Date: Sat, 4 Jan 2014
Subject: Cellular automaton
Thank you for your 2003 H. Paul Rockwood Memorial lecture on cellular automata. I just finished watching the YouTube version of it and I have learned substantially and I have been challenged. It was all quite brilliant.
In light of your work, I need to examine further several simple facts:
1. The universe is mathematically very small. Using base-2 exponential notation from the Planck Length to the Observable Universe, there are just 202.34 (NASA, Kolecki) to 205.11 (Paris, Luminet) notations, steps or doublings. This work (the mathematics) actually began in a high school geometry class 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 tetrahedrons in each face and the six octahedron in each corner. We kept going within until we found the Planck Length. It was easy to decide to multiply by 2 out to the Observable Universe. Then it was easy to standardize the measurements we just multiplied the Planck Length by 2 until we were in the range of the Observable Universe.
2. The small scale universe is an amazingly complex place. We had to assume the Planck Length is a singularity of one vertex and then we followed the expansion of vertices along each notation. By the 60th notation, of course, there are over a quintillion vertices and at 61st notation another 3 quintillion vertices are added. Yet, it all must start most simply and here the principles of computational equivalence has its a great possible impact. We are right now researching to see how and if AN Whitehead’s point-free geometries could also have applicability.
3. This little universe is readily tiled by the simplest structures.
4. Yet, the universe is delightfully imperfect. In 1959, Frank/Kaspers discerned the 7.38 degree gap with a simple construction of five tetrahedrons looking a lot like the Chrysler logo. The icosahedron can be constructed with two facing pentastars and a band of ten tetrahedrons between them. When made up of 20 tetrahedrons, the icosahedron is more than irregular, it is quite squishy. We call it quantum geometry in our high school. It is the opening to, or the beginning of, randomness.
5. The Planck Length as the next big thing. The behavior may not be so complicated on the surface, but far more complicated just below it. Computers generate rules and these simple rules might be what nature is using below the thresholds of measuring devices.
I could go on, but let’s see if these statements are at all helpful. Our work is just two years old yet relies on several assumptions that have been rattling around for 40 years. I’ll insert from references below.
Many thanks again for your cellular automaton lecture.