Physics

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Scientists unlock vital clue to strange quirk of static electricity

Scientists can now explain the prevailing unpredictability of contact electrification, unveiling order from what has long been considered chaos.

Static electricity—specifically the triboelectric effect, aka contact electrification—is ubiquitous in our daily lives, found in such things as a balloon rubbed against one’s hair or styrofoam packing peanuts sticking to a cat’s fur (as well as human skin, glass tabletops, and just about anywhere you don’t want packing peanuts to be). The most basic physics is well understood, but long-standing mysteries remain, most notably how different materials exchange positive and negative charges—sometimes ordering themselves into a predictable series, but sometimes appearing completely random.

Now scientists at the Institute of Science and Technology Austria (ISTA) have identified a critical factor explaining that inherent unpredictability: It’s the contact history of given materials that controls how they exchange charges in contact electrification. They described their findings in a new paper published in the journal Nature.

Johan Carl Wilcke published the first so-called “triboelectric series” in 1757 to describe the tendency of different materials to self-order based on how they develop a positive or negative charge. A material toward the bottom of the list, like hair, will acquire a more negative charge when it comes into contact with a material near the top of the list, like a rubber balloon.

The issue with all these lists is that they are inconsistent and unpredictable—sometimes the same scientists don’t get the same ordering results twice when repeating experiments—largely because there are so many confounding factors that can come into play. “Understanding how insulating materials exchanged charge seemed like a total mess for a very long time,” said co-author Scott Waitukaitis of ISTA. “The experiments are wildly unpredictable and can sometimes seem completely random.”

A cellulose material’s charge sign, for instance, can depend on whether its curvature is concave or convex. Two materials can exchange charge from positive (A) to negative (B), but that exchange can reverse over time, with B being positive and A being negative. And then there are “triangles”: Sometimes one material (A) gains a positive charge when rubbed up against another material (B), but B will gain a positive charge when rubbed against a third material (C), and C, in turn, will gain positive charge when in contact with A. Even identical materials can sometimes exchange charge upon contact.

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Microsoft demonstrates working qubits based on exotic physics

Microsoft’s first entry into quantum hardware comes in the form of Majorana 1, a processor with eight of these qubits.

Given that some of its competitors have hardware that supports over 1,000 qubits, why does the company feel it can still be competitive? Nayak described three key features of the hardware that he feels will eventually give Microsoft an advantage.

The first has to do with the fundamental physics that governs the energy needed to break apart one of the Cooper pairs in the topological superconductor, which could destroy the information held in the qubit. There are a number of ways to potentially increase this energy, from lowering the temperature to making the indium arsenide wire longer. As things currently stand, Nayak said that small changes in any of these can lead to a large boost in the energy gap, making it relatively easy to boost the system’s stability.

Another key feature, he argued, is that the hardware is relatively small. He estimated that it should be possible to place a million qubits on a single chip. “Even if you put in margin for control structures and wiring and fan out, it’s still a few centimeters by a few centimeters,” Nayak said. “That was one of the guiding principles of our qubits.” So unlike some other technologies, the topological qubits won’t require anyone to figure out how to link separate processors into a single quantum system.

Finally, all the measurements that control the system run through the quantum dot, and controlling that is relatively simple. “Our qubits are voltage-controlled,” Nayak told Ars. “What we’re doing is just turning on and off coupling of quantum dots to qubits to topological nano wires. That’s a digital signal that we’re sending, and we can generate those digital signals with a cryogenic controller. So we actually put classical control down in the cold.”

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Quantum teleportation used to distribute a calculation

The researchers showed that this setup allowed them to teleport with a specific gate operation (controlled-Z), which can serve as the basis for any other two-qubit gate operation—any operation you might want to do can be done by using a specific combination of these gates. After performing multiple rounds of these gates, the team found that the typical fidelity was in the area of 70 percent. But they also found that errors typically had nothing to do with the teleportation process and were the product of local operations at one of the two ends of the network. They suspect that using commercial hardware, which has far lower error rates, would improve things dramatically.

Finally, they performed a version of Grover’s algorithm, which can, with a single query, identify a single item from an arbitrarily large unordered list. The “arbitrary” aspect is set by the number of available qubits; in this case, having only two qubits, the list maxed out at four items. Still, it worked, again with a fidelity of about 70 percent.

While the work was done with trapped ions, almost every type of qubit in development can be controlled with photons, so the general approach is hardware-agnostic. And, given the sophistication of our optical hardware, it should be possible to link multiple chips at various distances, all using hardware that doesn’t require the best vacuum or the lowest temperatures we can generate.

That said, the error rate of the teleportation steps may still be a problem, even if it was lower than the basic hardware rate in these experiments. The fidelity there was 97 percent, which is lower than the hardware error rates of most qubits and high enough that we couldn’t execute too many of these before the probability of errors gets unacceptably high.

Still, our current hardware error rates started out far worse than they are today; successive rounds of improvements between generations of hardware have been the rule. Given that this is the first demonstration of teleported gates, we may have to wait before we can see if the error rates there follow a similar path downward.

Nature, 2025. DOI: 10.1038/s41586-024-08404-x  (About DOIs).

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Research Roundup: 7 cool science stories we almost missed


Peruvian mummy tattoos, the wobbly physics of spears and darts, quantum “cat states,” and more.

