We are all inspired in very different ways by the same facts and conjectures. It’s remarkable, the plasticity of human thought. Thanks again for all your good work and hard work! Nothing is easy.
Such a rare person you are. You know it, but now we know it. I hope you like our idiosyncratic view of the universe. It doesn’t have to be right; it’s just likeable.
Given your books, especially “Beyond Weird” and “Patterns in Nature” and “Flow” and “Shape” and “Branches” and … I hope we can open up a line of communication. Thanks. -Bruce
Second email: Apr 27, 2018, 9:12 AM
Phil –
You are a genius. Prolific-but-substantial. Thank you for what you do!
-Bruce
First email: October 21, 2017, 9:46 AM
RE: Base-2 from the Planck scale to the Age of the Universe
Dear Philip:
Thank you for all that you have so successfully written and have had published, a marvelous testament to you and your family. I am always so jealous of the depth of productivity of people like you. Along with John Barrow, Cliff Pickover, Penrose and so many others who walk around on the edge of knowledge, I sincerely congratulate you for all that you have done.
May I trouble you to look at some silly work of an idiosyncratic mind? In 2011 we naively walked into a base-2 model from the Planck scale to the Age of the Universe in just 202 notations. The first second from Planck Time is between Notation-143 and 144. The first 500 million years preparing for galaxy formation brings us up in between Notation-198 and 199. https://81018.com/chart
Shall I attempt to get on the Escher staircase and seek to publish beyond WordPress? Thank you.
It’s been six years since my last note to you. Though I was considered rather idiosyncratic back then, I am even more so today!
I’ve been reviewing your writing around dark matter, quantum gravity, and entanglement. To keep track of it all — you have such depth and breadth within your writings — I created a special page on our site about your work: https://81018.com/2018/09/26/choi/
As a review, our work on applying base-2 to the Planck scale began in December 2011. In 2016 that work within high schools got its own website. Also in 2016, with students now on to college, graduate school, and beyond, they also got their own site — http://81018.com — and it is where I do most of my work today.
I can see how extraordinarily busy you are. And since married, my goodness, you have more than enough to keep you writing. Yet, would you read the homepage today about gravity? In time, it’ll only be accessible through this url: https://81018.com/gravity/
I was so pleased to talk with you today. Thank you for returning my call. And, forgive me for my slowness to pick up; I am not sure if it is my hearing (substantially challenged) or my brain (slowing down after all these years).
You are as pleasant on the telephone as you appear in those photographs online!
From nanotechnologies to the LHC, I finally stopped and asked, “Who is this author?” Your website is so very gracious and giving. Besides your body of work, thank you for being so open and responsive. Let me forwarn you, my work has been described by John Baez in personal correspondence as being “idiosyncratic.” That is also the story of my life. In 1977 I was working on my PhD at Boston University, focused on the work of John Bell at CERN and the EPR paradox.
I visited with Bell a couple of times, but as I progressed, my ideas and work were indeed increasing idiosyncratic to my colleagues and professors. Though I knew a little quantum physics, my focus was on “perfected states” within space and time. After a brief stint in 1980 in Paris to study two conflicting points of view between physicists Olivier Costa de Beauregard and J.P. Vigier at the Institut Henri Poincare, I put my studies on hold. It was time to got a real job and get back to work. I had started a technology business in 1972 and they called on me to help shepherd the transition from a service bureau to one of the early software developers.
So, I have never been published in any of the scientific journals. In light of email below, it seemed to me that an interesting shortcut would be to put a rough draft up on Wikipedia and get the academics within these disciplines to shape it up. That was naive in more ways than one. First, Wikipedia editors mostly shape syntax and grammar; the initial content must come from peer-reviewed journals. I had assumed there were illusive papers that the web had not yet indexed. I would bring the article on base-2 exponential notation in as close as I could, and the experts could carry it from there. Wrong, wrong, wrong.
Simple logic sometimes flies in the face of established methodologies: 1. Why can we not multiply the Planck length by two? Even if it is a dimensionful number, it has an actual numerical number. A point becomes two points, then four, the eight, sixteen and onward. And, I think once multiplied, it is just a dimension about which many questions should be asked.
2. First, I would ask, “What are the possible structures points take?” We have the studies of tensors and manifolds to re-examine, then cobordism and so much more. I think such an approach can open doors for a new thought experiment and other explorations!
Still in my earliest stages after all these years, it seemed that you have a deep heart for the edges of knowledge and as a result of that, I penned this note (and the first one below) to you.
Warmly,
Bruce
First email: Sat, Jun 16, 2012
Hi Charles:
This is my first time to write to you…
Have you discovered that there seems to be some very basic academic oversights? I believe that I have discovered two that are related to simple geometries. At first, I thought it was my own unique stupidity… that I didn’t pay attention in that tenth grade geometry class. Then I started asking people who would know.
In fifteen years, I have found only a few pockets of people who intuitively know the answers to very simple questions.
Take the simple three-dimensional structure – the tetrahedron — and ask, “What is most perfectly-and-simply enclosed within a tetrahedron?” The solution is simple. Divide each edge in half, connect the points, and look. Most people are surprised to find an octahedron in the middle along with the four tetrahedrons in each corner.
Then the next question, “What is most perfectly-and-simply enclosed within that octahedron?” My old physics professor at BU, Robert Cohen, did not have a clue.
Of literally hundreds of very fine thinkers, even John Conway (Princeton – surreal numbers, geometry) had to stop and think about it. But even among the 1% who knew the answers, people like Conway were not much interested in exploring its interior structures further.
I think that is a huge academic oversight.
