Introduction. Commonsense tells us that subjects and objects exist independently. You are you; and, everybody and everything is apart from you. Things are things. That view was substantiated by Isaac Newton in 1687 within his book, the Principia.^{1} Not without controversy, lively arguments ensued and many persist to this day.^{2} The alternative view that emerged in that period is now labeled relationalism.^{3} The work of this website opens twelve key insights,^{4} all reasons that suggest that relationalism is a better formulation of the foundations of reality than Newton’s absolute space and time.
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We all know that there is something seriously off within our current scholarship. Today’s turmoil tells us that we need new definitions of who we are and why.
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Most scientists agree that the universe is 13.81-to-14.1 billion years old.^{5} It has a starting point. Yet, it also has an endpoint. Though it is constantly expanding, that endpoint is today, right now, the current time, or the Now. This is a new definition of time and it cannot be found within your grandfather’s old pocket watch. It is the fullness of time, or the totality of time; yet, it is always finite and quantized. It has a beginning and an end and it is derivative of light and space.
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Newton’s absolute space-and-time redefined infinity; absolute space and time was scientific and neutral. It didn’t take too long before that apparent neutrality became more acceptable than all other definition of infinity. Though less controversial, it gave things a special status of objectivity. Rather quickly that sense of things was widely adopted and became our scientific laboratory and then our commonsense worldview.
Questions: Have the old absolutes been obfuscating greater truths? How does the universe act if space and time are discrete, derivative and quantized manifestations of light? Can light define space and time and also help to define the infinite? Can there be a certain universal substance and texture within the infinite so we do not have to work around infinity and absolute space and time in order to get our physics (and other intellectual pursuits) to work?
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Background: First things first. While visiting with friends around the country, I provide updates about this work and explain the gist of my recent communications ^{7} with key thinkers about our most-simple, mathematical model of the universe. It appears to be too simple for most scholars. It is easy to brush it aside especially if those key conceptual transitions had not been engaged. So, as a result, this construction has not yet been rigorously analyzed by our academic community. Eventually it will be. This model is too important for these primary reasons:
• It is highly-integrated, totally-mathematical, 100% predictive and tracks a natural
Basic constructs. Often “new concepts” begin as an over-simplification of complex ideas and do not become a working platform for an integrative model. Our two Standard Models, one for particle physics and the other for cosmology, are proof of that statement. Our model begins with four of the most-basic units in science today and applies the simplest geometries, mathematics, and logic. Our goal is to build an extensible platform^{11} to add increasingly complex mathematical and geometric constructs eventually to begin to absorb both Standard Models. Though quite naive, until we are otherwise advised, it is among our goals on this road less traveled.
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There are leading thinkers and scholars in every discipline and within every flavor of every discipline. All of them are trying to get the attention of the others. As a result, it is difficult to get anyone’s attention. Very few constructs necessitate redefining space, time and infinity. This one does. That alone is worth the time to engage this material no matter what one’s discipline.
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Mathematics is the mathematics; and, logic is logic.^{12} Plus, this model is not without some precedent within popular culture.
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The First Mathematical Model and Scale of the Known Universe. In 1957, a Dutch schoolmaster, Kees Boeke wrote Cosmic View: The Universe in 40 Jumps.^{13} He was the very first to provide a base-10 scale of the universe that average people could readily grasp. His chart of his known universe measured progressions using just 40 images. He goes from the human scale out to the edges of the Milky Way and then he goes from the human scale down in size to the nucleus of a sodium atom. Forty years later, IMAX brought his book alive as a movie that dynamically moved from the smallest to the largest-known measurements by multiplying or dividing by 10. Today, most schoolchildren with access to the web are familiar with this perspective of the universe.
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The Starting Points: Discerning Planck’s Base Units, then the Smallest-Possible Measurements. The smallest and the largest generally-accepted measurements are still being studied and scrutinized. In 1899, Max Planck used universal constants to calculate his four base units. Although these numbers were generally ignored for 100 years, an MIT professor, Frank Wilczek, turned on the lights.^{14} His three articles in 2001, Scaling Mt. Planck, in Physics Today introduced Planck’s four base units to the world. For us these four derivative numbers became the foundations of our entire model, the possible start of our universe.
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That is a bold statement and it requires further study and debate. But again, logic is logic.
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We take Planck’s base units and apply what is known as base-2 notation. It just means that we double those original figures. Then we continue doubling each result until we reach a top limit. Multiplying by 2 or “doublings” is the most meaningful way to expand these numbers to render a scale universe.
We’ve all got to learn more about this mechanism. Today, it is still primarily associated with stacking cannonballs. It is rather ironic that an old, rather-obscure, mathematical problem, one that Kepler addressed, could hold one of the keys to unlock the secrets of our universe. Most speculatively, this mathematics may well open a passageway, perhaps a wormhole, to discover that we live in a very small universe^{16} after all. It is not unfathomably large after all.