Lasers revealed tattoos on the hand of a 1200-year-old Peruvian mummy. Credit: Michael Pittman and Thomas G Kaye

It’s a regrettable reality that there is never time to cover all the interesting scientific stories each month. In the past, we’ve featured year-end roundups of cool science stories we missed. This year, we’re experimenting with a monthly collection. January’s list includes papers on using lasers to reveal Peruvian mummy tattoos; the physics of wobbly spears and darts; how a black hole changes over time; and quantum “cat states” for error correction in quantum computers, among other fascinating research.

Tracking changes in a black hole over time

Left: EHT images of M87from the 2018 and 2017 observation campaigns. Middle: Example images from a general relativistic magnetohydrodynamic (GRMHD) simulation at two different times. Right: Same simulation snapshots, blurred to match the EHT’s observational resolution. Credit: EHT collaboration

In 2019, the Event Horizon Telescope announced the first direct image ever taken of a black hole at the center of an elliptical galaxy, Messier 87 (M87), located in the constellation of Virgo some 55 million light-years away. Astronomers have now combined earlier observational data to learn more about the turbulent dynamics of plasma near M87*’s event horizon over time, according to a paper published in the journal Astronomy and Astrophysics.

Co-author Luciano Rezzolla of Goethe University Frankfurt in Germany likened the new analysis to comparing two photographs of Mount Everest, one year apart. While the mountain’s basic structure is unlikely to change much in that time, one could observe changes in clouds near the peak and deduce from that properties like wind direction. For instance, in the case of M87*, the new analysis confirmed the presence of a luminous ring that is brightest at the bottom, which in turn confirmed that the rotational axis points away from Earth. “More of these observations will be made in the coming years and with increasing precision, with the ultimate goal of producing a movie of what happens near M87*,” said Rezolla.

Astronomy and Astrophysics, 2025. DOI: 10.1051/0004-6361/202451296 (About DOIs).

Lasers reveal Peruvian mummy tattoos

A tattooed forearm of a Chancay mummy

A tattooed forearm of a Chancay mummy. Credit: Michael Pittman and Thomas G Kaye

Humans across the globe have been getting tattoos for more than 5,000 years, judging by traces found on mummified remains from Europe to Asia and South America. But it can be challenging to decipher details of those tattoos, given how much the ink tends to “bleed” over time, along with the usual bodily decay. Infrared imaging can help, but in an innovative twist, scientists decided to use lasers that make skin glow ever so faintly, revealing many fine hidden details of tattoos found on 1,200-year-old Peruvian mummies, according to a paper published in the Proceedings of the National Academy of Sciences.

It’s the first time the laser-stimulated fluorescence (LSF) technique has been used on mummified human remains. The skin’s fluorescence essentially backlights any tattoos, and after post-processing, the long-exposure photographs showed white skin behind black outlines of the tattoo art—images so detailed it’s possible to measure density differences in the ink and eliminate any bleed effects. The authors determined that the tattoos on four mummies—geometric patterns with triangles and diamonds—were made with carbon-based black ink skillfully applied with a pointed object finer than a standard modern tattoo needle, possibly a cactus needle or sharpened bone.

PNAS, 2025. DOI: 10.1073/pnas.2421517122 (About DOIs).

Sforza Castle’s hidden passages

Ground-penetrating radar reveals new secrets under Milan's Sforza Castle

Ground-penetrating radar reveals new secrets under Milan’s Sforza Castle Credit: Politecnico di Milano

Among the many glories of Milan is the 15th-century Sforza Castle, built by Francesco Sforza on the remnants of an earlier fortification as his primary residence. Legends about the castle abound, most notably the existence of secret underground chambers and passages. For instance, Ludovico il Moro, Duke of Milan from 1494–1499, was so heartbroken over the loss of his wife in childbirth that he used an underground passageway to visit her tomb in the Basilica of Santa Maria delle Grazie—a passageway that appears in the drawings of Leonardo da Vinci, who was employed at the court for a time.

Those underground cavities and passages are now confirmed, thanks to a geophysical survey using ground-penetrating radar and laser scanning, performed as part of a PhD thesis. Various underground cavities and buried passageways were found within the castle’s outer walls, including Ludovico’s passageway and what have may have been secret military passages. Those involved in the project plan to create a “digital twin” of Sforza Castle based on the data collected, one that incorporates both its current appearance and its past. Perhaps it will also be possible to integrate that data with augmented reality to provide an immersive digital experience.

Physics of wobbly spears and darts

Image sequence of a 100-mm long projectile during a typical ejection in experiments.

Image sequence of a 100-mm-long projectile during a typical ejection in experiments. Credit: G. Giombini et al., 2025

Among the things that make humans unique among primates is our ability to throw various objects with speed and precision (with some practice)—spears or darts, for example. That’s because the human shoulder is anatomically conducive to storing and releasing the necessary elastic energy, a quality that has been mimicked in robotics to improve motor efficiency. According to the authors of a paper published in the journal Physical Review E, the use of soft elastic projectiles can improve the efficiency of throws, particularly those whose tips are weighted with a mass like a spearhead.

Guillaume Giombini of the Université Côte d’Azur in Nice, France, and co-authors wanted to explore this “superpropulsion” effect more deeply, using a combination of experimental data, numerical simulation, and theoretical analysis. The projectiles they used in their experiments were inspired by archery bows and consisted of two flat steel cantilevers connected by a string, essentially serving as springs to give the projectile the necessary elasticity. They placed a flat piece of rigid plastic in the middle of the string as a platform. Some of the projectiles were tested alone, while others were weighted with end masses. A fork held each projectile in place before launch, and the scientists measured speed and deformation during flight. They found that the wobble produced by the weighted tip projectiles yielded a kinetic energy gain of 160 percent over more rigid, unweighted projectiles.

