Top scholars concur that we do not understand space and time.


Redefine Both – Follow The Numbers

by Bruce Camber  Endnotes/Footnotes and References-Reflections-Resources

Introduction. We know our models of the universe are incomplete primarily because two of the most basic facets of our experience, space and time, need to be redefined:* (a) Newton was off.1 (b) Even our beloved Einstein didn’t have the complete story.2  (c) And, in 2011 we unwittingly began to redefine space and time. Key concepts went back to 1971.3

Background. Yes, in 2011 we created an outline of the universe using base-2 notation.4 Stating with the Planck base units, literally everything, everywhere, for all time, was encapsulated within 202 exponential notations.5 Those are big words for doubling key numbers at each step. We started with what we thought was logically the very first moment of time, Planck Time, and came right up to today, yes, right now, this instant.

Observations. The 202 steps from one end of the universe to the other constitute an actual working, mathematical model.6 Those numbers logically pull the universe together. Certainly, 202 steps doesn’t sound like much. And as small as that seems, our universe could be smaller!

We are now beginning to see possible shortcuts throughout the 202. Historically, scholars (like John Wheeler) called such shortcuts, wormholes.7 Today, the universe is currently unfolding and expanding uniquely within Notation-202.8  All other notations are fully symmetrical,  yet continue to evolve; yes, every notation is changing, adapting, and responding to Notation-202 and to each other. In this model the butterfly effect9a applies to the universe. Yes, this paradigm shift opens as many questions as it seems to address.9b

There is one thing we do know with some assurance from this model: this universe is a totally-connected, integrated, and a rather intimate place. Also, it would appear that the first thirty-to-fifty notations manifest perfections of continuity, symmetry and harmony. Somewhere, perhaps around the 50th notation, a geometric gap10 becomes part of the landscape.

It is a key gap; it opens an indeterminant infinitesimal universe.

First, Aristotle failed to grasp it and made incorrect assumptions about it.11 Then scholars repeated his mistake, over and over again, for about 1800 years. Within a simple configuration of five tetrahedrons sharing a common edge, there is a gap and then it is extended within both the icosahedral and the Pentakis dodecahedral structures. By Notations 64-to-67, that gap becomes systemic and quantum indeterminacy becomes dominant and the universe as we know it continues to unfold.

Conclusion. Our mathematical outline of the universe is slowly becoming a simple, logical, and mathematical model of the universe that fundamentally begins to redefine space-and-time as well as infinity.12


Footnotes & endnotes:

* The work of three dynamic scholars is lifted up: Nima Arkani-Hamid, Max Tegmark, and Neil Turok. The questions are abundant. New insights are not. Please Note: Scholars who have been referenced for March2020this homepage are sent a note to inform them.

1 Sir Isaac Newton. Absolute space and time is still the commonsense view of the world’s population. Even our best scholars defer to it although they know it is not right. But until people have an alternative that works, we all resort to what we know. Going back to Newton’s time, back to 1716, there are the makings of an alternative; Newton was arguing (through his associate, Samuel Clarke) with Gottfried Wilhelm Leibniz. That Leibnizian point of view could be an actual opening to an alternative understanding of space and time. More


2 Albert Einstein. Some of the best of Einstein’s students (and his students’ students) gathered in 1999 for a conference, Structure Formation in the Universe. Held at the Isaac Newton Institute (INI) of Cambridge University, it involved Andreas Albrecht, Savas Dimopoulos, George EfstathiouAlan Guth, Stephen Hawking, Juan Maldacena, Martin Rees, Joseph Silk, Paul Steinhardt, Leonard Susskind, Neil Turok, Joseph Silk, Gabriele Veneziano, Alex Vilenkin and a select group of scholars. A result of that effort was the emergence of models of the multiverse (i.e. Lisa Randall). Yet, at no time did a compelling redefinition of space-and-time truly emerge. More

3 Redefining Space and Time. In 1971, as a result of studying the Einstein-Podolsky-Rosen (EPR) thought formula of 1935, I asked, “What could be more fundamental than space and time?” Out of college in 1969 and part of an invention and problem-solving think tank in Cambridge (Massachusetts), it seemed that continuity was the basis for order which is experienced as time. Symmetries fundamentally defined relations and are experienced as space. And, then harmonies were the essence of dynamics, or interacting symmetries, and that is experienced as space-time moments. So, that was it — continuity (order-time), symmetry (relations-space) and harmony (dynamics-interacting symmetries) defined (and were) the infinite. Sir Isaac Newton was wrong. Space and time were not absolute, but derivative.

