Worldviews are incomplete. UniverseViews are inclusive and empowering.

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From the James Webb Space Telescope, left to right, Stephan’s Quintet, Southern Ring Nebula and the Cartwheel Galaxy

A Mathematically-Integrated UniverseView
by Bruce E. Camber, a working draft

Overview: The mathematics of the smallest things render things like stars, nebula, and galaxies. In 1874 in Dublin George Stoney* calculated an infinitesimally small unit for length and time using dimensionless constants. In 1899 in Berlin, Max Planck did similar calculations and got slightly different results. Symbolic placeholders, somewhere in their range of numbers is the very first unit of time. If we apply base-2 notation (doublings) to that assumption, it renders 202 logically-related groups right up to the current time. It is the most simple mathematical outline of our universe and it ontologically opens the universe with the smallest, most-basic units that make everything-everywhere-for all time. We begin to see how everything is connected to everything. And, as that math comes alive and begins to demonstrate its efficacy, a dynamic understanding of cosmology opens. Nothing will ever seem quite so far away or long ago; and, the universe becomes our home.

Simple mathematics. The universe is outlined by 202 base-2 notations from the Planck base units to the current time. The first 64 notations are below thresholds of direct measurement. It’s an infinitesimal area that has been, and continues to be, the unwitting subject of such diverse studies as Langlands programs, string theory (including M-Theory, F-theory, type II and its offshoots), supersymmetry (SUSY), loop quantum gravity (LQG), causal dynamical triangulation (CDT), causal set theory (CST), field theories (QFT, CFT, LFT), spectral standard model (SSM), hypothetical particles, and much more. These studies start simple and take us into complexity. And, each will defined on, as well as define this grid of the first 64 base-2 notations.[1]

Redefining time. Newton’s concept of absolute time became common-sense long before Einstein; yet Einstein’s alternative made very little sense. Is time an illusion? “No, but…” So, we’ve started to redefine time. It’ll be a major hurdle for each of us. The sense of past-present-future is hardly an illusion. Perhaps we need to think of it like we do a sense — seeing, hearing, smelling, etc. Linear time is quite real but transitory. Our guess is that it gets recompiled within exponential time within our sleep (See three paragraphs just below, nature of sleep cycles).[2]

Finite-and-infinite. This Janus-faced relation has been controversial throughout time. If we redefine it as the quantitative-qualitative in light of the continuity-symmetry-harmony of pi and in light of the other dimensionless constants found with the first 64 notations, then our historic and personal issues regarding infinity may eventually be seen in a new light.[3]

Perfection-imperfection. There has been a lack of engagement with (1) the geometries and physics of perfection, particularly of continuity-symmetry-harmony where there are no gaps and the universe is very smooth, and (2) the geometries and physics of imperfections where there are fluctuations and squishy or quantum geometries within an idealized Euclidean base. Our constructions are formative and, in part, unprecedented.[4]

The nature of sleep cycles. Within sentient and thinking things, there is a constant process by which linear time is recompiled within exponential time and the current moment of the universe. Notation-202, the Now, is always on the edge of the current expansion, could appear to be a time asymmetry but is forever being recompiled within the whole as everything that sleeps does so within the continuity-symmetry-harmony of infinity.[5]

Summary. These points are evolving and have been part of prior homepages. You can click back through those homepages from our list or go up to the top navigation bar on this page and cursor over HOME and select from that pull-down menu. You could scroll through every homepage since July 2016.

To review these five points as a checklist, try these pages. Thank you. -BEC


These points have pages within this website.

* George Johnstone Stoney is the first scholar to craft these natural units (1874). His report was published in 1881. Planck’s calculations were done in 1899.

The horizontal chart was a natural extension of our very first chart in December 2011, called the Big Board Little Universe. It is all just simple math and geometry.

[1] Math and Universals. Those nine studies involve the finest living scholars within mathematics and science today. Yet, we all need to know the boundaries and parameters within which we work. Our simple mathematical boundaries begin with the symbolic placeholders that were calculated in 1899 by Max Planck and in 1874 by George Stoney. These natural units of space, time, mass, and charge are a start. Applying a basic function — doublings — to those numbers creates a continuity equation that brings us to the current time in just 202 notations. This outline is independent of any ontology or cosmology; and taken as a given, we have a parameter set unlike any. It is worth exploring, even if as a thought experiment.

Also, there is much more. There are people like Julian Barbour with his shape dynamics, Dennis Deutsch and Chiara Marletto with their constructor theory, and the moonshine outliers starting with John Conway and more recently with Miranda Cheng. Our simple theory works with them all. So, yes, there’ll be many more steps…

[2] Finite time. The name of the file for our first exploration of the nature of time was /time/. The definition of time with which we are now working is, “Time is an equation; it makes numbering possible. And as a result, it makes measurement possible.” It is continuity. It is the never-ending, never-repeating numbers of pi. Our perception is the passage of time; the general perception is clocks that tick-tock. The reality is that its always and in every way dynamic.