Physical Review E, 2025. DOI: 10.1103/PhysRevE.00.005500  (About DOIs).

Quantum “cat states” for error detection

Left to right: UNSW researchers Benjamin Wilhelm, Xi Yu, Andrea Morello, and Danielle Holmes, all seated and each holding a cat on their lap

Left to right: UNSW researchers Benjamin Wilhelm, Xi Yu, Andrea Morello, and Danielle Holmes. Credit: UNSW Sydney/CC BY-NC

The Schrödinger’s cat paradox in physics is an excellent metaphor for the superposition of quantum states in atoms. Over the last 20 years, physicists have managed to build various versions of Schrödinger’s cat in the laboratory whereby two or more particles manage to be in two different states at the same time—so-called “cat states,” such as six atoms in simultaneous “spin up” and “spin down” states, rather like spinning clockwise and counterclockwise at the same time. Such states are fragile, however, and quickly decohere. Physicists at the University of New South Wales came up with a fresh twist on a cat-state that is more robust, according to a paper published in the journal Nature Physics.

They used an antimony atom embedded within a silicon quantum chip. The atom is quite heavy and has a large nuclear spin that can go in eight directions rather than just two (spin up and spin down). This could help enormously with quantum error correction, one of the biggest obstacles in quantum computing, because there is more room for error in the binary code. “As the proverb goes, a cat has nine lives,” said co-author Xi Yu of UNSW. “One little scratch is not enough to kill it. Our metaphorical ‘cat’ has seven lives: it would take seven consecutive errors to turn the ‘0’ into a ‘1.’” And embedding the atom in a silicon chip makes it scalable.

Nature Physics, 2025. DOI: 10.1038/s41567-024-02745-0  (About DOIs).

New twist on chain mail armor

how polycatenated architected materials look in their fluid or granular state, conforming to the shape of the vessel in which it is held.

Credit: Wenjie Zhou

Scientists have developed a new material that is like “chain mail on steroids,” capable of responding as both a fluid or a solid, depending on the kind of stress applied, according to a paper published in the journal Science. That makes it ideal for manufacturing helmets or other protective gear, as well as biomedical devices and robotics components. The technical term is polycatenated architected materials (PAMs). Much like how chain mail is built from small metal rings linked together into a mesh, PAMs are composed of various interlocking shapes that can form a wide range of different 3D patterns.

The authors were partly inspired by the lattice structure of crystals; they just replaced fixed particles with rings or cage-like shapes made out of different materials—such as acrylic polymers, nylon, or metals—to make small 3D-printed structures small enough to fit in the palm of one’s hand. They then subjected these materials to various stressors in the laboratory: compression, a lateral shearing force, and twisting. Some of the materials felt like hard solids, others were squishier, but they all exhibited the same kind of telltale transition, behaving more like a fluid or a solid depending on the stressor applied. PAMs at the microscale can also expand or contract in response to electrical charges. This makes them a useful hybrid material, spanning the gap between granular materials and elastic deformable ones.

W. Zhou et al., Science, 2025. DOI: 10.1126/science.adr9713  (About DOIs).

Kitty robot mimics headbutts

Any cat lover will tell you that cats show humans affection by rubbing their heads against the body (usually shins or hands). It’s called “bunting,” often accompanied by purring, and it’s one of the factors that make companion animal therapy so effective, per the authors of a paper published in ACM Transactions on Human-Robot Interactions. That’s why they built a small robot designed to mimic bunting behavior, conducting various experiments to assess whether human participants found their interactions with the kitty-bot therapeutic. The robot prototypes were small enough to fit on a human lap, featuring a 3D-printed frame and a head covered with furry polyester fabric.

The neck needed to be flexible to mimic the bunting behavior, so the authors incorporated a mechanism that could adjust the stiffness of the neck via wire tension. They then tested various prototypes with university students, setting the neck stiffness to low, high, and variable. The students said they felt less tense after interacting with the robots. There was no significant difference between the settings, although participants slightly preferred the variable setting. We know what you’re thinking: Why not just get an actual cat or visit your local cat cafe? The authors note that many people are allergic to cats, and there is also a risk of bites, scratches, or disease transmission—hence the interest in developing animal-like robots for therapeutic applications.

ACM Transactions on Human-Robot Interactions, 2025. DOI: 10.1145/3700600  (About DOIs).

Photo of Jennifer Ouellette

Jennifer is a senior writer at Ars Technica with a particular focus on where science meets culture, covering everything from physics and related interdisciplinary topics to her favorite films and TV series. Jennifer lives in Baltimore with her spouse, physicist Sean M. Carroll, and their two cats, Ariel and Caliban.

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Complexity physics finds crucial tipping points in chess games

For his analysis, Barthelemy chose to represent chess as a decision tree in which each “branch” leads to a win, loss, or draw. Players face the challenge of finding the best move amid all this complexity, particularly midgame, in order to steer gameplay into favorable branches. That’s where those crucial tipping points come into play. Such positions are inherently unstable, which is why even a small mistake can have a dramatic influence on a match’s trajectory.

A case of combinatorial complexity

Barthelemy has re-imagined a chess match as a network of forces in which pieces act as the network’s nodes, and the ways they interact represent the edges, using an interaction graph to capture how different pieces attack and defend one another. The most important chess pieces are those that interact with many other pieces in a given match, which he calculated by measuring how frequently a node lies on the shortest path between all the node pairs in the network (its “betweenness centrality”).

