Purpose of this group. To develop a special graciousness and openness about life and beliefs, this group is for the people who want to get along with believers and non-believers. Can we find a deeper truth that holds up some new insights that will embrace both sides of an equation by focusing on the nature of the relation. We’ll engage the edges of scientific research and its implications for our current theories about the universe and its origins, and about who we are and the meaning and value of life.
Overview: One of the best sources for a study of the relation between the finite and infinite are the sacred texts within our religious traditions. Many of us who grew up in the Christian tradition and like typical college students, we tend to reject the old to begin to self-actualize. Then we begin studying at the limits and boundaries of our knowledge and the challenges can become so daunting, they get left in those undergraduate and graduate classrooms. Personally I went out as far as I could on the edges of physics, working with Bob Cohen, then chairman of Boston University’s physics department, and then with physicists from around the world. I began discovering there are conceptual overlaps between all the departments within the university. The most extreme appeared to be those who were religious and those who demonized all religions.
What can be more different that the texts within The Bible, both Old Testament and the New Testament, and most texts within the scientific community, that is between Genesis 1 and John 1 and Stephen Hawking’s big bang theory. These sessions are designed to examine concepts within the sciences, philosophy, ethics, and mathematics to see how and where these overlap with concepts about eternity, infinity, light, and love. We start with an integrated view of the universe, and that begins to inform our understanding of the infinite and infinity.
Structure: This small group will have just nine gatherings, no longer than 90 minutes each. A goal for these sessions is to chart a way to empower people to create such a small group study. • The first two sessions. We will re-examine cosmological models of the universe (2 weeks). • The 3rd and 4th sessions: We will explore various ways of approaching an understanding of the finite-infinite relation. • The 5th and 6th sessions: We will explore a rather different understanding of light, a light that permeates and defines every notation and all of space and time. • The 7th and 8th sessions. We will explore the challenges to our understanding of basic concepts like space and time. Both become finite and transaction oriented. • The final session: Beyond the summaries, we will be searching for answers to the question, “What do we do now?”
Simple and small goals: The first goal is to open the door to a very simple orientation to science and faith that (1) works with science and mathematics and (2) allows for, and possibly informs, religious beliefs. The next goal is to explore the entry points between the finite and infinite. Another goal is to explore the physics, philosophy, and psychology of light. If we have even limited success, we’ll all begin to shrink space and time and open up an intimacy with the universe.
Précis: Whenever we look up into a clear night sky, often someone will say, “It goes on forever.” As children we learned to accept the infinitude of space and time. It is deeply ingrained within our thought structures. The problem is that this perception, in light of the base-2 exponentiation from the Planck units to the age and size of the universe, is probably not quite right.
History. Alchemist Isaac Newton was an experimenter and he made mistakes. He used trial and error. When he described space and time, I believe he was off the mark. Though a genius, he was overly sure of himself and was often arrogant and condescending. Perhaps his penultimate contribution to our universe of knowledge is his sense of space-time and the infinite. These lasting imprints, however, were only partially right.
Infinity: Newton was confused about the nature of infinity. And, his confusion became our confusion; and, it has become the world’s confusion. Infinity to this day remains a problem for many in the academic community because it is too often interlaced with theological and religious language. The God wars between the arrogant among religious thinkers have caused many intellectuals to avoid religious language. A possible resolution to that conundrum is to use those terms that describe the universals and constants that originate in mathematics and science. Those terms should capture facets, a certain essence, that is part of both the finite and the infinite.
Three Faces of Infinity. Though most of these studies on this website are of the finite, the infinite has a substantial, abiding and fundamental role. The infinite describes a never-ending, never-repeating perfection or completeness or a wholeness that is not fundamentally part of the finite. Within these studies the infinite is defined as continuity, that which creates order, sequences, and the nature of time. The infinite is symmetry, that which creates the foundations of relations, of balance and of the nature of space. And, the infinite is defined as harmony, that which creates dynamics, and creates a space-time moment. The use of religious or theological language and concepts is left to each reader. .
These three simple postulations about form-and-function assume a panoply of necessary-and-abiding transformations. When we look into the clear night sky, we “see” only as far as today’s transformations within this expanding universe. .
