|By Andrea Dibben
Originally published in the October 2011 Socionomist
In early 1982, the head of the laboratory where Daniel Shechtman worked came to his desk “smiling sheepishly.” Shechtman recalls what happened next:
He put a [crystallography] 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, ‘You know, I teach this book. I don’t need to read it. I know it’s impossible, but here it is. This is something new!’ That person expelled me … . 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. He was a good friend of mine.’1
What had this Israeli scientist done to deserve the disdain of his colleagues? He had discovered quasiperiodic crystals on April 8, 1982.2
Shechtman later described them as “fascinating mosaics of the Arabic world reproduced at the level of atoms.”3 Quasiperiodic crystals are regular; yet, they form non-repeating patterns that usually appear in aluminum alloys. X-rays first revealed the internal structure of crystals in 1912; and from that time forward, scientists concluded that all crystals possessed rotational symmetry and a periodic structure. This consensus held for more than 70 years.4 The accepted rule was that there were only five possible rotational symmetries: single, double, triangular, quadruple and hexagonal. Forms that were not regular and periodic (for example, the pentagonal form Shechtman identified) were deemed impossible.
When Shechtman first observed the five-fold symmetry, he thought it must be “twinning”—period crystals fusing at an angle. Yet, when he looked for twins and twin boundaries, they were not there.1 “If you look at historical materials, people probably had found quasicrystals before,” notes fellow chemist Patricia Thiel. “But they didn’t have the tools or the gumption to say what they were seeing. Danny had both.”5
Two years after Shechtman discovered quasicrystals, he finally succeeded in getting a paper published, but only after it was co-authored with Ilan Blech, a colleague at Technion; John Cahn, a senior scientist; and French crystallographer Denis Gratias.
The math behind Shechtman’s discovery dated from antiquity. Medieval Islamic artists used it in tile mosaics. But instead of curiosity about a potential breakthrough, the scientific community—often lauded for constantly questioning and innovating—effectively dismissed this new class of solid matter. Another Nobel laureate went so far as to say, “Danny Shechtman is talking nonsense. There is no such thing as quasicrystals, only quasi-scientists.”4
But new science breaks old paradigms. This October, 29 years after Shechtman’s discovery, the Royal Swedish Academy of Sciences awarded him the Nobel Prize in Chemistry for 2011.
Robert Prechter featured Shechtman’s research in The Wave Principle of Human Social Behavior (1999), when he wrote about how these newly identified objects are based on the Golden Ratio:
[Daniel Shechtman] discovered a type of crystal that contains spiral arrangements and is governed by Fibonacci mathematics. Initially believed impossible, the quasi-crystal has been verified by photographs made with an electron microscope. The quasi-crystal exhibits ‘five-fold symmetry,’ which means that a single rotation of the crystal exposed to an X-ray produces a symmetrical scattering pattern five times (p. 428).6
This characteristic of fiveness is found in the Wave Principle along with fractality, a relationship to the Fibonacci sequence of numbers, and robust self-similarity. And, similar characteristics were discovered in a 1993 study of DLA clusters by Alain Arneodo and four other scientists from the Centre de Recherche Paul Pascal and the École Normale Supérieure in France. In their concluding proposal, the researchers wrote the following:
The intimate relationship between regular pentagons and Fibonacci numbers and the golden mean…has been well known for a long time. …The recent discovery of ‘quasi-crystals’ in solid state physics is a spectacular manifestation of this relationship. This new organization of atoms in solids, intermediate between perfect order and disorder, generalizes to the crystalline ‘forbidden’ symmetries, the properties of incommensurate structures. Similarly, there is room for ‘quasi-fractals’ between the well-ordered fractal hierarchy of snowflakes and the disordered structure of chaotic or random aggregates (pp. 68-69).7
The study, like others, shows a greater level of order in apparently random processes than was previously expected. Prechter was interested in this new research because the Wave Principle proposes the same conclusion in relation to human social behavior.
Another important aspect of quasicrystals involves their mosaics, which are known as Penrose tiling. Previously, the consensus view was that all solid matter reflected only two patterns: completely random (glass) or perfectly ordered (periodic). Penrose tiling falls in between. In 1984, physicist Paul Steinhardt and graduate student Don Levine used computer-generated images to see what diffraction pattern Penrose tiling would reflect in a real atom. It produced a diffraction pattern in the middle of the two accepted outcomes.
Prechter discussed the mathematical similarities of Penrose tiles to the Elliott wave model of social-mood change:
It turns out that both the areas of the tiles and therefore the numbers of the tiles in any given (large) area, are in Fibonacci proportion, the same proportion that governs both the numbers and sizes of motive vs. corrective Elliott waves. … Penrose’s tiles support the applicability of the Fibonacci sequence to processes of structured yet infinitely variable partitioning and its inverse, structured yet infinitely variable building (p. 432).6
Shechtman’s story brings to mind the walls of skepticism other innovators have faced. Daniel Kahneman, who along with Vernon Smith was a pioneer of behavioral economics, recalls how some of his work was received: “We were also accused of spreading a tendentious and misleading message that exaggerated the flaws of human cognition.”8
Prechter, however, recognized the seminal importance of a market simulation that Smith conducted:
While these experiments were conducted as if participants could actually possess true knowledge of coming events and so-called fundamental value, no such knowledge is available in the real world. The fact that participants create a boom-bust pattern anyway is overwhelming evidence of the power of the herding impulse (pp. 153-154).6
Three years later, Smith and Kahneman were awarded a Nobel Memorial Prize in Economic Sciences.
History offers many instances of individuals who challenged conventional beliefs, and in turn were labeled heretics, ostracized, ridiculed and more often just plain ignored. This hostile response is not a thing of the distant past, but an ever-present deterrent to innovation. We applaud Daniel Shechtman for his discovery, and for the courage to challenge textbook orthodoxy in establishing a new perspective.■
1Interview with Technion Distinguished Professor Dan Shechtman. Science & Technology, YouTube, Retrieved from https://www.youtube.com/watch?v=EZRTzOMHQ4s.
2Chang, K. (2011, October 5). Israeli scientist wins Nobel Prize for chemistry. The New York Times, Retrieved from http://www.nytimes.com/2011/10/06/science/06nobel.html?_r=2&scp=1&sq=shechtman&st=cse.
3Nobel Prize in chemistry laureate Professor Dan Shechtman—Jerusalem (2011, October 9). Demotix, retrieved from http://www.demotix.com/news/865022/nobel-prize-chemistry-laureate-prof-dan-shechtman-jerusalem.
4Shtull-Trauring, A. (2011, January 4). Clear as crystal. Haaretz.com, Retrieved from http://www.haaretz.com/weekend/magazine/clear-as-crystal-1.353504.
5Marder, J. (2011, October 5). What are quasicrystals, and what makes them Nobel-worthy? PBS Newshour, Retrieved from http://www.pbs.org/newshour/rundown/2011/10/quasicrystals-win-chemistry-nobel.html.
6Prechter, R. (1999). The Wave Principle of Human Social Behavior. Gainesville, Georgia: New Classics Library.
7Arneodo, A., et al. (1993). Fibonacci sequences in diffusion-limited aggregation. Growth Patterns in Physical Sciences and Biology.
8Autobiography of Daniel Kahneman. Nobelprize.org, Retrieved from http://www.nobelprize.org/nobel_prizes/economics/laureates/2002/kahneman-autobio.html.
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