Response to Twitter Question: Quasicrystals’ Imprint on Reality

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A Twitter user asked us, “if the quasicrystals are fractal and fundamental, wouldn’t they leave an imprint on many levels of reality?”


Response by Klee:

They do leave an imprint on physical reality. For example, the universe may have icosahedral symmetry.

Solid-state physics provides evidence of golden ratio values related to the E8 lattice.

The golden ratio is a fundamental signature of quasicrystals found in nature whether that be 1-D, 2-D or 3-D.

Quantum mechanics has a fundamental relationship to the golden ratio as shown in the work of Lucien Hardy of the Perimeter Institute.

All of chemistry can be understood by all the understanding of the simplest atom, hydrogen. The work of Herovska, Suresh and Koga showed how the golden ratio is fundamentally related to the hydrogen atom.

Check out this presentation regarding the quasicrystalline nature of consciousness in the universe – it has more specific references to some of the above statements:

Late Night Discoveries

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By Fang Fang. October 18, 2016.

A few years ago I discovered that the dihedral angle of the 600-cell is exactly the same as the relative face rotational angle in the 20-group twist. When I told Klee about this, he had the intuition that this relationship cannot be simply a coincidence. He conjectured that there should be an inverse relationship between the curvature in the 600-cell (which is on a 3-sphere) and the twisting angle in the 20-group twist because they both encode the geometric frustration in the regular tetrahedral packing.

Klee has been very persistent on his conjecture although various scientists, both in and out of our group, have tried but not been able to prove it. Read More

Breakthrough: An Important Proof

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The other day, Fang sent out this exciting email. It started with the sentence, “Hi Klee, we solved your inverse proportionality puzzle!!!”

After congratulations were said and plans to toast with some wine and whiskey the following day were made,  I wrote the team the following email which I would like to share: Read More

The Arrow of Time and Other Things… Thoughts From Nepal

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Klee Irwin attending the 13th international conference on quasicrystals in Katmandu, Nepal

My trip to the 13th International Conference on Quasicrystals in Nepal was one of those things in life where one thing leads to another and where you really could never have predicted it but you just trusted the intuition to flow with something. The two big benefits that I needed for this trip but which I did not know that I needed prior to embarking on it is that I connected with one of the only theoretical physicists in the world who understand particle physics, cosmology and quasicrystal mathematics. Lantham Boyle. And he’s going to come out to California from the Perimeter Institute, where he works and do a workshop for us. Hopefully, that will lead to some important collaboration, where his involvement may resolve crucial pieces of our puzzle.

The other fortuitous thing that happened as a result of this trip is that I began writing a paper that moves our theoretical framework forward by an important leap. It is the connection, in a formal manner, between language theory, quasicrystals, and the second law of thermodynamics — which turns out not to be a law at all, as Erwin Schrodinger realized when he invented the term negentropy.

The second law of thermodynamics incorrectly says that things always dissolve into disorganization. This old idea is based on the experiment that, for example, when you have hot air in the bedroom and behind a closed door, you have cold air in the bathroom, the hot air can be understood as being organized in one space apart from the cold air that is organized in the other space. Entropy is the opposite of organization. It is disorder and homogeneity. So when we open the door, all the heat between them will commingle and evenly distribute homogeneously. This lower organized state is more entropic than when the door was closed. This is called the entropic arrow of time, where the idea is that the universe is moving toward a state of greater and greater disorder. Lack of order is lack of meaning or lack of information. But is this true? Is the second law of thermodynamics actually a law? It turns out that it is not. The universe is evolving toward higher and higher states of self-organization. Negative entropy. The arrow of time is going in the opposite direction from the direction most people are taught in high school physics classes. For example, most of the well established cosmological models, such as big bang theory, say that, a long time ago, the universe was in a higher entropy state as a homogenous quark plasma. After that, it self organized into a less homogenous hydrogen universe. And then it organized into solar systems and galaxies and galaxy clusters. The hydrogen atoms self-organized via solar processes into 81 stable elements. Those then self organized into millions of chemical compounds. Massively complex code-based molecules emerged, such as DNA. This then became the basis for biospheres, the most complex thing discovered in the universe so far. Biospheres evolve toward infinite self organization and complexity. So I am writing a paper, somehow prompted by this trip, on what emergence theory says should happen in our code theoretic framework with respect to entropy and negative entropy.

The Himalaya Mountains are stunning. I have never seen things reach so high into the sky. There are mountain ranges below the clouds which are themselves tall. And then, above the clouds, whitecapped peaks of the Himalayan mountain range sore even higher. Burnt orange monkeys with their babies are frolicking outside my balcony on the second story of a three-story hotel perched in the mountains overlooking the valley. The streets are chaotic and the poverty is remarkable. But the people have a calm gentleness and you feel safe. Like any city in a Third World country, people tend to press on their automobile horns a little too frequently for my western ears. But here in this land of melodic spoken language and Hindu and Buddhist influenced culture, all of the horns make a musical sound. And so from my room, I can hear the melodic roles of sequences of notes from the car horns in the city below. It is a beautiful place, and I may never have another opportunity to come here again. So I am glad that I did.

–Klee Irwin. Kathmandu, Nepal, September 22nd, 2016 (attending the 13th International Conference on Quasicrystals)

Musings On Where Humanity Is Headed

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There is probably life somewhere within most solar systems. But not necessarily high consciousness life. If a mutant lion strain become significantly more intelligent than its prey, it would destroy itself. This is how the biosphere grows and maintains symbiosis.

The shark is far more evolutionarily advanced than the homo sapiens. Some people have a distorted perception that humans are at the top of an evolutionary hierarchy. We are not more physically gifted or evolved than any other animal and we are less so than many.

There have been 100 million species so far on this planet. And that was over a duration of one third the age of the universe. And with that vast collection of different DNA instances, only once did an animal become so far out of balance and freakishly intelligent than the rest of the biosphere. Once. A statistician will tell you that is a throwaway number. You cannot presume that our sophisticated level of abstraction and intelligence and ability to discover mathematics and the code by which the universe works and to project our consciousness forward and backwards in time and create story and intrigue is something that occurs approximately once out of every 100 million species on a given biosphere. In fact, because it has only occurred once and not twice or thrice, a statistician will explain to you that it probably never occurs at all other than that one time. Why didn’t the biosphere correct this imbalance, as it usually does? After all, we almost wiped out much of the biosphere including ourselves in a nuclear holocaust.

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