Grünbaum, Branko

Branko Grünbaum


First email: Thu, Jan 9, 2014 at 5:21 PM

Dear Prof. Dr. Branko Grünbaum:

Is this just nonsense or should we pursue it further?
Some days I think it is a new path. Other days, I
think its nonsense.


1. The universe is mathematically very small.
Using base-2 exponential notation from the Planck Length
to the Observable Universe, there are somewhere over 202.34
and under 205.11 notations, steps or doublings. NASA’s Joe Kolecki
helped us with the first calculation and JP Luminet (Paris Observatory)
with the second. Our work began in our high school geometry
classes when we started with a tetrahedron and divided the edges
by 2 finding the octahedron in the middle and four tetrahedrons
in each corner. Then dividing the octahedron we found
the eight tetrahedron in each face and the six octahedron
in each corner. We kept going inside until we found the Planck Length.
We then multiplied by 2 out to the Observable Universe. Then it
was easy to standardize the measurements by just multiplying
the Planck Length by 2. In somewhere under 205.11 notations we go
from the smallest to the largest possible measurements of a length.

2. The very small scale universe is amazingly complex.
Assuming the Planck Length is a singularity of one vertex, consider
the expansion of vertices. By the 60th notation, of course, there are
over a quintillion vertices and at 61st notation well over 2 quintillion more
vertices. Yet, it must start most simply and here we believe the work
within cellular automaton and the principles of computational equivalence
could have a great impact. It’s mathematics of the most simple. We also
believe A.N. Whithead’s point-free geometries should have applicability.

3. This little universe is readily tiled by the simplest structure.
The universe can be simply and readily tiled with the four hexagonal plates
within the octahedron and by the tetrahedral-octahedral-tetrahedral chains.

4. And, the universe is delightfully imperfect.
In 1959, Frank/Kaspers discerned the 7.38 degree gap with a simple
construction of five tetrahedrons (seven vertices) looking a lot like the Chrysler
logo. As I said in the restaurant, we have several icosahedron models with its
20 tetrahedrons and call squishy geometry. We also call it quantum geometry
(just in our high school) and we guess, “Perhaps here is the opening to randomness.”

5. The Planck Length as the next big thing.
Within computational automata we might just find the early rules
that generate the infrastructures for things. Given your fermions and proton
do not show up until the 66th notation or doubling, what are we to do with those
first 65?

Bruce Camber

First principles:
The earlier edition:

That student’s related science fair project:

My working article about it all:

Wicked wanderings:

Other working references: