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My hope for you this day
by Bruce E. Camber
My hope for you this day is that you will begin to engage an integrated, mathematical view of the universe. It is a little thought experiment that starts with our first posting in 2011 while in a New Orleans high school. And, yes, it is a bit naive.
We start with Max Planck’s base units and assume those numbers define the first moment of time. We’ve been told that a smaller unit of time cannot be logically calculated. Then, doesn’t it follow, again using simple logic, the smallest unit of time is necessarily the first unit of time?
The appropriateness of that assumption is further discussed.
We then mapped the universe in 202 base-2 notations. Of course, the last notation, 202, includes the current time. The notation is 10.9+ billion years in duration. As you can imagine, from Planck Time to the first second takes us from Notation-0 to Notation-143. The first light year is within Notation-169. Essentially base-2 exponential notation gives us a mathematical model of the universe. The numbers are here: https://81018.com/chart/
Do you think it is possible that this universe is first and foremost an exponential universe?
If we take this construction as a thought experiment and assume it to be so, what might the first manifestation of space-time be? We were thinking about the role of pi in all of these constructions because an old professor friend from Brown University in Providence Rhode Island (USA) argued with me and said that the most simple construction in the universe (and necessarily the beginning point) is the sphere with its two vertices. It is simple and it is ubiquitous and it is historic and it is well-understood by many but not profoundly understood by any.
For us it had to be the first expression of spacetime. I wonder, “Is that a logical construct?“
For us, deep within the sphere, we discover continuity, symmetry, and harmony. Those three qualities exist in our minds; they each define pi and every circle and sphere. These qualities are not finite, so might we attribute them to infinity and open a finite-infinite relation so there is some causal efficacy for the numbers of spheres being generated per second if we follow the logic of Planck’s base units and one sphere per unit of Planck Time.
I know we are stretching logic and this construct, but where else can we go? Is our logic faulty?
When we consider the current measurements for particles, waves, and quantum fluctuations, we end up in the area of Notation-65 to Notation-67. How should we think about Notation-0 to Notation-64? I believe it holds great promise for understanding dark energy and dark matter, for grasping the basis for homogeneity and isotropy, and for deeming a natural inflation within our universe.
I hope this little thought experiment has been worth your time to consider. Our most current work to further define the very nature of a singularity, a blackhole, and a theory of everything is part of our little struggle to attempt to define an interface between the finite and infinite. It seems that now is the time!
Thank you for your time.
PS. Within this morning’s reading (August 5, 2021), I discovered a sweet, little article by a psychiatrist, Robert A. Faquet, of Santa Monica. Titled Finitude and Unboundedness, Constancy and Incommensurability, he opens with a question from Einstein, “How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?“
His title and that quote caught me. Then, Faquet caught me again with this statement: “There exists an intrinsic similarity between the human imagination (mind) and mathematical reality (body).” Faquet held my attention with a quote from Spinoza that I did not recognize: “…measure, time and number are nothing but modes of thought or rather imagination. Time and space are modes by which we think and not conditions in which we live.”
I asked myself, “Who is this guy?” when he unloads another quote; Faquet says that Jung asserted that “…mathematical reality, while certainly adhering to outer objects, is indisputably a reflection of our own mental structure.”
Then he stops me cold with this statement, “I should like to discuss the correspondence between mind and body by comparing the structures of inner space and the mathematical constant pi. In earlier work (of Jung) he had conceptualized the mind as a sphere. Inner space could be seen at once as finite (left hemisphere) and unbounded (right hemisphere). This structure permitted shifts, for example, from figure (finite) to background (unbounded), object to subject, particle to field, and thinker (I) to object (Self).” Faquet continues, “…the mathematical construct pi reveals that it is both a constant (finite) – reflecting the unchanging relation between two elements (the circumference and diameter of a circle) – and an incommensurable (unbounded) – an expression of an endless succession of digits for which there is no law predicting sequence.”
I wanted to know what else Faquet had written and who else would be among his references like his references to Kasner and Newman, Mathematics and the Imagination. Three cheers, Robert Faquet, MD! -Bruce