Back in 1979 I created a rather large display project under the dome at MIT. It focused on first principles within each of the academic disciplines and used Erwin Schrödinger’s book, What is life?, as a starting point. There were 77 living scholars who participated; many later became Nobel laureates.
David Bohm was among the 77. I learned about his death a year after he died in 1992. To stop and reflect a little about life and death, I took down his little book, Fragmentation and Wholeness, that he given me in a class on October 17, 1977. I was thinking about a discussion in a class when Bohm had us focus for several hours on points, lines, triangles, and tetrahedrons . Then it hit me, and I winced and said, “Bohm, you never asked, ‘What’s inside?'”
First, I wonder if you know what is most-perfectly-and simply enclosed by the octahedron? Are you aware of all the hexagonal and pentagonal bands?
That’s the start.
In 2011, my nephew asked if I would substitute teach his five high-school geometry classes. My assignment was to teach his classes about the five platonic solids. I had never made an icosahedron or dodecahedron; so in the process of preparing for the class, I made models of both with tetrahedrons.
The Basic Five. There is none simpler and from these all others evolve. An icosahedron of 20 tetrahedrons needs to be held in one’s hand. It’s squishy. It’s imperfect. Until Dan Shechtman kicked open that door on fivefold symmetries, there has been amazingly little discussion about it. Then, look throughout nature for the dodecahedral structures based on the pentagon. You’ll find little. But take each face and move that icosahedral model of five octahedrons within a loose pentagonal structure. I could not find that structure on the web. It seems so basic and simple.
Then, of course, I had to look inside of it. I found odd-shaped tetrahedrons and in the very middle, the icosahedron.
The nesting of these objects is significant, yet again, there is very little research of its meaning.
So, with my first classes, they made models and we all had fun.
My nephew asked if I would substitute on December 19, 2011. It would be my second time with these kids so I had to think what a natural sequel would be. I began thinking of Zeno’s paradox and the Russian dolls, nesting geometries and combinatorial geometries, and asked myself, “How many steps back would we have to go to get to the Planck length?” I assumed thousands of divisions by 2. There were just 112. I was flummoxed. “In how many other classes did you fall asleep?” I asked myself. Yet, in the Google search, I couldn’t find it.
I then asked, “How many steps to the edge of the observable universe (doubling each measurement successively)? Just another 90+ steps and we were there.
202.34 steps from the smallest to the largest.
Is that crazy? Too easy? Why haven’t we seen it? I pushed Wikipedia on it and they said, “Nope, it is original research.” I said, “You’re crazy… from a high school geometry class?”
So, what am I doing wrong? Why is this not part of our basic-basic education?
Introduction: A sixty-sided pentagonal figure of the (kind displayed) above is known as the Pentakis Dodecahedron. A sixty-sided pentagonal figure is also known as a cumulated dodecahedron or hexacontagon.
Earlier Work: We were learning about the tetrahedral-octahedral clusters. There are many possible combinations of tetrahedrons and octahedrons. The two can be used to tile and tessellate the universe in three dimensions, perfectly filling the container.
April 2011: This structure below was created with sixty tetrahedrons that create the outer layer. Of the five platonic solids (in discussions with high school geometry classes), it seemed that the flat pentagonal face of the simple dodecahedron was not readily evident throughout nature. It seemed to beg questions about “really-real” structure of the dodecahedron and its place in nature.
Why not make the dodecahedron with the rather odd three-dimensional pentagonal of five tetrahedrons? It is odd simply because there is a very small gap between the tetrahedrons.
This dodecahedron was created with twelve of those pentagonal objects, each made of five tetrahedrons.
The next step: Name this object. Smaller than a soccer ball, we did not know the name of this 60-sided object for many months. Finally, with a little help from Wolfram Research, it became apparent that it was in a class of objects called cumulated dodecahedrons. Hexacontagon is another class of 60-sided objects. Yet, the Pentakis dodecahedron seems to be most commonly accepted name.
More to come: Of course, pentagonal structures are ever abundant throughout nature as Nobel laureate Prof Dr. Dan Shechtman discovered, and botanists have known forever. More…
Observations: Number 5 is a prime number and in the systems of geometries we ask, “What is the next most simple geometrical or unique mathematical system?”
Spiral nebulae
What about the Fibonacci numbers? When might this sequence begin to apply to these notations? Reflecting on this question and the nature of an exponential universe, addition appears to be derivative of multiplication by 2. If the universe is fundamentally a multiplicative system, one might begin to think that addition occurs “within” notations, and in order to get “carried” across notations, it requires a mathematical function that provides the transport through the other notations. Let us be imaging the spiral nebulae. So, as of this writing, we are projecting the Fibonacci sequences might begin to engage possibly as late as the 144th notation where processing is just over one second. . From pentastars, tetrahedral rings, tetrahedral systems, to the icosahedral phase.
On April 8, 1982 Dan Shechtman (Nobel Prize in Chemistry 2011) actually saw for the first time what is now named the icosahedral phase; and as a result, hesingle-handedly opened the new field of quasiperiodic crystals. Prior to that day, an icosahedral phase barely existed in the minds of a very few mathematicians and geometers. Many of Shechtman’s colleagues thought he was a bit crazy. Nevertheless, he persevered — he knew what he could see was real — and as a result, he opened a new field of study with immediate applications that’d never existed prior to his work. More…
I believe the very foundations of the icosahedral phase begins within this 5th notation. Five perfect tetrahedrons, as pictured above, share eight vertices. With no less than 4096-to-32,768 vertices and possibly many more, this could be the notation within which complexity earnestly begins.
