“To infinity and beyond!”
Navigation: All footnotes link to the Endnotes-Footnotes-References-Resources just below (on this page). All other links open another page within this website. This is a working draft and your comments are most welcomed.
1. Key question: Can everything, everywhere, be mathematically encapsulated for all time?
The answer is: “Almost.” If we start with the Planck base units, doubling each, then doubling each result again and again, within the 202nd doubling, you will be at the Age of the Universe and the size of our universe today. Please check the numbers for yourself. This is unique, perhaps a first, whereby simple math integrates the universe. And, that process logically and mathematically creates the foundations for a dynamic construction project,3 a model to begin to answer the question posited just above. Although quite inclusive, this construction does not address the concept of infinity. And, it does not address the results of experimental work whereby a mass and a charge smaller than the Planck Mass and Planck Charge have been measured. But, most importantly, within this construction, time-and-space are discrete-derivative-and-quantized. Because it removes the two key attributes of infinity — space and time — our understanding of infinity must be redefined and that work is in process.
2. Key question: Does Max Planck’s formula for time-and-length work within this construction?
According to Max Planck, light is equal to Planck Length divided by Planck Time.5 Throughout our model with its 202 base-2 notations applied from the Planck base units, Planck’s little formula results in a variable speed of light notation-by-notation, yet always within .01% of the laboratory-defined speed of light. Also, given the role light commands within Planck Mass and Planck Charge, the very nature of light inextricably binds these four units throughout every notation. This definition of space and time, combined with Einstein’s definition of mass and energy creates a natural inflation of highly-integrated relations; and, all notations would appear to be forever active and necessarily interdependent. More…
3. Key question: Do all these notations, taken together, define the Now?
Within this model, the only expression of our sense of time is the Now. Although this construction always places the Now at the very top of the scale with the current expansion of the universe, that notation is actively dependent on all the prior notations and infinity. In some special measure, Notation 0-to-1 and the 202nd’s Now are a Janus face or the same. That concept is very much in process.
Although the first-64 notations are below thresholds for measurement, all 64 are constantly generating their respective four numbers, each a doubling of one of the Planck base units.
Our challenge is first to study the dynamics within each notation and then to consider the logic flow from one notation to the next.
Because the first second, and every subsequent second, is within the 143rd notation, this construction is mostly about the emergence of the universe.
Today, the notation within which the Now is defined is 202nd.6 The 202nd notation is 10.9816 billion years (and the prior notation is 5.4908 billion years). Acting together, the 202nd notation begins in 10.9816 billionth year, and if the universe is 13.79 to 13.81 billion years, then somewhere between 2.81-and-2.83 billion years of the 202nd notation have imprinted on the universe.
In some manner of thinking, one of our challenges is to discern how the 1st notation and the 202nd notation are one. More…
4. Key Question: Does this progression of doublings define a natural inflation?
The natural inflation defined by this construction project approximates the numbers that are still evolving within the ΛCDM model of cosmology. This construction project also appears to mitigate the need for big bang cosmology.
These comparisons tell the story. 7 Even at the first notation, there is no null or singularity but a convergence of formulas and dimensionless constants that are the beginning of this new reality that is actively and tangibly dependent on light and infinity. Those first 64 notations would appear to be the space-and-time whereby a possible unified theory of mathematics could emerge and begin to grow dynamically. Here, we believe, is the container for dark energy and dark matter,8 string theory,9 Langlands programs,10 amplituhedrons, cellular automaton, binary ops, scalar fields, bifurcation theory, and so much more (see line 11 of the chart). Chart…
5. Key question: What is the first manifestation of these numbers within space and time?
In earlier articles, we had suggested that the first manifestations are spheres and we proposed to call them Planckspheres. Planck often uses the factor, 4πr2 in his equations; it defines the surface area of a sphere. Yet, he did not say that the first manifestation of space and time is a sphere.
We also believe these spheres constitute the very nature of dark matter and dark energy. Because it wasn’t until 2001 when Frank Wilczek brought Max Planck’s work alive (over 100 years after it was initiated), and because nobody has proposed that such spheres are the fundamental building blocks of the universe within 202 base-2 notations, we will. Today the inclination is to brand them as UniverseSpheres. Perhaps a better name will emerge.
Pi is a key within each definition of the four base units. Then, these spheres are readily transformed into lines, triangles, and tetrahedrons-and-octahedrons11 and our little universe can be tiled and tessellated by any combination of planes and objects. This is the heart of simplicity. This is the beginning of the universe and the beginning of space-time spheres. It is simple and ubiquitous. More…
6. Key question: How shall we re-envision infinity?
Consider infinity12 in terms of light and its implied mathematics. Perhaps time is derivative of light’s continuity and this is the basis of order, a facet of infinity. In this model space is derivative of another facet of light, symmetry; it becomes the basis of primary relations. And, perhaps space-and-time, as the Janus face of each other, can be envisioned as a kind of harmony and it becomes the basis of all dynamics.
It would be easy to allow the energies within the studies of multiverses to cloud our thinking about infinity. Purely mathematical and surely a precursor of applied mathematics, multiverses (also known as Infinite Universes, Bubble Universes, Parallel Universes, Alternate Universes, Daughter Universes and more) are imaginative, mostly mathematical, yet entirely speculative. Yet, here is Buzz Lightyear going beyond a simple understanding of infinity. The work of the multiverse scholars reminds me of the early metaphorical work of religious scholars and writers, yet multiverse people have more credibility primarily because of their mathematics. Although we have no interest in the strictly speculative, we would encourage these two groups to get together to release all of our imaginations from the more simplistic worldviews generally held by people today. Perhaps people like JK Rowling, the author of the Harry Potter series, could help them with the language and images! Her imagination certainly could help to texture the infinite! More…
Yet, our three textures of infinity — continuity, symmetry, and harmony –are quite enough for now. Each has also become part of our grid or matrix when taken together, give rise to values and ethics. This redefinition of infinity gives us possible starting parameters. More…
7. Key Question: How do we re-envision time symmetry with the past and the future?
Many scientists, like Einstein, consider our sense of the past and the future to be an illusion. That’s disrespectful. It seems that our sense of time is more like the five standard senses. We know when we see, hear, touch, smell and taste. It is an activity of the brain related to particular stimuli.
We also know how exquisitely limited our human senses are.
Also, in light of the 13.8 billion years of the universe, we believe these senses have only come to be most recently. If the universe is always a composite constantly being imprinted by the evolution of our ever-expanding universe of things, interacting and reacting within that unfolding, only the very smallest part of that imprinting involves sentient beings. The human part of that imprinting is within an even more recent part (at most 400,000 years), all within a small part of the 202nd notation. Among all sentient activities, there is an emerging group who are also integrative beings, who knowingly and unknowingly, reach across several concurrent notations, integrating substantial skills and data sets.
Consciousness, then this level of consciousness, is a most recent phenomena. And, then the sciences that have emerged from within this level of consciousness is just a speck in light of the Age of the Universe.
Within computer programming we would say that data from different notations might be compiled and recompiled to be integrated within the whole. The emergence of this kind of activity would appear to be most recent, all within about 3000 years.
These are new thoughts for this website.
At the end of the year, 2016-to-2017, in a “Top Ten” listing, we entered this space of thinking — that we get our definition from multiple notations — for the first time. These paragraphs and this article attempts to extend that thinking. More to come…
Neil Turok’s group (Perimeter Institute) helped us with the idea that as a people we are active within multiple notations. In an article in June 2017 Turok said that the universe acts like it is constantly starting. That would be Notation #0, at the finite-infinite transformation, whereby spheres are constantly created. Though a concept that seems beyond the realms of possibility, we ask that you open your imaginations to this construct.
8. Key Question. What does consciousness (and sleep) have to do with the 202 notations?
Although the past and the future are profoundly part of our self perception, we are wrestling with concepts whereby consciousness is activated within the specific notations, speculated today to be 51-to-60, and that sleep is understood to act like a recompiler synching our particular conscious moments within these universal systems.
One conclusion: What we think, say and do affects the quality of the universe.
More to come: Is sleep essentially re-synching our waking span to universal time and adding a net-positive or net-negative imprint on the universe? See #6 and the basis for values and ethics.
More editing will be done on this article…
Endnotes, Footnotes, References and Resources:
2Dr. Pat Gary: “It’s a little like Buzz Lightyear.” Friends help us to see things differently. Here, a dear friend, Dr. Gary introduced me to the Disney-Pixar animation of Buzz Lightyear as a metaphor for how infinity informs value. Then a little later, Dr. Gary re-opened that discussion by engaging JK Rowling’s points of view. Do we participate within the infinite? Can one get beyond our limited understanding of infinity? These are open questions.
