Big Bang Cosmology Obfuscates Deeper Studies


12 Concepts/Formulas To Open Doors

To An Integrated, Mathematical Model of the Universe

by Bruce Camber. This is an outline, a working draft. There is much more work to be done. Projected to become a homepage before the end of the month. Others are being invited to contribute and even co-author. The Endnotes, Footnotes, References and Resources were just started.

Abstract: Big bang cosmology blocks the view of a simple mathematical construct that encapsulates the entire universe within ordered relations that provide an outline and possibly a new foundation and entirely different approach to space-and-time, mass-and-charge, and the finite-infinite relation, all basic concepts for the sciences, mathematics and commonsense.  These twelve key concepts are introduced and proposed for further exploration. 

The Approximate Age of the Universe in seconds
436,117,076,640,000,000± seconds

“436 quadrillion, 117 trillion, 76 billion, 900 million seconds”

A review of this very simple math begins to give us a sense that the universe is finite. It has a starting point and the current time is always the current expansion. What happens when we all know and can say, “The universe is just over 436 quadrillion years old!?!” Also, if the world had an active Universe Clock, it just might help us all feel some commonality with each other within this world and well beyond.

We can do it: We’ll need a little advice from those who calculated the age of the universe which is currently estimated to be between 13.772-and-13.82 billion years (with an uncertainty of just 59 million years). How did they arrive at that figure?  How did they calculate the number of days in a year? We are on a Solar-Time System based on the Sun. The rest of the universe is not involved. Our year has 365 days except for Leap Year when it has 366 days.  The question is simple; for every thousand years, should we add 250 days?  We can all readily do the easy work of calculating the number of seconds in a minute (60),  an hour (3600), a day (86,400), and then a 365-day year (31,536,000 seconds). There are 31,556,952 seconds in a 365.2425 day year. And, there are 31,557,600 seconds in a 365.25 days per year. We have chosen 365.2425 days per year for 31,556,952 seconds/year or 31,556,952,000,000,000 in a billion years (an aeon). If we multiply 31,556,952,000,000,000 by 13.82, we get 436,117,076,640,000,000 billion years. At this time, we are considering adding to this number. We need to approximate how much time has passed since that expert measurement was made with the data from the Hubble Space Telescope or ESA Planck satellite. It could well be over 10 years old and getting older each day.  Stay tuned!

Observation: The value of a second was established by a consortium of government agencies around the world. They unofficially began cooperating and sharing insights as early as 1841. The first official actions began in 1947 with the formation of the International Organization for Standardization (ISO). One of their jobs is to define a second. The ancient approximation was 1/86,400 of the time that it takes the Earth to rotate once on its axis. Then, in the 1700s it was determined by the pendulum swing of a carefully-defined grandfather clock, but most recently by the very stable calibrations within the cesium 133 atom. We’ve been advocating that the second could be defined by an exact multiple of Planck Time. At Notation 143, it is .60116 seconds. Why not add that fraction that brings it closest to the current one second mark? This kind of thinking began back in 2012 when we were advocating that a standard length be based on an exact multiple of Planck Length.  In 2012 a retired NASA scientist thought it was an interesting proposal.

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Encapsulate everything, everywhere, for all time:
202 notations from the first moment to Now.

By definition, the Planck base units are the key initial quantities for physical reality. Of course, pi and other dimensionless constants are part of the dynamics. Taken as a given, if these base units are doubled, then doubled again and again, in just over 202 doublings, the current time (the full Age of the Universe) and the current size of the universe are inscribed. There are well over 1000 numbers that are generated within our chart (horizontally-scrolled). It is entirely predictive and each notation necessarily builds on the prior notation. The first second of this universe emerges between notations 143 and 144. The first  year emerges within notation 169. The first thousand years, a sweet little millennium, emerges between notation 178 and 179,  The first million years, an aeon, is between the 188th and 189th notations; and, the first billion, an aeon, is between notation 199 and 200. All of human history and most of the history of this Planet Earth are within Notation 202.

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Dark energy and dark matter:
Defined by the first 64 notations

Now let us review the first 64 notations out the 202 base-2 notations. The first six notations are initially displayed when one opens the chart.  Horizontally-scroll through those. Especially observe the first 64 notations (or doublings). If taken together, the first 64 notations have a rather substantial mass and charge. At just the 64th notation, the Planck Mass multiple is now 4.01495×1011 kilograms and Planck Charge multiple is 34.5986 Coulombs. Yet, the Planck Length and Planck Time multiple are still infinitesimally small. The first possible measurement of a multiple of the Planck Length is between Notations 65 and 67 and the first possible measurement of time is within the 84th notation.

Simple logic tells us those first 64 or 65 notations define dark energy and dark matter.

Check this work:  Again, to derive the 202 steps or notations from the Planck base units to the approximate age and size of the Universe today, we multiplied the four Planck base units by 2, (and the results by 2, over and over again). Perhaps the easiest concept to observe is the Planck Time multiple as it goes up to and beyond the current age of the universe at Notation 202.

More Observations: Particularly watch lines 5 and 6 within our large horizontally-scrolled chart:  We start with Planck Mass (2.176.470×10-8 kilograms) and Planck Charge (1.875×10-18 Coulombs). And it bears repeating — at the 64th notation, the time and length  measurements are still below our ability to measure, yet Planck Mass has increased to 4.01495×1011 kilograms and Planck Charge has increased to 34.59863 Coulombs. That’s amazing, but then it goes extreme.

Just beyond the first second of the universe at 1.2023 seconds at the 144th notation, these values have exponentially increased to 4.8537×1034 kilograms and 4.1827×1025 coulombs. Today we are within the 202nd notation and the age and size of the universe. Planck Mass and Planck Charge, of course, are ginormous. Some percentage of the total is below our thresholds for measurement, and so, yes, here is the ever-so-illusive dark energy and dark matter.

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Also, follow the horizontally-scrolled chart, lines 5 and 6:

Redefine the infinite.
We start with the equation for π.

pi-formulaWe will be studying and surveying many of the dimensionless concepts. The most simple, most ubiquitous, never-ending, never-repeating ratio is pi. In some measure, as the most simple constant, it defines and redefines the infinite and opens a definition of a finite-infinite bridge. The abiding concepts that flow within the finite-infinite relation are continuity (order), symmetry (relations) and harmony (dynamics). There three concepts are also the backbone of the finite, particularly our sciences, the finite-infinite-bridge, and the infinite. And, it all starts with π (pi). 

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Also, see: and 

(working on a new page that unites all three)

Mathematically confirm the speed of light.

Here, based just on the accuracy of the determination of the Planck Time value and the Planck Length value, the speed of light is confirmed mathematically. At one second, the Planck Time value is 1 and Planck Length is the distance of the speed of light in one second: 299,792,458 meters/second.  The experimentally-defined speed of light is 299,792,458 m/s in a vacuum.

Of course, it is not at all surprising that the Planck Time, Planck Length, and the speed of light correlate throughout the chart given that both Planck Time and Planck Length are defined by the speed of light.

What is surprising is that this simple formula begins to corroborate the basic integrity of the chart, base-2 exponentiation with the speed of light, and it all begs for a much deeper analysis.

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Yes, the speed of light is approximated at every other notation. It generally ranges around ± 1% of the laboratory defined speed, 299,792,458 meters/second.  Just 1% of that value is 2,997,924.58 m/s which gives us a range of  296,794,523.42 to 301,790,382.58 m/s. 

Our current highest calculation is 299,982,157 (Notation #16) and the lowest (#3) is 299,768,509.931, so, that lowest figure has to be further analyzed. It just may be a simple mathematical error on my part.  I’ve been call me sloppy in the past!.

So, Planck’s little equation for Planck Time, Planck Length (lP) divided by light equals tP, seems to be telling us an important story throughout all 202 notations. 

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Compare their intellectual expansion to our mathematical expansion.

There is a concresence between the events of the current big bang theory and our mathematically-defined quiet expansion. This analysis opens many questions based on the fact that observational data from the intellectual definition of the Big Bang actually works within the mathematical inflation of our “Quiet Expansion.” 

Editor’s note regarding the Quiet Expansion: 20-to-20,000 Hz is the generally accepted range of audible frequencies for human hearing convert to wavelengths of anywhere from 17 meters to 1.7 centimeters or from the 109th to the 120th notations.

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Analyze the logic of six samples from across the 202.

Becoming aware of the parameters that define this chart is not a trivial activity. Thinking of the universe as exponential at its core is difficult. Thinking about time as an interval without a past but as encoded as a necessary effect within the entire universe even stretches our sense of relationality. And, I suspect it will do the same for you.  The net-net of studying the simple doubling formulas is an entirely different orientation to our little universe of just 202 notations.

For more, go to:  and Also, if you have not studied the chart of numbers, please do:

Sphere stacking is at the heart of all doublings.

Sphere to tetrahedron-octahedron coupletThis simple dynamic image tells many sorties. Sphere stacking is the first chapter. This Planck scale compared to the atom is like the atom compared to our solar system.  Yet, here we surmise  that those Planck spheres which have a small mass and charge, literally fill the universe (See #2). This most simple dynamic of the universe interacts with all other spheres, centerpoint to centerpoint to centerpoint, creating geometries, points, lines, triangles, tetrahedrons and octahedrons that literally tile and tessellate the universe. 