The icosahedral structures involve 20 tetrahedrons within what we call quantum geometry, a squishy geometry where there are many of degrees of freedom. Within this model, there are two groups of five tetrahedrons with a band of ten tetrahedrons separating the two. All twenty all share the same centerpoint. Or, there are also three groups of five tetrahedrons with a cluster of four and a single tetrahedron such that each cluster shares only one edge with another cluster and, of course, they all share the same centerpoint.
It is a wonderful model, easily put together, and an entirely transformative experience to feel the first instances of squishy quantum geometries. n my more adventuresome moments, I propose that by the 60th notation, these simple structures give us quantum fluctuations.
Chrysler’s Pentastar
Eventually I will make a short video demonstrating how the five tetrahedrons actually have movement within confined spaces and how the 20 tetrahedrons seem to do their thing.
We are only on the fifth notation, five steps beyond the nexus of transformations between the finite and infinite. That amalgamation of equations and ratios are necessarily an intimate part of this notational definition. These most simple and most perfect equations are all using pi to create the geometries and symmetries that become our first forms with real numbers (Planck base units) and real formulas.
Some of the people, publications, and organizations with whom we have been in contact. The list is very incomplete and it will continue to be so. All links go to a page within this website. No responses to these communications will ever be published unless authorized and encouraged by their author (such as this note from Freeman Dyson). Boldface entries are mostly from 2022. Those in gray have died. Go to this listing to find those whose work is most intriguing.
A | B | C | D | E | F | G | H | I | J | K | L | M | N| O | P | Q | R | S | T | U | V | W | X | Y | Z
a b c d e f g h i/j k l m n/o p q/r s t/u/v w x/y/z
About: People give us hope and insight by what they write and think and do. I thank people for their efforts. Here are over 500 such people listed here. -BEC
Also, please note: We do not share the correspondence that we receive from scholars unless they encourage us to do so. I can only guess that once the concept of a base-2 outline of the universe from Planck Time and Planck Length is entertained, most scholars would say, “It just a bunch of numbers. Cute, but not particularly meaningful.”
The most-highly recognized thought leaders of our time, people like Hawking, ‘t Hooft, Penrose, Rees, Zichichi, I can well imagine, if they ever actually read our email to them, the first judgment would be, “Too idiosyncratic. It’d take too much time to respond.” They would intellectually pat our head and gently smile, “Someday you may understand.” We sometimes get such responses, …not sure what to make of it, …not an area in which I have any expertise, or something like, …good luck and have fun.
There are actually new concepts that emerge from out of the corners of our communities, yes, from far out near the left field wall. Such concepts are just hard to conceive.
These are five basic concepts that first need to be internalized:
• Ordering principles come within the Planck base units. Taken as given, all the dimensionless constants that give rise to these Planck units also come along inside. There are many more concepts than initially meet the eye. • An infinitesimal sphere is projected to be the first manifestation of physicality. That sphere brings with it all the dimensionless constants and interior dynamics, i.e. functions like the Fourier transform. There are many other dynamics we are also trying to grasp. • Expansion at One Plancksphere per Plancksecond • Base-2 is the next ordering principle created through simple sphere stacking. • A finite-infinite relation is assumed and it is defined most simply and is limited to it. • Here is a domain of at least 64 notations to accommodate Langlands programs, string theory, consciousness and all those discoveries below the thresholds of measurement.
On the homepage today, first paragraph, with Eugene Wigner, we are building on your Mathematical Universe. More references and links to your pages will be forthcoming. I thought you would want to know. Thanks for all that you do to stimulate discussions about first principles and initial conditions.
Warmly,
Bruce
Tenth email: 23 January 2022 at 5 PM
Of course the hadron didn’t cut it. Composites aren’t fundamental. None of the subs are. It’s got to be more like a perfect sphere.
Aren’t spin dynamics manifestations of sphere dynamics?
Compared to the Planck base units or Stoney base units, all the subs and hypotheticals are rather large and clunky.
Of course, historically these “Planck Particles” have been considered tiny blackholes while others insist such entities simply do not exist.
Picking up on your theme that we need to redefine spacetime and infinity, perhaps you would like to get involved with these explorations:
The first second is still alive, well and moving outward 13.8 billion years later!
Or, today’s expansion of the universe is also the first moment of the universe.
Blackholes aren’t just sucking everything in; they (Type B) are also pushing it out at levels (sizes) that our measuring devices will never pick up.
Thanks. Warmly, Bruce
PS. I think the current homepage is worth a quick read: https://81018.com/empower/ Also, I know you get too much email so I will not send another email to you without an invitation to do so. -BEC
Along with Nima and Neil, you three constitute a force in physics and are three of my favorites among the legions of the brilliant. Today’s homepage — https://81018.com/uni-verse/ — has links to you three, plus to one of my very favorite pages: https://81018.com/redefinition/
Our idiosyncratic model of the universe is different: 1. The infinite-finite relation is unique — the infinite is the qualitative expression of continuity (order), symmetry (relations), and harmony (dynamics) while the finite is the quantitative expression of continuity, symmetry, and harmony. For me, any other definition of the infinite has too much historicity that is limited within time. 2. The initial perfections of the qualitative is challenged by the geometric gap of the five tetrahedral configuration. It becomes the grounds for quantum fluctuations which becomes systemic before Notation-64 where particles and waves begin to manifest.
The fact that the speed of light is confirmed within .01% of laboratory-defined speed at the one second mark between Notation-143 and Notation-144 and then again with a light year between Notation-168-and-169 is sweet.
When it comes to testing new ideas, we are all fools albeit some of us more foolish than others given those quantum leaps and impatience with incrementalism.
