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Opening New Answers To Old Questions

By Bruce Camber Related: CommonsenseCritical AnalysisFoundational Concepts  Future: Radical Chic

Back in December 2011, a simple mathematical chart of the universe started at the very  smallest units of the Planck Scale and went to the size of the universe in just 202+ doublings. It was the first time such a chart was introduced and it raised questions:

1. Is the power of 2 a cornerstone of this model (and the universe)?

Answer: Yes. It’s in the geometry. Between 1972 and 1980 I formally studied finite-infinite relations, the Einstein-Podolsky-Rosen thought formula and Bell’s inequalities (primarily at BU and Harvard). Continuity and symmetry were key concepts within my work, but it wasn’t going anywhere, so I went into business. Thirty years later, exploring Zeno’s paradox while helping a nephew with his high school geometry classes, we followed the embedded geometries of the tetrahedron and octahedron back to the Planck scale.

Dividing or multiplying by 2 (base-2, doublings, or the power of 2) is inherent within that geometry (see illustration). Continuity and symmetry are as well.

Totals: 24 small tetrahedrons and 10 small octahedrons. Please notice three of four hexagonal plates in the center octahedron.

After we mathematically touched Planck’s wall, it didn’t take long to ask, “What happens if we multiply those units by 2?” We went within 112 steps to the wall, then it took just 90 steps to go out to the edges of the universe. We were using the most recent measurements from the Hubble Space Telescope. That story is here: https://81018.com/home/ So, yes, our base-2 applications began with this model:  https://81018.com/tot/

Even more simple geometries came out of the Planck scale. We take as a given that the Planck scale is a baseline for length and time and that Max Planck’s numbers are close enough for the simple conceptual work that we were doing.

We received some early encouragement back in 2013 when Frank Wilczek in his MIT office encouraged us to continue our explorations inside the Planck base units. Wilczek’s three articles about Scaling Mt. Planck appeared in 2001 in Physics Today and opened the door for the rest of science to engage these units. It was now a very young science even though Max Planck had started his work back in 1899.

2. How are the Planck base units organized? Although defined by certain dimensionless constants, how and why is there coherence?

Sphere to tetrahedron-octahedron couplet
The next layer: octahedrons

Pi (π) was the most simple, most ubiquitous of the dimensionless constants. It was then assumed that planckspheres are the most simple manifestation of the Planck Length and Planck Time.

Then, in studying spheres, there was an abundance of work around sphere stacking.

In 2016, while preparing an initial analysis of numbers, I discovered this image from a discussion in Wikipedia about sphere stacking —  ccp, hcp and fcp. That dynamic image caught me. It didn’t take long to begin to see the spheres as planckspheres and the graphic as a representation of the first moments of space and time. The progression of thinking can be followed through the emergence of these pages:

From Doublings to Period-Doubling Bifurcation and other studies. In April 2018 an “Open Letter” to many of my friends became a homepage. Then, this page on the dynamics of doublings emerged.

3. Where and when do all other dimensionless constants come in?

Quick answer: Of course, many are already there within that first doubling.  These are the constants that define the Planck units. We’ll find there rest of them! There are so many times when I’ve had to caution myself, “This is your first time to go over this information. This is new. Be patient now.”  I often wondered, “What other numbers should we be considering? What are all these dimensionless constants? How many are there?” It was anybody’s guess. Though pi was first on many lists, others like e were well into the future for me. Euler’s work was not yet in my beingness. I say somewhat apologetically, “Maybe I’ll get there before I die!” https://81018.com/number/

I would rhetorically ask, “e, oh e, why do you equal to 2.7182818?”

Digging deeper, trying to make the strange familiar, many factors were pushing me. I had re-opened Frontiers of Time, a preprint from John Wheeler. He became a de facto mentor and his work to define quantum foam which seemed entirely foundational had caught my attention.

I have always assumed a finite-infinite bridge since I was a kid. So even back in the earliest days, I’d ask, “How can we talk about infinity using more scientific language?” By 1972, I emerged with three concepts: (1) continuity/order, (2) symmetry/relations, and (3) harmony/dynamics. Quite in the face of David Hilbert, I saw manifestations of the finite-infinite bridge everywhere, yet the mathematics of it all had eluded me. But now,  this new framework could be where we actually begin thinking about how to test very general and rough ideas.

The first group of notations began to taunt me. What’s there? Below the CERN-scale of measurements, there were a lot of data sets to explore. My first feeble attempts humbled me. I knew each set would have to be addressed one at a time. That’s when I created a grid for each of the 202 notations as a constant reminder and challenge.

Throughout it all the first 64 notations stood out. Of the 202+ doublings, those 64 are well-below the threshold for particles and measurable physicality. Here I assumed that mathematics and logic must dominate and our challenge is to formulate how mathematics builds upon itself. I would allow the 18 primes to each take on their special role of introducing new mathematical functionality. For now, I continue with my assumption that those 18 primes within the first 64 notations, along with the necessary relations given within each doubling, give rise to the basic physical structures of the universe.

What fits? Perhaps that’s too much little like the New York Times, however, each step of the way, I will rely on experts to advise the process, “What numbers work next? What fits?”  It is within these 18 steps that “e = 2.7182818” will be tested. All those fundamental constants of Lord Martin Rees will be tested. And, we’ll have their help! He’s on the sidelines expecting questions as is Freeman Dyson and a host of others.

4. What about the age of the universe?

The number is thought to be settled science. When Steven Weinberg engaged the question for his 1977 book, The First Three Minutes, he concluded 13.7 billion years. More recently scholars seem to be pushing it to 13.81 billion years. There are others out of  the mainstream who go out as  far as 40 billion years. That range is not substantial within this model. If notations or doublings amount to 202, 203, 204 or 205, the base-2 chart can be readily extended once there is general consensus about that number.

This chart is all about how the earliest notations participate in the current notation.

5. Where does dark matter and dark energy come in?

Dark matter and dark energy within this chart might well be the building of an endless stream of planckspheres over the 202 notations, especially focusing on the first 64 notations. This chart seems to suggest that all notations as active, integrated, interdependent, and necessary. Of course, the nature of time takes on a very different texture and Neil Turok’s perpetual big bangs just may be the net-net of the first 64.  This issue will be further addressed in the next homepage.

There are more questions just below!


Editor’s Notes about Navigation and Other Points of Interest:

  • Navigation: Scroll to the top of the page. Cursor over the word HOME and a very long drop down menu will be displayed. It can be scrolled. There is a link to every homepage within this site from its beginning in September 2016.
  • Homepage. Click on Our Universe in 202+ Doublings to go to the current homepage.
  • That second header contains links to the past 20 homepages. “Just Prior” always goes to the most recent, then each number is active to the next prior homepage.  The image goes to the horizontally-scrolled chart as does its tagline.
  • Values and ethics: Universals and constants give rise to a sense of value that gives rise to values and ethics. The antithesis is nihilism which opens dystopia.
  • Related Letters: Times Literary Supplement
  • Wayback:  

The current struggle: Who will lead us? Who can break the impasse?

Might the seven First Ladies of oldest trade routes of our world break the impasse?


More key evocative questions:

Back in my very early days at Synectics Education Systems (1971-    ), in the days of metaphors and analogies, one of the most important activities was trying to engage key evocative questions. Here are a few of those questions explored within this site:

Join us. Challenge us. Help us.  We need all the help we can get!

An excellent resource to translate any of our pages by its URL:

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