Set within the 202 base-2 notations from the Planck base units to this current moment, the Now, it challenges us to see how the entire universe is bound together within what is initially a most-simple mathematical and geometrical system that profoundly redefines space-and-time and our relation to the universe. In 2011 the first name of the project was “Big Board – little universe.” Those 202 steps, all active, make for a rather intimate place.
Our conclusion: “We live in a highly-integrated, exponential universe.” .
The continuity-symmetry-harmony concepts were first written down in 1970-72 to define the three faces of a perfected state in space-and-time. Each seemed to hold plausible answers to deeper questions about life and to such practical things as superconductors, quantum fluctuations, heartbeats, sleep, consciousness, reproduction… but the articulation of those facets of the transformations was too weak and generalized. There was no systemic application or coherence until it was discovered that our entire universe is contained within those 202 base-2 notations. So profoundly and deeply integrated, this chart gave us our first introduction to the first 67 notations that provide the footings to explain the homogeneity and isotropy of the universe. Here was the story of the Chessboard and Wheat all over again. There is so much space-and-time, every strain of mathematics will have its place within these first notations. There is enough room for consciousness, ethics, psychology and all other disciplines that have never had a place on a scientific grid.
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• Multiply by 2. Start with the smallest units of measurement, the Planck Time and Planck Length, multiply each by 2, then the result by 2, and continue right up to the largest possible measurements, the Age of the Universe and the Observable Universe. Though both are still constantly expanding, your result will quickly be a totally, mathematically-integrated model of the universe that includes everything, everywhere, for all time in just 202 notations.
Just one more time: Most scientists and scholars now believe that Planck Length and Planck Time are the very smallest possible measurements. If you double them, then double them over and over again, in just 202 doublings, you will have reached the size of our Universe and you will have gone from the beginning of time to this present moment in time. It sounds impossible, but the math is the math.
• Rather special. Though simple logic, simple math, it’s still just a model. As a challenge, take this model as a given, to explore in what ways it could be an outline for the initial structures of the universe. Also, if simple logic and math do not work from the Planck Scale to the CERN scale to the Large Scale Universe, then logic and math should not work anywhere. Continuity is continuity. Order is order.
Eventually we added Planck Charge and Planck Mass to our doublings and continued to study how the numbers and the inherent logic worked together. We have been exploring this model since December 2011 and have discovered that it seems quite sustainable! No scientists or scholars have seriously challenged it. Of course, it is idiosyncratic and it does raise rather unusual questions. Notwithstanding, the universe within just 202 doublings (clusters, containers, domains, layers, notations, sets and/or steps), so far, actually does seem to cohere 1(Footnotes/endnotes at bottom).
• Sweet. By the 31st notation, Planck Mass has increased to 103 pounds. That may be an ideal weight for some, yet in this notation, space and time are still so small that science has always considered these values meaningless. We do not. Though an entirely novel concept, we take it as a given that there was a time when the universe was just 103 pounds. Though necessarily defined by point free vertices, it already has more active ratios than our imaginations can grasp (1.23794×1027). It exceeded one million vertices by the eighth notation, one billion at the 11th, and one trillion at the 15th, and a quintillion vertices at the 17th notation. To follow that quiet expansion, look at line 9 in the chart below.More…
• In this model each notation is more than just a simple doubling.The next notation doubles in size and doubles in contentand each notation it would appear is currently defining our universe. As we live with the model, grasping the first notation as the start of the universe and the current notation as our current moment in time, all the notations come alive as a process that gradually builds upon itself, every notation changing and growing because of the others. To think about this very different sense of space-time, I did a sampling of six of the notations somewhat evenly spaced across the 202 notations. Of course, these Planck scale doublings are all predictive numbers. Within these six notations that were sampled, each demonstrates a natural inflation that is a quiet expansion. A sampling…Prime numbers...2
• Being natural is good. If one were to wonder about the basis for bifurcation theory, chemical bonding, cellular development, and isotropy-and-homogeneity, we may have found a new opening to explore. Then, if one were ask about the source of this thrust, again I think we may have found another good opening to explore.