I wish you well. We all must try to stay healthy in these very odd times.
Most sincerely, Bruce
Sixth email: Thu, Jun 1, 2017 at 5:39 PM
Subject: Fwd: Do our simple mathematics at all jive? I hope so.
Hi Max –
Whenever I quote somebody’s work, I send a copy of that reference.
We all should know your work and your thinking. To that end, we have a Max Tegmark page within our website (Editor’s note: This page!)
We live in such crazy times and I believe a lot of it has to do with Stephen Hawking’s dystopian, nihilistic bang. Also, to address your desire to throw out infinity, I have offered a redefinition (only highlighted here within this document).
Our naive model has a simple logic, a most-simple start, and simple mathematics. It is all-inclusive yet particularized. And, it also has a simple logical start for infinity, indeterminacy, fluctuations, incompleteness, and imperfections.
So I ask myself, “Why not try to integrate it with the Standard Model of Physics, with quantum gravity, and with the ΛCDM model?” Would you advise us? Thank you.
Most sincerely, Bruce ********* Bruce (as the Editor) answers his own note on 27 March 2020: “Advice…? So, you want advice? Here’s my advice as a question: What, are you crazy?”
Your endearing smile and wonderful openness should have the world on your doorstep. Congratulations on all that you do.
Of course, the big bang is one of those answers that only a fool would dare question. So, here I stand among the fools. We’re just high school folks; we claim no special status, so maybe we can be excused for being nicely idiosyncratic and naive!
I think you might enjoy seeing the numbers all filled in from the Planck base units to the Age of the Universe using base-2 notation. Boeke’s Cosmic View looks a little timid by comparison. Even ‘t Hooft’s Time in the Powers of Ten misses too much. If you have a moment — it is looking for a special critique.
Is it solipsistic poppycock? That chart is big; it is horizontally-scrolled, starts with the five Planck base units (and some simple geometries), and it is carried out the 202 notations to the Age of the Universe. You can follow the changes of each base unit in contrast to the others. There are over 1000 simple-simple-simple calculations. But, simple is good. It tells a bold and dramatic story but it may have more to do with fantasy than reality… but I don’t think so. I respect you too much to waste your time that way.
Is it possible that the universe started with those infinitesimally small numbers and grew quietly and rather prodigiously and all rather quickly? Of the 200+ notations, the first second is between 143 and 144. The first light year is between 168 and 169. And the first million years between 188 and 189.
That small scale universe, 1-67, could be a new science and math. Maybe Langlands is on the right path after all. Below I’ll post some of the other work-in-progress asking for critical review! Thank you.
I am now a groupie of sorts. Too old and too naive to be deeply informed.
You encourage me with your great spirit while I’ve begun working through your “Dimensionless constants, cosmology and other dark matters.” http://arxiv.org/abs/astro-ph/0511774
From the perplexing place we were within my first note, to the questioning within the third, would you tell us why our basic concept is wrong headed and “to take a break.” A Simple View of the Universe: https://www.linkedin.com/pulse/simple-view-universe-bruce-camber
Your website is sensational! Thank you for all that you do to stimulate scholarship and creative thinking!
-Bruce
An automated response: September 22, 2014:
Thanks for your LinkedIn invitation, which I’m going to accept shortly! Although there’s essentially no information on my LinkedIn page, I have an active public Facebook page where you can connect and discuss with me and others intrigued by science and life’s big questions. I very much hope you’ll join me there! Just surf over to the link below and click “like”:
I was 20 when you came into this world, I suspect you came in feet first. So much standing comedy in all that you are and do. It is entirely refreshing. I am enjoying your pages-and-writing immensely.
I am on a search for simple wisdom. I’m a simple person.
But, I do have a seriously silly question for you. It started when I was asked to substitute for my nephew a couple of years ago. He was to have a second child and I got his five geometry classes for a few days. I wanted to stand them on their head a little, so they actually made models of the “Big Five.” They took a tetrahedron, divided the edges in half, connected the new vertices, and bingo, there is a tetrahedron in each corner and an octahedron in the middle. Then, the same with the octahedron, with six baby octahedrons in the corners and eight tetrahedrons in the faces, all sharing a centerpoint.” That’s a goldmine and you kids have got to go in there and start digging!”
That was the beginning of my regression. The next time, Stevie wanted to take his bride on a fifth-anniversary cruise and left me with those buggers on the last day of class before the Christmas recess, Monday, December 19, 2011.
“Come one, come all, see the universe and everything in it from the smallest to the largest measurement in about 202 steps!”
We used the Planck Length and started multiplying by 2. Within a relatively short time, we had the entire universe looking like a Planck Factory. Everything had a place. Geometry was pervasive. Here was the homunculus of all homunculi. One part Plato, add a little relativistic aether, and mix well into the first sixty steps — nobody seems to have explored 2-to-60, possibly 64 (just before getting hit with any sensibility and a neutrino and quark).
Absolutely crazy?!? Worth exploring further??? Or, shall I tell the kids to come out of that cave?
Please, help me to debunk this crazy Alice-in-Wonderland hole that I’ve dropped into….
I am a television producer. But recently, I was asked to substitute for a high school geometry teacher, a nephew. He asked me to introduce the kids to Plato’s five. It would be my second time with them, so I had to expand my own horizon a bit for my visit on December 19, 2011.
The first time I had them, back in March 2011, they made icosahedrons out of 20 tetrahedrons. I called it squishy geometry and said that it probably fits into quantum geometries or imperfect geometry somewhere and somehow, but I couldn’t find any online references to it. This link goes to pictures of those icosahedrons.