He also calculated so-called “fragility scores,” which indicate how easy it is to remove those critical chess pieces from the board. And he was able to apply this analysis to more than 20,000 actual chess matches played by the world’s top players over the last 200 years.

Barthelemy found that his metric could indeed identify tipping points in specific matches. Furthermore, when he averaged his analysis over a large number of games, an unexpected universal pattern emerged. “We observe a surprising universality: the average fragility score is the same for all players and for all openings,” Barthelemy writes. And in famous chess matches, “the maximum fragility often coincides with pivotal moments, characterized by brilliant moves that decisively shift the balance of the game.”

Specifically, fragility scores start to increase about eight moves before the critical tipping point position occurs and stay high for some 15 moves after that. “These results suggest that positional fragility follows a common trajectory, with tension peaking in the middle game and dissipating toward the endgame,” he writes. “This analysis highlights the complex dynamics of chess, where the interaction between attack and defense shapes the game’s overall structure.”

Physical Review E, 2025. DOI: 10.1103/PhysRevE.00.004300  (About DOIs).

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Researchers optimize simulations of molecules on quantum computers

The net result is a much faster operation involving far fewer gates. That’s important because errors in quantum hardware increase as a function of both time and the number of operations.

The researchers then used this approach to explore a chemical, Mn4O5Ca, that plays a key role in photosynthesis. Using this approach, they showed it’s possible to calculate what’s called the “spin ladder,” or the list of the lowest-energy states the electrons can occupy. The energy differences between these states correspond to the wavelengths of light they can absorb or emit, so this also defines the spectrum of the molecule.

Faster, but not quite fast enough

We’re not quite ready to run this system on today’s quantum computers, as the error rates are still a bit too high. But because the operations needed to run this sort of algorithm can be done so efficiently, the error rates don’t have to come down very much before the system will become viable. The primary determinant of whether it will run into an error is how far down the time dimension you run the simulation, plus the number of measurements of the system you take over that time.

“The algorithm is especially promising for near-term devices having favorable resource requirements quantified by the number of snapshots (sample complexity) and maximum evolution time (coherence) required for accurate spectral computation,” the researchers wrote.

But the work also makes a couple of larger points. The first is that quantum computers are fundamentally unlike other forms of computation we’ve developed. They’re capable of running things that look like traditional algorithms, where operations are performed and a result is determined. But they’re also quantum systems that are growing in complexity with each new generation of hardware, which makes them great at simulating other quantum systems. And there are a number of hard problems involving quantum systems we’d like to solve.

In some ways, we may only be starting to scratch the surface of quantum computers’ potential. Up until quite recently, there were a lot of hypotheticals; it now appears we’re on the cusp of using one for some potentially useful computations. And that means more people will start thinking about clever ways we can solve problems with them—including cases like this, where the hardware would be used in ways its designers might not have even considered.

Nature Physics, 2025. DOI: 10.1038/s41567-024-02738-z  (About DOIs).

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How to get a perfect salt ring deposit in your pasta pot

Deposit morphologies for a settling particle. When increasing either the injection volume or the settling height, the deposit radius increases.

Deposit morphologies for a settling particle. When increasing either the injection volume or the settling height, the deposit radius increases. Credit: M. Souzy et al., 2025

They used spherical borosilicate glass beads of varying diameters to represent the grains of salt and loaded different fixed volumes of beads into cylindrical tubes. Then they slid open the tube’s bottom to release the beads, capturing how they fell and settled with a Nikon D300 camera placed at the top of the tank. The tank was illuminated from below by a uniform LED light screen and diffuser to get an even background.

The physicists found that gravity will pull a single particle to the bottom of the tank, creating a small wake drag that affects the flow of water around it. That perturbation becomes much more complicated when many large particles are released at once, each with its own wake that affects its neighbors. So, the falling particles start to shift horizontally, distributing the falling particles in an expanding circular pattern.

Particles released from a smaller height fall faster and form a pattern with a clean central region. Those released from a greater height take longer to fall to the bottom, and the cloud of particles expands radially until the particles are far enough apart not to be influenced by the wakes of neighboring particles such that they no longer form a cloud. In that case, you end up with a homogeneous salt ring deposit.

“These are the main physical ingredients, and despite its apparent simplicity, this phenomenon encompasses a wide range of physical concepts such as sedimentation, non-creeping flow, long-range interactions between multiple bodies, and wake entrainment,” said Souzy. “Things get even more interesting once you realize larger particles are more radially shifted than small ones, which means you can sort particles by size just by dropping them into a water tank. It was a great overall experience, because we soon realized our simple observation of daily life conceals a rich variety of physical mechanisms.”

Those phenomena are just as relevant outside the kitchen, according to the authors, most notably in such geophysical and industrial contexts as “the discharge of dredged materials and industrial waste into rivers lakes and oceans,” they wrote. “In scenarios involving contaminated waste, comprehending the behavior of both the solid waste and the interacting fluid is crucial.”

Physics of Fluids, 2025. DOI: 10.1063/5.0239386  (About DOIs).

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Did Hilma af Klint draw inspiration from 19th century physics?


Diagrams from Thomas Young’s 1807 Lectures bear striking resemblance to abstract figures in af Klint’s work.

Hilma af Klint’s Group IX/SUW, The Swan, No. 17, 1915. Credit: Hilma af Klimt Foundation

In 2019, astronomer Britt Lundgren of the University of North Carolina Asheville visited the Guggenheim Museum in New York City to take in an exhibit of the works of Swedish painter Hilma af Klint. Lundgren noted a striking similarity between the abstract geometric shapes in af Klint’s work and scientific diagrams in 19th century physicist Thomas Young‘s Lectures (1807). So began a four-year journey starting at the intersection of science and art that has culminated in a forthcoming paper in the journal Leonardo, making the case for the connection.

Af Klint was formally trained at the Royal Academy of Fine Arts and initially focused on drawing, portraits, botanical drawings, and landscapes from her Stockholm studio after graduating with honors. This provided her with income, but her true life’s work drew on af Klint’s interest in spiritualism and mysticism. She was one of “The Five,” a group of Swedish women artists who shared those interests. They regularly organized seances and were admirers of theosophical teachings of the time.

It was through her work with The Five that af Klint began experimenting with automatic drawing, driving her to invent her own geometric visual language to conceptualize the invisible forces she believed influenced our world. She painted her first abstract series in 1906 at age 44. Yet she rarely exhibited this work because she believed the art world at the time wasn’t ready to appreciate it. Her will requested that the paintings stay hidden for at least 20 years after her death.

Even after the boxes containing her 1,200-plus abstract paintings were opened, their significance was not fully appreciated at first. The Moderna Museum in Stockholm actually declined to accept them as a gift, although it now maintains a dedicated space to her work. It wasn’t until art historian Ake Fant presented af Klint’s work at a Helsinki conference that the art world finally took notice. The Guggenheim’s exhibit was af Klint’s American debut. “The exhibit seemed to realize af Klint’s documented dream of introducing her paintings to the world from inside a towering spiral temple and it was met roundly with acclaim, breaking all attendance records for the museum,” Lundgren wrote in her paper.

A pandemic project

Lundgren is the first person in her family to become a scientist; her mother studied art history, and her father is a photographer and a carpenter. But she always enjoyed art because of that home environment, and her Swedish heritage made af Klint an obvious artist of interest. It wasn’t until the year after she visited the Guggenheim exhibit, as she was updating her lectures for an astrophysics course, that Lundgren decided to investigate the striking similarities between Young’s diagrams and af Klint’s geometric paintings—in particular those series completed between 1914 and 1916. It proved to be the perfect research project during the COVID-19 lockdowns.

Lundgren acknowledges the inherent skepticism such an approach by an outsider might engender among the art community and is sympathetic, given that physics and astronomy both have their share of cranks. “As a professional scientist, I have in the past received handwritten letters about why Einstein is wrong,” she told Ars. “I didn’t want to be that person.”

That’s why her very first research step was to contact art professors at her institution to get their expert opinions on her insight. They were encouraging, so she dug in a little deeper, reading every book about af Klint she could get her hands on. She found no evidence that any art historians had made this connection before, which gave her the confidence to turn her work into a publishable paper.

The paper didn’t find a home right away, however; the usual art history journals rejected it, partly because Lundgren was an outsider with little expertise in that field. She needed someone more established to vouch for her. Enter Linda Dalrymple Henderson of the University of Texas at Austin, who has written extensively about scientific influences on abstract art, including that of af Klint. Henderson helped Lundgren refine the paper, encouraged her to submit it to Leonardo, and “it came back with the best review I’ve ever received, even inside astronomy,” said Lundgren.

Making the case

Young and af Klint were not contemporaries; Young died in 1829, and af Klint was born in 1862. Nor are there any specific references to Young or his work in the academic literature examining the sources known to have influenced the Swedish painter’s work. Yet af Klint had a well-documented interest in science, spanning everything from evolution and botany to color theory and physics. While those influences tended to be scientists who were her contemporaries, Lundgren points out that the artist’s personal library included a copy of an 1823 astronomy book.

Excerpt from Plate XXIX of Young’s Lectures Niels Bohr Library and Archives/AIP

Af Klint was also commissioned to paint a portrait of Swedish physicist Knut Angstrom in 1910 at Uppsala University, whose library includes a copy of Young’s Lectures. So it’s entirely possible that af Klint had access to the astronomy and physics of the previous century and would likely have been particularly intrigued by discoveries involving “invisible light” (electromagnetism, x-rays, radioactivity, etc.).

Young’s Lectures contain a speculative passage about the existence of a universal ether (since disproven), a concept that fascinated both scientists and those (like af Klint) with certain occult interests in the late 19th and early 20th centuries. In fact, Young’s passage was included in a popular 1875 spiritualist text, Unseen Universe by P.G. Tait and Balfour Stewart, that was heavily cited by Theosophical Society founder Helena Petrovna Blavatsky. Blavatsky in turn is known to have influenced af Klint around the time the artist created The Swan, The Dove, and Altarpieces series.

Lundgren found that “in several instances, the captions accompanying Young’s color figures [in the Lectures] even seem to decode elements of af Klint’s paintings or bring attention to details that might otherwise be overlooked.” For instance, the caption for Young’s Plate XXIX describes the “oblique stripes of color” that appear when candlelight is viewed through a prism that “almost interchangeably describes features in af Klint’s Group X., No. 1, Altarpiece,” she wrote

(a) Excerpt from Young's Plate XXX. (b) af Klint, Parsifal Series No. 68. (c and d) af Klint, Group IX/UW, The Dove, No. 12 and No. 13.