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Ever-Expanding, Ever-Aging: The Largest Measurements. The numbers at top of the scale are ever-changing. These four base units continue to become larger with every moment, so the current best estimate of the Age of the Universe is a key; and, by most accounts, it is quite accurate. That number gives us a size of the container with which to work at this moment. By definition, we know it is the largest, most-meaningful measurement of our universe right now.
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If Kees Boeke had used both of these parameters — seconds and meters — to determine his jumps, he would have expanded that base-10 model by another twenty to 21 jumps. If one applies base-2, doubling each (essentially multiplying by 2 just like we did in the second and third grades), that more granular scale renders 202 notations (a key conceptual transition).
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Since December 2011, this chart with its 202 doublings or notations has been the subject of our study. Yet, in seven years, we have barely scratched the surface. Eventually we recognized that what we backed into the work to create some kind of unified theory of mathematics ^{17}. In this model it would grow in complexity, notation by notation, whereby we must now discern and learn about the causality from one notation to the next.
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Encapsulate the universe, everything, everywhere, for all time: Sounds ridiculous, but that is exactly what is happening here.
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Consider the logic: If nothing is smaller, and this seed structure exponentially increases in size, how can there be anything else? As it expands, it creates the conditions for everything else to emerge. One notation at a time, each notation doing its required function, building on each other, always, constantly. The first to publish such a concept was Prof. Dr. Neil Turok, director of the Perimeter Institute (Waterloo, Ontario). He was once a colleague and co-author with Stephen Hawking. Turok says our first notation, the first instant of creation, is never ending.^{18} So, if you will, please accept for the moment that there is such a small unit of time where the conditions for exponential growth are created and that smallest unit of time is Planck Time.
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Does simple logic tell us that the smallest unit of time would also be the first moment in time?
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Just so you can see and become familiar with the look and feel of these Planck base units, I will insert the actual formulas and the results. Eventually… it could take several years, my hope is that you’ll start recognizing these numbers and eventually each fourmula and that each becomes like an old friend.
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We should start with Planck Time. It is incredibly small, a very exacting number written using notation as 5.39116(13)×10^{-44} seconds. The more classic way to write that number is:
.0000000000000000000000000000000000000000000539116 seconds. As the first notation, it is also the first instance of the universe and a current instance defined by Planck Time.
• Between notation 143 and 144 the universe is processing one second.
• Between notation 169 and 170 it is constantly processing everything that is one-year old.
• Between notation 197 and 198 it is processing everything that takes 300 million years.
It is such a different orientation, it’ll take awhile for it to begin to settle in. Without question, this construction project is mostly about the earliest universe, the place where we have the least amount of information.
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Yes, these time measurements are not so much an indication of time past, they are a nexus of relations that defines a notation. It is derivative of light and a ratio with space and all the dimensionless constants that define both. By the way, as a result of thinking about this, I need to check out an important detail. CERN Labs measures interactions within the 67th notation. What are they measuring? Do they think they are measuring any time intervals? How?
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The current fastest calculation of a time interval falls within the 84th notation.^{20} That calculation was done in Garching, Germany at the Max Planck Institute (Max-Planck-Institut für Quantenoptik) where scholar-scientist, Dr. Vladislav S. Yakovlev told us that their measurement of an attosecond is within Notation 84 which is indicated by the red zero in the actual numbers for Planck Time just above. There are about five more doublings (the green “0”) to reach down into the CERN-scale measurements and another 20 (3.333 per base-10 units or about 66 or so to reach Planck Time).
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The Simple Planck Formula: You can see Max Planck’s complete formula deep within the footnotes. Here you see the simple part of formula; it is a little like e=mc^{2}. And quite naturally, you can apply that simple formula to each notation and to each other.
Planck’s equation binds space and time with light. Einstein’s formula binds mass and energy with light. These Planck base units are necessarily bound throughout all 202 notations.
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Summary:
1. 202 base-2 notations or doublings, our container universe.
2. There is a fullness of time that is quantitative, derivative, and finite. There is no absolute time.
3. Space and time are redefined by Max Planck’s formula for Planck Time.
4. Doublings are a basic mechanism of the universe.
5. The first manifestation of space-and-time-and-charge-mass is the sphere.
6. The model is an extensible platform for a unified theory of mathematics to include the Standard Models, Langlands programs and string theory.
7. There is a natural inflation within this universe.
8. The universe is fundamentally exponential. Euler’s identity got it right.
9. Infinity through qualities of light is primary continuity, symmetry and harmony.
10. Continuity (order), symmetry (relations), and harmony (dynamics) are qualitative.
11. The qualitative opens the way to value and ethics.
12. All notations (doublings) define boundaries and each is always active and never the same.
Of course, there is more to come. Each of these key ideas will have a page like this one for the first key idea. It’ll take time and your comments, questions, and insights are most welcomed.
This article is based on the key points of the prior posting, “To infinity and beyond!?!” Several told me that it was too hard to understand, “What does it mean? How does it work?” Hopefully, this discussion of the first key idea will help a little to clarify this young model.