I thought, “…speculative, fanciful thinking, probably just nonsense.”
Yet, just after that first encounter, I became impatient with my little paper model of a dodecahedron. I took the same pentagonal groups of five tetrahedrons, and attached twelve of them together. I filled it with PlayDoh, then tried to discern what was inside.
A smaller icoshedron was in the center of the thing. Fascinating for me. No study of it online yet. I found a name – hexacontagon — but none in the shape of this particular pseudo-dodecahedron.
I’ve been looking inside those five-tetrahedral structures for awhile. A week before that class, I asked, “How far within, how many steps by dividing by 2, would I have to go to get to the range of Planck’s length?” I assumed thousands. Nope. Just 118 steps! There I was, dividing one meter by 2 and then by 2 again u.s.w until 1.6×10−35or Planck’s length. Then I thought about the large scale universe and in 91 steps I was out in the range of 1027 meters and the edge of the observable universe.
I hadn’t seen such an application of scientific notation so I made it up and produced a colorful chart for the class: https://81018.com/big-board/
Image of quasicrystals by Daniel Shechtman, Nobel Prize winner in Chemistry, 2011, Technion University
The Nobel Prize. Though an exclusive little committee in Norway and Sweden, the Nobel Prize people do have some of the best scientific advisers in the world. It is worth looking at their selections each year. It is worth taking time to listen to the lectures of Nobel laureates.
The 2011 Nobel Prize in Chemistry: Daniel Shechtman The scientific community at first ridiculed and even scorned this man for his work and his conclusions about 30 years before he received the prize. It took him awhile to sell his concepts and to have enough others replicate his research so others believed. He stood his ground on simple truths and won on principle.
Evolving concepts: From our Universe to a Multiverse There are bridges being constructed by thought leaders like Lisa Randall between this universe and mathematically-defined multiverses.
Shechtman’s work is significant because it opens the way to re-examine the nature of the five basic structures of geometry and and their applications from everything from physics to chemistry to biology to our mind. Also, it is within these simple, basic structures — the tetrahedron, octahedron, cube, dodecahedron and icosahedron — we just might find clues to the very nature of the mathematics the appears to be a bridge to another universe.
Most people do not know these simple structures nor what is naturally and sometimes perfectly inside each of them. There is exquisite complexity within the simplicity of each. Although the following letter is within the correspondence section, it is duplicated here because there is a profound link between quantum physics, the gap and indeterminacy, and the imperfections of the quasicrystals. It is here to remind us to think about it all.
I listened to your video reflections online (produced by Technion) about the early reception of your work and your pointed encouragement of those of us who have rightly or wrongly been treated as speculative fools. Unfortunately, I needed to make a living so in 1980, I went back to a business that I had started before my doctoral work in perfected states within space-time.
Perhaps I would have been one of the early enthusiasts around your work.
In 1970-1972 I worked within a group at Harvard called the Philomorphs with Prof. Arthur Loeb. Bucky Fuller was a frequent visitor. I was smitten with the notion of perfection within the imperfect, quantum world. The EPR Paradox was my starting point. Victor Weisskopf (Physics, MIT) was on my path and befriended me. Under his guidance, I visited with John Bell at CERN and later I had a six month study with Olivier Costa de Beauregard and JP Vigier in Paris where we looked in on the work of Alain Aspect on Bell’s Inequality theorem and the EPR paradox. In 1977 I spent a day with David Bohm and his doctoral candidates talking about points, lines, triangles and the tetrahedron.
When I first learned of Bohm’s death, I pulled down a book he had given to me from that day, Fragmentation & Wholeness, and realized he never asked what was perfectly enclosed within the tetrahedron. A year later I asked the question about the octahedron.
Business has been good, but demanding. Only this year have I slowed down a little. I have been playing with models that I created by having molds made to knock out thousands of tetrahedrons and octahedrons. I am still a novice, but I think you might be interested in my approach.
My guess right now is that the dodecahedron is really a sixty-sided cluster and each of the pentagonal faces are a cluster of five tetrahedrons. That they are imperfect intrigues me. I have begun a most speculative page and it is the height of stupidity to share it with a new Nobel laureate, but you were so very warm and kind in that video and you have walked over the coals for almost 30 years.
I have just started working on this little page and, though I know you are inundated with requests and demands on your time, I thought you might appreciate it.
May 2007. I believe a simple conceptual bottleneck that has been starring at us for many, many centuries exists in pure geometry. I may be totally mistaken, but I do not believe our best scholars throughout time and around the world have answered three very simple, basic questions:
What are the simplest three-dimensional structures?
What is most simply and perfectly enclosed within those structures?
What is most simply and perfectly enclosed within each of those parts?
When David Bohm died in 1992, I took down his little book, Fragmentation & Wholeness, he had given me in class and I started reading just one more time. Then, it hit me. “What is perfectly enclosed within the tetrahedron?” I did not know. “Four half-sized tetrahedrons and an octahedron.” Discovering what was inside the octahedron was a major breakthrough for me. Since 1994 I have asked literally hundreds of people those three questions. Chemists, biologists, architects, mathematicians, physicists, crystallographers, geologists, and geometers — few had quick answers. Only one, John Conway, had an answer to the third question.
The tetrahedron. The answer to the first question is the basic building block of biology, chemistry, geometry and physics. The answer is the tetrahedron. Many, many people answered that question. The tetrahedron has four sides and is made of four equilateral triangles. It is not a pyramid (that has a square base and it is half of an octahedron).
You will discover the octahedron, four of its faces are the “middle” face of the tetrahedron, and four are interior.
