Do we live in an exponential universe?

Center for Perfection Studies: Continuity-Symmetry-Harmony • Austin, Texas • USA • December 2017
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From the chart:  Just 72 of the 202  doublings from the Planck Scale to this day.

Is this Quiet Expansion exponential?

by Bruce Camber  (First posted on November 16, 2017. Most recent update, February, 2018)

The 202 doublings of the Planck base units from the Planck Scale to the Age of the Universe appear to tightly weave together the most basic assets, forms and functions that define our universe.

Light is equal to Planck Length divided by Planck Time

  • Yet, our chart with its successive doublings of the Planck base units in 202 steps to the Age of the Universe raises questions:
  • Does each of the 202 steps uniquely define light (c)?
  • Within every step, every layer, every doubling, space-and-time seems to reveal a discrete, quantitative universe. Is it?
  • What does it mean?
  • Does this progression have anything to do with Euler’s equation [1]?
  • Does this progression and any way capture an exponential universe as in Euler perfect little equation?Euler

It is perhaps the most-simple view of a highly-integrated universe.

By contrast the infinitely hot, infinitely dense big bang [2]  is an imaginative-but-complicating  theory [3]. Big bang observations begin within the 197th notation of our simple model. For notations 1 to 197, the big bang theory is a series of informed guesses based on measurements that do not easily cohere within that “infinitely dense and infinitely hot” speculation.

Within our chart [4], the numbers within each step fully accommodate all the cosmological measurements and projections (epochs) within a natural inflation that is coherent and 100%-predictable and utilizes the most basic mathematics in our armory of tools, multiplying by 2 and pi (π). Driven by the simple math, simple logic, and irrational (transcendental) numbers and equations, this chart is evolving, however, the current numbers provide enough layers of detail to extend invitations to scholars to come in and do a much needed, deeper analysis.

Yes, this article is our standing invitation to our academic, scholarly and scientific communities, “Please check it out; we are reaching the limits of our abilities.”

Key articles include:
• A not-so-deep, initial analysis of just six notations out of 202:
• Our very first analysis of cosmological epochs:
. . Also linked in the second paragraph above [1], this is the quiet expansion.
• The chart of 202 notations:
. . Also linked from 81018 in the top navigation bar and from the second paragraph [2]
• A discussion of the nature of thrust: (accommodate inflation)
• An outline of work done to date on this model:
. .Also, always on the top navigation bar, HOME
• An index of all the writings to date:
Also, always on the top navigation bar, INDEX.

What is an exponential notation machine?

Think about it for a second. Autonomically, unwittingly, nothing to do with the conscious you, every cell of your body is constantly doubling.  It doesn’t double in size. It just doubles.  Perhaps that has to do with the fact that we are exclusively within the 202nd notation.  This current notation is the one in which we are living right now, and it is the same one that contains all of our history and most of the history of our solar system.

The 202nd notation is a total of 10.9816 billion years and we are in the earliest part of it! (Calculation: The 201st notation is 5.49 billion years and all the other notations added up to the 201st also equals 5.49 billion years.)

Wheat & Chessboard or Checkerboard & Penny

There are many web-based stories about the Wheat & Chessboard.  I encourage you to read them. Bottomline: by the 64th square (doubling) there is more wheat that the world’s annual harvest. It sounds as unlikely as the version of the story, dubbed the Checkerboard & Penny.

Screen Shot 2017-11-10 at 1.34.38 PM
$184.467 quadrillion dollars

The Checkerboard & Penny calculation is a bit more contemporary.  Start with a penny. Use exponential notation and watch the last row of eight doublings! [5] The first doubling is the first square. Four pennies in the second. Eight pennies in the third. Doubling. Doubling. Doubling, all the way to the 64th square. That is 264 and it equals 18,446,744,073,709,551,615 (for whole number, i.e. dollars).  Calculated in pennies doesn’t effect it too-too much: $184,467,440,737,095,516.15. Rounding up, that would be: $184.467 quadrillion dollars (Billion-Trillion-Quadrillion-Quintillion).

What is the estimated global debt? Some have added up the debt for all the nations and their people and estimate $215 trillion in 2017.  That is a lot, but you could readily retire all the global debt and still have $184.2 quadillion dollars left over.  It appears that there has been no time in human history that 264 has been extended to 2202 as a possible construct for the known and unknown universe.  More… just the numbers

To begin to grasp 2202 will take time.  We first began looking for common numbers that were part of our everyday experiences. That resulted in a rather primitive analysis of six notations: The first stop was at the 31st notation where Planck Mass has doubled 31 times and has become a very svelte 103 pounds, yet it is still so small, its density would easily rival a neutron star. Within the Planck Length at the 67th notation, CERN labs in Geneva comes into the picture. Planck Charge is now equivalent to a few lightning bolts. Planck Time is still infinitesimally small.  The current world record brings it “down” to notation 84 in the attoseconds range. Just beyond notation 143 comes our first second. One day is between notations 160 and 161, the first year between 168 and 169.  The first 1000 years is between  178 and 179. The first million years is between 188 and 189.  At notation 197 we have crossed 343 million years. All the time added prior to it amounts to another 343 million years so the truly large scale structures of the universe have just now begun to unfold.  More…  

Stretching:  Current work

• Have you seen the first draft of the Exascale universe?
• A dialogue with the universe with Charles Jencks
• Eight concepts To Grasp A Simple Model Of The Universe


[1]  The fabric of the universe begins with pi which is a key to Euler’s equation and opens a confrontation with big bang mystery:
[2]  The infinitely hot, infinitely dense big bang:    Subsequent analysis has also pushed our these first principles: 
[3]   Imaginative-but-complicating  theory:
[4]  The chart:
[5]  Watch the last row of eight doublings!


seem to define a bridge, an infrastructure between the finite and the infinite. We experience that bridging as continuity, symmetry and harmony that respectively create order, relations and dynamics within every moment.

whereby these basic components of our common experience.

One thought on “Do we live in an exponential universe?

  1. We encourage your comments, the more specific, the better! We backed into this model and need the insights of scholars who have been studying these issues for their lifetime! Thanks. -Bruce


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