Endnotes, Footnotes, References and Resources:
^{1}Philosophiæ Naturalis Principia Mathematica a/k/a Principia. Considered a classic, one of the greatest publications for all times, science has put Newton’s major work on such a high pedestal, it is hard for anyone to criticize it, especially a person with so few credentials. My old geology professor, John Harrington (1966, Wofford College, Spartanburg, SC), told me that I was destined to be a gadfly! He was right. Nobody will deny that Newton laid the foundations for empirical science where mathematics and measurements reign. Notwithstanding, if his first principles are off, major sections of science become largely locked behind impervious walls. Over the years, the truth has a way of drilling holes in those walls until they become so weak…
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^{2}Newton-versus-Leibniz to Hawking-versus-Penrose: The arguments are substantial and voluminous. Throughout my writing those discussions are bearing down on it. The major work that is often open on this desktop include the following:
^{3}Substantialism versus Relationalism: Points of view become schools of thought where the primary arguments are shaped and it all becomes quite encyclopedic. All too often, these documents are opened on this desktop:
^{4}Key insights from Max Planck and others: To date, there are twelve key conceptual transitions that appear to be somewhat original thoughts. Either these are right or they are wrong. If wrong, I am anxious to learn why and to fill in that information where I have had no knowledge. Every page throughout this web site focuses on at least one key transition. There are several pages where many are summarized. The prior homepage is a case in point. Eight keys concepts are reviewed. Just prior to that, twelve were reviewed. Right from the early years, back in 2012 and 2014, there has been a fair amount of speculation about the meaning of our chart of Planck base units doublings that encapsulate the universe. A working list is below.
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^{5}Age of the Universe. There are many ongoing studies, however, most now agree that the universe is anywhere from 13.79 to 13.81 billion years old. We take the the higher figure as our given. The precise number is not as important as it is to have a number which is generally accepted. The Wikipedia study is constantly being updated. Plus, articles like this one from June 11, 2017 in Space.com by Nola Taylor Redd are helpful.
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^{6}Retire space, time and infinity: Three very serious professors, Turok, Akani-Hamed, and Tegmark truly want to retire the concepts. Too quick and not-quite intuitive, after all we all grew up learning about the three dimensions of space and the additional dimension of time, it begs the question, “What are we missing?” First, we did not grow up on Max Planck’s formulas for length and time. Newton’s absolute time and space have held us in check too long. To begin to break out, engage the 202 doublings from Planck Time to the Age of the Universe. Also: Why now?
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^{7}Letters to Leaders and Scholars: These listings that are online today are quite mixed. This list is being sorted by categories. See the drop down menu when you cursor over CONTACTS in the top navigation bar.
^{14}Frank Wilczek. In November 2012 searching the web from our home in New Orleans, I discovered Frank Wilczek’s three articles about Max Planck’s base units. All three articles are a spirited embrace of basic concepts of reality: A Must-Read. Wilczek wrote them in 2001 and 2002. Published in Physics Today, there are, however, many other references to Wilczek’s work within this site; many are linked from our “Wilczek reference page.”
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^{15}Doublings. In this model, the first emergence of a space-time moment is a sphere. We’ve called them Planckspheres, yet that is being reviewed. Many would have us begin with human cells. These appear to double by splitting into two to make a pair. Human cells are huge. Along our scale they begin at their smallest with the male sperm cell within Notation 99 and the largest cell, the female egg, at 103. Therein is the mystery of life spanning the center of this scale. You are about to be introduced to the very simple mechanism within that mystery.
^{17}Unified Theory of Mathematics. That first notation is a complexity of mathematics even before there is a measurable manifestation of space and time. In June 2016 in a rambling post, that place was initially described as a transformation nexus, the so-called singularity. There was so much mathematics going on, I went looking for help. I asked, “Who is studying and writing about all this dynamic simplicity?” Through Edward Frenkel’s work, I found Robert Langlands. In November 2017, there was a series of four homepages within this site that eventually confessed my struggles to understand Langlands programs. My math was just too weak, but with some help, the Langlands programs will continue to be studied.
^{19}Large-scale structure formation – Galaxies. This model is about the early universe. Out of 202 notations or doublings, 197 notations bring us to about 300 million years (out of 13.81 billion). The next five notations bring us to the current time.
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First, please notice that Planck Length [1.616229(38)×10^{-35 }(meters)] divided by Planck Time [5.39116(13)×10^{-44} (seconds )] [equals 299,792,437.99 meters/second] does approximate the speed of light in a vacuum [299,792,458 m/s]. At about the one second mark within notation 143, the calculation is 299,773,654.24. It is always within less than .1% of the experimental value.
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.”
More References, Resources, and Research
Though part of the intellectual debates about boundaries, 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 ask, “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 effort 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 more recently, Steven Weinberg re-formalized 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 this 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 with KG Wilson: “His work in physics involved formulation of a comprehensive theory of scaling: how fundamental properties and forces of a system vary depending on the scale over which they are measured. He devised a universal divide-and-conquer strategy for calculating how phase transitions occur, by considering each scale separately and then abstracting the connection between contiguous ones, in a novel appreciation of renormalization group theory.