a personal reflection by Bruce Camber about a National Science Fair project by Bryce Estes entitled, *Walk the Planck*

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##### Multiply the Planck Length by 2, over and over again (base-2 exponential notation). What can we say about the first 60 notations? Is it helpful and meaningful to see the entire universe in 202-to-206 notations?

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**Background**: In September 2013 a student emailed me for advice on a possible science fair project suggested by his physics teacher. This student had been part of a December 19, 2011 class where the Big Board-little universe (BiBo-lu) was first discussed in a classroom. Having no immediate interest in chaos theory and perfect shuffles, I asked him, “Would you be interested in making Bibo-lu into a presentation? Of course, we would have to get quite creative to come up with a hypothesis that you could test.”

His physics teacher was entirely open for him to do something that interested him. Between the three of us, an hypothesis emerged and a science fair project was underway. One of the student’s first tasks was to write research paper. He did an excellent job summarizing the work of Max Planck and Albert Einstein as well as the concepts of gravity, relativity, quantum mechanics, fractals and chaos theory. Scientists have been wrestling with the relations between the fundamental forces of nature for hundreds of years. The latest iteration is CERN’s work with the Large Hadron Collider to better understand the Standard Model and the Higgs Boson or so-called *God Particle*. The student’s implied open question for which he does not have an answer is, “What happens to all these forces as one approaches the Planck Length?”

If he could answer that question, he would quickly be recognized as the next Einstein.

**The appeal of wholeness**: There is something deep within the human psyche that dislikes discontinuities. We want standards. We want things to cohere. We want things to work together. For some reason, we do not like loose ends. So, that has become the challenge that is called, “Science.” And her proponents, the scientists, have a simple task, “Tighten up all those loose ends!”

On July 5, 1687 with the publication of his *Principia*, Sir Isaac Newton was the first to unify the laws of motion and universal gravitation; it was ostensibly the first unified field theory. James Maxwell followed in 1869 by demonstrating that electricity, magnetism, and optics were manifestations of the same electromagnetic field. Einstein formally coined the term, Unified Field Theory; and throughout the 20th century there have been numerous approaches by many to determine the relations between different kinds of dynamic systems. In the 1974 that term was reworked and dubbed a Grand Unified Theory or GUT. Then, in 1986 it was reworked again as a Theory of Everything (TOE).

The Big Board-little universe has no illusions. It is not about TOEs or GUTs or Unified Anythings. It is about simple geometry and simple mathematics. By taking the simplest geometry (Plato’s solids) and simple mathematics (multiplying by 2), we have a way of making the strange familiar and the familiar strange. That is, we are able to make a few interesting observations and ask a few new questions in possibly new ways.

These observations and questions could eventually effect the way we go about seeing fragmentation and wholeness.

**December 19, 2011: the last day before the Christmas break**. You can be sure I was thinking, “What a day to be a substitute teacher!” I quickly asked myself, “How does one keep their attention? What might catch their imagination?” The first and only other time with these students was used to build models of Plato’s five solids, the tetrahedron, the octahedron, the square, the icosahedron and the dodecahedron. That was fun. The students explored the simple inside structures of the tetrahedron and octahedron. A simple paper model of the dodecahedron (pictured) needed to be re-thought, “How do we make it a bit more interesting?” One retort, “Why not make each face of that dodecahedron out of the five tetrahedrons (pictured) conveniently call a pentastar?”

Making the familiar strange opens creativity. Making the strange a bit more familiar does, too.

So, we took twelve sets of pentastars and taped them together. That object, known most often as the Pentakis Dodecahedron, could be used as a replacement soccer ball. We filled the inside cavity (pictured) with Play Doh. In a few days, we carefully removed the outer layer of pentastars. An unusual object made of Play Doh faced us. We then removed a layer of odd shaped terahedrons, and deep in the center was a percect icosahedron made of twenty tetrahedrons. Of course, we knew within each tetrahedron, perfectly filling it, are four half-size tetrahedrons and an octahedron that shares edges with those four tetrahedrons; and within that octahedron are six half-size octahedrons and eight half-size tetrahedrons all sharing a common centerpoint.

In this process the key evocative question was asked, “How many steps within to get to the Planck length?” We assumed thousands and found just over 100. Flummoxed! “Why haven’t we used this before? Could it be that it’s just too simple?”

**Naively in search of the Planck Length**. If one takes on a naive point of view, relatively easy for a high school student and an uninformed person, the Planck Length can be wonderfully fascinating to explore. If one knows science, it is difficult. There is nothing smaller than particle physics and the Planck Length is so far removed from this physics, it is like trying to study an ant when the atoms are the size of galaxies. And, if particles and atoms are the constituents of all that exists in space and time, what can you say? What do you study?

With a naive point of view, one attempts to abandon all those presuppositions… not easy to do.

