A case of Kuhn, quasicrystals & communication – Part III

The doctrine of incommensurability arises out of the conflict between two paradigms and the faltering of communications between the two adherent factions.

According to Kuhn, scientists are seldom inclined to abandon the paradigm at the first hint of crisis – as elucidated in the previous section – and instead denounce the necessity for a new paradigm. However, these considerations aside, the implications for a scientist who proposes the introduction of a new paradigm, as Shechtman did, are troublesome.

Such a scientist will find himself ostracized by the community of academicians he belongs to because of the anomalous nature of his discovery and, thus, his suddenly questionable credentials. At the same time, because of such ostracism, the large audience required to develop the discovery and attempt to inculcate its nature into the extant paradigm becomes inaccessible.

As a result, there is a communication breakdown between the old faction and the new faction, whereby the former rejects the finding and continues to further the extant paradigm while the latter rejects the paradigm and tries to bring in a new one.

Incommensurability exists only during the time of crisis, when a paradigm shift is foretold. A paradigm shift is called so because there is no continuous evolution from the old paradigm to the new one. As Kuhn puts it (p. 103),

… the reception of a new paradigm often necessitates a redefinition of the corresponding science.

For this reason, what is incommensurable is not only the views of warring scientists but also the new knowledge and the old one. In terms of a finding, the old knowledge could be said to be either incomplete or misguided, whereas the new one could be remedial or revolutionary.

In Shechtman’s case, because icosahedral symmetries were altogether forbidden by the old theory, the new finding was not remedial but revolutionary. Therefore, the new terms that the finding introduced were not translatable in terms of the old one, leading to a more technical form of communication breakdown and the loss of the ability of scientists to predict what could happen next.

A final corollary of the doctrine is that because of the irreconcilable nature of the new and old knowledge, its evolution cannot be held to be continuous, only contiguous. In this sense, knowledge becomes a non-cumulative entity, one that cannot have been accumulated continuously over the centuries, but one that underwent constant redefinition to become what it is today.

As for Dan Shechtman, the question is this: Does the media’s portrayal of the crisis period reflect any incommensurability (be it in terms of knowledge or communication)?

How strong was the paradigm shift?

In describing the difference between “seeing” and “seeing as”, Kuhn speaks about two kinds of incommensurability as far as scientific knowledge is concerned. Elegantly put as “A pendulum is not a falling stone, nor is oxygen dephlogisticated air,” the argument is that when a paradigm shift occurs, the empirical data will remain unchanged even as the relationship between the data changes. In Shechtman’s and Levine’s cases, the discovery of “forbidden” 3D icosahedral point symmetry does not mean that the previous structures are faulty but simply that the new structure is now one of the possibilities.

However, there is some discrepancy regarding how much the two paradigms are really incommensurable. For one, Kuhn’s argument that an old paradigm and a new paradigm will be strongly incommensurable can be disputed: he says that during a paradigm shift, there can be no reinterpretation of the old theory that can transform to being commensurable with the new one.

However, this doesn’t seem to be the case: five-fold axes of symmetry were forbidden by the old theory because they had been shown mathematically to lack translational symmetry, and because the thermodynamics of such a structure did not fall in line with the empirical data corresponding to crystals that were perfectly crystalline or perfectly amorphous.

Therefore, the discovery of QCs established a new set of relationships between the parameters that influenced the formation of one crystal structure over another. At the same time, they did permit a reinterpretation of the old theory because the finding did not refute the old laws – it just introduced an addition.

For Kuhn to be correct a paradigm shift should have occurred that introduced a new relationship between different bits of data; in Shechtman’s case, the data was not available in the first place!

Here, Shechtman can be attributed with making a fantastic discovery and no more. There is no documented evidence to establish that someone observed QC before Shechtman did but interpreted it according to the older paradigm.

In this regard, what is thought to be a paradigm shift can actually be argued to be an enhancement of the old paradigm: no shift need have occurred. However, this was entirely disregarded by science journalists and commentators such as Browne and Eugene Garfield, who regarded the discovery of QCs as simply being anomalous and therefore crisis-prompting, indicating a tendency to be historicist – in keeping with the antirealism argument against scientific realism as put forth by Richard Boyd.

