# Daniel Shechtman and His Fivefold Symmetry

**The Nobel Prize**. Though an exclusive little committee in Norway and Sweden, the Nobel Prize people do have some of the best scientific advisers in the world. It is worth looking at their selections each year. It is worth taking time to listen to the lectures of Nobel laureates.

**The 2011 Nobel Prize in Chemistry: Daniel Shechtman** The scientific community at first ridiculed and even scorned this man for his work and his conclusions about 30 years before he received the prize. It took him awhile to sell his concepts and to have enough others replicate his research so others believed. He stood his ground on simple truths and won on principle.

**Evolving concepts: From our Universe to a Multiverse** There are bridges being constructed by thought leaders like Lisa Randall between this universe and mathematically-defined multiverses.

Shechtman’s work is significant because it opens the way to re-examine the nature of the five basic structures of geometry and and their applications from everything from __physics to chemistry to biology to our mind__. Also, it is within these simple, basic structures — the tetrahedron, octahedron, cube, dodecahedron and icosahedron — we just might find clues to the very nature of the mathematics the appears to be a bridge to another universe.

Most people do not know these simple structures nor what is naturally and sometimes perfectly inside each of them. There is exquisite complexity within the simplicity of each. Although the following letter is within the correspondence section, it is duplicated here because there is a profound link between quantum physics, the gap and indeterminacy, and the imperfections of the quasicrystals. It is here to remind us to think about it all.

## An Open Letter to Daniel Shechtman

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.

Here are a few related links:

• **First principles**: https://81018.com/foundations/

• **Historic perspective**: https://81018.com/home/

• **The icosahedron**: https://81018.com/icosahedron/

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.

Warmly,

-Bruce

Continuity, Symmetry & Harmony

Evocative questions about the basic basics:

Let us study five-fold symmetry

Assorted references (though each still needs to be vetted):

1. Roger Penrose five-fold tiling and the Golden Ratio

3. Molecules With Five-Fold Symmetry As A Two-Dimensional Crystal? Not So Impossible Any More

and many more reference and much more discussion to come