On following the work of the AAAS, Science Magazine and Holden Thorp…

H. Holden Thorp, Editor-in-Chief, Science
American Association for the Advancement of Science

Books: Our Higher Calling
Google Scholar

First email: 27 February 2020 @ Noon

RE: An Appeal to you and your readers to help us solve a basic math and logic problem

Dear Prof. Dr. H. Holden Thorp:

In 2011 our high school geometry classes were studying the tetrahedron and octahedron. By dividing the edges in half and connecting those new vertices, we could see fitting perfectly within the tetrahedron are four “half-sized” tetrahedra, one in each corner, and an octahedron in the middle. Within the octahedron we found six “half-sized” octahedra, one in each corner, and a tetrahedron, one in each of the eight faces.

While looking at our model, someone asked, “How far down inside can we go?” We discovered it only took 45 “halving” steps to get down into the measurements of particle physics and just another 67 to get down within the Planck scale. To standardize those measurements, we then used the Planck length as the size of our edge and multiplied by 2. In 112 steps we were back in the classroom, but most surprisingly, in just another 90 steps we were out to the age and size of the universe.

We were more than surprised!  202 steps or notations or groups, that’s all it took to map the universe. It stopped us cold. We hadn’t see anything like it! We decided it would be our own home-grown STEM tool.

We looked to find out what the experts were saying about our little puzzle. We couldn’t find anything from the scholars. We did find Kees Boeke’s work in 1957 in a Dutch high school where he created a base-10 scale of universe in 40 jumps. Our approach was quite a bit more ordered and granular. It had a structure. More than adding another zero, our progression forced us to think, “What is a group? How are things related? Where do we stop?” So, we learned about Max Planck’s work. Surely Zeno didn’t have such a mentor! We also continued our studies of that tetrahedral-octahedral cluster. We touched on combinatorics,  learned a little about Euler and  base-2 exponentiation, and a little about cubic close packing of equal spheres, then asked, “Could something as simple as sphere-stacking account for the expansion of the universe?”

We were flummoxed.

It has been remarkable journey; but our little map was out of sync with so much of physics and cosmology, we began asking ourselves, “Has our logic failed us?” It is clearly an idiosyncratic model. We must be doing something wrong, but what? Might you or the readers of Science have some ideas? Thank you.

Most sincerely,
Bruce Camber


Future research: Halving lines in fission (MIT),  Density Matrix Renormalization Group Reference Wavefunction (China),

1. The first 67 notations constantly prodded us. What’s there?  We began studying the work of Robert Langlands, Ed Witten and others. There were many proposed ideas, but no integrative structure within which to work.

We have continued to poke at our map. We added Planck Time (2014), then the other Planck base units (2015) and said, “Voila. A Base-2 Map of the Universe.” Totally predictive, it is 100% simple mathematics but from the little that we understand, we have come to realize that is is an entirely idiosyncratic way of looking at our universe.

Where do simple math and logic go astray? The Planck base units and all the constants that define each are called a “singularity” but it is more like an “alphabet-and-number soup” it has so many equations defining it. Naturally inflating, it seems to encapsulate all the appropriate epochs of the big bang without a bang.

2. We pulled the first two paragraphs out because they could readily be considered patronizing:

“You are an all American, a symbol statement of what makes this country great… a lover of life, adventuresome, bold, questioning, prodding, a risk taker, a dream maker, the perfect person to become the editor-in-chief of Science. And, wouldn’t you agree, that it is “…the world’s most important publication for the sciences.”

Given your extraordinarily roles in life, you are one of the best people to whom we can turn with a very basic problem. We’ve backed into a conundrum.


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