Thus, the comparison to The Structure that held up all this time fails.

There are many reasons why this could have been so, not the least of which is the involvement of Pauling and his influence in postponing the announcement of the discovery (Pauling’s credentials were, at the time, far less questionable than Shechtman’s were).

Linus Carl Pauling (1901-1994) (Image from Wikipedia)

As likely as oobleck

Alan I. Goldman, a professor of physics at the Iowa State University, wrote in the 84th volume of the American Scientist,

Quasicrystals … are rather like oobleck, a form of precipitation invented by Dr. Seuss. Both the quasicrystals and the oobleck are new and unexpected. Since the discovery of a new class of materials is about as likely as the occurrence of a new form of precipitation, quasicrystals, like oobleck, suffered at first from a credibility problem.

There were many accomplished chemists who thought that QCs were nothing more than as-yet not fully understood crystal structures, and some among them even believed that QCs were an anomalous form of glass.

The most celebrated among those accomplished was Linus Pauling, who died in 1994 after belatedly acknowledging the existence of QCs. It was his infamous remark in 1982 that bought a lot of trouble for Shechtman, who was subsequently asked to leave the research group because he was “bringing disgrace” on its members and the paper he sought to publish was declined by journals.

Perhaps this was because he took immense pride in his works and in his contributions to the field of physical chemistry; otherwise, his “abandonment” of the old paradigm would have come easier – and here, the paradigm that did include an observation of QCs is referred to as old.

In fact, Pauling was so adamant that he proposed a slew of alternate crystal structures that would explain the structure of QCs as well as remain conformant with the old paradigm, with a paper appearing in 1988, long after QCs had become staple knowledge.

Order and periodicity

Insofar as the breakdown in communication is concerned, it seems to have stemmed from the tying-in of order and periodicity: crystallography’s handing of crystalline and amorphous substances had ingrained into the chemist’s psyche the coexistence of structures and repeatability.

Because the crystal structures of QCs were ordered but not periodical, even those who could acknowledge their existence had difficulty believing that QCs “were just as ordered as” crystals were, in the process isolating Shechtman further.

John Cahn, a senior crystallographer at NBS at the time of the fortuitous discovery, was one such person. Like Pauling, Cahn also considered possible alternate explanations before he could agree with Shechtman and ultimately co-author the seminal PRL paper with him.

His contention was that forbidden diffraction patterns – like the one Shechtman had observed – could be recreated by the superposition of multiple allowed but rotated patterns (because of the presence of five-fold symmetry, the angle of rotation could have been 72°).

A crystal-twinning pattern in a leucite crystal

This was explained through a process called twinning, whereby the growth vector of a crystal, during its growth phase, could suddenly change direction without any explanation or prior indication. In fact, Cahn’s exact response was,

Go away, Danny. These are twins and that’s not terribly interesting.

This explanation involving twinning was soon adopted by many of Shechtman’s peers, and he was repeatedly forced to return with results from the diffraction experiment to attempt to convince those who disagreed with the finding. His attempts were all in vain, and he was eventually dismissed from the project group at NBS.


All these events are a reflection of the communication breakdown within the academic community and, for a time, the two sides were essentially Shechtman and all the others.

The media portrayal of this time, however, seems to be completely factual and devoid of deduction or opining because of the involvement of the likes of Pauling and Cahn, who, in a manner of speaking, popularized the incident among media circles: that there was a communication breakdown became ubiquitous fact.

Shechtman himself, after winning the Nobel Prize for chemistry in 2011 for the discovery of QCs, admitted that he was isolated for a time before acceptance came his way – after the development of a crisis became known.

At the same time, there is the persisting issue of knowledge as being non-accumulative: as stated earlier, journalists have disregarded the possibility, not unlike many scientists, unfortunately, that the old paradigm did not make way for a new one as much as it became the new one.

That this was not the focus of their interest is not surprising because it is a pedantic viewpoint, one that serves to draw attention to the “paradigm shift” not being “Kuhnian” in nature, after all. Just because journalists and other writers constantly referred to the discovery of QCs as being paradigm-shifting need not mean that a paradigm-shift did occur there.