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Abstract: Five reasons are given to consider a highly-integrated model of the universe using simple math and logic. This model reopens basic questions within cosmology, particularly about the the big bang theory. Starting with base-2 exponential notation from the Planck base units to the Age of the Universe, it encapsulates everything, everywhere throughout all time. Advocates for the big bang theory argue that there has not been a better alternative. Work on this base-2 model began in December 2011; in the Spring of 2016 it began to become apparent that this simple model simulates the big bang without the bang by using an all-natural inflation and relational concepts of space-time and finite-infinite.
Pictured above are 36 of 202 base-2 exponential notations that capture the universe from the very first moment of time to the current Age of the Universe.
Introduction. Using base-2 notation from the Planck scale to the Age of the Universe, there are a total of just over 202 notations.1 The chart has not been formally critiqued by the academic community. The first 60+ notations are of particular interest. These notations are well-below the measuring threshold of instrumentation. Several have said, “Those notations are too small to be relevant.” Mostly physicists, they approach the challenge of defining the foundations-of-our-foundations in light of historic research of atoms, particles and hypothetical particles.2 The approach here is to define the boundaries and boundary conditions, and then to engage the universe as one dynamic, highly-integrated system. An active imagination can readily speculate and instantiate meaning and purpose in each of the first 60+ notations. Yet, number theory, simple geometries, and the base-2 expansion of the Planck base units of time, length, charge and mass provide a wide range of data to evaluate.
Observations. There are five key observations from analyzing all that data that may open a means to define new foundations for ontology, epistemology and cosmology:
1. Natural inflation.3 The first second of creation within the base-2 model occurs between the 143rd notation (.60116 seconds) and 144nd notation (1.2023 seconds). Using a whole number multiple of Planck Time, consider the other three Planck numbers at Notation 144. Planck Length is now 360,424.632 km or 223,957.48 miles. To have a comparative sense of that number, the average distance between the earth and the moon is 238,900 miles. Planck Mass at Notation 144 is now a daunting 2.4268×1034 kilograms. As a comparison, the weight of the earth is 5.972×1024 kilograms and the weight of the sun is 1.989×1030 kilograms (sun’s radius, 432,288 miles). The smallest and densest stars known to exist are neutron stars. Wikipedia says, “With a radius on the order of 10 km, they can, however, have a mass of about twice that of the Sun,” so the mass of the universe at 1.2023 seconds is within the known ranges of current science.
The coulomb progression from Planck Charge is line 6 within the chart. Within Notation 144 it is 2.0913×1025 Coulombs. Given a coulomb is the amount of electricity carried in one second of time by one ampere of current, it converts to 2.0913×1025 joule/volts. That compares well to the total energy output of the Sun each second (3.8×1026 joules).
Sectional summary: Our earliest universe at just over one second has naturally inflated at a size, mass and energy that are within ranges known to our sciences. But more importantly, the progression of base-2 numbers appears to create a natural inflation and a rather good simulation of the epochs of big bang cosmology4 BUT without the bang.
2. Homogeneous and isotropic universe.5 Notations 1-to-144 provide a progression of simple numbers from the Planck base units. Notwithstanding, our work in this area began with geometries and symmetries,6 particularly following embedded tetrahedrons and octahedrons within tetrahedrons and octahedrons. Our attention was then focused on a new definition of the small-scale universe, Notations 1-to-67. The human scale seemed to be naturally defined from 67 to 134 and the large-scale universe from 134 to 202. This entire universe could be easily and perfectly tiled and tessellated using a tetrahedral-octahedral couplet (pictured). Yes, that simple structure can readily and perfectly fill all the space in the universe. Though an imputed geometry, its potential role in this very small-scale universe was studied in light of bifurcation theory, cellular automaton, fractals, cubic close packing, Langlands programs, and more.7 This range of possible constructions falls well-below our measuring devices but are clearly within the scope of the human mind, mathematics (numbers and geometries), and logic.
An initial analysis of the concepts was written up as a top ten countdown to the end of the year 20158 (in the style of Late Night television host, David Letterman9). In January 2016 there was an initial analysis of how numbers and geometries might be generated from scratch.
Natural transitions from the ubiquitous circle and sphere were found within several most-simple constructions. This example on the right is the transformation to lines, triangles, tetrahedrons and octahedrons. Here the simple quickly becomes intricately complex and often chaotic. The integration of several such examples within our studies of our universe view will be reviewed and updated in light of the following questions:
- Is this domain the foundation for isotropy and homogeneity?
- Does everything in the universe share this space-and-time?
- Is it one of the many bridges between the finite and infinite?
- Is it what is now characterized as dark energy / dark matter?
The anticipated answer to all four questions is “Yes!”
3. Compactification and super densities.10 Compactification within big bang theory is a formal study. The concept of the universe being compacted, as Stephen Hawking says about the big bang, “…infinitely small …infinitely dense point” seems beyond commonsense, intuition, and simple logic. It begs the open questions about the transitions from a neutron star to a black hole to a gravitational singularity. Is there a better way? If the science of compactification cannot define that “infinitely-small and infinitely-dense” universe for the big bang, shouldn’t we keep the door open for other possibilities and explorations? An affirmative response is just commonsense.
Surely, it will be instructive to learn more about the very nature of the compactification of a neutron star!
4. Finite-Infinite. To promote a scientific theory as fact requires a special assurance. To encourage continued debate and dialogue requires a special openness and integrity. To attempt to close debate is arrogant and solipsistic. Stephen Hawking wields enormous intellectual influence throughout the world. With it comes responsibilities, especially to people who believe differently. Gracious scientists would at least make an attempt to provide a path for the billions of people of faith to have some intellectual and scientific access to their belief systems. There has been very little attempt by today’s intellectual leaders of the big bang theory to begin to provide such access. Adamant atheism curtails such discussions.
To eliminate the infinite as a concept altogether has even been proposed. Max Tegmark (MIT), among others, has been such an advocate.11 But, infinity plays a key role throughout math and physics. How do we address the issue of non-ending, non-repeating numbers like pi and dimensionless physical constants? Is it enough to suggest that just those two facets of numbers, geometries, and constants describe qualities of infinity?
The base-2 model, starting with the Planck base units and going out to the current age of the universe, gives space and time a finite, discrete, derivative, quantized status. These two also become necessarily-related, a space-time ratio so it follows that our universe is finite, discrete, derivative, and quantized. If that’s true. what can be said about the nature of the infinite with words that have a scientific character?
Three sets of words12 seem to capture the simple progression of logic that is the backbone of the sciences as well as the “scientific” nature of the infinite:
- order-continuity (numbers)
- relations-symmetry (geometries)
- dynamics-harmony (numbers and geometries in concert)
This description of the infinite could readily provide an access path for believers whose history includes widely-divergent metaphors to describe their Infinite as well as a scientific way to describe boundary conditions between the finite and infinite.
5. Space-time. If, along with the three sets that describe the infinite, these four general topics described above are taken as a given, our understanding of space-time is fundamentally challenged [See Newton-Leibniz]. Addressed briefly in the end-of-year reflections of December 2015, this model suggests that the first notation is still the first notation and each notation supports each subsequent notation and each is actively defining the fullness of the universe and life at this moment. Nothing is past. It is always the now and every notation is constantly being imprinted by each of us every second of every day. There is time symmetry within most microscopic physical theories, yet within any macroscopic setting, all events are irreversible. There is a direction of our universe.
Today, we minimize ourselves and our influence within this ever-so-small universe. That may be about to change.
Summary and conclusions. In 1899 Max Planck first wrote about fundamental or natural units based on constants within physics and mathematics. His work was mostly ignored for over a century. In 2001 MIT’s Frank Wilczek wrote a series of articles, Scaling Mt. Planck (Physics Today), and the scholarly community began to pay attention. It still took the better part of a decade before for the rest of the scientific community began to catch up with Wilczek and a few others.
Today the Planck base units are a core part of scientific research.
Though base-10 had been introduced by Kees Boeke in 1957 (Cosmic View: The Universe in 40 Jumps), he did not start at Planck Time nor did he stop at the Age of the Universe. He missed between 22-to-24 jumps! Nevertheless, that model was popularized by many. Most recently the Huang twins Scale of the Universe has received substantial attention. Not until December 2011 had anybody applied a much more granular base-2 to this scale using the Planck length. In December 2014 Planck time was added to that base-2 model. And then, in 2015 Planck Charge and Planck Mass were added. A line for Planck Temperature was added as a place holder.
Perhaps it requires a certain naivete to do this kind of modelling. Using base-2 is 3.333 times more granular than base-10 and it encapsulates the universe within just 200+ steps. The roots for the base-2 model, just like base-10, also go back to a high school. Although base-2 is totally-predictive, as of this writing, it is yet to be critically reviewed by the scholarly community. And, yes, that may be about to change, too.
Endnotes and Footnotes:
1 The chart. Work began in April 2016 on this horizontally-scrolled version of the February 2015 vertical chart. The vertical chart was difficult to use to follow the numbers along the 202 columns. The horizontally-scrolled chart provides an immediate comparative analysis with the progression of the other Planck base units.
2 Foundations of foundation. This legacy extends back to Leucippus and his student, Democritus, in and around 450 BC. Systems theory, by contrast, began with Ludwig von Bertalanffy, perhaps as early as 1937.
3 Natural inflation. Having just discovered “natural Inflation” as a formal study, there are several dozen papers now being analyzed. That includes: Natural Inflation: Consistency with Cosmic Microwave Background Observations of Planck and BICEP2 by Katherine Freese (Univ. of Michigan), William H. Kinney (Univ. at Buffalo, SUNY); Natural Inflation, Planck Scale Physics and Oscillating Primordial Spectrum by Xiulian Wang, Bo Feng, Mingzhe Li, Xue-Lei Chen, Xinmin Zhang; and Natural Inflation: Particle Physics Models, Power Law Spectra for Large Scale Structure, and Constraints from COBE by Fred Adams, J. R. Bond, Katherine Freese, Joshua Frieman, Angela Olinto. Your recommendations are encouraged.
4 Epochs of big bang cosmology. This posting was initiated on June 1, 2016. Because it began to get a little long and labored (according to my initial reader), I started another for the general public: https://81018.com/bigbang/ Both are considered to be first-drafts because neither posting has been critically reviewed. Real feedback is needed so the post can be appropriately updated.
5 Homogeneous and isotropic universe. Homogeneity and isotropy in cosmology is a formal, active area of study, and it has many highly-credible experts. Current work being reviewed includes that of scholars such as Andrei Linde of Stanford with his 2014 report, Inflationary Cosmology after Planck 2013 (84-pages). Also there is the September 2016 article by Xingang Chen and Hossein Namjoo of the Institute for Theory and Computation (Harvard-Smithsonian Center for Astrophysics) and Mohammad Yi Wang of the Hong Kong University of Science and Technology, A Direct Probe of the Evolutionary History of the Primordial Universe. Again, your recommendations are encouraged.
6 Geometries and symmetries. The initial chart was based on the Planck Length. It would be our initial venture into the Planck Scale. Given its heuristic value, it was immediately dubbed a Science-Technology-Engineering-Mathematics (STEM) tool for high school students. Though the data from notation 67 with its protons and fermions to notation 202± with the Observable Universe was instructive, those first 60+ notations remained a mystery.
7 “On Constructing the Universe From Scratch.” This working paper began as an attempt to fill-in the many blank lines within the first 60± notations of the Big Board – little universe chart. It has opened many new doors of inquiry so this work will be constantly reviewed and developed. It is a start and the best living scholars in several disciplines are being consulted.
8 “Top Ten Reasons to give up those little worldviews for a much bigger and more inclusive UniverseView” This posting will also be constantly reviewed and developed. First, there will be an annual update for the countdown to the New Year. This “Top Ten” will always be an answer to question, “What are the most important conclusions derived from the base-2 model?”
9 Top Ten. Over his 33 years as the host of a television show during the late night hours, David Letterman did 4605 Top Ten lists. Again, our intention is to do only this one list but continually update it!
10 M-theory opens this discussion. Ed Witten enlivens it. Yet, by his own admission, so much of it is conjecture and pure magic. More to come.
11 Max, Max, Max. Although you, Max Tegmark, are naturally filled with vim and vigor, there is a reason you have adopted George Miller’s dystopian moniker, Mad Max. I am not sure the rest of science and mathematics will follow you off that cliff, but it is in keeping with your style!
12 Back to the foundations. First formulated in 1972, this set was to answer the question, “What are the faces of a perfected state system?” That is, religions seemed to be making a mess of our world so I asked the question, “What is the core of most religious systems?” Perfection, among many possible answers, seemed to encapsulate the most conceptual richness with the least philosophical overhead. This work is a natural outgrowth of that exploration. More to come.
1. Supersolids: http://physics.aps.org/articles/v4/109
2. Super Yang-Mills at Finite Heavy-Quark Density: https://arxiv.org/abs/1410.4466
Anton F. Faedo, Arnab Kundu, David Mateos, Javier Tarrio 16 Oct 2014