Tag: quasicrystals

• Quasicrystal, heal thyself

  Scientists have uncovered a remarkable self-healing property in a strange class of materials known as quasicrystals, revealing their ability to grow into a perfect, single structure even when faced with obstacles. The discovery challenges a long-held understanding of crystal formation and opens the door to creating large, strong materials free of defects for a new generation of applications.

  Imagine you’re tiling a massive bathroom floor. You could use identical square tiles, laying them in a simple, repeating grid. This is analogous to a regular crystal. The pattern is predictable and repeats perfectly. When the arrangement of atoms repeats at fixed intervals, called periodicity, you have a conventional crystal.

  But as you’re laying these tiles, you come across a pipe sticking out of the floor. To get around it, you would have to cut tiles into awkward shapes, breaking your perfect pattern. The lines where the mismatched tiles meet would also create a permanent scar on your floor. In the world of materials, these ‘scars’ are called defects or grain boundaries.

  These defects are often the weakest points in a material, making it more prone to breaking or corrosion. Say you’ve a chair that’s starting to crack: the odds are the crack would’ve originated at a grain boundary. For many decades, a major goal for materials scientists has been to create large single crystals: materials with no grain boundaries and thus maximum strength and performance.

  Now, what if instead of squares, you were tiling with a special set of tiles, say a mix of two different diamond shapes (see below). You could cover the entire floor without gaps, creating a pattern that looks ordered and intricate. But then you notice the catch: the pattern never exactly repeats. This is the essence of a quasicrystal. It has long-range order—its atoms are arranged in a pattern you can predict—but that pattern doesn’t repeat.

  

  This fundamental difference led scientists to ask a critical question: what happens when a growing quasicrystal encounters an obstacle like that pipe in the floor? Does it also form messy, weakening defects or does its unique, more flexible structure give it a way to grow around the disruption and ‘fix’ itself on the other side?

  In a new study in Physical Review Letters, researchers from the University of Michigan, Ann Arbor, hypothesised that quasicrystals possess a unique “self-healing” ability. They’ve written that this ability stems from special atomic rearrangements, known as phasons, that are only possible in quasicrystals. To test this, they decided to watch a specific type of quasicrystal, a decagonal quasicrystal, grow around a common, bubble-shaped obstacle found in metal alloys called shrinkage pores.

  To watch this microscopic drama unfold, the researchers used a two-part strategy in which they combined a real-world experiment with a sophisticated computer simulation.

  For the experiment, they used a technique called synchrotron X-ray microtomography. Think of it as a super-powered CT scan for materials. They took a small cylinder of an aluminium-cobalt-nickel alloy, melted it, and then carefully cooled it down. As the alloy solidified, quasicrystals began to form and grow, eventually running into the shrinkage pores that were already present in the material. The X-rays allowed the scientists to capture rapid, 3D “movies” of this process in real-time, tracking the crystal’s growth as it navigated the porous landscape.

  To understand the atom-level mechanics behind what they were seeing, the team ran molecular dynamics simulations. This is like creating a virtual universe in a computer, where they could build a model quasicrystal atom by atom. They then programmed a virtual pore in its path and let the simulation run to watch exactly how the individual atoms rearranged themselves as the crystal grew and enveloped the obstacle.

  The results were astonishing: both the live-action X-ray movies and the computer simulations showed the quasicrystal growing around the pores without forming any permanent defects.

  As the growing front of the quasicrystal met a pore, it momentarily distorted its shape to flow around the void. Then when the two fronts met on the far side of the pore, they merged together perfectly. The crystal continued to grow as if the pore had never been there, resulting in a single, flawless quasicrystal that had simply swallowed the obstacle.

  The key evidence from the experiments was the smoothness of the final quasicrystal’s surface. In a normal crystal, if a defect like a grain boundary had formed where the two fronts met, it would have created a permanent groove on the surface. The fact that the quasicrystal’s surface healed into a smooth, convex shape confirmed that no such defect was present.

  

  The computer simulations revealed the secret to this ability: the phasons. A phason flip is one pattern of tiles changing into another without disrupting the overall order. When the growing crystal collided with the pore, it created localised stress. But through a cascade of these phason flips, the quasicrystal was able to distribute this stress and seamlessly stitch its structure back together. The scientists described this as an err-and-repair mechanism because the quasicrystal makes a temporary “mistake” at the collision point, then quickly corrects it. The result: perfect structure.

  The finding has profound implications for materials science. First, it suggests that creating large, defect-free single crystals—currently a notoriously difficult and expensive process for conventional materials—could be dramatically easier with quasicrystals. Their built-in fault tolerance means they might be grown perfectly using simpler and cheaper methods.

  The ability to easily create large, single-grain quasicrystals could also better unlock their incredible potential. Lacking the weak points of grain boundaries, quasicrystals could be used to create exceptionally strong, hard, and lightweight alloys for aerospace and industrial applications. Their unique structure also gives them interesting properties like low friction and low adhesion, making them ideal as durable nonstick coating.

  The err-and-repair mechanism is also a form of self-healing at the most fundamental level. Understanding this process could inspire the design of a new class of “smart” materials. For instance, imagine a composite that when cracked or damaged can automatically absorb the defect and ‘repair’ its own atomic structure, maintaining its integrity and performance. The principles revealed in this study could be applied to other fields, such as creating more durable catalysts for the chemical industry that can resist degradation from internal pores.