At first, we referred to the Planck Length as a point. But, points are associated with space within time. A point creates a position, but theoretically has no other definition. No properties. No length. No volume. And, no other kind of dimensional characteristics. With tongue-in-cheek, we ask, “Could it be any more ephemeral and less definitive?” That it actually occupies space and time seems a bit much. So, after referring to the Planck Length as a point for almost two years, we are re-thinking that position. First, the Planck Length is by its very nature a very definitive length. So, for awhile, we said it was a special case of a point called a vertex. Yet, most everywhere a vertex is defined as a point. That is until we discovered the work of Alfred North Whitehead and his development of a point-free geometry. Could a point-free geometry have vertices that in some way actually begin to define space and time? Perhaps.

We are still just at the beginning of this study, however, we have a lot of data with which to work.

In March 2012, writing the very first two articles about this exploration, it seemed that a good place to publish these articles would be Wikipedia. All the students could readily edit both documents and help shape and move the concepts forward. And, though we could not find direct scholarly references to *base-2 exponential and geometric notation from the Planck Length to the Observable Universe*, we could find enough other scholarship around the concepts. Besides, there already was an existing Wikipedia article about *base-10 scientific notation*. We assumed that we could find more definitive work of the scholarly community on base-2 and simple geometries; “It has to be out there somewhere.”

It wasn’t. The Wikipedia people, particularly a young MIT professor, said that the article was not appropriate for Wikipedia, “This is original research.” That paper was up for part of the month of April 2012 yet deleted the first week in May 2012.

We never submitted the second article. of just the numbers (1) of vertices as they expand to the Observable Universe and (2) the lengths as they double, both with each notation. And, it was in writing this second article, primitive questions were asked about the Planck Length, the following 60 notations, and a point-free geometry.

Unfazed and undaunted, and now having these thoughts incubate for almost two years, it is time to share this work with others, particularly to submit each for critical review. The major discussions will focus on the way geometries emerge and pervade the universe, the thrust of life, and the role of the first 60 notations, steps, domains, layers or doublings within a dynamic universe that has continutiies, symmetries and harmonies.

We will look at a simple periodicity based on simple divisions. The first, a simple bell curve, by dividing in half, gives us the range of steps 101 to 103. We’ll be looking at that much more closely to see what we are missing. Then, at the division by a third, we’ll continue our initial studies of steps 67-to-68, then 134-to-136, and 201-to-204. Then the relations between other key notations will be be studied:

Quarter: 51, 102, 153, and 204

Fifths: 41, 82, 123, 164 and 205

Sixths: 34, 68, 102, 136, 170, and 204

Sevenths: 29, 58, 87, 116, 145, 174, and 203

Eighths: 26, 52, 78, 104, 130, 156, 182, and 208

Ninths: 23, 46, 69, 92, 115, 138, 161, 184, and 207

Tenths: 20.4, 40.8, 61.2, 81.6, 102, 122.4, 142.8, 163.2, 183.6, and 204

Soon to come will be attempts to normalize the Planck Length so its units are totally based on Planck Units such that each notation becomes a whole number and all the measurements currently based on meters or feet (inches, miles, etc) become the derivative measurement. We believe we can more readily discover correlations between notations across the 202-to-205 current steps. We also believe that there will be a more obvious correction to the mathematics of Pi and Phi.

What this seems to be about is to discern the boundary conditions between perfection and imperfection, between quantum physics and relativity. Extending Benoit Mandelbrot’s scope of fractal geometry down into the small scale and up into the large scale should teach us something. Focusing on basic geometric structures may also help. For example, we believe there is much more to be learned in studying all the work within chemistry that has been extended from the Frank & Kaspers article documented in 1959 (Acta ) who appear the first to document a 7.38 degree gap within a five-tetrahedral cluster, sometimes known as a pentastar. The icosahedron is a 20-tetrahedral object that has different configurations, one is with two pentastars separated by a band of ten tetrahedrons. The other has three pentastars with a cluster of four tetrahedrons touching each of them and a single tetrahedron also touching the three pentastars.

We are not sure what all this means yet, but we will continue our naive analysis.

Once we have a new paper we will link it here.

Forthcoming are:

-Space filling and tiling with the tetrahedral-octahedral chains

-Imperfections of the pentastar, icosahedron and Pentakis dodecahedron and quantum geometries

-Pentastar as the beginning of a disc and icosahedron the beginnings of a sphere and Pi.

-Frank-Kaspers, Cambridge Database Cluster, Bangalore Indian Institute of Science

-Six tetrahedral star on a plane as the basis for Phi

So, of course, there is more to come.

References:

http://www.hawking.org.uk/space-and-time-warps.html

http://plato.stanford.edu/entries/lewis-metaphysics/spacetime-points.html

http://plato.stanford.edu/entries/lewis-metaphysics/index.html

http://plato.stanford.edu/entries/lewis-metaphysics/humean-supervenience.html

http://www.fas.harvard.edu/~phildept/hall.html