Hawking’s big bang theory has reached its limits.

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The Challenge: Expand A Nascent Theory
How we see the start affects how we see ourselves.
by Bruce E. Camber, a first draft (for collaborations)

Abstract: The big bang theory stretches commonsense and logic. We’ve never met anyone who can really imagine everything in the universe being compressed into a singularity.* That first moment of time about which Stephen Hawking said, “.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” (PBS-special, Genius, May 2016). That’s a theory. Our more simple theory assumes there are structures and functions below the thresholds of our measuring devices that begin with the natural units calculated in 1899 by Max Planck. Today known as base units, the first calculation of natural units was in 1874 in Dublin by George Stoney. If base-2 notation is applied to those units, there are about 64 successive doublings prior to an actual measurement of a length and 74 prior to measuring a unit of time (zeptosecond, 10-21 or a trillionth of a billionth of a second). Within that gap from Notation 0-to-64, there are possibilities for most every kind of geometry-mathematics prior to particles, waves and fluctuations.[†]

Introduction: A challenge to big bang cosmology. There are 202 base-2 notations from a well-defined start, about 13.81 billion years ago to this day.[1] The defenders of the big bang do not know this chart. It wasn’t in their books. Without precedent, the 202 notations were defined in 2011 in a New Orleans high school geometry class. There has been no peer-reviewed article about that start — an infinitesimal sphere originates from a functional infinity that we know through the qualitative values of continuity- symmetry-harmony within pi (π), the three inherent qualities of scale-invariant spheres (so, yes, this definition is circular for now).

There is a growing discontent and tensions within this little world which we attribute it to the inherent nihilism of the big bang theory, so there is a sense of urgency to expand this nascent theory and the positive qualities within pi (π).

Perpetual starts. In 2017 Neil Turok[2] who today sits in the Higgs Chair of Edinburgh University says the universe is perpetually starting[3]. Logically not the Big Bang, our Notation-1 is perpetually starting. All 202 notations are always active. Turok and his team use the mathematics of Solomon Lefschetz, yet those articles and that mathematics have not sparked a growing following or flood of experimental work. That same criticism can be leveled on many other attempts to break through with a more compelling theory, all alternatives, potential replacements, about the start-and-art of our universe.[4]

The veracity of a theory is when others are able to build on it. So with this page, we will attempt to interview Turok, Job Feldbrugge, Jean-Luc Lehners (and their other co-authors) to follow-up our first reports from 2017. We’ll try to get their first-hand insights and explanations of the current place of their work. We will also focus on those nine alternative approaches by diverse scholarly groups around the world.

That’s the thesis. The antithesis is where there has been an explosion of excitement and experimental work involving hundreds-of-thousands of scholars and scientists.


Real data, right now: The James Webb Space Telescope (JWST). The JWST is a challenge to Stephen Hawking’s old, tired, fantastical theory.[5] In July 2022 the first images came back from the most advanced telescope in human history. It began confirming what the Hubble telescope had glimpsed. The early universe is just too smooth for big bang cosmology… much too smooth. There’s nothing there to grab to start to build a universe. Every scholar in the know is scrambling to come up with a better theory. The world is desperate for new Ideas, yet there are tried-and-true concepts with wisdom that may serve us very well. Let’s go over pi (π) one more time to see if we can learn anything new about it. Let’s go smaller and deeper, be even more inclusive, integrative, and diverse. In the spirit of E.P. Wigner, let us declare that the universe is totally-integrated, an amalgamation of most ubiquitous equations. We already know that pi (π) is integral to our most important equations. Notations 0-to-201 are nonlocal. Locality is limited to each person’s unique space-and-time (universally recompiled within sleepmore to come).


The synthesis: A new model. Structure and dynamics are built into the infinitesimal spheres and these structures (geometries) immediately begin to shape this universe. Langlands programs and string and M theories need to be dropped into this base-2 container. The projection is that Langlands and strings will finally be on the grid. The concept of a singularity is put on hold until our understanding of that grid is expanded. The structures emerging could easily be confused with points or vertices, but these have dimensional qualities, including qualities defined by the Fourier transform and attractors and repellers (Milnor and Smale).

In 2020 an article was prepared for the Foundational Questions Institute (FQXi)[6] It was, at that time, the most comprehensive review of our model and nascent theory. Notwithstanding, it was not reviewed within that scholarly community. It is so idiosyncratic, it didn’t get beyond an initial, casual review within one of their competitive challenges.


History. The model is simple mathematics (algebra) and geometries. The first outline was developed by chasing tetrahedrons and octahedrons further and further within themselves. In about 45 steps from our classroom, by dividing the edges by 2 and connecting those new vertices, we were in the range of fermions (10−15 meters). Quarks, theoretically in the range of 10−18 meters, would be in Notations 56-59. From the fermions, there are 67 additional steps within to be in the range of the Planck base units (10−33 meters). Going out from the classroom, by multiplying the edges by 2 and connecting those imaginary vertices, there are just 90 steps to inscribe an approximate size and age of the universe, all just simple doublings.[7]

Summary. This model is dynamic, wholistic, intimate, and inclusive. Here our universe is a huge, hyper-sensitive grid, one that some might think is overly sensitive, because it appears to respond to the thoughts, words and deeds of everyone as everything-everywhere becomes part of the face of the universe.


Brief Review. Our first outline of the universe was first created by applying base-2 notation to the simple geometries of the tetrahedron and octahedron, then the same process was applied to the Planck base units. The result is a mathematical and geometrical outline of just 202 rather comprehensive, natural doublings from the first moment of time to the Now. We believe it is a chart worth studying, an easy-yet-unprecedented map of the universe.[8]


Possible Action Plans: Specific steps governments, schools and people can take today.

First, we need to acknowledge the problem; the weaknesses and strengths of big bang theory[9] need to be even more clearly articulated. Wikipedia has started this process within its sections of unsolved problems in physics, cosmology, and mathematics. The open issues from big bang cosmology are mostly covered within one section, Cosmology and general relativity.[10]

Also, a place for alternative theories needs to be lifted up. Important within this process is to come to terms with the fact that we are all fallible. We make mistakes. We learn by doing. Successive approximations are okay. We need to be gentle with each other.[11]

Yes, second, all people should be constantly gentle with all others. Inherent within the 202 base-2 notations, there is a valuation determined by continuity, symmetry, and harmony, each a face of pi (π) and infinitesimal spheres. Beside the mistakes, at times we are even duped.[12]

Third, we must start educating everybody starting with the leaders with access to our most horrific weapons of war, and also with our children and our decision makers. Again, we would begin with the chart of numbers and the map of the universe because both are easy to understand and learn. We would also introduce the circle of value and qualities as noted at the very beginning of this brief article.

Around the globe, politics brings out the worst and the best within people.
It has since time immemorial
. This chart and map should help to bring out the best.

Fourth, we should get the prize people to focus on the issue so there is a reward at the end of these many tunnels exploring these issues. We should recognize the best theory each year until there is a consensus among most of our active scholars. Thank you. -BEC

Key pages:


Endnotes & Footnotes
These points already have pages within this website.

[*] Singularities. In 2017 the concept of a singularity was first examined within this website. It is a primary concept in big bang cosmology but it doesn’t work very well. There is dimensionality down to the Planck scale. With this homepage, we will begin immediately reworking that page about singularities with resources and experts until it is consistent with the past five years of our work.

[†] Geometries and mathematics of fluctuations. Also, in 2017 the concept of fluctuations was first explored within this website. We were had just learned about Aristotle’s gap. The icosahedral gaps were just being modeled. Five years later we would discover an octahedral gap. There was not scholarly precedent for it. New light was being shined on a primary unsolved problem. So, with this work, we will begin rethinking this page about fluctuations with more current resources and experts until it, too, is consistent with the past five years of our discoveries. More…

[1] Early history, No Start, Abundant Nihilism. The 202 notations were defined in December 2011. Our working chart was first posted in 2016. Our second attempt to publish was a re-work of a letter to editors of big three publication, Scientific American, Nature, and AAAS Science. It became our STEM article yet was never accepted for publication. James Peebles, a Princeton Nobel laureate (2019) and an early developer of our understanding of the Cosmic Microwave Background Radiation (CMBR), most directly confronts the lack of a starting point for the big bang theory. It has, for example, no concept that incorporates the Planck base units. Big bang cosmology has also failed to recognize the simple progressions of geometry and algebra using base-2 notations or doublings thus excluding ways to incorporate major studies along the grid within those first 64 notations. Also, science and her theories are not value neutral. The big bang theory as understood by Stephen Hawking captures his extreme skepticism that life has any deep, inherent meaning, or intrinsic value. Some have labelled that orientation, postmodernity. Some extend a sense of neutrality for mathematics; however, we found a value structure based on simple geometries and a sense of perfection inherent within those geometries. Within the sphere and pi (π) alone, there are perfections of continuity, symmetry and harmony.

