**Robbert Dijkgraaf**

Director, Institute for Advanced Studies (Video Tour)

Leon Levy Professor (since July 2012)

Nadine Thomspon (Executive Assistant to the Director)

Princeton, New Jersey

ArXiv: 1of 51 (sample, *Baby Universes in String Theory*)

Homepage

Master Class

Twitter: @RHDijkgraaf

Video I and Video II of many videos

Website

Wikipedia

YouTube: And others

First email: Saturday, 15 November 2014 @ at 6:12 PM (links updated)

RE: The Past and Future of Unification

Dear Prof. Dr. Robbert Dijkgraaf,

Earlier today I signed up for your Master Class. And just now, I have spent some time on those websites with citations to you and your work.

Congratulations on all your contributions past. Quite remarkable. May you continue to be inspired to continue to challenge us all to think ever more creatively and responsibly! We are a bit impulsive and probably much to quick to jump to conclusions.

I sent you a little Tweet earlier today about some work we backed into from within our high school geometry classes.

It is obvious that we do not have a current or deep understanding of physics, advanced mathematics, or cosmology/astrophysics. Nevertheless, we are using our little paradigmatic base-2 notation from the Planck Length to Observable Universe as an outline to learn more. That we started with a tetrahedron and octahedron also imputes simple platonic geometries. Just those two dynamics have raised more questions than we have found answers. That has not stopped us from guessing and making a few wild-and-crazy speculations.

Our work is posted in three places on the web. I’ll paste in a sample below so you can easily check us out. Do you have any words of wisdom for us?

Of course, your cautions and comments will be read with the greatest respect. Thank you.

Most sincerely,

-Bruce

___________________

Bruce Camber

Austin, Texas

http://81018.com

P.S. A sample page from our work is below.

Overview to timeline: https://81018.com/bec

This page was first posted on the web: 9 September 2017

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**Is There Order In The Universe?**

Our high school geometry classes created a simple, mathematically and geometrically-ordered view of the known universe. We also found an inherent geometry for disorder.

**Yes, rather unwittingly we backed into developing what we now call our Universe View**. We used a very simple logic and math. First, we divided an object by 2 until we were down in the range of the smallest measurement of a length, then we multiplied the object by 2 until we were finally out around the largest-known measurement of a length.

Our work began in December 2011. That simple exercise resulted in measurements which opened paths to challenging facts, rather fun concepts, obviously wild-and-crazy ideas, and truly playful speculations.

There are nine references to other pages that are also linked at the bottom of the page. Also, please be advised, that this project will always be a work in progress.

1. **The Power of 2**. There are at around 202 doublings starting at the Planck Length (the smallest conceptual measurement of a length in the universe) to the Observable Universe (the largest). That is a fact (Reference #1) and it is just simple mathematics. Although a Dutch high school teacher, Kees Boeke, used base-10 in 1957 and found about 40 notations (the very first mathematically-driven Universe View), our work began with an inherent geometry; it was not just a process of adding and subtracting zeros. Plus, base-2 is so much more informative, granular, and natural; it mirrors the processes in biological reproduction and chemical bonding.

2. **Inherent Geometries**. We were studying tetrahedrons and octahedrons, two of the most simple Platonic solids. We started our project by dividing each edge of a tetrahedron in half. We connected those six new vertices and discovered a half-sized tetrahedron in each of the four corners and an octahedron in the middle.

We did that same process with the octahedron and found six half-sized octahedrons in each of the six corners and a tetrahedron within each of the eight faces (link opens a new window). We did that process of going within about 112 times. On paper, in about 45 steps we were inside the atom; and, rather unexpectedly, within another 67 steps we were *in the range* of the Planck Length.

We then multiplied our two objects by 2 and within about 90 notations or steps, we were *in the range* of the Observable Universe. Then, to standardize our emerging model, we began at the Planck Length and multiplied it by 2 until we were at the edges of the known universe. We had some help to calculate the number of notations. We settled for a range from 202.34 to 205.1 (Reference 2 – See point #4 within those 15 points).

Because we started with a geometry, we learned ways to tile the universe with that geometry. It is simple. It puts everything within a mathematically-compact relation that over the years has had a wide range of names from the aether (or ether), continuum, firmament, grid, hypostases, matrix, plenum to vinculum. We call it, *TOT tilings*. The TOT fills three-dimensional space perfectly. Also, there are two-dimensional tilings everywhere! There are many triangular tilings, square tilings, hexagonal tilings and combinations of the three. The most fascinating are the four plates of hexagons within the octahedron, all at a 60 degree angle to another sharing a common center vertex. It is all so fascinating, we are now exploring just how useful these models can become.

That tiling is a perfection, however, imperfections were readily discovered. Using just the tetrahedron, we found that not all constructions fit together perfectly.For example, the pentastar, a five-tetrahedral cluster, cannot perfectly tile space; it creates gaps. Those gaps have been thoroughly documented yet to the best of our knowledge, it was first written up by two mineralogists, Frank & Kaspers, in 1958 (opens in a new tab or window). In our simplicity, we concluded that this was the beginning of imperfections and it extended out to the 20 tetrahedral cluster known as the icosahedron, and then out to the 60 tetrahedral cluster, the Pentakis Dodecahedron. We dubbed these figures, *squishy geometry;* the constructions have considerable play. Yet in more temperate moments, we call this category of figures that do not fit perfectly together, *quantum geometry*.

