We don’t know what we don’t know.
Notes: Until this letter is published, we will post our history of emails to the “Letters to the Editor” department of major scientific publications.
Dear AAAS Senior Editor:
In December 2011 our high school geometry class was following the simple logic of base-2 exponentiation. We had discovered an infinite regression, or at least what seemed like such, going inside the tetrahedron and octahedron. Within the tetrahedron, by dividing each edge in half, there are four half-sized tetrahedrons in the corners and an octahedron in the middle. Inside the octahedron, dividing each edge in half and connecting those new vertices, there are six half-sized octahedrons in each corner and a tetrahedron in each of the eight faces.
How far within can we go? Where would Zeno stop? Where would Max Planck stop?
We had fun mapping the universe using base-2 notation (https://81018.com/chart). We were quite surprised to find there were less than 45 steps within to get down to the size of particle physics and just another 67 steps within to get down to the Planck scale. The next day we multiplied by two. In about 90 steps we were out to the Observable Universe. That is a total of 202 notations to encapsulate the universe.
We didn’t know what we didn’t know. We couldn’t believe it. Are we doing something wrong? Where does our simple logic break down?
We were glad to find Kees Boeke’s base-10 work, but found no base-2. We kept looking for almost a year and discovered bits and pieces, but no map of the universe using base-2 with its very special granularity. For the past five years we continued poking at our map. We added Planck Time, then the other Planck base units and said, “Voila. A Base-2 Map of the Universe.” Totally predictive, it is 100% simple mathematics but it tells a radically different story about the universe. Starting with the Planck base units and all the constants that define each, this “singularity” 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.
It is all a bit much to swallow; it is altogether too simple; and hardly anybody has truly wrestled with it. We must be doing something wrong, but what? Thank you.
Endnotes/Footnotes: To date, no scientific publication has printed this simple letter. So we ask again, “What are we doing wrong? What are we missing? What is so sacred about big bang cosmology that a more simple explanation could not at least be explored, discussed, and, if need be, discounted.”
History of submissions and responses:
Email: Monday, January 18, 2021: Aeon Magazine
Email: Monday, June 5, 2017 to Scientific American. To this day, we have not received a response.
Email: Friday, March 31, 2017 2:59 pm to AAAS, Science, No response
Email: March 31, 2017 to Journal of Cosmology, No response