  Overall, this research reshapes our understanding of how ordered matter can form and provides a blueprint for a new generation of resilient materials built from the atom up.

  2025.10.21

• A new beast: antiferromagnetic quasicrystals

  Scientists have made a new material that is both a quasicrystal and antiferromagnetic — a combination never seen before.

  Quasicrystals are a special kind of solid. Unlike normal crystals, whose atoms are arranged in repeating patterns, quasicrystals have patterns that never exactly repeat but which still have an overall order. While regular crystals have left-right symmetries, quasicrystals have unusual rotational ones.

  For decades, scientists wondered if certain kinds of magnetism, but especially antiferromagnetism, could exist in these strange materials. In all materials the electrons have a property called spin. It’s as if a small magnet is embedded inside each electron. The spin denotes the direction of this magnet’s magnetic field. In ferromagnets, the spins are aligned in a common direction, so the materials are attracted to magnets. In antiferromagnetic materials, the electron spins line up in alternating directions, so their effects cancel out.

  While antiferromagnetism is common in regular crystals, it’s thus far never been observed in a true quasicrystal.

  The new study is the first to show clear evidence of antiferromagnetic order in a real, three-dimensional quasicrystal — one made of gold, indium, and europium. The findings were published in Nature Physics on April 14.

  The team confirmed such a material is real by carefully measuring how its atoms and spins are arranged and by observing how it behaves at low temperatures. Their work shows that even in the weird world of quasicrystals, complex magnetic order is possible, opening the door to new discoveries and technologies.

  The scientists created a new alloy with the formula Au₅₆In_28.5Eu_15.5. This means in 1,000 atoms’ worth of the material, 560 will be gold, 285 will be indium, and 155 will be europium. The composition tells us that the scientists were going for a particularly precise combination of these elements — which they could have known in one of two ways. It might have been trial-and-error*, but that makes research very expensive, or the scientists had reasons to expect antiferromagnetic order would appear in this material.

  They did. Specifically, the team focused on Au₅₆In_28.5Eu_15.5 because of its (i) unique positive Curie-Weiss temperature and (ii) rare-earth content, and (iii) because its structural features matched the theoretical criteria for stable antiferromagnetic order. Previous studies focused on quasicrystals containing rare-earth elements because they often have strong magnetic interactions. However, these compounds typically displayed a negative Curie-Weiss temperature, indicating dominant antiferromagnetic interactions but resulting only in disordered magnetic states.

  A positive Curie-Weiss temperature indicates dominant ferromagnetic interactions. In this case, however, it also suggested a unique balance of magnetic forces that could potentially stabilise antiferromagnetic order rather than spin-glass behaviour. Studies on approximant crystals — periodic structures closely related to quasicrystals — had also shown that both ferromagnetic and antiferromagnetic orders are stabilised only when the Curie-Weiss temperature is positive. In contrast, a negative temperature led to spin-glass states.

  The scientists of the new study noticed that the Au-In-Eu quasicrystal fit into the positive Curie-Weiss temperature category, making it a promising candidate to have antiferromagnetic order.

  For added measure, by slightly altering the composition, e.g. adding an impurity to increase the electron-per-atom ratio, the scientists could make the antiferromagnetic phase disappear, to be replaced by spin-glass behaviour. This sensitivity to electron concentration further hinted that the composition of the alloy was at a sweet spot for stabilising antiferromagnetism.

  Finally, the team had also recently discovered ferromagnetic order in some similar gold-based quasicrystals with rare-earth elements. The success encouraged them to explore the magnetic properties of new compositions, especially those with unusual Curie-Weiss temperatures.

  The Au-In-Eu quasicrystal is also a Tsai-type icosahedral quasicrystal, meaning it features a highly symmetric atomic arrangement. Theoretical work has suggested that such structures could support antiferromagnetic order in the right conditions, especially if the atoms occupied specific sites in the lattice.

  To make the alloy, the scientists used a technique called arc-melting, where highly pure metals are melted together using an electric arc, then quickly cooled to form the solid quasicrystal. To ensure the mixture was even, the team melted and flipped the sample several times.

  Then they used X-ray and electron diffraction to check the atomic arrangement. These techniques passed X-rays and electrons through the material. A detector on the other side picked up the radiation scattered by the material’s atoms and used it to recreate their arrangement. The patterns showed the material was a primitive icosahedral quasicrystal, a structure with 20-sided symmetry and no repeating units.

  The team also confirmed special arrangement of atoms by the way the diffraction patterns followed mathematical rules that are special to quasicrystals. Team members also used a magnetometer to track how much the material was magnetised when exposed to a magnetic field, from temperatures as low as 0.4 K to up to 300 K. Finally they also measured the material’s specific heat, i.e. the amount of heat energy it took to raise its temperature by 1º C. This reading can show signs of magnetic transitions.

  

  To confirm how the spins inside the material were arranged, the team used neutron diffraction. Neutrons are adept at passing through materials and are sensitive to both atoms’ positions and magnetic order. By comparing patterns at temperatures above and below the suspected transition point, they could spot the appearance of new peaks that signal magnetic order.