I wrote it up, but it had no math and no container; it was just a feel-good idea. More

4 An Outline of the Universe. In 2011 within a high school geometry class, we divided the edges of a tetrahedron in half, connected the new vertices, and like Zeno, we kept on going until we hit Max Planck’s wall. There were just 112 steps. When we multiplied our classroom tetrahedron by 2, in just 90 steps we were out to the edges and age of the universe. Much like the Sierpinski Triangle (base on the equilateral) and Sierpinski space, it was disconcertingly simple and the numbers told wild and crazy stories. Yet, at no time has our little naive outline of the universe been discussed by the scholarly community.  I’ve tried (and will continue to do so). And, things could change. FQXi, a scholarly group, invited papers for March 2020 around some of these issues and I’ve submitted one. It is still quite rough, so I continue to update it within these homepages. Given this work started in a high school, our construct is entirely too simple for most. More

5 202 Base-2 Notations. It appears to be the first model to begin space-and-time with the Planck base units, Planck Length, Planck Time, Planck Mass and Planck Charge. It appears to be the first model to apply base-2 notation that resulted in 202 notations. A series of charts emerged. More…

6 Chart of the Universe. The charts are all very helpful; finally there was a bit of causal efficacy for everything, everywhere, for all time. Every number was 100% predictive. And, it all went back to the first manifestation of space-time, an infinitesimal sphere. It was the first object and it totally fills space-and-time, defines space-and-time, and is space-and-time. The first dynamics of the universe: Sphere generation and then sphere stacking. The universe became emergent. More…

7 Shortcuts throughout the universe. Base-2 is magical because it is so simple. Doublings, as we’ve examined sphere stacking, generate the simplest geometries. There is cohesion and there are structures within structures. We could see how the universe literally was growing together. Then that vision began started checking out. At one second, between the 143rd and 144th notations, the number is within .01% of the laboratory-defined speed of light.

There will be many more self-validations within this model. Those 202 notations are simple math and reality should follow. And, if base-2 works, perhaps base-3 and every other prime-base between Notation-1 and Notation-202 will as well. Of course, the prime numbers have been called  “the atoms of mathematics.” Those primes up to Notation-199 are here-on-in considered the most fundamental among all primes.

Observations: If base-2 works, then base-3 should be scrutinized closely. Base-3 goes from Notation-3 to Notation-201 in 67 jumps. It is fully symmetrical. Each of its 67 notations are “completely filled” with planckspheres as it works right alongside base-2 and Notation-202 which is being populated now as the current expansion, literally filling up with planckspheres.

Note: The count of the jumps includes from Notation-0, the Planck base units, to the prime number base.

If base-2 and base-3 work, then base-5 should work. It would jump to Notation-200 in 40 steps. Of course, all the other possible bases will also require analysis. Base-7 jumps goes to Notation-196 in 28 steps. We might think of these primes to be like an express train to its highest notation closest to 202, then you would go to a transfer station to the local trains, where a “local” base would then bring that base into the present moment within Notation-202.

Base-11 jumps to Notation 198 in 18 steps. Base-13 jumps to Notation 195 in 15 steps. Base-17 jumps to 188 in 11, base-19 jumps to 190 in 10, base-23 to 184 in 8, and base-29 to 174 in 6. Base-31 goes to 186 in six jumps. Base-37 goes to Notation 175 in five jumps.

Just what is this passageway? Right now, that’s anybody’s guess. I’d say, mathematical possibilities are actively being explored with the addition of every new plancksphere.

We can readily calculate that base-41, base-43 and base-47 reduce the jumps to 4. Base-53, base-59, base-61, and base-67 reduce the jumps to 2. The following primes, 71, 73, 79, 83, 89, 97, and 101, reduce the jumps to 1 and, of course, it would always be working with base-2.

The nineteen primes thereafter — 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197, and 199 — are themselves an especially unique place within the universe. Each new notation initially replicates all prior notations, yet each evolves with its unique functionality.

For more see: (1) Wormholes, (2) Matt Visser’s Lorentzian Wormholes (1996) (letter/references), (3) Misner and Wheeler, “Classical physics as geometry” (Ann. Phys. 2 (6): 525, 1957), and (4).Francisco S. N. Lobo,  traversable wormholes (April 2016).

8 Notation-202 and the symmetry of the universe. The current notation is still filling with infinitesimal spheres exactly like the first one to emerge and all 200 that have since emerged. All are still currently active. Notation-202 is directional and will continue to be directional until it is filled with infinitesimal spheres and the next notation begins. Yes, our current notation is Notation-202; it has a duration of 10.98+ billion years. Only about 2.82 billion years has transpired. That creates directional, asymmetric moments. Symmetry is needed for our Standard Models, our physics and mathematics. Enter sleep. Consider sleep to be like an overnight recompile of a computer. All the programs are reset and re-calibrated so everything, everywhere, for all time works in conjunction with each other. Symmetries are momentarily restored. Of course, there is more to come.

9 Among the conceptual problems within current scholarship. This model just might addresses a few of the unsolved problems in physics and astrophysics. Key among them is dark energy/matter and homogeneity and isotropy. It also pushes a more inclusive application of the butterfly effect within chaos theory. There is so much more work to be done.

10 Geometric gap: 0.12838822+ radians and 7.35610317245345+° degrees. Even today, April 2020, this gap is little studied and less known. Our first encounter with it was in 2016 upon writing the article, “Which numbers are the most important and why?”  At that time, it seemed like Chrysler Corporation had branded  that geometry as the pentastar. And though it is a five-tetrahedral representation, they never looked uniquely at the gap of 7.35610+° also defined by 0.12838822+ radians. Two chemists (Frank & Kasper) came closest to opening the discussion in the 1950s. Two academics, Lagarias and Zong, did a preliminary analysis that has been a tremendous help, yet the relation of this gap to the deeper geometries of life remains a challenge. Our modest start is here:  Also, see the icosahedron and Pentakis Dodecahedron.

The guess is
that little gap
just above is
the beginning
of quantum

11Aristotle’s failure is our failure. Perhaps the gravity and nature of this error is only now beginning to be understood. We all make mistakes. When we are challenged, we defend our concepts as best we can, and then adapt. We change or our associates change.

Some people become larger than life within their own time. Three examples are Aristotle, Newton and Hawking. All three were wrong about one key impression about the nature of life, yet their egos and their position and their person were so illuminated, it became increasingly difficult to challenge their assumptions.

Aristotle’s geometric gap, Newton’s absolute space and time, and Hawking’s infinitely hot big bang have each misled scholarship and then, most of us lost the scent and direction of the chase with its resultant discovery and creativity. We’ve been blinded by basics that were not basic enough.  Throughout our ever-so-youthful human history, such people can readily continue to mislead us. We have to be vigilant to review and re-review all the concepts we hold near-and-dear and begin to adjust them appropriately.

12 New definitions of space-and-time and infinity. A rather uncomfortable view of space-and-time, certainly non-intuitive, this model pushes us to consider the four Planck base units are so tightly wrapped together — always and forever an active, bundled expression — the five faces of the speed of light are what we first experience and observe: light, space, time, matter and energy. Those five faces are each uniquely defined as a Planck unit and then collectively-and-uniquely defined in relation to the entire universe. Yes, though unique, each is ever-changing in relation to the entire universe.  This finite universe has wholeness and thingness. Yet, it is balanced within an infinite continuity, symmetry and harmony.