(a) Excerpt from Young’s Plate XXX. (b) af Klint, Parsifal Series No. 68. (c and d) af Klint, Group IX/UW, The Dove, No. 12 and No. 13. Credit: Niels Bohr Library/Hilma af Klint Foundation

Art historians had previously speculated about af Klint’s interest in color theory, as reflected in the annotated watercolor squares featured in her Parsifal Series (1916). Lundgren argues that those squares resemble Fig. 439 in the color plates of Young’s Lectures, demonstrating the inversion of color in human vision. Those diagrams also “appear almost like crude sketches of af Klint’s The Dove, Nos. 12 and 13,” Lundgren wrote. “Paired side by side, these paintings can produce the same visual effects described by Young, with even the same color palette.”

The geometric imagery of af Klint’s The Swan series is similar to Young’s illustrations of the production and perception of colors, while “black and white diagrams depicting the propagation of light through combinations of lenses and refractive surfaces, included in Young’s Lectures On the Theory of Optics, bear a particularly strong geometric resemblance to The Swan paintings No. 12 and No.13,” Lundgren wrote. Other pieces in The Swan series may have been inspired by engravings in Young’s Lectures.

This is admittedly circumstantial evidence and Lundgren acknowledges as much. “Not being able to prove it is intriguing and frustrating at the same time,” she said. She continues to receive additional leads, most recently from an af Klint relative on the board of the Moderna Museum. Once again, the evidence wasn’t direct, but it seems af Klint would have attended certain local lecture circuits about science, while several members of the Theosophy Society were familiar with modern physics and Young’s earlier work. “But none of these are nails in the coffin that really proved she had access to Young’s book,” said Lundgren.

Photo of Jennifer Ouellette

Jennifer is a senior writer at Ars Technica with a particular focus on where science meets culture, covering everything from physics and related interdisciplinary topics to her favorite films and TV series. Jennifer lives in Baltimore with her spouse, physicist Sean M. Carroll, and their two cats, Ariel and Caliban.

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why-solving-crosswords-is-like-a-phase-transition

Why solving crosswords is like a phase transition

There’s also the more recent concept of “explosive percolation,” whereby connectivity emerges not in a slow, continuous process but quite suddenly, simply by replacing the random node connections with predetermined criteria—say, choosing to connect whichever pair of nodes has the fewest pre-existing connections to other nodes. This introduces bias into the system and suppresses the growth of large dominant clusters. Instead, many large unconnected clusters grow until the critical threshold is reached. At that point, even adding just one or two more connections will trigger one global violent merger (instant uber-connectivity).

Puzzling over percolation

One might not immediately think of crossword puzzles as a network, although there have been a couple of relevant prior mathematical studies. For instance, John McSweeney of the Rose-Hulman Institute of Technology in Indiana employed a random graph network model for crossword puzzles in 2016. He factored in how a puzzle’s solvability is affected by the interactions between the structure of the puzzle’s cells (squares) and word difficulty, i.e., the fraction of letters you need to know in a given word in order to figure out what it is.

Answers represented nodes while answer crossings represented edges, and McSweeney assigned a random distribution of word difficulty levels to the clues. “This randomness in the clue difficulties is ultimately responsible for the wide variability in the solvability of a puzzle, which many solvers know well—a solver, presented with two puzzles of ostensibly equal difficulty, may solve one readily and be stumped by the other,” he wrote at the time. At some point, there has to be a phase transition, in which solving the easiest words enables the puzzler to solve the more difficult words until the critical threshold is reached and the puzzler can fill in many solutions in rapid succession—a dynamic process that resembles, say, the spread of diseases in social groups.

In this sample realization, sites with black sites are shown in black; empty sites are white; and occupied sites contain symbols and letters.

In this sample realization, black sites are shown in black; empty sites are white; and occupied sites contain symbols and letters. Credit: Alexander K. Hartmann, 2024

Hartmann’s new model incorporates elements of several nonstandard percolation models, including how much the solver benefits from partial knowledge of the answers. Letters correspond to sites (white squares) while words are segments of those sites, bordered by black squares. There is an a priori probability of being able to solve a given word if no letters are known. If some words are solved, the puzzler gains partial knowledge of neighboring unsolved words, which increases the probability of those words being solved as well.

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delve-into-the-physics-of-the-hula-hoop

Delve into the physics of the Hula-Hoop

High-speed video of experiments on a robotic hula hooper, whose hourglass form holds the hoop up and in place.

Some version of the Hula-Hoop has been around for millennia, but the popular plastic version was introduced by Wham-O in the 1950s and quickly became a fad. Now, researchers have taken a closer look at the underlying physics of the toy, revealing that certain body types are better at keeping the spinning hoops elevated than others, according to a new paper published in the Proceedings of the National Academy of Sciences.

“We were surprised that an activity as popular, fun, and healthy as hula hooping wasn’t understood even at a basic physics level,” said co-author Leif Ristroph of New York University. “As we made progress on the research, we realized that the math and physics involved are very subtle, and the knowledge gained could be useful in inspiring engineering innovations, harvesting energy from vibrations, and improving in robotic positioners and movers used in industrial processing and manufacturing.”

Ristroph’s lab frequently addresses these kinds of colorful real-world puzzles. For instance, in 2018, Ristroph and colleagues fine-tuned the recipe for the perfect bubble based on experiments with soapy thin films. In 2021, the Ristroph lab looked into the formation processes underlying so-called “stone forests” common in certain regions of China and Madagascar.