• Sweet. (1) The quiet expansion continues its doublings until finally at the 67th the folks at the CERN labs (Geneva) are able to pick up something and our core sciences start to evolve. (2) Truly sweet is that this natural inflation approximates all the cosmological epochs that were defined by big bang theorists; however, in this model there is no bang. (3) The 67 notations provides more than enough “room” for every possible system of mathematics to be applied. Remember the 64 doublings within the Checkerboard story! More…And more...
• That is very special. Light, Time and Length are being redefined by each other and by Charge and Mass.3
Please take note that between the 143rd and 144th notation, the universe is finally one second old and Planck Length has grown to the size defined by the distance that light travels within that second.
It is simple math and simple logic yet it re-engages us to expand and begin to understand a rather extended spectrum of light, of course, well beyond the visible spectrum and well beyond where it has been defined to date.
This work has given new meaning to an old song (1977), “You light up my life.” The very final refrain goes something like this: “It can’t be wrong when it feels so right…” More…
• Sweet. Here is the first time light, defined by another very simple mathematical formula, can be found within a simple mathematical progression. The formula from Planck predates Einstein’s! More…
• The Gnarls and Knots of Space-and-Time. Definitively cast in stone in 1686 when Newton released his blockbuster, Principia, time-and-space took on an absolute frame of reference and this view became our commonsense worldview. It became a realism (and naturalism) whereby our external reality is assumed to exist as it is given and experienced. Both concepts — space-and-time — have been problematic and now some really smart scholars want to throw them both out; we believe it would be better to redefine them in light of our model with its 202 notations. Here, the universe begins within the Planck Scale. Our challenge is to figure out how the universe evolved within those initial notations, and then how it continued to the 202nd notation and to this very second within our expanding universe.
• It is a very special and rather non-intuitive challenge. There are so many people today who still affirm Newton. They unwittingly do so when one of them looks up into the clear, night skies, observing the panoply of stars, and says, “It goes on forever.” Those wrestling with this new model would say, “We are looking out at our expanding universe. It is still expanding within the 202nd doublings and has been for about 13.82 billion years.” What happens is that no notation goes away and recedes into a past. Instead, each notation participates in the current definition of the universe and space-and-time, as the fabric of the universe, absorbs every imprint for all time-and-space.
Let’s turn on the clock. There are about 31,556,952 seconds per year so at some time we will be adding at least four years of seconds, somewhere over 126 million additional seconds, to bring the total to the current time. A hundred years is just 3.1556 billion seconds. Extend that to 1000 years (31.556 billion seconds), a million years (31.556 trillion seconds), and a billion years (31.556 quadrillon seconds). Our earth and solar system are approximately 4.5 to 4.6 billion years old. The estimates for the Milky Way galaxy are about 13.7 billion years (yes, among the original galaxies formed). Yet, none of it is old; it is all current. All the cosmological epochs are now understood to be ongoing processes of the universe. More…
• Science and mathematics have made great use the concept of the infinite; philosophers and theologians have as well. Yet, over the years we have seen how these disciplines tend not to work very well together, especially those elitists among them, particularly among those religionists and theologians who too frequently don’t work well with anybody except their own.
• We suggest a shakedown. First, let us shake out all the concepts that have anything to do with faith statements — these are too often argumentative, emotional, and sometimes even hostile. Within the quiet expansion model, there are several conceptual assumptions that begin to bind the finite and infinite in special-and-heretofore unexplored ways. These concepts include: continuity-order, symmetry-relations, and harmony-dynamics. Though an unusual combinations of words, some element of each can be readily understood.
• We can do this. The word combinations may be a little gray, but we’ve all used each word at one time or another. Taken together and in this sequence, these words become very rare concepts because each reflects a face of the finite (our beingness, whether it is science, mathematics, psychology, philosophy or religion) and also a face of the infinite. More…Foundations…Ethics-and-values…
• Numbers. Perfect, unshakeable continuity occurs within numbers that are called incommensurables, transcendentals and the irrational. These numbers are never-ending and never-repeating. Our old friend, yes, a very dear friend of every circle and sphere, is Pi. Its very close cousin is e, for Euler’s number. Euler’s equation also defines the universe. It is the heart of our exponential universe. Also, meet Pi once again.
