everything, everywhere for all time.
- Here are the beginnings of a smooth inflation,8 where every successive notation is building on the priors. All notations are eternally active, and there are just 202 notations to the current time.
- By the 136th notation, the temperature (which started close to absolute zero Kelvin) is now hot enough to initiate the quark-gluon plasma. This expansion of mass/energy (charge) correlates well with time/space. This chart helps to visualize these continuums.
- Yes, the first second comes within Notation-143, the first year in Notation-169, the first 1000 years in Notation-179, and the first million years in Notation-189. Large-scale structure formation between 150-to-300 million years begins in Notations 197-198.
- Highly-ordered, highly-structured, it pushes us to expand our understanding of time and infinity and in so doing we discover the qualitative9a all over again.
The most-simple mathematics of the finite-infinite relation results in the emergence of the first possible moment of space-time and mass-energy.
POINT OF VIEW: Too many within our world are nihilistic9b drifting toward dystopian. It’s obvious; we need a more integrative model of who we are and why. The question is asked, “How do we open a deeper understanding of infinity and the foundations of science and values?”
HISTORY: Since 2011 I have been actively seeking the help of scholars to interpret the data given within a chart of 202 base-2 notations from Planck Time to the current Age of the Universe today. We call it a Mathematically-Integrated View of the Universe.
OUR LEADING QUESTIONS.
• Did Aristotle’s 1800-year old mistake where he missed a simple geometric gap, help to conceal the geometries that give rise to quantum fluctuations?
• Did Newton’s absolute time precondition us so we could not grasp Max Planck’s simple 1899 equation for length and time? Also see: https://81018.com/bridge/
• Did Hawking’s infinitely-hot start of our universe block our view of a more simple cold start?
• Are the 202 base-2 notations from the Planck units a more relational model because each notation builds off the prior, all notations are always active, the role of infinity is integral, and the universe is open?
OPEN SEARCH. The work of specialized groups of scholars helps. They question aspects of big bang cosmology. I am especially researching the form and function of the earliest possible structures of the universe. Although wrapped a little tightly within their discipline, increasingly I appeal to such specialists as these scholars.
THE CHALLENGE. A concept, more than an idea, orders information. It becomes a good concept when it seems to integrate many “facts” from our observations and measurements. If a more simple concept appears to integrate everything that a “good” concept does, yet more consistently and deeply, it should be tested.
That is where we are today with our Mathematically-Integrated View of the Universe.11 It readily absorbs and integrates all but the first fraction of a nanosecond of big bang cosmology. The most speculative part of the big bang, the first-three epochs out of their sixteen, need to be understood as on-going processes, not discrete epochs. Neil Turok testifies to it.
SCHOLARS & OUR MODEL. Many of the key scholars within theoretical physics and astrophysics have been challenged to engage this mathematically-integrated, exponential model with its concepts and numbers. Most seem quite surprised to be introduced to a base-2 chart of the universe. A little like Kees Boeke’s 1957 base-10 chart, our model is more granular, it starts with Planck’s base units, and it generates geometries as well as periodicity and spin. That’s helpful. The first infinitesimal spheres and sphere stacking define a natural inflation and a continuum from the first moment in time to this very day. In so doing, it absorbs big bang cosmology right back to Lemaître’s 1927 cold start theory.
VALUES. Big bang cosmology appears to be value neutral but, de facto, it encourages a solipsism that tends toward nihilism. The infinite is acknowledged but only as a mathematical concept and expression. Within our base-2 exponentiation model, infinity reveals itself as the source of infinitesimal circles and spheres transforming its non-dimensional qualitative values — continuity, symmetry and harmony — into quantitative values. The earliest notations, well prior to quantum fluctuations, appear to constitute a perfected state 12 within a range of notations — much too infinitesimal to be measured — yet still further defining an emerging space-time.
ENCAPSULATION. That base-2 chart of 202 notations or doublings of the Planck base units logically encapsulates the entire universe, everything, everywhere, for all time.
TENACITY. This project has also been introduced to wonderful groups of scholars whose only goal is to understand the fundamentals of life more deeply. For the appropriately-named Foundational Questions Institute (FQXi), I summarized our nine years of work.
Also, I had been following the work of three generations of the Templeton Foundation. Their charter is to build bridges between theology and science and each year they recognize a person who seems to be leading that charge best. I have been asking their scholars for help since around 1975.
By asking all these scholars for help and clarity to analyze these notations, we can only hope new insights and a few new answers will be forthcoming. There’s an abundance of questions about the integration of information about length, time, mass and energy (charge) with corresponding information within the current epochs that define big bang cosmology. The past two years (since 2018) resulted in 72 top-level posts (a homepage on this site). The most-recent three, top-level posts are the current focus.
