Key references are below.
Thank you for your lecture, A New Kind of Science. Although over ten years ago, I have learned and have been challenged.
Intellectually, you are quite compelling.
Yet, a few facts and a few ideas may need to be further examined:
- 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 2011 in a high school geometry class when we started with a tetrahedron and divided the edges by 2 finding the octahedron in the center and four tetrahedra 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 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 by just multiplying the Planck Length by 2.
- The small-scale universe is an amazingly complex place.
Assuming the Planck Length is a singularity of one vertex, we also noted the expansion of vertices. By the 60th notation, of course, there are over a quintillion vertices and at 61st notation well over 3 quintillion vertices. Yet, it must start most simply and here the principles of computational equivalence have a possible impact. AN Whitehead’s point-free geometries could also have applicability.
- This little universe is readily tiled by the simplest structures.
The universe can be simply and readily tiled with the four hexagonal plates within the octahedron and by the tetrahedral-octahedral-tetrahedral chains.
- 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 with 20 tetrahedrons is squishy. We call it quantum geometry in our high school. It is the opening to randomness.
- The Planck Length could become 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 this might be what nature is using.
I could go on, but let’s see if these statements are at all helpful. Our work began in December 2011 within a high school, however, it relies on several assumptions — order (continuity), relations (symmetry), and dynamics (harmony) — that have been waiting to be engaged since 1972. I’ll insert a few references below.
Many thanks again for your cellular automaton lecture.
References to pages within our blogs and websites:
First principles: http://bigboardlittleuniverse.wordpress.com/2013/03/29/first-principles/
Earlier edition: http://smallbusinessschool.org/page869.html
Next Big Thing: http://tinyurl.com/PlanckLength
One of our student’s related science fair project: http://walktheplanck.wordpress.com/2013/12/03/p1/
References to your work:
UCSD Institute of Neural Computation, 2003 H. Paul Rockwood Memorial lecture 4/30/2003
How does structure take shape in the universe?
What are the fundamental problems to this approach?
What does it mean to be a universal system?
Rule 30 and 110 and computational equivalence