Most recent email: 1 September 2020 @ 12 noon
Dear Prof. Dr. Daniel Shechtman:
We are picking up on an email that I sent you back in 2011. We are now following all your efforts with fivefold symmetry; it is a major study for us yet in a most idiosyncratic way.
Not long after this note you (below), our high school geometry classes began exploring the interiority of the tetrahedron and octahedron: https://81018.com/home/ Essentially we started following Zeno deeper and deeper inside. In about 45 steps we were down among the fermions, and in another 67 steps we were up against the Planck Wall. We did an about-face, but this time we used the Planck Length as our standard measurement. Doubling each step, in 112 steps we were back in the classroom and in another 90 steps we were at the edge and age of the universe. It became our STEM tool of choice. After all, we created it! …all with the Planck base units.
It was our base-2 map of the universe! It had the Planck base units, our simple geometries (tiling and tessellating the universe), all in 202 notations. Then it started asking us questions and now we are struggling.
Might you have any thoughts about it all?
First email: Thursday, October 20, 2011,10:25 PM
Dear Prof. Dr. Daniel Shechtman:
I listened to your video reflections online (produced by Technion) about the early reception of your work and your pointed encouragement of those of us who have rightly or wrongly been treated as speculative fools. Unfortunately, I needed to make a living so in 1980, I went back to a business that I had started before my doctoral work in perfected states within space-time.
Perhaps I would have been one of the early enthusiasts around your work.
In 1970-1972 I worked within a group at Harvard called the Philomorphs with Prof. Arthur Loeb. Bucky Fuller was a frequent visitor. I was smitten with the notion of perfection within the imperfect, quantum world. The EPR Paradox was my starting point. Victor Weisskopf (Physics, MIT) was on my path and befriended me. Under his guidance, I visited with John Bell at CERN and later I had a six month study with Olivier Costa de Beauregard and JP Vigier in Paris where we looked in on the work of Alain Aspect on Bell’s Inequality theorem and the EPR paradox. In 1977 I spent a day with David Bohm and his doctoral candidates talking about points, lines, triangles and the tetrahedron.
When I first learned of Bohm’s death, I pulled down a book he had given to me from that day, Fragmentation & Wholeness, and realized he never asked what was perfectly enclosed within the tetrahedron. A year later I asked the question about the octahedron.
Business has been good, but demanding. Only this year have I slowed down a little. I have been playing with models that I created by having molds made to knock out thousands of tetrahedrons and octahedrons. I am still a novice, but I think you might be interested in my approach:
Only recently have I begun to consider the icosahedron.
The original file was posted here: http://smallbusinessschool.org/page2168.html
My guess right now is that the dodecahedron is really a sixty-sided cluster and each of the pentagonal faces are a cluster of five tetrahedrons. That they are imperfect intrigues me. I have begun a most speculative page and it is the height of stupidity to share it with a new Nobel laureate, but you were so very warm and kind in that video and you have walked over the coals for almost 30 years.
I have just started working on this little page; and, though I know you are inundated with requests and demands on your time, I thought you might appreciate it.
Notes: Scaling theory of localization: Absence of quantum diffusion in two dimensions / pp. 673-676. doi:10.1103/PhysRevLett Phys.Rev.Lett.,42,10 42.673. (p. 138).