6 The Now: Past, present, and future all meld together for the entire universe. There is only one time for this universe and it is called, The Now. We all share this instant of the expanding universe.
7 ΛCDM Epochs Compared to our Horizontally-Scrolled Chart: There are three comparisons to consider: (1) A notation-by-notation comparison with the epochs of the big bang. (2) A comparison between the epochs of the ΛCDM model with the processes that define our Quiet Expansion. (3) A consideration of line 11 within the horizontally-scrolled chart. Most of the intellectual pursuits found on line 11 are prior to the 67th notation and none have ever been part of a grid or matrix. Consciousness is hypothesized to be within those notations currently defined as Systems, Notations 51 to 60.
8Dark energy and dark matter: Since around the year 1920, scientists have attempted to define these two illusive, yet measurable entities. Within the context of the first 64 notations which are beyond any possible direct measurement, this mystery can be seen in a new light.
10Langlands programs Initiated by Robert Langlands of the Institute for Advanced Studies in Princeton, New Jersey, his construction project now involves many scholars working to develop the first unified theory of mathematics. Currently this work does not start simply; it requires a thorough grounding in mathematics to begin to engage it.
11 Spheres and Emergence. Sphere-stacking within cubic-close packing (CCP) opens this conceptual area for study. It is simple, logical, and mathematical; and, it is an active area of study within crystallography and the material sciences. Going from spheres to lines, triangles, and tetrahedrons-and-octahedrons is the key and the dynamic image linked on this page demonstrates it well.
The past and the future are profoundly part of our self perception, so we are wrestling with concepts whereby both are delimited as a special form of space-time that occurs between sleep events such that sleep is understood to act like a recompiler synching us within universal systems.
Which concept is strongest? Which is weakest?
Key documents that were recently homepages:
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An excellent resource to translate any of our pages by its URL:
Afterthoughts and ruminations:
Change does not come easy for most of us. We adopt a view of the world that works with our image of ourself, and that’s that “…and I’m sticking to it. It’s just commonsense.” A key part of that commonsense worldview is called “absolute space and time.”
Though part of the intellectual debates going back 3000 years and more, our particular brand of it comes from Sir Isaac Newton, a point of view formalized in his 1687 book, generally known as The Principia.
If you look up into the heavens on a clear, crisp evening, it looks like it goes on forever. That’s Newton. Another person might say, “It goes just as far as the current expansion of the universe.” To which one of the kids quickly asks, “Well, what’s behind that?” To which I would reply, “Infinity.” And, of course, that begs the question, “What’s infinity?”
Infinity is not an easy concept to grasp. As a recent college graduate in 1969, I remember asking myself, “How can we take religion out of infinity and make it more accessible to everyone?” The efforts by scholars has become a formal discipline called renormalization. And like so much of scholarship, it is not easy for regular people to understand. Even scholars have problems with it. Freeman Dyson worked on it back in 1949 and Steven Weinberg reformalized it in 1986. Infinity is such a character, it needs to be corralled so the work of mathematicians and physicists can go on. Of course, it can’t be corralled, but it can appear to be tamed enough to carry on one’s work without getting bitten too badly.
Physicists developed a means to avoid engaging the concept of infinity, then they made that work an art form, and then a fine science unto itself. Initially called renormalization, the process began in earnest… (Wilson history)
On Planck’s quote: https://quoteinvestigator.com/2017/09/25/progress/
Living With Infinities, Steven Weinberg: https://arxiv.org/pdf/0903.0568.pdf
The Net Advance of Physics:
Baez: “…assume you vaguely know what a Lagrangian for a quantum field theory looks like.”
Feynman, QED: Strange Theory of Matter and Light: https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter
A Quantum Pioneer Unlocks Matter’s Hidden Secrets by Elizabeth Gibney (Nature, Sept. 2017): “What if each quantum critical point is just the beginning of another generation? …probing the boundaries around those states could reveal more phases, and studying the boundaries of those could reveal yet more, with discoveries unfolding in a fractal manner.” https://en.wikipedia.org/wiki/Gilbert_George_Lonzarich
On the Revolutions of the Internal Spheres: A New Theory of Matter and the Transmission of Light, K. Troy.