• Through our Looking Glass. Most looking glasses are mirrors. This looking glass can also be a magnifying glass. Isn’t it unusual that a number can seemingly go on forever without repeating itself and with no special pattern or repetition? Doesn’t that define a certain kind of uniqueness? …diversity? Within this class of numbers there is a group that is also known as dimensionless constants. There are quite a lot of them. Yet, in all the discussions about the many scholarly blogs, papers, articles and books, there does not appear to be any discussion about how these numbers must define some aspect of infinity. Isn’t that an oversight? If we take it as a given within our new definition of infinity, this very special kind of continuity and order can also be understood as uniqueness and diversity. That’s rather special.
Now of all the scholars I know, perhaps Clifford Pickover or John Barrow have started a process of looking at infinity in this simpler way; we’ll be digging further into their scholarship. More…
But, for now, let’s see if we can take it one step further. Let us take as a given that these rather unique numbers (1) originate within the infinite, (2) tell us about the nature of the infinite, and (3) define the transformation between the finite and infinite.
• Pi leads the way. Leading the way out of the infinite is pi. Perfect equal circles, then spheres, then multiple spheres, then stacks of equal and doubled spheres. We are probably within the first ten notations or doublings. And then, a radius discovers a radius and the first line is created. Then the radii begin discovering radii and lines and dimensionless, point free, vertices are created. Vertices discover vertices and the first triangles are created. Triangles discover triangles and the first tetrahedron is created. Lines, vertices and triangles discover each other and then the first octahedron is created within the tetrahedron. And, quickly, hexagonal plates are discovered. Triangular plates are discovered. And diversity begins to move into high gear in a perfectly simple, yet increasingly complex manner. Symmetries abound. Perfection is in the air. But the imperfect and asymmetrical are not far behind. More…
• Dynamics. Euler’s number is somehow holding pi’s hand! The two are working those continuity and symmetry relations and are making a universe one step at a time. More…
• That is a very special challenge. All shapes and forms and sizes and every manner of symmetry relations are being created. The pulse of energy known as Planck Charge creates a thrust, an energy, a direction, a motion, and soon our little universe is pulsing with activity. More…
First, called the Planck Scale, it transmogrifies into what some call a Grand Unification. Here is the first doubling. But for all intents and purposes, it is within a self-discovery mode. Yet, rather quickly (understatement), that self-discovery process organizes and begins what we call the Inflationary Processes right up to and including the 67th notation. Now declared to be the Electroweak Processes, Planck Charge is huge. Planck Mass is huge. Planck Length has become manageable. Planck Time is still too small to be considered anything other than a placeholder. More…
• Sweet. The rest of the cosmological epochs seem to follow rather naturally in line with the continued expansions (doublings and notations) of these Planck base units. Even Planck Temperature, which was placed at the top of the scale because everything begins simply, is now substantial enough to warm things up and to begin looking like our little universe. More…And more…
• The first 60 or so notations will never be observed by our machines. These domains are much too small to be picked up by our measuring devices. If there can be no validation by our machines, then we must rely on logic and mathematics. This special domain has a very special word to describe it; it’s call hypostatic. We actually create a real reality when shared by another. It is a really real reality when shared by many. As more people adopt that structure, we press meaning and purpose into it. Then we ask, “Is this helpful? Does it seem to describe a real reality for people within our time?”
• Yes, this is very special challenge for all of us. Because everything, everywhere, for all time must be logically included on this grid — nothing is exempt — we will hypostatize a place for philosophy, psychology, mathematics, quantum fluctuations, the cosmological constant, religions, the mind, consciousness, sleep, and qualities. More…
• So we have a bit of work to do. And, we recognize that this work just started in December 2011 and it is still quite naive and young. The initial goal was to give our high school students a very special chart to integrate Science, Technology, Engineering and Mathematics (also known as a STEM tool). Today this project is known as the Big Board -little universe.
That was cool. But now, the real work begins. We know we are onto something and have opened a door that is worth exploring. We’ve begun to study some of the older problems within science with such names as inertial frame of reference, point processes, scalar fields and scalar field theory, and path integral formulation. Many of those subjects are listed on line 11 of our horizontally-scrolled chart.
We struggle with it all most everyday so your advice, insight, and help are most welcomed! Thank you.