  This way, the team reported that at 6.5 K, the magnetisation curve showed a sharp change, known as a cusp. This is a classic sign of an antiferromagnetic transition, where the material suddenly changes from being unordered to having a regular up-and-down pattern of spins. The specific heat also showed a sharp peak at this temperature, confirming something dramatic was happening inside the material.

  The scientists also reported that there was no sign of spin-glass behaviour — where the spins are pointing in random directions but unchanging — which is common in other magnetic quasicrystals.

  Below 6.5 K, new peaks appeared in the neutron diffraction data, evidence that the spins inside the material were lining up in the regular but alternating pattern characteristic of antiferromagnetic order. The peaks were also sharp and well-defined, showing the order was long-range, meaning they were there throughout the material and not confined to small patches.

  The team also experimented by adding a small amount of tin to the alloy, which changed the balance of electrons. This little change caused the material to lose its antiferromagnetic order and become a spin glass instead, showing how delicate the balance is between different magnetic states in quasicrystals.

  The findings are important because this is the first time scientists have observed antiferromagnetic order in a real, three-dimensional quasicrystal, settling a long-standing debate. They also open up a new field of study, of quasiperiodic antiferromagnets, and suggest that by carefully tuning the composition, scientists may be able to find yet other types of magnetic order in quasicrystals.

  “The present discovery will stimulate both experimental and theoretical efforts to elucidate not only its unique magnetic structure but also the intrinsic properties of the quasiperiodic order parameter,” the scientists wrote in their paper. “Another exciting aspect of magnetically ordered quasicrystals is their potential for new applications such as functional materials in spintronics” — which use electron spins to store and process information in ultra-fast computers of the future.

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  * Which is not the same as serendipity.

  Featured image credit: Nature Physics volume 21, pages 974–979 (2025).

  2025.07.11

• Why do quasicrystals exist?

  Featured image: An example of zellij tilework in the Al Attarine Madrasa in Fes, Morocco (2012), with complex geometric patterns on the lower walls and a band of calligraphy above. Caption and credit: just_a_cheeseburger (CC BY)

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  ‘Quasi’ means almost. It’s an unfair name for quasicrystals. These crystals exist in their own right. Their name comes from the internal arrangement of their atoms. A crystal is made up of a repeating group of some atoms arranged in a fixed way. The smallest arrangement that repeats to make up the whole crystal is called the unit cell. In diamond, a convenient unit cell is four carbon atoms bonded to each other in a tetrahedral (pyramid-like) arrangement. Millions of copies of this unit cell together make up a diamond crystal. The unit cell of sodium chloride has a cubical shape: the chloride ions (Cl^–) occupy the corners and face centres while the sodium ions (Na⁺) occupy the middle of the edges and centre of the cube. As this cube repeats itself, you get table salt.

  The structure of all crystals thus follows two simple rules: have a unit cell and repeat it. Thus the internal structure of crystals is periodic. For example if a unit cell is 5 nanometres wide, it stands to reason you’ll see the same arrangement of atoms after every 5 nm. And because it’s the same unit cell in all directions and they don’t have any gaps between them, the unit cells fill the space available. It’s thus an exercise in tiling. For example, you can cover a floor of any shape completely with square or triangular tiles (you’ll just need to trim those at the edges). But you can’t do this with pentagonal tiles. If you do, the tiles will have gaps between them that other pentagonal tiles can’t fill.

  Quasicrystals buck this pattern in a simple way: their unit cells are like pentagonal tiles. They repeat themselves but the resulting tiling isn’t periodic. There are no gaps in the crystal either because instead of each unit cell just like the one on its left or right, the tiles sometimes slot themselves in by rotating by an angle. Thus rather than the crystal structure following a grid-like pattern, the unit cells seem to be ordered along curves. As a result, even though the structure may have an ordered set of atoms, it’s impossible to find a unit cell that by repeating itself in a straight line gives rise to the overall crystal. In technical parlance, the crystal is said to lack translational symmetry.

  Such structures are called quasicrystals. They’re obviously not crystalline, because they lack a periodic arrangement of atoms. They aren’t amorphous either, like the haphazardly arranged atoms of glass. Quasicrystals are somewhere in between: their atoms are arranged in a fixed way, with different combinations of pentagonal, octagonal, and other tile shapes that are disallowed in regular crystals, and with the substance lacking a unit cell. Instead the tiles twist and turn within the structure to form mosaic patterns like the ones featured in Islamic architecture (see image at the top).

  

  The discovery of quasicrystals in the early 1980s was a revolutionary moment in the history of science. It shook up what chemists believed a crystal should look like and what rules the unit cell ought to follow. The first quasicrystals that scientists studied were made in the lab, in particular aluminium-manganese alloys, and there was a sense that these unusual crystals didn’t occur in nature. That changed in the 1990s and 2000s when expeditions to Siberia uncovered natural quasicrystals in meteorites that had smashed into the earth millions of years ago. But even this discovery kept one particular question about quasicrystals alive: why do they exist? Both Al-Mn alloys and the minerals in meteorites form in high temperatures and extreme pressures. The question of their existence, more than just because they can, is a question about whether the atoms involved are forced to adopt a quasicrystal rather than a crystal structure. In other words, it asks if the atoms would rather adopt a crystal structure but don’t because their external conditions force them not to.