The very first equation gives us the circle and sphere, then tetrahedrons and octahedrons. The next equation begins to count the rate by which those infinitesimal spheres come to be. It is a “new cosmological constant” that can be calculated. Planck Time and Stoney Time give us a range between 539-to-4605 tredecillion infinitesimal spheres per second.

[3] Infinite: Continuity, symmetry, harmony. Also, redefine space; it’s tethered to time and light (Einstein’s equation) and necessarily to continuity-symmetry-harmony. These dynamic equations manifest as space. It is the actualization of symmetries. As a space-time moment, those equations also may be experienced as a most profound harmony and equally profound finite-infinite relation. Next steps

[4] Perfect-Imperfect. Specialized astrophysicists have concluded that the universe started very smooth, so smooth some scholars are suggesting that it is begging for a new physics. Our prediction is that as they peer either further away or back in time, they might even call that smoothness, perfection. Harvard’s Avi Loeb said, “If the anomaly in S8 and the Hubble constant stands the test of time, then both may imply new physics.”
Our Unexpectedly Smooth Universe May Point To New Physics, Govert Schilling, Sky & Telescope, July 31, 2020.

When we begin to acknowledge that it took 1800+ years to uncover Aristotle’s mistake, we know that we all make mistakes; we even repeat the mistakes of others, even the very best among us. One of the three key mistakes that science is making even today is to ignore that legacy of Aristotle. Gaps within basic geometries matter. Imperfection can be geometrical.

[5] Nature’s sleep. Do all living things sleep? Are all living things aware of a passage of time? Is there a sense of time? Among living things, all that which is organic, is there a group of just those that reflect on the past, dwell in the present, and project their future? Earlier I’ve placed all thinking living things in this group.

These are just a few of the questions with which we will be working. Thank you.


Editor’s note: As this posting begins receiving questions and feedback, these endnotes will be updated and extended; and, footnotes may be added. This is a working document.


References & Resources
As these references are studied, key references and resources will be added.within this website.

• Cycles of Time, Roger Penrose, Knopf, 2011. In this book, Penrose proposes his Conformal Cyclic Cosmology (CCC) within the backdrop of the big bang cosmology. Our next step in our development will be to contrast the mathematically-integrated view of the universe with various cosmologies that have been proposed over the years. Penrose’s CCC is the first to be considered.

Our pivotal agreement is when he says, “The circular boundary itself represents infinity for this geometry (CCC), and it is this conformal representation of infinity as a smooth finite boundary…” (CoT, 2011, Knopf USA, page 67)

Penrose is now over 90 years old, yet still active, so it will be of interest to see if he responds to our note (also linked below).

• Our Unexpectedly Smooth Universe May Point To New PhysicsGovert Schilling, Sky & Telescope, July 31, 2020

• Khodadi, M., Nozari, K. & Hajkarim, F., On the viability of Planck scale cosmology with quartessenceEur. Phys. J. C 78, 716 (2018).

• Foundations of the new field theory, Max Born and Leopold Infeld, 29 March 1934.


There will be emails to many of our scholars about these five points.

• Who shall we write to next? Any suggestions?
Karen Keskulla Uhlenbeck, Institute for Advanced Study, Princeton, NJ
Alexander F. Ritter, Associate Professor, University of Oxford, September 13, 2022
Valerie Jamieson, The Fusion Cluster, UKAEA, September 13, 2022 (update of Sept 6 email)
Matt Strassler, Center for Fundamental Laws of Nature, Harvard, Cambridge, MA, Sept. 12, 2022
Sir Roger Penrose, Oxford University, Oxford, UK, September 12, 2022
• Avi Loeb, Center for Astrophysics, Harvard University, Cambridge, MA, September 10, 2022
• Yair Shenfeld, MIT, Cambridge, Massachusetts USA September 7, 2022
(Questions about the geometry of gaps. Yair is an expert on Brownian motion.)


There will also be many instant messages to thought leaders about these five points.


Matt Strassler, a theoretical physicist, tweeted, “So, the news from #Kharkiv is surprisingly good, but very worrying. This is not retreat, it is collapse. (Izium, already!) #Putin cannot tolerate more humiliation. I fear he will lash out.”

9:16 AM · Sep 11, 2022 To which I replied, “You are right. The world needs to be giving him (Putin) off ramps everyday. Let’s get creative!


Participate. .. You are always invited.


Keys to this page, mathematical-universe

• This page became a homepage on September 9, 2022.
• The last update was September 24, 2022.
• This page was initiated on Wednesday, September 6, 2022.
• The URL for this file is
• The prior homepage: Challenged by the James Webb Space Telescope: What is space?…time?
• The headline for this article: Mathematically-Integrated UniverseView
• First byline is: On going from a worldview to an integrated view of our universe
Second: What’s your worldview? Does it absorb all space-time from the very start?
Third: Do you have a worldview? Wouldn’t an ordered UniverseView be better?
Fourth: Worldviews: Too vague. A well-ordered UniverseView: Liberating.
Fifth: Worldviews are incomplete. UniverseViews are inclusive and liberating.