The octahedron. The answer to that third question requires a quick analysis of the octahedron. Only one person knew the answer to the question, “What is perfectly enclosed within an octahedron?” Yet, he hesitated and said, “Let’s figure it out.” That was Princeton professor, John Conway, who invented surreal numbers and is one of the most renown geometers living in the world today.
An octahedron with a smaller octahedron in each of the six corners and a tetrahedron in each of the eight faces.
Within each corner there is an octahedron. There are six corners. With each face is a tetrahedron. There are eight faces. The tape inside define four hexagonal plates that share a common center point. Notice the tape comes in four different colors.
Here are the two most basic structures in the physical world and most people do not know what objects are most simply enclosed by each. Yet, these are simple exercises. School children should have quick answers to all three questions.
When questioned about my focus on this gateway to interior space, my standard answer is, “…because we do not know.” And, as I look through the history of knowledge, I do not know why it hasn’t been part of our education. It is too simple.
I will predict that once more of the complexity-yet-simplicity of these basic interior relations are discerned, the mathematics will follow and these forms will beget new functions as we discovered within nanotechnologies, i.e. nanoparticles (buckyballs or fullerenes) and quasiparticles (Dan Shechtman’s work). I believe the results will impact every major discipline, including religion, ethics, ontology, epistemology and cosmology.
In physics we’ll have a new look at the weak and strong interactions, gravity and polarity or electromagnetism, and deep internal symmetry transformations.
In chemistry, the four hexagonal plates crisscrossing the center point should open a new understanding of bonding. I even believe there will be a new science of “cross-dimensional bonding” in quantum chemistries.
Within biology, the sciences of RNA/DNA sequencing, genomics, applied biosystems, and even quantum biology will go deeper and become more cohesive.
In psychology, learning, memory, and even identity can be more richly addressed.
This apparent intellectual oversight does not seem to know any physical, cultural, religious or political boundaries. I have not been able to find references to the interiority of simple structures in any culture to date.
Surely my friends who have worked with R. Buckminster Fuller and Arthur Loeb, would take exception to the comment. Yet, Bucky’s two volumes, Synergetics I and Synergetics II, are virtually impermeable to the average person and neither work has been widely used for common tasks or applied sciences. Buckyballs or fullerenes are now being used widely within nanotechnologies, but that is all in its earliest stages of development as a reduction-to-practice.
The answer to the question about the octahedron renders a model with a profound complexity and simplicity. Again, if you can picture an eight-sided object, essentially the two square bases of the pyramid pushed together, you’ll have an image of an octahedron.
Divide each of the edges in half and connect the points. You will find an octahedron in each of the four corners of the base square and an octahedron on the top and bottom. In each of the eight faces is a tetrahedron.
There are very few models of the parts and whole relation. There are fewer still that describe the interior relations of these objects.
Let us take a look.
This third picture from the top in the right column is of a tetrahedron. There is a tetrahedron in each of the four corners and an octahedron in the middle.
The fourth picture is the octahedron. Again, there is an octahedron in each of the six corners and a tetrahedron in each face.
The TOT. The picture on the right is a tetrahedral-octahedral-tetrahedral truss or chain. I dubbed it a TOT line. The first time I thought I was observing it in action as a trusss system to support the undulating roof system of the Kansai Airport in Japan. In February 2007, I realized that truss was actually just half a TOT when I actually made the model pictured here. It is a simple parallelogram that can be found in many basic geometry textbooks. Yet, it seems that this tetrahedral-octahedral chain has not been examined in depth.
Geologists have been studying natural tetrahedral-octahedral layers within nature that is known as a TOT layer. We will look extensively at the natural occurrences of TOT formations much later in this work.
In the photograph, it is two tetrahedrons facing on an edge with an octahedron in the middle. Each face of the TOT is an equilateral triangle on the surface which, of course, opens to the inner cavity of either an octahedron or a tetrahedron.
These are simple models that have been largely unexamined by the academic communities.
Towards a Theory of Everything Similar
With the TOT line, I believe we are looking at the structure of perfection. Pure geometry. And, I believe that geometry once expressed in the physical world, manifested within space and time, becomes rather randomly quantized and infinitely variegated.
I believe our chemists should look into chemical bonding that goes beyond the usual two-dimensional diagrams to these these three-dimensional interactions and then to the multi-dimensional complexity when correlated within the necessary plates of a yet deeper, internal tetrahedron, octahedron, or tetrahedral-octahedral structure.
Here we open the very nature of chemical bonding to new possibilities. The bonding (the function) is interior to a pure structure (the form).
Simple complexity. If you were to keep going deeper within each octahedron and tetrahedron, as you might guess, the number of cells or objects expands quickly. By the tenth step within (and not yet using dimensional analysis), there are 131,323,456 tetrahedrons and 10,730,656 octahedrons for a total of 142 million objects.
At the eleventh step there are over a billion tetrahedrons and 63,859,648 octahedrons within. The total, just taking 11 steps within, are 1,110,412,992 objects.
At the twelfth step there are over 8 billion tetrahedrons and 381 million octahedrons. That level of complexity within such simplicity allows for a wide range of diversity.
A footnote and timeline: Yes, this particular document was written in May 2007. The first iterations that lead up to this document were written in 1994.
I wanted to invite them to a conference in July 1979 at MIT for the World Council of Churches. Over 4000 people would gather to discuss, Faith, Science, and the Future. Being on the organizing committee, it seemed to me that the ideas of the finest scholars from the area, and then from the world, should be part of that discussion.
At that time, those leading scholars were not invited. The committee thought they would dominate and possibly overwhelm the discussions; so as a consolation, they allowed me to organize this display project.