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  This post benefited from feedback from Adhip Agarwala.

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  Often a good way to understand the effects of extreme conditions on a substance is using the tools of thermodynamics — the science of the conditions in which heat moves from place to another. And in thermodynamics, the existential question can be framed like this, to quote from a June paper in Nature Physics: “Are quasicrystals enthalpy-stabilised or entropy-stabilised?” Enthalpy-stabilised means the atoms of a quasicrystal are arranged in a way where they collectively have the lowest energy possible for that group. It means the atoms aren’t arranged in a less-than-ideal way forced by their external conditions but because the quasicrystal structure in fact is better than a crystal structure. It answers “why do quasicrystals exist?” with “because they want to, not just because they can”. Entropy-stabilised goes the other way. That is: at 0 K (-273.15º C), the atoms would rather come together as a crystal because a crystal structure has lower energy at absolute zero. But as the temperature increases, the energy in the crystal builds up and forces the atoms to adjust where they’re sitting so that they can accommodate new forces. At some higher temperature, the structure becomes entropy-stabilised. That is, there’s enough disorder in the structure — like sound passing through the grid of atoms and atoms momentarily shifting their positions — that allows it to hold the ‘excess’ energy but at the same time deviate from the orderliness of a crystal structure. Entropy stabilisation answers “why do quasicrystals exist?” with “because they’re forced to, not because they want to”.

  In materials science, the go-to tool to judge whether a crystal structure is energetically favourable is density functional theory (DFT). It estimates the total energy of a solid and from there scientists can compare competing phases and decide which one is most stable. If four atoms will have less energy arranged as a cuboid than as a pyramid at a certain temperature and pressure, then the cuboidal phase is said to be more favoured. The problem is DFT can’t be directly applied to quasicrystals because the technique assumes that a given mineral has a periodic internal structure. Quasicrystals are aperiodic. But because scientists are already comfortable with using DFT, they have tried to surmount this problem by considering a superunit cell that’s made up of a large number of atoms or by assuming that a quasicrystal’s structure, while being aperiodic in three dimensions, could be periodic in say four dimensions. But the resulting estimates of the solid’s energy have not been very good.

  In the new Nature Physics paper, scientists from the University of Michigan, Ann Arbor, have reported a way around the no-unit-cell problem to apply DFT to estimate the energy of two quasicrystals. And they found that these quasicrystals are enthalpy-stabilised. The finding answer is a chemistry breakthrough because it raises the possibility of performing DFT in crystals without translational symmetry. Further, by showing that two real quasicrystals are enthalpy-stabilised, chemists may be forced to rethink why almost every other inorganic material does adopt a repeating structure. Crystals are no longer at the centre of the orderliness universe.

  

  The team started by studying the internal structure of two quasicrystals using X-rays, then ‘scooped’ out five random parts for further analysis. Each of these scoops had 24 to 740 atoms. Second, the team used a modified version of DFT called DFT-FE. The computational cost of running DFT scales increases according to the cube of the number of atoms being studied. If studying four atoms with DFT requires X amount of computing power, 24 atoms would require 8,000 times X and 740 atoms would require 400 million times X. Instead the computational cost of DFT-FE scales as the square of the number of atoms, which makes a big difference. Continuing from the previous example, 24 atoms would require 400 times X and 740 atoms would require half a million times X. But the lower computational cost of DFT-FE is still considerable. The researchers’ solution was to use GPUs — the processors originally developed to run complicated video games and today used to run artificial intelligence (AI) apps like ChatGPT.

  The team was able to calculate that the resulting energy estimates for a quasicrystal was off by no more than 0.3 milli-electron-volt (meV) per atom, considered acceptable. They also applied their technique to a known crystal, ScZn₆, and confirmed that its estimate of the energy matched the known value (5-9 meV per atom). They were ready to go now.

  When they applied DFT-FE to scandium-zinc and ytterbium-cadmium quasicrystals, they found clear evidence that they were enthalpy-stabilised. Each atom in the scandium-zinc quasicrystal had 23 meV less energy than if it had been part of a crystal structure. Similarly atoms in the ytterbium-cadmium quasicrystal had roughly 7 meV less each. The verdict was obvious: translational symmetry is not required for the most stable form of an inorganic solid.

  

  The researchers also explored why the ytterbium-cadmium quasicrystal is so much easier to make than the scandium-zinc quasicrystal. In fact the former was the world’s first two-element quasicrystal to be discovered, 25 years ago this year. The team broke down the total energy as the energy in the bulk plus energy on the surface, and found that the scandium-zinc quasicrystal has high surface energy.

  This is important because in thermodynamics, energy is like cost. If you’re hungry and go to a department store, you buy the pack of biscuits that you can afford rather than wait until you have enough money to buy the most expensive one. Similarly, when there’s a hot mass of scandium-zinc as a liquid and scientists are slowly cooling it, the atoms will form the first solid phase they can access rather than wait until they have accumulated enough surface energy to access the quasicrystal phase. And the first phase they can access will be crystalline. On the other hand scientists discovered the ytterbium-cadmium quasicrystal so quickly because it has a modest amount of energy across its surface and thus when cooled from liquid to solid, the first solid phase the atoms can access is also the quasicrystal phase.