DEEPER DYNAMICS. Max Tegmark of MIT wants to retire infinity. We want to expand our understanding of infinity. Our key question is to discern how that finite-infinite relation gives rise to infinitesimal spheres, sphere stacking, and cubic-close packing of equal spheres, and how it is that this special mix renders basic geometries, emergence, and a natural inflation.
SUCCESS. Now, it is well-past time to write some of these posts in a style for peer-reviewed publications. Of course, they’ll have to be accepted and that is a substantial hurdle. On the other side, there is enough material now for a short book. Successful acceptance of an article or a book will generate new discussions about our current understanding of infinity, space-time, light and the start of our universe and that would spell success..
* Bridges between the finite-and-infinite. In our exploration of possible bridges between the finite and infinite, Lemaître’s 1927 cold start model is re-engaged. The 20-to-30 dimensionless constants (needed to support the parametrization of ΛCDM (Lambda cold dark matter) are explored as derivatives of three basic concepts, continuity-symmetry-harmony. These pages continue with explorations of pi and emergence.
 Define the very first instant of the universe with Planck’s four base units. If you studied physics much before 2010, the Planck base units were considered strange little numbers that Max Planck calculated long ago. Paul Dirac had his large numbers. Max had his infinitesimal numbers. Well, here they are directly related and there is an all-natural continuum between them. There is causal efficacy and this website has been charged to figure that out:
• All 202 notations were part of our school curriculum for a year.
• The most important and mysterious notations are the first 64 notations.
 Assume a sphere is the very first manifestation of space-time. The most historical and most-studied shape in the universe, there are many pages to engage. First, take a look at the current state of activity when calculating pi. Consider all the work that has gone into Pi Day analysis and into the analysis of numbers. Of all the scholars in the world, Steven Strogatz (Cornell) is one of my favorites. He is a mathematics wizard and one of the world’s experts regarding pi.
 Assume sphere stacking is the next dynamic. Yes, something as simple as sphere stacking which in 1587 became an academic subject developed by Thomas Harriot, then further in 1611 by Johannes Kepler. It continues to be studied and developed, the most prominent work being done by Thomas Hales. Of course, the work of John Thomas Conway, Salvatore Torquato, Chaunming Zong and Jeffrey Lagarias have been specifically noted. That Aristotle thought the universe could be tessellated by tetrahedrons is perhaps the biggest error in history of geometries. Surely, it is the most-longstanding at over 1800 years. Six tetrahedrons create a flat face and that face certainly can be used to tile the universe
 Assume cubic-close packing of equal spheres is the next. Dating back to 1587, at that time it was about maximizing the storage of cannonballs on the deck of a ship. Eventually it was moved down in size to consider an atomic packing factor (APF). Here we take it down to the infinitesimal sizes of the Planck base units.
 The universe expands quickly — from Notation-0-to-144 in a second! Anything that goes from 0-to-144 in second (of just about anything) would be considered fast, but here we are talking about a fundamental-core process of the universe; it is one that never stops and connects everything- everywhere, that is defined by a second.
 A smooth, natural inflation from a very cold start. One of the enigmatic problems with big bang cosmology is the homogeneity and isotropy of the universe. There is no current scientific explanation for it. Here there is. Just follow the numbers from 0-to-144. But, it only works within base-2 exponentiation. It suggests something fundamental about this function within mathematics: the universe is fundamentally exponential. What else?
 The first 64 notations. There are no other known studies of the first 64 base-2 notations (out of the 202 that actually encapsulate the entire universe). These 202 notations are both a logical and mathematical system yet these 64 notations can not be empirically validated. All are below the thresholds of our measuring devices. Yet, there are numbers that can be validated between notations 67 and 202 and as that work continues, once it becomes compelling, we then might assume that the numbers below those thresholds of measurement approximate a real reality.
 Here are the beginnings of a smooth inflation. Not just a smooth inflation, it would appear to be a perfect inflation within the first groups of notations. The five-tetrahedral configuration with the shared edge eventually manifests within this expansion; however, we project that it is around Notation-50. That is also when and where we also project the emergence of systems as in systems theory. With systems theory, we are also projecting that it is the beginning of the most primitive consciousness. A huge subject with plenty of mystery, here we anticipate that it can begin to be demythologized with mathematics and logic.
[9a] The quantitative-qualitative divide: An historic philosophical and scientific question, within this model of the universe where the infinite is defined as continuity (order), symmetry (relations) and harmony (dynamics), the entire qualitative expression is an aspect of the infinite such that values can be placed within a chart that overlays the 202 notations. There is no finite-infinite divide and there is no quantitative-qualitative divide. All are in a dynamic, constant relation understood within dynamic ratios.