That display project, titled What is Life? after Erwin Schrödinger’s book of the same title., is being renewed here today. Early stages of it can be found on other pageswithin this website. BEC
The purpose of this project was to summarize those comprehensive worldviews and powerfully suggestive ideas of living scholars (bold equals the “still living” the last time we checked!). All vetted back in 1979 within their community as leading thinkers, the hope was that there might be a dynamic exchange and synthesis of ideas and information that would open new and deeper insights and wisdom. Based on their experiences, observations, historical analysis, hypotheses and testing, informed speculations, and even visionary insights, each person’s work was placed within one of three perspectives: The Small-Scale Universe, The Human-Scale Universe, and The Large-Scale Universe. And then, with each perspective, there were three groups of scholars: (1) Natural Scientists, (2) Philosophers/Theologians and (3) The Boldly Speculative.
Small-Scale Universe To Be – Reality. What is it? Scholars seek to define fundamental units of reality, experience and/or being.
Human Scale Universe To Know – Ways of Knowing Scholars seek to understand basic interactions from cells to populations of people. What makes life human? What gives life meaning?
Large-Scale Universe To Envision the Cosmos Scholars seek to understand cosmology — the parts, laws, and operations of the universe. They seek to know the origin and nature of the universe.
1979: All Living Scholars. Selected by their peers Listings are alphabetical listings of Scientists, Philosophers and Theologians. Each listings is followed by a school designation and links go to published work.
Who would disagree with the observation that our world has deep and seemingly unsolvable problems? It is obvious there is something missing. So, what is it? Is it ethics, morality, common sense, patience, virtues like charity, hope and love? We have hundreds of thousands of books, organizations and thoughtful people who extol all of these and more. Those lists are robust. The work is compelling, but obviously it is not quite compelling enough.
Everybody seems to have their own unique spin to solve the world’s problems. Yet, we have discovered that one person’s spin does not easily integrate with another. Listen to those with their finger on nuclear triggers and those who are trying to be among them. Thoughtful people in every part of the globe are deeply concerned.
MIT lobby 7 at 77 Mass. Avenue
For years, I had been smitten with some of the insights of a theoretical physicist, David Bohm. In 1977, I went for a visit at Birkbeck College in London where he gathered a group of graduate students together to be like a child to examine everything we knew about points, lines, triangles and tetrahedrons. We were trying to discern what makes for fragmentation and what makes for wholeness.
In 1979 I proposed and developed a display project at MIT (image on right) to focus on first principles within the major academic disciplines. For that project, I wrote, “The human future is becoming increasingly complex and problematical. Proposals for redirecting human energies toward basic, realizable, and global values appear simplistic. Nevertheless, the need for such a vision is obvious.”
The focus was on cross-disciplinary scholarship of living scholars around the world who were attempting to define a more integrative and comprehensive understanding of physical and human nature.
Our first posting of this list on the web was back in 1999. It is being updated here and here.
***
Obviously progress has been slow. There is an obvious bottleneck somewhere. And, that is what this article seeks to address.
I believe a simple conceptual bottleneck that has been starring at us for many, many centuries exists within pure geometry. I may be totally mistaken, but I do not believe our best scholars throughout time and around the world have answered three very simple, basic questions:
Since 1994 I have asked literally hundreds of people those three questions. Chemists, biologists, architects, mathematicians, physicists, crystallographers, geologists, and geometers — few had quick answers. Only one had an answer to the third question.
The tetrahedron. The answer to the first question is the basic building block of biology, chemistry, geometry and physics. The answer is the tetrahedron. Many, many people answered that question. The tetrahedron has four sides and is made of four equilateral triangles. It is not a pyramid (that has a square base and it is half of an octahedron).
What is perfectly enclosed within the tetrahedron? The answer to this second question eluded most people. To figure out the simple-perfect answer, divide each of the six edges of the tetrahedron in half and connect the new vertices. You will quickly see a “half-sized” tetrahedron in each of the four corners, but, there is a middle object and it often requires a model to see it. You will discover the octahedron, four of its faces are the “middle” face of the tetrahedron, and four are interior.
The octahedron. The answer to this third question requires a quick analysis of the octahedron. Only one person knew the answer to the question, “What is perfectly enclosed within an octahedron?” Yet, he hesitated and said, “Let’s figure it out.” That was Princeton professor, John Conway, who invented surreal numbers and was one of the most renown geometers in the world at that time.
Within each corner there is an octahedron. There are six corners. Within each face is a tetrahedron. There are eight faces. The tape inside defines four hexagonal plates that share a common center point. Notice the tape comes in four different colors.
Here are two of the most basic structures in the physical world and most people do not know what objects are most simply enclosed by each. Yet, these are simple exercises. School children should have quick answers to all three questions.
When I am questioned about my focus on this gateway to interior space, my standard answer is, “…because we do not know.” And, as I look through the history of knowledge, I do not know why it hasn’t been part of our education. It is just too simple.
This simplicity became the basis for my initial work with first principles.
Why pursue this domain of information?
First, it is there to be examined. It is what is. This is not speculative. It just is. Second, it is truly rich with more information. Third, and here I’ll be speculative, it just may open a door to some of the most basic, unanswered academic questions that, if answered, might build bridges and open new ways to an integrative understanding of life (that link goes to such a door that opened on December 19, 2011).
I will predict that once more of the complexity-yet-simplicity of these basic interior relations are discerned, the mathematics will follow and these forms will beget new functions, i.e just look within nanotechnologies, i.e. nanoparticles (buckyballs or fullerenes) and quasiparticles (Shechtman’s work). I believe the results will impact every major discipline, including religion, ethics, ontology, epistemology and cosmology.