3. **Numbers and Potential Geometries Gone Wild.** By the 10th doubling there are 1024 vertices. Assuming 1 for the Planck Length, there are then 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024. The simple aggregation of all notations up to 10th would be 2000+ vertices. Within just the 20th doubling (notation) there are over 1-million vertices, within just the 30th notation over 1-billion, the 40th notation over 1-trillion, and the 50th over a quadrillion vertices. By the 60th notation, a quintillion more vertices are created and that measurement is still below the range of our elementary or fundamental particles.

Imagining all the possible hidden complexities has become a major challenge!

Although this rapid expansion of vertices within each doubling is entirely provocative, it could be even greater if we follow the insights of Freeman Dyson (Reference #3 – point #11). Dyson is Professor Emeritus, Mathematical Physics and Astrophysics at the Institute for Advanced Studies in Princeton, New Jersey. He said, “Since space has three dimensions, the number of points goes up by a factor eight, not two, when you double the scale.” We are trying to figure out what that means and how to use his insight correctly.

4. **Driving Concepts**. The simple mathematics provides a basic order and continuity that we have imposed on the universe. The simplest geometries provide a robust range of symmetries and relations. Add time and put these objects in motion, folding and enfolding within each other like a symphony, and we can begin to intuit a very special dynamics and a range for harmony (Reference #4). When those concepts were first written up back in the 1970s, it seemed to describe a perfected state within space and time, but it was too vague. It needed a domain or container within which to work and it seems that this just may be it (opens in a new window or tab).

5. **Big Board-little universe and the Universe Table** (__Reference #5__). By September 2013, a class of sixth grade students got involved and a core group of about 40 high school students continued to study this formulation. First, it seemed like an excellent way to visualize the entire universe in a systematic way and on a single piece of paper. Second, as a simple ordering tool, it placed most of the academic disciplines in the right sequence. Mathematics, logic, philosophy, theology and ethics seemed to apply to every notation.

That was all very helpful, but then, we began observing some very simple correlations and let our imaginations work a little overtime.

That seems like a concrescence of meaning.

We are just starting to parse the 205.1 notations in thirds, fourths, fifths… using musical notation as the analogue and metaphor.

7. **The first 60+ notations, doublings, or layers are unchartered**. We asked, “What could possibly be there?” To get some ideas, we started going back throughout history and philosophy. We placed Plato’s Forms (*Eidos*) within the first ten notations. Aristotle’s *Ousia* (Essence) became the next ten from 11 to 20. Substances were 20-30, Qualities from 30-40, Relations 40-50 and then Systems 50-60. Within Systems we project a place for *The Mind* (Reference #7).

It was great fun to be so speculative!

“The cellular automata (of the Wolfram code) belong right within the Forms.” Of course, that’s just a simple guess. We continued, “And within Systems, we have all those academic subjects that have never had a place on a scientific grid or scale of the universe.”

We dubbed this domain “the really-real Small-Scale Universe.”

8. **Einstein-Rosen Bridges, Wormholes & Intergalactic Travel** The imagination can readily get ahead of facts, yet bridges and tunnels appear everywhere in nature. So, when we partitioned our known universe in thirds, we discovered that elementary particles and atoms began to emerge in the transition area from the first-third, our Small-Scale Universe, to the second-third, our Human-Scale. Well then, what happens in the transition to the third-third, from the Human-Scale to the Large-Scale Universe?

We decided to be wildly speculative.

In the grand scheme of things, the transition from the second-third begins with notations 136, 137 and 138. At Notation 136 you could be 874 miles above earth. At Notation 137, you would be about 1748 miles up and at Notation 138, just 3500 miles up.

What happens? “Einstein-Rosen!” was the charge. “It’s the beginning of wormholes!”

That raised a few eyebrows. After all, we surely need a shortcut to explore the Large-Scale Universe. So, now we are calling on our most entrepreneurial space cadets (Reference #8), especially Elon Musk of SpaceX, “Go out looking, but don’t go inside any of those wormholes yet. We all need to be thinking a bit more about their structure.” If we take it as a given that space is derivative of geometry, and time derivative of number, we begin to see the universe quite differently. Of course, we have far more questions than we have insights so we truly welcome yours.

9. **A system for value, thinking, logic, reasoning and more**. As you can see, our evolving Universe View was quickly becoming a structure for a rather idiosyncratic style of thinking, reasoning and logic (Reference #9).

The concept of a perfected moment in space-and-time was pushing us to think about order, relations and dynamics in new ways. Continuity, symmetry and harmony were becoming richer than space and time. This marks our first attempt to begin writing about this perception of our interior universe where our numerical-geometrical structure of the universe became its own inherent logic. It wasn’t long before we began thinking about how this structure could also be applied to thinking itself, then reasoning, and so much more.

A mentor and friend from long ago, John N. Findlay, might call it an architecture for the thrust or zest for life.

This system seems to have within it many possibilities for seeing wholeness where today information and systems do not cohere, so we are glad to share these skeletal models (including the one just below) for your inspection. We hope you find it all as challenging as we have, and that you have enjoyed taking this rather quick tour through this work.

rhd@wins.uva.nl

rdijkgraaf@ias.edu