Tag: three-dimensional geometry

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.

Conclusion

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.

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.

Conclusion

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.