In physics we’ll have a new look at the weak and strong interactions, gravity and polarity or electromagnetism, and even the deeper internal symmetry transformations.
In chemistry, the four hexagonal plates crisscrossing the center point should open a new understanding of bonding. I even believe there will be a new science of “cross-dimensional bonding” in quantum chemistries.
Within biology, the sciences of RNA/DNA sequencing, genomics, applied biosystems, and even quantum biology will go deeper and become more cohesive.
In psychology, learning, memory, and even identity can be more richly addressed.
This apparent intellectual oversight does not seem to know any physical, cultural, religious or political boundaries. I have not been able to find references to the interiority of simple structures in any culture to date.
Surely my friends who have worked with R. Buckminster Fuller and Arthur Loeb, would take exception to the comment. Yet, Bucky’s two volumes, Synergetics I and Synergetics II, are virtually impermeable to the average person and neither work has been widely used for common tasks or applied sciences. Buckyballs or fullerenes are now being used widely within nanotechnologies, but that is all in an early stage of development as a reduction-to-practice.
The answer to the question about the octahedron renders a model with a profound complexity and simplicity. Again, if you can picture an eight-sided object, essentially the two square bases of the pyramid pushed together, you’ll have an image of an octahedron.
Divide each of the edges in half and connect the points. You will find an octahedron in each of the four corners of the base square and an octahedron on the top and bottom. In each of the eight faces is a tetrahedron.
There are very few models of the parts and whole relation. There are fewer still that describe the interior relations of these objects.
Let us quickly review.
This third picture from the top is of a tetrahedron. There is a tetrahedron in each of the four corners and an octahedron in the middle.
The fourth picture is the octahedron. Again, there is an octahedron in each of the six corners and a tetrahedron in each face.
TOT layer
The TOT. The fifth picture from the top is a tetrahedral-octahedral-tetrahedral chain. I dubbed it a TOT line. The first time I thought I was observing it in action as a truss system to support the undulating roof system of the Kansai Airport in Japan. In February 2007, I realized that truss was actually just half a TOT when I actually made the model pictured here. It is a simple parallelogram that can be found in many basic geometry textbooks. However, I have not yet found this tetrahedral-octahedral chain examined in depth.
Geologists have been studying natural tetrahedral-octahedral layers within nature that is known as a TOT layer. We will look extensively at the natural occurrences of TOT formations much later in this work.
In the photograph, it is two tetrahedrons sharing edges with the octahedron in the middle. Each face of the TOT is an equilateral triangle on the surface which, of course, opens to the inner cavity of either an octahedron or a tetrahedron.
These are the most simple models but still have much more to teach the academic communities.
Towards a Theory of Everything Similar
With the TOT line, I believe we are looking at the structure of perfection. Pure geometry. And, I believe that geometry once expressed in the physical world, manifested within space and time, becomes rather randomly quantized and infinitely variegated.
I believe our chemists should look into chemical bonding that goes beyond the usual two-dimensional diagrams to these these three-dimensional interactions and then to the multi-dimensional complexity when correlated within the necessary plates of an internal tetrahedron or octahedron.
Here we open the very nature of chemical bonding to new possibilities. The bonding (the function) is interior to a pure structure (the form).
The Numbers: Simple complexity. If you were to keep going deeper within each octahedron and tetrahedron, as you might guess, the number of cells or objects expands quickly. By the tenth step within, there are 131,323,456 tetrahedrons and 10,730,656 octahedrons for a total of 142 million objects.
At the eleventh step there are over a billion tetrahedrons and 63,859,648 octahedrons within. The total, just taking 11 steps within, are 1,110,412,992 objects.
At the twelfth step there are over 8 billion tetrahedrons and 381 million octahedrons. That level of complexity within such simplicity allows for a wide range of diversity.
A footnote and timeline: This particular document was written in May 2007. The first iterations that lead up to this document were written in 1994.
1979 brochure at MIT
The precursor to it all is pictured in the top right: “A Display Project of First Principles.” It began as a list of some of the most-speculative, integrative thinkers within the major academic disciplines at that time.
I wanted to invite them to a conference in July 1979 at MIT for the World Council of Churches. Over 4000 people would gather to discuss, Faith, Science, and the Human Future. Being on the organizing committee, it seemed to me that the ideas of the finest scholars from the area, and then from the world, should be part of that discussion.
Those leading scholars were not invited. The committee thought they would dominate and possibly overwhelm the discussions; so as a consolation, they allowed me to organize this display project.
The display project was titled What is Life? after Erwin Schrödinger’s book of the same title. This work is being renewed through this website: https://81018.com/ – BEC
Introduction: A sixty-sided pentagonal figure of the (kind displayed) above is known as the Pentakis Dodecahedron. A sixty-sided pentagonal figure is also known as a cumulated dodecahedron or hexacontagon.
Why not make the dodecahedron with the rather odd three-dimensional pentagonal of five tetrahedrons? It is odd simply because there is a very small gap between the tetrahedrons.
The TOT. The picture on the right is a tetrahedral-octahedral-tetrahedral truss or chain. I dubbed it a TOT line. The first time I thought I was observing it in action as a trusss system to support the undulating roof system of the Kansai Airport in Japan. In February 2007, I realized that truss was actually just half a TOT when I actually made the model pictured here. It is a simple parallelogram that can be found in many basic geometry textbooks. Yet, it seems that this tetrahedral-octahedral chain has not been examined in depth.
Worldviews limit perspective 