In 2021, his lab built a working Tesla valve, in accordance with the inventor’s design, and measured the flow of water through the valve in both directions at various pressures. They found the water flowed about two times slower in the nonpreferred direction. In 2022, Ristroph studied the surpassingly complex aerodynamics of what makes a good paper airplane—specifically, what is needed for smooth gliding.

Girl twirling a Hula hoop, 1958

Girl twirling a Hula-Hoop in 1958 Credit: George Garrigues/CC BY-SA 3.0

And last year, Ristroph’s lab cracked the conundrum of physicist Richard Feynman’s “reverse sprinkler” problem, concluding that the reverse sprinkler rotates a good 50 times slower than a regular sprinkler but operates along similar mechanisms. The secret is hidden inside the sprinkler, where there are jets that make it act like an inside-out rocket. The internal jets don’t collide head-on; rather, as water flows around the bends in the sprinkler arms, it is slung outward by centrifugal force, leading to asymmetric flow.

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ten-cool-science-stories-we-almost-missed

Ten cool science stories we almost missed


Bronze Age combat, moral philosophy and Reddit’s AITA, Mondrian’s fractal tree, and seven other fascinating papers.

There is rarely time to write about every cool science paper that comes our way; many worthy candidates sadly fall through the cracks over the course of the year. But as 2024 comes to a close, we’ve gathered ten of our favorite such papers at the intersection of science and culture as a special treat, covering a broad range of topics: from reenacting Bronze Age spear combat and applying network theory to the music of Johann Sebastian Bach, to Spider-Man inspired web-slinging tech and a mathematical connection between a turbulent phase transition and your morning cup of coffee. Enjoy!

Reenacting Bronze Age spear combat

Experiment with experienced fighters who spar freely using different styles.

An experiment with experienced fighters who spar freely using different styles. Credit: Valerio Gentile/CC BY

The European Bronze Age saw the rise of institutionalized warfare, evidenced by the many spearheads and similar weaponry archaeologists have unearthed. But how might these artifacts be used in actual combat? Dutch researchers decided to find out by constructing replicas of Bronze Age shields and spears and using them in realistic combat scenarios. They described their findings in an October paper published in the Journal of Archaeological Science.

There have been a couple of prior experimental studies on bronze spears, but per Valerio Gentile (now at the University of Gottingen) and coauthors, practical research to date has been quite narrow in scope, focusing on throwing weapons against static shields. Coauthors C.J. van Dijk of the National Military Museum in the Netherlands and independent researcher O. Ter Mors each had more than a decade of experience teaching traditional martial arts, specializing in medieval polearms and one-handed weapons. So they were ideal candidates for testing the replica spears and shields.

Of course, there is no direct information on prehistoric fighting styles, so van Dijk and Mors relied on basic biomechanics of combat movements with similar weapons detailed in historic manuals. They ran three versions of the experiment: one focused on engagement and controlled collisions, another on delivering wounding body blows, and the third on free sparring. They then studied wear marks left on the spearheads and found they matched the marks found on similar genuine weapons excavated from Bronze Age sites. They also gleaned helpful clues to the skills required to use such weapons.

DOI: Journal of Archaeological Science, 2024. 10.1016/j.jas.2024.106044 (About DOIs).

Physics of Ned Kahn’s kinetic sculptures

Ned Kahn's Shimmer Wall, The Franklin Institute, Philadelphia, Pennsylvania.

Shimmer Wall, The Franklin Institute, Philadelphia, Pennsylvania. Credit: Ned Kahn

Environmental artist and sculptor Ned Kahn is famous for his kinematic building facades, inspired by his own background in science. An exterior wall on the Children’s Museum of Pittsburgh, for instance, consists of hundreds of flaps that move in response to wind, creating distinctive visual patterns. Kahn used the same method to create his Shimmer Wall at Philadelphia’s Franklin Institute, as well as several other similar projects.

Physicists at Sorbonne Universite in Paris have studied videos of Kahn’s kinetic facades and conducted experiments to measure the underlying physical mechanisms, outlined in a November paper published in the journal Physical Review Fluids. The authors analyzed 18 YouTube videos taken of six of Kahn’s kinematic facades, working with Kahn and building management to get the dimensions of the moving plates, scaling up from the video footage to get further information on spatial dimensions.

They also conducted their own wind tunnel experiments, using strings of pendulum plates. Their measurements confirmed that the kinetic patterns were propagating waves to create the flickering visual effects. The plates’ movement is driven primarily by their natural resonant frequencies at low speeds, and by pressure fluctuations from the wind at higher speeds.

DOI: Physical Review Fluids, 2024. 10.1103/PhysRevFluids.9.114604 (About DOIs).

How brewing coffee connects to turbulence

Trajectories in time traced out by turbulent puffs as they move along a simulated pipe and in experiments, with blue regions indicate the puff

Trajectories in time traced out by turbulent puffs as they move along a simulated pipe and in experiments, with blue regions indicate puff “traffic jams.” Credit: Grégoire Lemoult et al., 2024

Physicists have been studying turbulence for centuries, particularly the transitional period where flows shift from predictably smooth (laminar flow) to highly turbulent. That transition is marked by localized turbulent patches known as “puffs,” which often form in fluids flowing through a pipe or channel. In an October paper published in the journal Nature Physics, physicists used statistical mechanics to reveal an unexpected connection between the process of brewing coffee and the behavior of those puffs.