[9b] Solipsism, Narcissism, Nihilism, Dystopian. In what is described as postmodernity, solipsism becomes the de facto ground of being and meaning within big bang cosmology. It breeds narcissism as a way of life. Various manifestations of obscurantism become abundant and a nihilism progressively grows and many become advocates of various forms of dystopia and anarchism.
 Duped by Aristotle, Newton, and Hawking. A top-level post (homepage) in June 2020 that focuses on how we have been not been open to seek a deeper truth because it flies in the face of our historical heroes.
• Aristotle was wrong about very basic geometry. He misled us for over 1800 years.
• Newton didn’t give an inch to Leibniz. He should have. More…
• Hawking had plenty of detractors of big bang cosmology, yet he held firm, even in light of compelling alternatives by trusted associates.
 Notation-0 is the Planck units. And, Notation-202 is the current notation defining the current time and expansion. Planck’s calculation for temperature is still enigmatic and appears to have only a derivative role. Our mathematical model of the universe begins to capture the big bang at 1.8751×109 Kelvin (Notation-127) and surely within Notation-136 at 1.9201×1012 Kelvin. The universe is less than one-hundredth of second from its start and may have a diameter of 1750 miles. A natural inflation is generated by light, the Planck charge, and the mix of dimensionless constants. A natural symmetry is created within Notation-1 to Notation-201 because although “complete” they are still dynamic and “pushing up and out” Notation-202 where the very first sphere is possibly at the point of the current expansion.
 A Domain of Perfection. Hypothesized, hypostatized and intuited, this domain is not part of any accepted academic work today. Perfection was thrown out of the academic world when quantum physics was fully embraced. Notwithstanding, if there is such a domain, it impacts physics, cosmology, ontology, epistemology…
There is good reason to test the logic. First, it is a major enigma for big bang advocates that the earliest universe is so smooth. In our model of the physical world, it begins with an infinitesimal sphere defined by the Planck base units. Nothing within space and time can be smaller and that sphere manifests the perfections of the circle and sphere: continuity, symmetry, and harmony (given through the Fourier transform). You can almost feel the perfections of sphere stacking and the generation of tetrahedrons and octahedrons from cubic-close packing of equal spheres.
We made some projections in our 2014 Universe Table. Notation-0 to Notation-10 were reserved for Plato’s Forms, Langlands’ automorphic forms, and Witten’s strings. Notations 11-to-30 were reserved for Aristotle’s Ousia and for substance-structure. Notations 31-to-40 were for the earliest possible definition of Qualities; Notations 41-50 were for the first principles of Relations and 51-to-60 were for Systems including consciousness. That was a first draft in 2014. Today, I would also include the 18 prime numbers between Notation-0 and Notation-64. Being wildly speculative, prime numbers 2, 3, 5, 7, 11, 13 and 17 may each be the beginning of the seven notes that give rise to all music. Primes 19, 23, 29, 31, and 37 may be tested to see if in any way each could give rise to one of our five most basic senses.
Primes from 2 to 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, to 199 are all being subject to increasing scrutiny. We are asking the question, “What unique mathematically-generated aspect of reality might manifest at this point of ‘this particular expansion‘ of the universe?”
- Pi Day: How One Irrational Number Made Us Modern, Steven Strogatz, New York Times, March 14, 2019
- The physics of infinity, George F. R. Ellis, Krzysztof A. Meissner and Hermann Nicolai, Nature Physics, Vol. 14, Aug 2018, pp.770–772
- George F R Ellis, Mathematics Dept, University of Cape Town
- Emergence in Solid State Physics and Biology, June 30, 2020
- The Causal Closure of Physics in Real World Contexts, June 30, 2020
- Physics, Determinism, and the Brain, August 2020
- Emergence of time, George F R Ellis and Barbara Drossel, Nov. 2019
- “Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation”, The Astrophysical Journal Supplement Series; Komatsu, E.; Smith, K. M.; Dunkley, J.; Bennett, C. L.; Gold, B.; Hinshaw, G.; Jarosik, N.; Larson, D.; Nolta, M. R.; Page, L.; Spergel, D. N.; Halpern, M.; Hill, R. S.; Kogut, A.; Limon, M.; Meyer, S. S.; Odegard, N.; Tucker, G. S.; Weiland, J. L.; Wollack, E.; Wright, E. L. (1 February 2011). 192 (2): 18. arXiv:1001.4538.Bibcode:2011ApJS..192…18K. doi:10.1088/0067-0049/192/2/18.
