A case of Kuhn, quasicrystals & communication – Part II

Did science journalists find QCs anomalous? Did they report the crisis period as it happened or as an isolated incident? Whether they did or did not will be indicative of Kuhn’s influence on science journalism as well as a reflection of The Structure’s influence on the scientific community.

In the early days of crystallography, when the arrangements of molecules was thought to be simpler, each one was thought to occupy a point in two-dimensional (2D) space, which were then stacked one on top of another to give rise to the crystal. However, as time passed and imaginative chemists and mathematicians began to participate in the attempts to deduce perfectly the crystal lattice, the idea of a three-dimensional (3D) lattice began to catch on.

At the same time, scientists also found that there were many materials, like some powders, which did not restrict their molecules to any arrangement and instead left them to disperse themselves chaotically. The former were called crystalline, the latter amorphous (“without form”).

All substances, it was agreed, had to be either crystalline – with structure – or amorphous – without it. A more physical definition was adopted from Euclid’s Stoicheia (Elements, c. 300 BC): that the crystal lattice of all crystalline substances had to exhibit translational symmetry and rotational symmetry, and that all amorphous substances couldn’t exhibit either.

An arrangement exhibits translational symmetry if it looks the same after being moved in any direction through a specific distance. Similarly, rotational symmetry is when the arrangement looks the same after being rotated through some angle.)

In an article titled ‘Puzzling Crystals Plunge Scientists Into Uncertainty’ published in The New York Times on July 30, 1985, Pulitzer-prize winning science journalist Malcolm W Browne wrote that “the discovery of a new type of crystal that violates some of the accepted rules has touched off an explosion of conjecture and research…” referring to QCs.

Malcolm W. Browne

Paper a day on the subject

In the article, Browne writes that Shechtman’s finding (though not explicitly credited) has “galvanized microstructure analysts, mathematicians, metallurgists and physicists in at least eight countries.”

This observation points at the discovery’s anomalous nature since, from an empirical point of view, Browne suggests that such a large number of scientists from fields as diverse have not come together to understand anything in recent times. In fact, he goes on to remark that according to one estimate, a paper a day was being published on the subject.

Getting one’s paper published by an academic journal worldwide is important to any scientist because it formally establishes primacy. That is, once a paper has been published by a journal, then the contents of the paper are attributed to the paper’s authors and none else.

Since no two journals will accept the same paper for publication (a kind of double jeopardy), a paper a day implies that distinct solutions were presented each day. Therefore, Browne seems to claim in his article, in the framework of Kuhn’s positions, that scientists were quite excited about the discovery of a phenomenon that violated a longstanding paradigm.

Shechtman’s paper had been published in the prestigious Physical Review Letters, which is in turn published by the American Physical Society from Maryland, USA, in the 20th issue of its 53rd volume, 1984 – but not without its share of problems.

Istvan Hargittai, a reputed crystallographer with the Israel Academy of Sciences and Humanities, described a first-hand account of the years 1982 to 1984 in Shechtman’s life in the April 2011 issue of Structural Chemistry. In these accounts, he says that,

Once Shechtman had completed his experiment, he became very lonely as every scientific discoverer does: the discoverer knows something nobody else does.

In Shechtman’s case, however, this loneliness was compounded by two aspects of his discovery that made it difficult for him to communicate with his peers about it. First: To him, it was such an important discovery that he wanted desperately to inquire about its possibilities to those established in the field – and the latter dismissed his claims as specious.

Second: the fact that he couldn’t conclusively explain what he himself had found troubled him, kept him from publishing his results.

At the time, Hargittai was a friend of a British crystallographer named Alan Mackay, from the Birkbeck College in London. Mackay had, a few years earlier, noted the work of mathematician Roger Penrose, who had created a pattern in which pentagons of different sizes were used to tile a 2D space completely (Penrose had derived inspiration from the work of the 16th century astronomer Johannes Kepler).

In other words, Penrose had produced theoretically a planar version of what Shechtman was looking for, what would help him resolve his personal crisis. Mackay, in turn, had attempted to produce a diffraction pattern simulated on the Penrose tiles, assuming that what was true for 2D-space could be true for 3D-space as well.

An example of a Penrose tiling

By the time Mackay had communicated this development to Hargittai, Shechtman had – unaware of them – already discovered QCs.

There was another investigation ongoing at the University of Pennsylvania’s physics department: Dov Levine, pursuing his PhD under the guidance of Paul Steinhardt, had developed a 3D model of the Penrose tiles – again, unaware of Shechtman’s and Mackay’s works.

