Is our universe fundamentally exponential?

Homepages: Just Prior|Concepts|Dialogue|Finite-Infinite|Education|Original

Let’s examine this Quiet Expansion

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 weave together the most basic assets, forms and functions that define our universe. Our chart with its successive doublings of the Planck base units in 202 steps to the Age of the Universe raises questions:

Light is equal to Planck Length divided by Planck Time
  • Do the 202 steps uniquely defining light (c) or does light define them?
  • Within every step (layer or doubling), space-and-time reveals a discrete, quantitative universe.
  • How does this progression reflect Euler’s equations [1]?
  • How does an exponential universe integrate with Euler identity?Euler
  • Does this simple view of our universe open new doors?

By contrast the infinitely hot big bang [2]  is an imaginative-but-complicating theory [3]. Big bang observations begin within the 197th notation of our simple model (343 million years). 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 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 have reached the limits of our abilities and our learning curves are rather steep.”

Key articles include:
• An initial analysis of 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, having 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 54th square (doubling) there is more wheat than in the world’s annual harvest in 2020 (by a wide margin). It sounds as unlikely as the version dubbed the Checkerboard & Penny.

The Checkerboard & Penny calculation is more of a stretch.  Start with a penny. Use base-2 exponential notation and watch the last two rows of eight doublings! [5]

The first doubling: Just two pennies. Four pennies in the next. Doubling. Doubling. Doubling, all the way to the 64th square. That is 264 and it equals 18,446,744,073,709,551,615.  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 $303 trillion in 2021.  That is a lot, but you could readily retire all the global debt and still have $184.1 quadrillion 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 place it within the family of 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 2016 world record for a measurement of a unit of time, 247 zeptoseconds (10-21) brings it “down” to about Notation-78. 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 cross 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…  


• Have you seen the first draft of the Exascale universe?
• Thinking about the universe of Charles Jencks
• Eight concepts to grasp a simple model of the universe


[1]  With this model the fabric of the universe would appear to begin with pi which is a key to Euler’s equation —  —  and opens a confrontation with big bang mysteries:
[2]  The infinitely hot, infinitely dense big bang:
[3]   Imaginative-but-complicating  theory:
[4]  The chart:
[5]  Watch the last row of eight doublings!


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