  This is an important discovery: the researchers found that a phase diagram alone can’t be used to say which phase will actually form. Understanding the surface-energy barrier is also important, and could pave the way to a practical roadmap for scientists trying to grow crystals for specific applications.

  The big question now is: what special bonding or electronic effects allow atoms to have order without periodicity? After Israeli scientist Dan Shechtman discovered quasicrystals in 1982, he didn’t publish his findings until two years later, after including some authors on his submission to improve its chances with a journal, because he thought he wouldn’t be taken seriously. This wasn’t a silly concern: Linus Pauling, one of the greatest chemists in the history of subject, dismissed Shechtman’s work and called him a “quasi-scientist”. The blowback was so sharp and swift because chemists like Pauling, who had helped establish the science of crystal structures, were certain there was a way crystals could look and a way they couldn’t — and quasicrystals didn’t have the right look. But now, the new study has found that quasicrystals look perfect. Perhaps it’s crystals that need to explain themselves…

  2025.06.26

• The calculus of creative discipline

  Every moment of a science fiction story must represent the triumph of writing over world-building. World-building is dull. World-building literalises the urge to invent. World-building gives an unnecessary permission for acts of writing (indeed, for acts of reading). World-building numbs the reader’s ability to fulfil their part of the bargain, because it believes that it has to do everything around here if anything is going to get done. Above all, world-building is not technically necessary. It is the great clomping foot of nerdism.

  Once I’m awake and have had my mug of tea, and once I’m done checking Twitter, I can quote these words of M. John Harrison from memory: not because they’re true – I don’t believe they are – but because they rankle. I haven’t read any writing of Harrison’s, I can’t remember the names of any of his books. Sometimes I don’t remember his name even, only that there was this man who uttered these words. Perhaps it is to Harrison’s credit that he’s clearly touched a nerve but I’m reluctant to concede anymore than this.

  His (partial) quote reflects a narrow view of a wider world, and it bothers me because I remain unable to extend the conviction that he’s seeing only a part of the picture to the conclusion that he lacks imagination; as a writer of not inconsiderable repute, at least according to Wikipedia, I doubt he has any trouble imagining things.

  I’ve written about the virtues of world-building before (notably here), and I intend to make another attempt in this post; I should mention what both attempts, both defences, have in common is that they’re not prescriptive. They’re not recommendations to others, they’re non-generalisable. They’re my personal reasons to champion the act, even art, of world-building; my specific loci of resistance to Harrison’s contention. But at the same time, I don’t view them – and neither should you – as inviolable or as immune to criticism, although I suspect this display of a willingness to reason may not go far in terms of eliminating subjective positions from this exercise, so make of it what you will.

  There’s an idea in mathematical analysis called smoothness. Let’s say you’ve got a curve drawn on a graph, between the x- and y-axes, shaped like the letter ‘S’. Let’s say you’ve got another curve drawn on a second graph, shaped like the letter ‘Z’. According to one definition, the S-curve is smoother than the Z-curve because it has fewer sharp edges. A diligent high-schooler might take recourse through differential calculus to explain the idea. Say the Z-curve on the graph is the result of a function Z(x) = y. If you differentiate Z(x) where ‘x’ is the point on the x-axis where the Z-curve makes a sharp turn, the derivative Z'(x) has a value of zero. Such points are called critical points. The S-curve doesn’t have any critical points (except at the ends, but let’s ignore them); L-, and T-curves have one critical point each; P- and D-curves have two critical points each; and an E-curve has three critical points.

  With the help of a loose analogy, you could say a well-written story is smooth à la an S-curve (excluding the terminal points): it it has an unambiguous beginning and an ending, and it flows smoothly in between the two. While I admire Steven Erikson’s Malazan Book of the Fallen series for many reasons, its first instalment is like a T-curve, where three broad plot-lines abruptly end at a point in the climax that the reader has been given no reason to expect. The curves of the first three books of J.K. Rowling’s Harry Potter series resemble the tangent function (from trigonometry: tan(x) = sin(x)/cosine(x)): they’re individually somewhat self-consistent but the reader is resigned to the hope that their beginnings and endings must be connected at infinity.

  

  You could even say Donald Trump’s presidency hasn’t been smooth at all because there have been so many critical points.

  Where world-building “literalises the urge to invent” to Harrison, it spatialises the narrative to me, and automatically spotlights the importance of the narrative smoothness it harbours. World-building can be just as susceptible to non-sequiturs and deus ex machinae as writing itself, all the way to the hubris Harrison noticed, of assuming it gives the reader anything to do, even enjoy themselves. Where he sees the “clomping foot of nerdism”, I see critical points in a curve some clumsy world-builder invented as they went along. World-building can be “dull” – or it can choose to reveal the hand-prints of a cave-dwelling people preserved for thousands of years, and the now-dry channels of once-heaving rivers that nurtured an ancient civilisation.

  HiRISE Epigrammata
  
  “The world is like the impression left by the telling of a story.”
  