- To see what a black hole looks like, Daniel Clery, AAAS, Apr. 10, 2019. Heino Falcke, Radboud University, Nijmegen, the Netherlands, says, “It feels like looking at the gates of hell… This is the end of space and time.” Falcke is one of the leaders of the Event Horizon Telescope (EHT) collaboration.
- More resources from among our scholars will be added.
1. Select emails to Templeton Prize winners to be added.
2. An update of an email to Alvin Plantinga: “If knowledge of infinity is not possible then beliefs in God would be unreasonable” (from a review of Plantinga’s Warranted Christian Belief –PDF)
3. ArXiv (48): “… string theory has not yet answered many of the thorniest questions at the intersection of QM and GR, such as the black-hole information puzzle or the nature of the big bang.”
Dear Prof. Dr. Matthew Headrick of Brandeis University:
Instead of “What if” questions, I more deferentially ask, “Might we assume…?
- Might Max Planck’s base units help open the logjam at the intersection of QM and QR?
- Might we assume that Planck Time is the first unit of time?
- Might we assume a thrust given with light and the Planck Charge that energizes whatever it is that manifests as those four Planck base units?
- Might we assume that an infinitesimally small sphere — some might call it a PlanckSphere, planckion, or Planck Particle or quantum foam — would manifest?
- Might we then assume many spheres and sphere stacking?
- Might we assume cubic-close packing of equal spheres? Here we have a transformation from sphere to tetrahedrons and octahedrons.
To begin to impart some order, could we assume base-2 notation to follow that expansion of spheres?
We mapped 202 notations from Planck Time to the current age of the universe. Does it tell us anything? We think so, but we need critical reviews to avoid making mistakes (…more mistakes). We’ve probably already made many egregious mistakes.
PS. I’ve been on the Brandeis campus many times over the years. It is still the quiet jewel within the Boston area. -BEC
- @gcaw @TheAtlantic @Yale@newrepublic @DeutschePostDHL @CFR_org Worldviews cut us short. A mathematically-integrated view of the universe is the only possible opening to a platform that could lead to a comprehensive understanding of who we are and why: https://81018.com/chart/
- More select tweets to Templeton Prize winners will be added shortly.
- Tweets/emails to people associated with Ralph Burhoe and Zygon.
- Select Tweets to current Templeton project-and-program administrators
- In this hyper-partisan, highly-emotional election season, we all need a new model of ourselves and our universe. Partisans have too much ego involved. It may not be the best idea, but here is a sample from Sunday, August 16, 2020: @JohnKasich We need a truly unifying vision to move us beyond small-minded party politics within limited worldviews. A way to break through it all is an integrated view of the universe. Here’s a start: https://81018.com/chart/ It is relational and turns the concept of time upside down and inside out.
Please do not hesitate to contact us with comments and questions.
Have you ever heard of the Templeton Foundation? Much of the work of this page is a result of the Templeton Foundation’s ongoing challenge to the world to bring the issues of universal beliefs, particularly of those within religions, in harmony with the universal beliefs of science.
In-and-around 1975 I first became aware of the work of Sir John Templeton. He was born in 1912 in Winchester, Tennessee, became a British citizen in 1964, but lived in the Bahamas. In 1972 he had begun awarding an amount always greater than the Nobel Prize to a person he (and a panel of his judges) believed made the greatest contribution in grasping the real relations between the sciences and theology.
Over the years, I have gotten to know many of the award winners personally including Frère.Roger (1974), Ralph Burhoe (1980), Carl Friedrich von Weizsäcker (1989), Charles Birch (1990), Michael Novak (1994), Paul Davies (1995), Freeman Dyson (2000), Arthur Peacocke (2001), and Bernard d’Espagnat (2009). Others with whom I have corresponded include Francis Collins (2020), Alvin Plantinga (2017), 14th Dalai Lama, Tenzin Gyatso (2012), Martin Rees (2011), George F. R. Ellis (2004), John D. Barrow (2006), John Polkinghorne (2002), Ian Barbour (1999), Thomas F. Torrance (1978), and Stanley Jaki (1987).
Please note: These links just above to the Templeton Award winners will continue to be updated until there is a page on this site that analyzes the work of each person.
This article was initiated on Tuesday, August 11, 2020.
Just-a-Second became a homepage or top-level post: August 25, 2020.
Last update: Friday, September 11, 2020
The Prior Homepage: https://81018.com/open-envelope/
The URL for this page: https://81018.com/just-a-second/
The initial tagline: A Gut Check About A Dream I Had0
Another tagline: So much happens in just a second — it’s a quiet start, a natural inflation.