He was fired by two time Nobel Prize winner Linus Pauling. As of today he is the recipient of his own Nobel Prize for defending the very “impossible” form of matter he was fired over. His story of ridicule, ostracism, hostility, and rejection by the mainstream scientific community for affirming something anomalous/discordant to the predominant scientific paradigm reads like something straight out of Thomas Kuhn’s The Structure of Scientific Revolutions. But he was right! The scientifically impossible in this case was not only possible, it was actual.
“For a couple of years I was alone, I was ridiculed, I was treated badly by my peers and my colleagues, and the head of my laboratory [two-time Nobel Prize recipient Linus Pauling] came to me smiling sheepishly and he put a book on my desk and said ‘Danny, why don’t you read this and see that it is impossible, what you are saying.’ And I said, ‘I teach this book… I know what it says, and I know it’s impossible, but here it is! This is something new!’ That person expelled me from his group He said ‘you are a disgrace to our group; I cannot bear this disgrace,’ and he asked me to leave the group. So I left the group. And he was a good friend of mine! But he could not stand that people would say ‘this nonsense came from your group!’ This was the atmosphere. People not only did not believe in what I said: people were hostile! The community of non-believers was very large in the beginning. In fact it included everybody! The leader of the group was Linus Pauling, a two-time Nobel laureate. He was a very important figure, and the idol of the American Chemical Society, and to his last day he was standing on stages and publishing papers saying that Danny Shechtman is talking nonsense.
“Two years later I came back to Technion, and here I met professor Ilan Blech who was the first person to believe in my observations, and we linked forces and he proposed a physical model that explains how these crystals could form. And the two of us for publication in a journal, the Journal of Applied Physics, and the paper was rejected on the grounds that it would not interest the community of physicists. And so that summer of 1984 I went back to NBS and met another colleague of mind, John Cahn who was the chief scientist there. Then he invited another scientist, from France named Denny Gratius, and the four of us published another paper (D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “A Metallic Phase with Long Ranged Orientational Order and No Translational Symmetry”), which was published very quickly, and then hell broke loose, because it did interest the community, and many scientists around the world started to work on these materials, and they called me from around the world: ‘I have it! I have it! I have it too!’” And so the community of believers grew, slowly; the community of unbelievers shrunk. The new form of matter which had different symmetries than known before, which is called quasi-periodic crystals, or in short quasicrystals, is accepted into the community of crystal. So the definition of crystals was broadened to include crystals which were not known before.” -Dan Shechtman
The Geometric pattern of Penrose tiling which occurs physically in quasicrystals was completely unknown even to mathematicians until the 1970s when it was presented as a mathematical model by Roger Penrose. As the tiling pattern expands over larger ratios it converges to the ever present Fibonacci/Golden Ratio known as phi intrinsic to a vast swath of diverse yet similar structures including spiral galaxies, snowflakes, neural connections, flowers, electromagnetic field borders, circulatory and pulmonary structure, basic chemical arrangements (tetrahedron, icosahedron, etc.), and so on (see my article Fibonacci, Fractals, and Inorganic Teleology for further details and implications).
 “For icosahedral quasicrystals [see image below], each approximant may be characterized by a rational approximant T,, = Fn,+1/Fn (Fn is a Fibonacci number) to the golden mean T. As TnT the lattice constants and the number of atoms contained in a lmit cell tend to inﬁnity. The lattice constant of an nth order cubic approximant to an icosahedral quasicrystal may be expressed where aqc is a quasilattice constant – the edge of the golden rhombohedral tile. Each next approximant therefore has a lattice constant that is approximately 1.62 times larger. The volume of the next approximant, and correspondingly also the number of atoms in the unit cell, increase by a factor of T^3 = approximately 4.24. In practice, a third or fourth generation approximant is essentially indistinguishable from the inﬁnite quasicrystal” (J. B. Suck, Michael Schreiber, Peter Häussler, Quasicrystals: An Introduction to Structure, Physical Properties, and Applications, p. 397).
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