  Yoga Vasistha pic.twitter.com/ic5sazW5XQ

  — HiRISE: Beautiful Mars (@HiRISE) October 27, 2019

  My principal objection to Harrison’s view is directed at the false dichotomy of writing and world-building, and which he seems to want to impose instead of the more fundamental and more consequential need for creative discipline. Let me borrow here from philosophy of science 101, specifically of the particular importance of contending with contradictory experimental results. You’ve probably heard of the replication crisis: when researchers tried to reproduce the results of older psychology studies, their efforts came a cropper. Many – if not most – studies didn’t replicate, and scientists are currently grappling with the consequences of overturning decades’ worth of research and research practices.

  This is on the face of it an important reality check but to a philosopher with a deeper view of the history of science, the replication crisis also recalls the different ways in which the practitioners of science have responded to evidence their theories aren’t prepared to accommodate. The stories of Niels Bohr v. classical mechanics, Dan Shechtman v. Linus Pauling and the EPR paradox come first to mind. Heck, the philosophers Karl Popper, Thomas Kuhn, Imre Lakatos and Paul Feyerabend are known for their criticisms of each other’s ideas on different ways to rationalise the transition from one moment containing multiple answers to the moment where one emerges as the favourite.

  In much the same way, the disciplined writer should challenge themself instead of presuming the liberty to totter over the landscape of possibilities, zig-zagging between one critical point and the next until they topple over the edge. And if they can’t, they should – like the practitioners of good science – ask for help from others, pressing the conflict between competing results into the service of scouring the rust away to expose the metal.

  For example, since June this year, I’ve been participating on my friend Thomas Manuel’s initiative in his effort to compose an underwater ‘monsters’ manual’. It’s effectively a collaborative world-building exercise where we take turns to populate different parts of a large planet with sizeable oceans, seas, lakes and numerous rivers with creatures, habitats and ecosystems. We broadly follow the same laws of physics and harbour substantially overlapping views of magic, but we enjoy the things we invent because they’re forced through the grinding wheels of each other’s doubts and curiosities, and the implicit expectation of one creator to make adequate room for the creations of the other.

  I see it as the intersection of two functions: at first, their curves will criss-cross at a point, and the writers must then fashion a blending curve so a particle moving along one can switch to the other without any abruptness, without any of the tired melodrama often used to mask criticality. So the Kularu people are reminded by their oral traditions to fight for their rivers, so the archaeologists see through the invading Gezmin’s benevolence and into the heart of their imperialist ambitions.

  2019.10.27

• A case of Kuhn, quasicrystals & communication – Part IV

  Dan Shechtman won the Nobel Prize for chemistry in 2011. This led to an explosion of interest on the subject of QCs and Shechtman’s travails in getting the theory validated.

  Numerous publications, from Reuters to The Hindu, published articles and reports. In fact, The Guardian ran an online article giving a blow-by-blow account of how the author, Ian Sample, attempted to contact Shechtman while the events succeeding the announcement of the prize unfolded.

  All this attention served as a consummation of the events that started to avalanche in 1982. Today, QCs are synonymous with the interesting possibilities of materials science as much as with perseverance, dedication, humility, and an open mind.

  Since the acceptance of the fact of QCs, the Israeli chemist has gone on to win Physics Award of the Friedenberg Fund (1986), the Rothschild Prize in engineering (1990), the Weizmann Science Award (1993), the 1998 Israel Prize for Physics, the prestigious Wolf Prize in Physics (1998), and the EMET Prize in chemistry (2002).

  As Pauling’s influence on the scientific community faded with Shechtman’s growing recognition, his death in 1994 did still mark the complete lack of opposition to an idea that had long since gained mainstream acceptance. The swing in Shechtman’s favour, unsurprisingly, began with the observation of QCs and the icosahedral phase in other laboratories around the world.

  Interestingly, Indian scientists were among the forerunners in confirming the existence of QCs. As early as in 1985, when the paper published by Shechtman and others in the Physical Review Letters was just a year old, S Ranganathan and Kamanio Chattopadhyay (amongst others), two of India’s preeminent crystallographers, published a paper in Current Science announcing the discovery of materials that exhibited decagonal symmetry. Such materials are two-dimensional QCs with periodicity exhibited in one of those dimensions.

  The story of QCs is most important as a post-Second-World-War incidence of a paradigm shift occurring in a field of science easily a few centuries old.

  No other discovery has rattled scientists as much in these years, and since the Shechtman-Pauling episode, academic peers have been more receptive of dissonant findings. At the same time, credit must be given to the rapid advancements in technology and human knowledge of statistical techniques: without them, the startling quickness with which each hypothesis can be tested today wouldn’t have been possible.

  The analysis of the media representation of the discovery of quasicrystals with respect to Thomas Kuhn’s epistemological contentions in his The Structure of Scientific Revolutions was an attempt to understand his standpoints by exploring more of what went on in the physical chemistry circles of the 1980s.

  While there remains the unresolved discrepancy – whether knowledge is non-accumulative simply because the information founding it has not been available before – Kuhn’s propositions hold in terms of the identification of the anomaly, the mounting of the crisis period, the communication breakdown within scientific circles, the shift from normal science to cutting-edge science, and the eventual acceptance of a new paradigm and the discarding of the old one.

  Consequently, it appears that science journalists have indeed taken note of these developments in terms of The Structure. Thus, the book’s influence on science journalism can be held to be persistent, and is definitely evident.