References, reflections, and resources:

Please note: In the course of compiling data-information-and-insights, writing about them, editing and re-engaging new concepts, there is much that no longer fits, however, it is still worthy and perhaps should be preserved as a reference, resource, or reflections about the roots for this article.

scholars-April4-20201. Questions about groups and sets: Does each notation or step or doubling complete a set? Can those sets can be grouped? In quite a different light, there are three groups of scholars to which we re-engaged for this rather brief article. These are: FQXi, the Physics of Quantum Electronics (PQE) group, and the 1999 Structure Formation attendees.

2. Poetry about the small universe? Consider the intimate part of our universe. The simple part. Perhaps once we learn something about the very small (infinitesimal) universe, the big-complicated universe, larger-than-life and rather overwhelming, will get a new handle and the universe will come home.

What seems so far away, “…back at the very beginning,” begins to become accessible. So, let us start with that infinitesimal circle that becomes a sphere, and one sphere follows with another and another. Here is the youngest universe; forever young, ebullient, reaching out to you like a baby. Yes, here is our evolving universe, always beginning, even today (See Turok).

3. Working models. Do you see that very small stack of spheres (just below)? No sphere is empty. There’s always a centerpoint, an active radius; there’s dancing. There’s music, too. There’s particularity; there’s continuity. There are relations and symmetries. The infinite (qualitative) has become the finite (quantitative). And, the harmonies of the universe begin.

4. Definitions: The infinite is the qualitative expression of continuity (order), symmetry (relations), and harmony (dynamics) and the finite is the quantitative expression of the same. Yes, although there are many people would like to retire infinity as a concept, we do not.

Sphere to tetrahedron-octahedron couplet
A Study of Numbers:

5. A little science, math, and geometry, too.
•  The hand-and-glove of our knowledge and this reality
…letters to Steven Strogatz, our mathematics bard
•  The Universe is properly parsed by 202 base-2 notations which includes “everything, everywhere, for all time,” starting at the Planck base units and coming through to today, the Now, this very moment in time. It all began in local high school.
letters to Frank Wilczek who boldly opened a way.
•  Then, a simple formula opened another door, c=pl:pt
…letter to (and letter from) Espen Gaarder Haug
•  The universe starts perfectly (Spherical Perfections)
…letters to Ethan Siegel, a political, emotional, big-bang advocate

The so-called Plancksphere, a first-order of physicality.
letter to Howard Georgi (Unparticle Physics)
Cubic-close packing of equal spheres (first-order activity)
…letters to Mitchel Feigenbaum and Thomas Hales
Planck-scale units that enliven the Fourier Transform and Poincaré spheres are well-below the ability of our machines or devices to measure.

6. Spacetime. I began reading the work of  Stephen Wolfram. He watched his incredibly simple algorithms generate incredibly complex results; but, to do so. it requires a computer to be in the mix. Even quantum computing doesn’t get simple enough.

speed of light
Image as it appears in Wikipedia

7. Max Planck: He has a rightful place within the continuum of development of an accurate definition of the speed of light. The chart on the right is from Wikipedia. Our more inclusive version follows. Take Planck’s Length — 1.616255×10-35 meters — divided by Planck’s Time  — 5.391247×10-44  seconds and you have 299,792,22.8 meters per second. He didn’t claim it, so we’ll shout it out for him.Planck-in-light-list8.  Header: Image by R. Wesson,La Silla Paranal Observatory, European Organization for Astronomical Research, La Higuera, Coquimbo, Chile (Google Maps)
• “
We all now know how small our world is. We may be surprised to discover our universe is, too!”
• “Many scholars concur, ‘We do not understand space and time.’ And, i
t just may turn out that this universe is not so large after all.”
•  “
Replace that Big Bang Theory with this!”

Please send along your comments or questions:

A work in progress….
Started on March 16, 2020 at 11 PM
First homepage date: 24 March 2020
Last edit: Saturday,  April 11, 2020

This page is: