CENTER FOR PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS.April 2017
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The First 64 Notations, A Truly Small-Scale Universe
by Bruce Camber (Your comments are always welcomed.)
|Reflections about modeling the universe using base-2 exponential notation. We are somewhat cautious with any description of the first 64 notations. Most every line item in that range is just a number, the simple doubling of the prior number, each a multiple of one of the Planck base units. When looking at the Planck Length continuum, there are no known physical measurements of anything below that 64th notation. Of course, there is plenty of math, but no measurements qua measurements. It is all so infinitesimally small, it is beyond our current measuring devices and would appear to be destined to remain mysterious. Yet, I don’t think that’s its destiny. If an emergent mathematics can be assumed, the numbers will follow and studies might be performed to validate them. So, I’d project just the opposite, “It all won’t be mysterious much longer. A door just may be opening.”|
Those of us who are curious are not going to stop our explorations. The deepest mysteries of our universe will continue to be explored and people will make breakthroughs. Within our emerging model of the universe, every notation is interrelated and interconnected so analogical constructions should work to guide our thinking. Our logic, mathematics (especially geometry and number theory), physics and philosophy should open the way to a rather new domain, first for thought experiments and then for actual experiments.
At one time scholars referred to the Planck units as a singularity assuming that all the forces of nature, all the constants and universals, are pulled into this exquisitely small space to create a totally-magical point. Their model, the big bang, has always been counter intuitive to me; our base-2 progression has a quiet expansion and a natural inflation. Within our model, that first moment at the Planck scale is more like a convention than a singularity; there are strings of ratios all jockeying to be the first vertex. To track it, we created a line item within our chart of numbers to begin to follow these assumed “construction vertices” within each simple doubling. After some analysis of the numbers, we also assumed it began with the simplest geometries initially manifest by pi. There are, however, other possibilities.
In our very early stages of asking around about the logic of multiplying the Planck units by 2, Freeman Dyson, one of the early expositors of dimensional analysis and renormalization, suggested that we should be multiplying by 8. Though initially perplexed, we did; and, we watched amazed as that progression made a very formidable rise. If taken to be construction vertices, anything seemed possible.
Yet, starting from virtually nothing was still perplexing.
By exploring essentials within philosophy, logic, and mathematics, we made generalized guesses back in December 2011 to create our first chart of the universe. It was rather awkward working with a five-foot by one-foot board so we then created a smaller chart (2013) modeled after the Periodic Table of Elements.
The first box in the first ten notations of our new chart were the Forms or the Eidos of Plato. The second group of ten notations became the Ousia or Structures of Aristotle. The third group of ten notations were regarded as the beginning of Substances. The fourth group generated Qualities. The fifth group of ten notations manifested Relations and the sixth group of ten was the emergence of Systems (which included consciousness).
That gave us a very generalized, rather casual, initial structure within which to consider any additional data, and there was a lot to come. We went back to the Newton-Leibniz debate of 1715 and began revisiting old friends that had been ignored for many years. Alfred North Whitehead had asked questions about dimensionless, pointfree geometries which opened the way to study ontology, systems theory and complex systems.
When the numbers for Planck Time to the Age of the Universe were added in 2014, it became even more mysterious. Out of a total of just over 202 notations, the first second of the universe emerged between notations 143 and 144. That turned our understanding of time on its head. We as people with our brief history did not emerge until the 202nd notation. All of human history seemed so small. The year, 1715, was as if yesterday. The paradigm was shifting and time was feeling ever so discrete and obviously quite quantized. Every notation began and ended within a very particular fraction of a second. It was finite. And because of our prior work with numbers and geometries, it seemed quite derivative.
Time began to take on a special flavor of its own. It didn’t pass by and it wasn’t gone forever, but appeared to be an active, present, part of the whole. Somehow each notation was starting to come alive with a dynamic, functional purpose within-and-for the entire universe.
We needed to study periodicity, cycles and frequency to see how the Small Scale manifests in the larger. What we had considered to be the Human Scale using just Planck Length, was fully within the first second of the life of the universe. So, we asked, “How does the Small Scale manifest within the “Human Scale” which then manifests within macroscopic or Large-Scale universe?“
The 202nd notation contains the current time, the Now, and all of human history.
With the addition of Planck Charge and Planck Mass, this first group of 67 notations began to reveal their special flavor and charm. Though beyond the reach of experimentation, here is a domain that appears to hold the secrets for homogeneity and isotropy as well as for dark energy and dark matter. This deep mysterious infrastructure is waiting to be explored, yet it can only be penetrated by the mind, mathematics and logic. In a very real sense of the word, it is hypostatic. Used throughout the centuries to describe the foundation of foundations, it seems appropriate to call this domain hypostatic. Although there is a fair amount of hocus-pocus around the word, in time, that can be demythologized as it is increasingly defined mathematically and logically.
Within this domain of information, the finite-infinite relation will be opened to examination in very new ways. Never-ending, never repeating numbers will be less irrational and more transcendental–and–transfinite as the infinite takes on the faces of continuity (creating order), symmetry (creating relations), and harmony (creating dynamics) while the simplest geometries of the imperfect give rise to the statistical-probabilistic-and-predictive, and to creativity, the creative will, and choice within the finite.
In time, we just may emerge with a hypostatic way of learning and knowing.
News / Research
• Open Letter to the editors of Science (magazine) of the American Association for the Advancement of Science
• Letters: Stephen Hawking, Clifford Pickover (IBM)…
• Simple View of the Universe
• Universe View: What is your expertise? There are many blanks within many cells — over 2000 of them in the entire chart — so, we assume it will always be “under construction.”
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