[2] Neil Turok. A key part of the history of Neil Turok is when he held the Chair of Mathematical Physics at the University of Cambridge, Department of Applied Mathematics and Theoretical Physics (DAMTP). He is the director emeritus of Canada’s Perimeter Institute for Theoretical Physics (2008-2020). And, in 2020 he was appointed to the Inaugural Higgs Chair of Theoretical Physics at the University of Edinburgh.

At DAMTP, Turok co-authored the following articles with Hawking:
Gravitational Waves in Open de Sitter Space (2000)
Open Inflation, the Four Form and the Cosmological Constant (1998)
Open Inflation Without False Vacua (1998)
Comment on `Quantum Creation of an Open Universe’, by Andrei Linde (1998)

At Perimeter, Turok began his criticism of Hawking’s work:
No Rescue for the No Boundary Proposal (2017)
No smooth beginning for spacetime (2017)

The general press most-often quoted these three paragraphs from the Perimeter press release:

“Professor Neil Turok, director of the Perimeter Institute in Canada, has long-questioned Hawking’s vision of the Big Bang, when space, time and matter are thought to have burst into existence.” London Daily Mail, June 29, 2017

“Now he has published research suggesting that the basic maths behind Hawking’s views is incorrect and that science must rethink the origins of the universe.”

“Our research implies that we either should look for another picture to understand the very early universe, or that we have to rethink the most elementary models of quantum gravity,” said Job Feldbrugge, one of Turok’s co-authors.” Sunday Times, 25 June 2017

In the summer of 2022 he opened questions about big bang in light of the strong CP Problem. Although it initially sounds like he is re-engaging the big bang, more study is needed. We have asked Elizabeth Gibney, a journalist with Nature magazine if she might consider doing a deeper analysis!

[3] Perpetually starting. Of course, if this universe is perpetually starting, it can’t be a “big bang.” So what is it? In our 2017 overview of the Turok team’s work, we were delighted to find scholars who made a claim similar to our own. This time around we are going to understand their conclusions and the Picard-Lefschetz theory. Turok and his team do not yet recognize the simple logic for perfections of the earliest notations. They do not recognize the continuity-symmetry-harmony inherent within the infinitesimal spheres. They do not recognize the first 64 infinitesimal notations (out of the 202 base-2 notations that encapsulate the universe from the first moment of time until now). Hypothetical particles, most often considered point particles within more traditional studies, have dimensionality, mass, charge, and all the facets of the dimensionless constants that define them. So, we will enter Picard-Lefschetz theory and the work of Solomon Lefschetz and Émile Picard to see if they contributed to Turok team’s reluctance to embrace these natural units as given.

[4] Potential alternatives. Those first 64 base-2 notations may well serve as an outline for the foundations of our universe. However, there are no less than nine studies with literally thousands of people associated with them that define some part of those first 64 notations. The nine studies are: (1).Langlands programs, (2).string theory (including M-Theory, F-theory, type II and offshoots), (3).supersymmetry (SUSY), (4).loop quantum gravity (LQG), (5).causal dynamical triangulation (CDT), (6).causal set theory (CST), (7).field theories, (8).spectral standard model (SSM), and (9).all the hypothetical particles.

[5] James Webb Space Telescope (JWST). There’ll be many senior scholars who will hold onto the big bang cosmology until they die. A 1949 statement by Max Planck proclaims that truth. They’ll have the company of great scholars like Dr. John Mather, Nobel Laureate (2006) and James Webb Space Telescope Senior Project Scientist. As the smoothness of the early universe gets deeper and deeper (older and older), the big bang will slowly lose its grip on the mythopoetics around the start of the universe. The nine groups of potential alternatives (just above), all within the outline of the 202 notations, will define a powerfully entangled grid with pi at its core driving our most significant formulas, foremost among them being that for the infinitesimal sphere.

[6] FQXi. The Foundational Questions Institute was started by Max Tegmark and Anthony Aguirre with financial help from the Templeton Foundation. This concrescence of interest and abilities is a key to make a breakthrough. Tegmark, with Turok and others have called for a fundamental rethinking of space, time and infinity. Yet, among the defenders of the big bang faith, the deep believers, do not easily question the fundamentals of those beliefs. Our abiding hope is that FQXi can help us all out of our ruts of misunderstanding. https://81018.com/3u/

[7] Simple doublings. Doublings, multiplying and dividing by 2, is something we learn as a child. There is a special delight in feeling that process unfold. We have failed to grasp that process within three-and-four dimensional geometries. The interiority of the octahedron will surprise most scholars. It is more complex and more simple at the same time. There is a linear doubling and exponentiation where a linear doubling becomes systemic and we get the numbers within our chart.

[8] STEM: Science-Technology-Engineering-Mathematics. There is a common core within these four disciplines. Continuity-symmetry-harmony. All four require the three. The key article is: https://81018.com/stem/.