  2012.10.23

• 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).

  

  As likely as oobleck

  Alan I. Goldman, a professor of physics at the Iowa State University, wrote in the 84^th 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°).

  

  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.

  2012.10.23

• 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.

  

  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 20^th issue of its 53^rd 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 16^th 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.

  

  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.

  

  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.

  

  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.

  2012.10.21

• A case of Kuhn, quasicrystals & communication – Part I

  Dan Shechtman’s discovery of quasi-crystals, henceforth abbreviated as QCs, in 1982 was a landmark achievement that invoked a paradigm-shift in the field of physical chemistry.

  However, at the time, the discovery faced stiff resistance from the broader scientific community and an eminent chemist of the time. Such things made it harder for Shechtman to prove his findings as being credible, but he persisted and succeeded in doing so.

  We know his story today because of its fairly limited coverage in the media, and especially from the comments of his peers, students and friends; its revolutionary characteristic was well reflected in many reports and essays.

  Because such publications indicated the onset of a new kind of knowledge, what merits consideration is if the media internalized Thomas Kuhn’s philosophy of science in the way it approached the incident.

  Broadly, the question is: Did the media reports reflect Kuhn’s paradigm-shifting hypothesis? Specifically, in the 1980s,

  1. Did science journalists find QCs anomalous?
  2. Did science journalists identify the crisis period when it happened or was it reported as an isolated incident?
  3. Does the media’s portrayal of the crisis period reflect any incommensurability (be it in terms of knowledge or communication)?

  Finally: How did science journalism behave when reporting stories from the cutting edge?

  The Structure of Scientific Revolutions

  Thomas S. Kuhn’s (July 18, 1922 – June 17, 1996) book, The Structure of Scientific Revolutions, published in 1962, was significantly influential in academic circles as well as the scientific community. It introduced the notion of a paradigm-shift, which has since become a principal when describing the evolution of scientific knowledge.

  

  Kuhn defined a paradigm based on two properties:

  1. The paradigm must be sufficiently unprecedented to attract researchers to study it, and
  2. It must be sufficiently open-ended to allow for growth and debate

  By this definition, most of the seminal findings of the greatest thinkers and scientists of the past are paradigmatic. Nicholas Copernicus’s De Revolutionibus Orbium Coelestium (1543) and Isaac Newton’s Philosophiae Naturalis Principia Mathematica (1687) are both prime examples that illustrate what paradigms can be and how they shift perceptions and interests in the subject.

  Such paradigms, Kuhn said (p. 25), work with three attributes that are inherent to their conception. The first of the three attributes is the determination of significant fact, whereby facts accrued through observation and experimentation are measured and recorded more accurately.

  Even though they are the “pegs” of any literature concerning the paradigm, activities such as their measurement and records are independent of the dictates of the paradigm. Instead, they are, in a colloquial sense, conducted anyway.

  Why this is so becomes evident in the second of the three foci: matches of fact with theory. Kuhn claims (p. 26) that this class of activity is rarer in reality, where predictions of the reigning theory are compared to the (significant) facts measured in nature.

  Consequently, good agreement between the two would establish the paradigm’s robustness, whereas disagreement would indicate the need for further refinement. In fact, on the same page, Kuhn illustrates the rarity of such agreement by stating

  … no more than three such areas are even yet accessible to Einstein’s general theory of relativity.

  The third and last focus is on the articulation of theory. In this section, Kuhn posits that the academician conducts experiments to

  1. Determine physical constants associated with the paradigm
  2. Determine quantitative laws (so as to provide a physical quantification of the paradigm)
  3. Determine the applications of the paradigm in various fields

  In The Structure, one paradigm replaces another through a process of contention. At first, a reigning paradigm exists that, to an acceptable degree of reasonableness, explains empirical observations. However, in time, as technology improves and researchers find results that don’t quite agree with the reigning paradigm, the results are listed as anomalies.

  This refusal to immediately induct the findings and modify the paradigm is illustrated by Kuhn as proof toward our expectations clouding our perception of the world.

  Instead, researchers hold the position of the paradigm as fixed and immovable, and attempt to check for errors with the experimental/observed data. An example of this is the superluminal neutrinos that were “discovered”, rather stumbled upon, at the OPERA experiment in Italy that works with the CERN’s Large Hadron Collider (LHC).

  When the experiment logs from that fateful day, September 23, 2011, were examined, nothing suspicious was found with the experimental setup. However, despite this assurance of the instruments’ stability, the theory (of relativity) that prohibits this result was held superior.

  On October 18, then, experimental confirmation was received that the neutrinos could not have traveled faster than light because the theoretically predicted energy signature of a superluminal neutrino did not match with the observed signatures.

  As Kuhn says (p. 77):

  Though they [scientists] may begin to lose faith and then to consider alternatives, they do not renounce the paradigm that has led them into crisis. They do not, that is, treat anomalies as counterinstances, though in the vocabulary of philosophy of science that is what they are.