PS. There may be more footnotes inserted in the forthcoming days. If you are observing changes in the post, it is because this post is edited every day. It will change, and undoubtedly grow a little longer.
Friends from New Orleans came for a visit. Their two images have been in my mind’s eye as I worked on this page. I have been constantly asking myself, “Is there a way to write this up so they understand it?” -BEC
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Our most simple assumptions and insights for an alternative theory:
The relation between the Finite and the Infinite is rather hotly debated, mostly between people who equate the infinite with God and those who have no place for any kind of god. Yet, the infinite also creates conundrums within science. In 2014, MIT physicist, Max Tegmark advocated, “I’m betting that we also need to let go of it.” He wants to retire what he and others call an incorrect assumption – infinity. His friend, Stephen Hawking, opened that door with his 1983 No Boundary Proposal that holds that the universe has no beginning or end.1
“Not so fast y’all” as it is said along the banks of the Mississippi River in New Orleans. With these two thought leaders, Hawking and Tegmark, it should be acknowledged that both are being speculative and that their concepts are brilliantly incomplete.
In the Big Board-little universe model using base-2 notation from the Planck Time to the Age of the universe, the entire physical universe is contained within just over 200 notations that are highly-integrated and totally-predictive. Notations are also known as clusters, doublings, groups, sets or steps. Within the first second of the universe, there is more than enough “natural inflation” from the Planck Charge to get “things” going. As a result of studying and working with this model since December 2011, there are many-many facets to explore, however one of the most important is that this model logically suggests that time is derivative and that the finite and the infinite are perhaps best understood in terms of continuity, symmetry and harmony.
Continuity. Though an unusual way to define infinity, even with quantum indeterminacy, continuity throughout the universe is the bedrock of science, logic, and rational thought. Numbers clarify this continuity. If we were to carry our measurements out a billion places, the universe and its systems around us would still replicate day after day with utmost precision.
Within this model, continuity is more fundamental than time; it begets time. It is the initial condition of order. More…
Symmetry. The second face of the infinite is symmetry. Though so much of life is asymmetrical, the deepest examination of any physical thing begins to reveal deeper symmetries. Numbered relations define those symmetries, relations are created, and the universe appears to be tiled and tessellated deeply within every notation throughout the model. Here symmetry is more fundamental than space; it begets space. More…
Harmony. Speculating, it is hypostatized that two symmetries begin interacting within a notation and then across notations, dynamics are created, and though not quite perfect, the interaction of the symmetries perfects the moment for the observer or for the notations involved. Therefore, we have moments of perfection within our experiences of the universe.2 More…
Our studies. At this point in our studies, there is not much more we can say about how the infinite defines the model and what the model says about the very nature of the infinite. These three insights, although reflective of the model, in part come out of a study of a moment of perfection in 1972,3 then from studies of the book, Finite and Infinite: A Philosophical Essay (Austin Farrer, Oxford, Dacre Press, Westminster, 1943), and from an application to a business model.4 More…
These three qualities became the bedrock for our model of the universe and for discussions about the shared nature of the finite and infinite.
What difference does it make? First, it is a clear contrast to the nihilism of big bang cosmology. Building in strength and popularity over the past 30 years, that nihilism has had a lot to do the fraying of our little world. So much is out of control and spinning apart. Money is not the issue. What we believe and how we believe is. Hope is. Charity is. Integrity is.
The finite and infinite relation has been the focus of humanity for as long as we have been recording our ever-so-short history. In light of 13.8+ billion years, five thousand years of records is, of course, quite short. We’ve just begun to make sense of it all.
Today in history. The finite is usually associated with physical, limited things. The infinite is often capitalized and associated with godly things, the eternal and everlasting. To our knowledge, Max Tegmark is the first theoretical physicist who has suggested that the concept of the infinite be abandoned. His rationale is that it gets in the way. He cannot make it work for the science he wants to create. Within these many articles, we hope to convince him, Hawking, Guth and so many others to re-engage our simple definition of the infinite. It does not require a religion or religious beliefs. Notwithstanding, it also does not necessarily fly in the face of those who believe in a much more robustly-defined Infinite.
We can all begin to tolerate each other.
This is our simple introduction to a very large topic and we will return to this page often to expand its range and its depth.