At long last we find our old aether. Michelson-Morely can relax. How appropriate that this is the time we celebrates 400 years of Johannes Kepler’s 1619 work, Harmonices Mundi. It all started with a cannonball; and with this image, it opens both projective and Euclidean geometries.

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Opening up period doubling bifurcation
δ = 4.669 201 609 102 990 671 853 203 821 578

In 1975 mathematician, Mitchell Feigenbaum, discovered a limiting ratio for each bifurcation interval. It was a constant. The plain vanilla version of period doubling were guided by such constants, yet nobody could discern why simply because nobody could look below that 64th notation and nobody was motivated to do so. Simple concepts had been blown out of our consciousness by big bang cosmology. Here we can begin to discern why all period doublings occurs. We look to sphere stacking. We are currently dancing in this sphere of influence which in a recent article, I said that it “ included Mandelbrot’s work on fractals, the Santa Fe Institute and their work on complexity and chaos theory, and Stephen Wolfram on computational irreducibility. In 2006 Ari Lehto refocused his work as he explored period doubling at the Planck scale and in 2014 Charles Tresser added insights regarding its universality.though new to us, is huge and diverse from fractals.”

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The Fourier transform dynamics at the Planck scale

Fourier A

There are so many equations within the Fourier transform, everybody who is anybody would have their heads spinning rather quickly.  Period doubling captures the moment when things become two.  Here we discover how every two things are related to every other thing. The Fourier transform has a wide diversity of applications that touch every part of our life. At no time has its inherent power been brought down to the Planck scale.

File:Circle cos sin.gif
Fourier B

Again, hidden by big bang cosmology, the Fourier transform at the Planck scale even opens a new discussion of the very nature of “gravitational weak” and “electromagnetic and strong.”  Just observe the two graphics on the right. Click on each to images to dig into it all. 

More coming from equations of motion, structural dynamics…

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Living in an exponential universe and among all things infinite

This chart is an application of Euler’s exponentiation. Euler’s formula, named after Leonhard Euler, is a mathematical formula that establishes the fundamental relationship between our basic and our more complex mathematics. If the universe is fundamentally exponential, that changes everything. We all have to re-learn the basics. We all have a lot of studying and thinking to do. There are a lot of concepts to be reconsidered. There are many very assured articles, books, videos and movies to be update and rewrite, and a whole new universe needs to be explored.

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Saturday, 14 September 2019 at 6 PM

You’ve caught up with me!  Here I am doing today’s work.  Your comments and suggestions are always welcomed! Let’s work together on these concepts!

The geometries of imperfection and fluctuations

More to come…  In our high school we also called it squishy geometry.  More

Endnotes, Footnotes, References and Resources

1  Any seconds for the “Planck Second” in between Notations 143 and 144 second?  Contact:  



2  Peter Mohr <> Cross sections at sub-Coulomb energies






The idea of T-duality was first noted by Bala Sathiapalan in an obscure paper in 1987[1].

CODATA Task Group on Fundamental Constants: F. Cabiati, Istituto Nazionale di Ricerca Metrologica, Italy; J. Fischer, Physikalisch-Technische Bundesanstalt, Germany; J. Flowers (deceased), National Physical Laboratory, United Kingdom; K. Fujii, National Metrology Institute of Japan, Japan; S. G. Karshenboim, Pulkovo Observatory, Russian Federation and Max-Planck-Institut für Quantenoptik, Germany; E. de Mirandés, Bureau international des poids et mesures; P. J. Mohr, National Institute of Standards and Technology, United States of America; D. B. Newell, National Institute of Standards and Technology, United States of America; F. Nez, Laboratoire Kastler-Brossel, France; K. Pachucki, University of Warsaw, Poland; T. J. Quinn, Bureau international des poids et mesures; C. Thomas, Bureau international des poids et mesures; B. N. Taylor, National Institute of Standards and Technology, United States of America; B. M. Wood, National Research Council, Canada; and Z. Zhang, National Institute of Metrology, People’s Republic of China.

Newtonian constant of gravitation
Newtonian constant of gravitation over h-bar c
Planck constant
Planck constant in eV/Hz
Planck length
Planck mass
Planck mass energy equivalent in GeV
Planck temperature
Planck time
reduced Planck constant
reduced Planck constant in eV s
reduced Planck constant times c in MeV fm
speed of light in vacuum
vacuum electric permittivity
vacuum magnetic permeability


Initiated in private on September 5, 2019
Projected soft posting: Thursday, September 12, 2019
Projected to become a homepage:
Most active editing: September 9 to September 13, 2019