  However, this state of disagreement is not perpetual because, as Kuhn concedes above, an accumulation of anomalies forces a crisis in the scientific community. During a period of crisis, the paradigm reigns, yes, but is also now and then challenged by alternately conceived paradigms that

  1. Are sufficiently unprecedented
  2. Are open-ended to provide opportunities for growth
  3. Are able to explain those anomalies that threatens the reign of the extant paradigm

  The new paradigm imposes a new framework of ideals to contain the same knowledge that dethroned the old paradigm, and because of a new framework, new relations between different bits of information become possible. Therefore, paradigm shifts are periods encompassing rejection and re-adoption as well as restructuring and discovery.

  Kuhn ties together here three postulates: incommensurability, scientific communication, and knowledge being non-accumulative. When a new paradigm takes over, there is often a reshuffling of subjects – some are relegated to a different department, some departments are broadened to include more subjects than were there previously, while other subjects are confined to illogicality.

  During this phase, some areas of knowledge may no longer be measured with the same standards that have gone before them.

  Because of this incommensurability, scientific communication within their community breaks down, but only for the period of the crisis. For one, because of the new framework, some scientific terms change their meaning, and because multiple revolutions have happened in the past, Kuhn assumes the liberty here to conclude that scientific knowledge is non-accumulative. This facet of evolution was first considered by Herbert Butterfield in his The Origins of Modern Science, 1300-1800. Kuhn, in his work, then drew a comparison to visual gestalt (p. 85).

  

  Just as in politics, when during a time of instability the people turn to conservative ideals to recreate a state of calm, scientists get back to a debate over the fundamentals of science to choose a successor paradigm. This is a gradual process, Kuhn says, that may or may not yield a new paradigm that is completely successful in explaining all the anomalies.

  The discovery of QCs

  On April 8, 1982, Dan Shechtman, a crystallographer working at the U. S. National Bureau of Standards (NBS), made a discovery that would nothing less than shatter the centuries-old assumptions of physical chemistry. Studying the molecular structure of an alloy of aluminium and manganese using electron diffraction, Shechtman noted an impossible arrangement of the molecules.

  In electron diffraction, electrons are used to study extremely small objects, such as atoms and molecules, because the wavelength of electrons – which determines the resolution of the image produced – can be controlled by their electric charge. Photons lack this charge and are therefore unsuitable for high-precision observation at the atomic level.

  When accelerated electrons strike the object under study, their wave nature takes over and they form an interference pattern on the observer lens when they are scattered. The device then works backward to reproduce the surface that may have generated the recorded pattern, in the process yielding an image of the surface. On that day in April, this is what Shechtman saw (note: the brightness of each node is only an indication of how far it is from the observer lens).

  

  The diffraction pattern shows the molecules arranged in repeating pentagonal rings. That meant that the crystal exhibited 5-fold symmetry, i.e. an arrangement that was symmetrical about five axes. At the time, molecular arrangements were restricted by the then-36-year old crystallographic restriction theorem, which held that arrangements with only 2-, 3-, 4- and 6-fold symmetries were allowed. In fact, Shechtman had passed his university exams proving that 5-fold symmetries couldn’t exist!
  

  At the time of discovery, Shechtman couldn’t believe his eyes because it was an anomaly. In keeping with tradition, in fact, he proceeded to look for experimental errors. Only after he could find none did he begin to consider reporting the discovery.

  

  In the second half of the 20^th century, the field of crystallography was beginning to see some remarkable discoveries, but none of them as unprecedented as that of QCs would turn out to be. This was because of the development of spectroscopy, a subject that studied the interaction of matter and radiation.

  Using devices such as X-ray spectrometers and tunneling electron microscopes (TEM), scientists could literally look at a molecule instead of having to determine its form via chemical reactions. In such a period, there was tremendous growth in physical chemistry because of the imaginative mind of one man who would later be called one of the greatest chemists of all time as well as make life difficult for Shechtman: Linus Carl Pauling.

  Pauling epitomized the aspect of Kuhn’s philosophy that refused to let an old paradigm die, and therefore posed a significant hindrance to Shechtman’s radical new idea. While Shechtman attempted to present his discovery of QCs as an anomaly that he thought prompted crisis, Pauling infamously declared, “There is no such thing as quasi-crystals, only quasi-scientists.”
  

  Media reportage

  The clash between Pauling and Shechtman, rather the “old school” and the “new kid”, created some attrition within universities in the United States and Israel, who with Shechtman was affiliated. While a select group of individuals who were convinced of the veracity of the radical claims set about studying it further, others – perhaps under the weight of Pauling’s credibility – dismissed the work as erroneous and desperate. The most important entity classifiable under the latter was the Journal of Applied Physics, which refused to publish Shechtman’s finding.

  In this turmoil, there was a collapse of communication between scientists of the two factions. Unfortunately, the media’s coverage of this incident was limited: a few articles appeared in the mid-1980s in newspapers, magazines and journals; in 1988 when Pauling published his own paper on QCs; in 1999 when Shechtman won the prestigious Wolf Prize in mathematics; and in 2011, when he won the Nobel Prize in chemistry.

  Despite the low coverage, the media managed to make known the existence of such things as QCs to a wider community as well as to a less-sophisticated one. The rift between Pauling and Shechtman was notable because, apart from reflecting Kuhn’s views, it also brought to light the mental block scientists professed when it came to falsification of their work, and how that prevented science as such from progressing rapidly. Anyway, such speculations are all based in the media’s representation of the events.

  2012.10.20