Thus, it is conspicuous how the anomalous nature of discoveries – which are unprecedented by definition because, otherwise, they would be expected – facilitates a communication-breakdown within the scientific community. In the case of Levine, who was eager to publish his findings, Steinhardt advised caution to avoid the ignominy that might arise out of publishing findings that are not fully explicable.

In the meantime, Shechtman had found an interested listener in Ilan Blech, another crystallographer at NBS. They prepared a paper together to send to the Journal of Applied Physics in 1984 after deciding that it was imperative to get across to as many scientists as possible in the search for an explanation for the structure of QCs.

However, since they had no explanation of their own, the paper had to be buried “under a mountain of information about alloys,” which prompted the Journal to write back saying the paper “would not interest physicists.”

Shechtman and Blech realized that, as a consequence of reporting such a result, they would have to spruce up its presentation. Shechtman invited veteran NBS crystallographer John Cahn, and Cahn in turn invited Denis Gratias, a French crystallographer, to join the team.

Even though Cahn had been sceptical of the possibility of QCs, he had since changed his mind in the last two years, and his presence awarded some credibility to the contents of the paper. After Gratias restructured the mathematics in the paper, it was finally accepted for publication in the Physical Review Letters on November 12, 1984.

(Clockwise from top-left corner) Danny Shechtman, Istvan Hargittai, Roger Penrose, Paul Steinhardt, and Dov Levine with Steinhardt

And by the time Browne’s article appeared a year later, it is safe to assume that at least 50-70 papers on the subject were published in the period. Whether this was a rush to accumulate anomalies or to discredit the finding is immaterial: the threat to the existing paradigm was perceptible and scientists felt the need to do something about it; and Browne’s noting of the same is proof that science journalists noted the need, too.

In fact, how much of an anomaly is a finding that has been accepted for publication? Because after it has been carefully vetted and published, it becomes as good as fact: other scientists can now found their work upon on it, and at the time of publication of their papers, cite the parent paper as authority.

However, it must be noted that there are important exceptions, such as the infamous Fleischmann-Pons experiment in cold fusion in 1989-1990. For these reasons, let it be that a paradigm is considered to have entered a crisis period only after it is established that it cannot be “tweaked” after each discovery and allowed to continue.

Three years of falsifications

Browne, too, seems to conclude that despite a definite discovery having been made three years earlier,

… only recently has experimental evidence overwhelmed the initial skepticism of the scientific community that such a form of matter could exist.

For three years, the community could not allow a discovery to pass, and subjected it repeatedly to tests of falsifications. A similar remark comes from science writer and crystallographer Paul Steinhardt, Levine’s PhD mentor, who, in a paper titled ‘New perspectives on forbidden symmetries, quasicrystals and Penrose tilings’, remarked upon the need for “a new appreciation for the subtleties of crystallographically forbidden symmetries.”

Shechtman’s QCs exhibited rotational symmetry but not a translational one. In other words, they demanded to be placed squarely between crystalline and amorphous substances, sending researchers scurrying for an explanation.

In a period of such turmoil, Browne’s article states that some researchers were willing to consider the arrangement as existing in six-dimensional (6D) hyperspace rather than in 3D space-time.

A hexeract (or, a geopeton)

Now, someone within the community had considered physical hyperspace to be an explanation way back in 1985. Even though mathematical hyperspace as a theory had been around since the days of Bernhard Riemann (Habilitationsschrift, 1854) and Ludwig Schläfli (Theorie der vielfachen Kontinuität, 1852), the notion of physical hyperspatial theory with a correspondence to physical chemistry is still nascent at best.

Therefore, Browne’s suggestion only seems to supplant his narrative of intellectual turbulence, that scientists had stumbled upon a phenomenon so anomalous that it alone was prompting crisis.


Did science journalists find QCs anomalous? Yes, they did. Browne, Hargittai and Steinhardt, amongst others, were quick to identify the anomalous nature of the newly discovered material and point it out through newspaper reports and articles published within the scientific community.

Thomas Kuhn’s position that scientists will attempt to denounce a paradigm-shift-inducing theory before they themselves are forced to shift is reflected in the writers’ accounts of Dan Shechtman in the days leading up to and just after his discovery.

Did they, the journalists, report the crisis period as it happened or as an isolated incident? That they could identify the onset of a crisis as it happened indicates that they did recognize it for what it was. However, it remains to be seen whether these confirmations validate Kuhn’s hypothesis in their entirety.