[9] Strengths and weaknesses of big bang theory. Starting with the work of Jayant Narlikar in his 1992 review, Strengths and weaknesses of big bang theory, we will continue his work in a separate section of this website. Our goal is to get everyone talking about it.

[10] Wikipedia Unsolved Problems. Within Wikipedia there is a discipline called Unsolved Problems. Within this website, we are most concerned with physics, mathematics, and astronomy, particularly cosmology. With physics, there is also a section called Cosmology and general relativity. So many of these unsolved problems will be addressed within the 202 notations.

[11] One step at a time, and often two steps forward, one step back. It is not easy. All the great scholars of all times made mistakes. It is part of life. We are all on a learning curve all the time. Aristotle should become a new icon for this most basic failing. We all need to know about Aristotle’s error and how it was repeated for 1800 years and how the implications of that overlooked gap still taunts our intellectual well-being today. https://81018.com/aristotle/

[12] Even the best make mistakes. Aristotle, Newton and Hawking unknowingly built on each others mistake. It’s too important. It’s symbolic. We all make mistakes: https://81018.com/duped/


References & Resources
As these issues are studied, key references and resources will be added.

Causal Dynamic Triangulation
A non-perturbative Lorentzian path integral for gravity (PDF), Ambjørn, Jurkiewicz, Loll, 2000
Scaling in four dimensional quantum gravity (PDF), Jan AmbjornJerzy Jurkiewicz (1995)

Strengths and weaknesses of the big bang cosmology, Narlikar, Jayant V., Astronomical Society of India, Bulletin (ISSN 0304-9523), vol. 20, no. 2, p. 1-12, March 1992
Strengths: The predictions of the expanding universe, the abundances of light nuclei, and the MW background.
Weaknesses: Evidence for anomalous redshift, the age problem, the low abundances of helium, and the failure to find any feature in the microwave background as predicted by the theories of structure formation.

Day One Project (of the Federation of Atomic Scientist): https://www.dayoneproject.org/
The team: https://fas.org/fas-experts/ Ryan Buscaglia: URL: https://fas.org/expert/ryan-buscaglia/

Follow-up of these key pages is on-going: https://81018.com/communicate/#4z (Cover-ups)

David N. Spergel (2015), “The Dark Side of Cosmology: Dark Matter and Dark Energy,” Science, 347[6226]:1100-1102, March.


There will be emails to many of our scholars about the key points.

7 December at 10:01 PM: Dr. Lisa Randall, Harvard
6 December 2022: Elizabeth Gibney, Nature magazine, London

12 November at 3:31 PM: Dr. Hans Havlicek, Vienna
10 November at 2:23 PM: Dr. Lisa Randall, Harvard
9 November at 3:26 PM: Dr. Cumrun Vafa, Harvard
7 November 2022 at 5:14 PM: Dr. Geraint F. Lewis, Sydney Institute for Astronomy
6 November at 3:48 PM: Dr. Zeeya Merali, FQXi
6 November 2022 at 3:21 PM: Dr. John Mather, JWST, Senior Project Scientist
5 November 2022 (Sat) at 1:45 PM: Dr. Shadab Alam, University of Edinburgh, Scotland UK
3 November 2022: Dr. Arnab Dasgupta, University of Pittsburgh
2 November 2022 (re-evaluated): Sent 10 October 2022, Dr. Fabienne Casoli, Paris Observatory
Related email to Stephen Hawking in 2016


There will also be many instant messages to thought leaders about the key points.

9:55 AM · Nov 12, 2022 @skdh Musk-Twitter. Programming-applications- communications to be good require continuity-and-symmetry-that-creates-harmony. That’s Musk’s raison d’être. It’s yours, too. All three faces of the sphere and pi are our universals that drive us. Twitter will become better. -BEC

2:25 PM · Nov 7, 2022 Geraint F. Lewis, @Cosmic_Horizons @Sydney_Uni Go inside the tetrahedron (divide the edges by 2, connect new vertices) and in 45 steps you’ll be among the elementary particles and in another 67 steps you’ll be at the Planck base units. Now multiply by two, over and over, 202 times and you have the universe: https://81018.com A little math and geometry go a long way!


Participate You are always invited.


Keys to this page, old-theory

• This page became the homepage on November 6, 2022.
• The last update was December 7, 2022.
• This page was initiated on October 30, 2022.
• The URL for this file is https://81018.com/old-theory/
• The headline for this article: The Challenge: Expand A Nascent Theory
• First byline is: Hawking’s big bang theory has reached its limits..