Traditional mathematical models of percolation date back to the 1940s. Directed percolation is when the flow occurs in a specific direction, akin to how water moves through freshly ground coffee beans, flowing down in the direction of gravity. There’s a sweet spot for the perfect cuppa, where the rate of flow is sufficiently slow to absorb most of the flavor from the beans, but also fast enough not to back up in the filter. That sweet spot in your coffee brewing process corresponds to the aforementioned laminar-turbulent transition in pipes.

Physicist Nigel Goldenfeld of the University of California, San Diego, and his coauthors used pressure sensors to monitor the formation of puffs in a pipe, focusing on how puff-to-puff interactions influenced each other’s motion. Next, they tried to mathematically model the relevant phase transitions to predict puff behavior. They found that the puffs behave much like cars moving on a freeway during rush hour: they are prone to traffic jams—i.e., when a turbulent patch matches the width of the pipe, causing other puffs to build up behind it—that form and dissipate on their own. And they tend to “melt” at the laminar-turbulent transition point.

DOI: Nature Physics, 2024. 10.1038/s41567-024-02513-0 (About DOIs).

Network theory and Bach’s music

In a network representation of music, notes are represented by nodes, and transition between notes are represented by directed edges connecting the nodes. Credit: S. Kulkarni et al., 2024

When you listen to music, does your ability to remember or anticipate the piece tell you anything about its structure? Physicists at the University of Pennsylvania developed a model based on network theory to do just that, describing their work in a February paper published in the journal Physical Review Research. Johann Sebastian Bach’s works were an ideal choice given the highly mathematical structure, plus the composer was so prolific, across so many very different kinds of musical compositions—preludes, fugues, chorales, toccatas, concertos, suites, and cantatas—as to allow for useful comparisons.

First, the authors built a simple “true” network for each composition, in which individual notes served as “nodes” and the transitions from note to note served as “edges” connecting them. Then they calculated the amount of information in each network. They found it was possible to tell the difference between compositional forms based on their information content (entropy). The more complex toccatas and fugues had the highest entropy, while simpler chorales had the lowest.

Next, the team wanted to quantify how effectively this information was communicated to the listener, a task made more difficult by the innate subjectivity of human perception. They developed a fuzzier “inferred” network model for this purpose, capturing an essential aspect of our perception: we find a balance between accuracy and cost, simplifying some details so as to make it easier for our brains to process incoming information like music.

The results: There were fewer differences between the true and inferred networks for Bach’s compositions than for randomly generated networks, suggesting that clustering and the frequent repetition of transitions (represented by thicker edges) in Bach networks were key to effectively communicating information to the listener. The next step is to build a multi-layered network model that incorporates elements like rhythm, timbre, chords, or counterpoint (a Bach specialty).

DOI: Physical Review Research, 2024. 10.1103/PhysRevResearch.6.013136 (About DOIs).

The philosophy of Reddit’s AITA

Count me among the many people practically addicted to Reddit’s “Am I the Asshole” (AITA) forum. It’s such a fascinating window into the intricacies of how flawed human beings navigate different relationships, whether personal or professional. That’s also what makes it a fantastic source of illustrative common-place dilemmas of moral decision-making for philosophers like Daniel Yudkin of the University of Pennsylvania. Relational context matters, as Yudkin and several co-authors ably demonstrated in a PsyArXiv preprint earlier this year.

For their study, Yudkin et al. compiled a dataset of nearly 370,000 AITA posts, along with over 11 million comments, posted between 2018 and 2021. They used machine learning to analyze the language used to sort all those posts into different categories. They relied on an existing taxonomy identifying six basic areas of moral concern: fairness/proportionality, feelings, harm/offense, honesty, relational obligation, and social norms.

Yudkin et al. identified 29 of the most common dilemmas in the AITA dataset and grouped them according to moral theme. Two of the most common were relational transgression and relational omission (failure to do what was expected), followed by behavioral over-reaction and unintended harm. Cheating and deliberate misrepresentation/dishonesty were the moral dilemmas rated most negatively in the dataset—even more so than intentional harm. Being judgmental was also evaluated very negatively, as it was often perceived as being self-righteous or hypocritical. The least negatively evaluated dilemmas were relational omissions.

As for relational context, cheating and broken promise dilemmas typically involved romantic partners like boyfriends rather than one’s mother, for example, while mother-related dilemmas more frequently fell under relational omission. Essentially, “people tend to disappoint their mothers but be disappointed by their boyfriends,” the authors wrote. Less close relationships, by contrast, tend to be governed by “norms of politeness and procedural fairness.” Hence, Yudkin et al. prefer to think of morality “less as a set of abstract principles and more as a ‘relational toolkit,’ guiding and constraining behavior according to the demands of the social situation.”

DOI: PsyArXiv, 2024. 10.31234/osf.io/5pcew (About DOIs).

Fractal scaling of trees in art

De grijze boom (Gray tree) Piet Mondrian, 1911.

De grijze boom (Gray tree) by Piet Mondrian, 1911. Credit: Public domain

Leonardo da Vinci famously invented a so-called “rule of trees” as a guide to realistically depicting trees in artistic representations according to their geometric proportions. In essence, if you took all the branches of a given tree, folded them up and compressed them into something resembling a trunk, that trunk would have the same thickness from top to bottom. That rule in turn implies a fractal branching pattern, with a scaling exponent of about 2 describing the proportions between the diameters of nearby boughs and the number of boughs with a given diameter.

According to the authors of a preprint posted to the physics arXiv in February, however, recent biological research suggests a higher scaling exponent of 3 known as Murray’s Law, for the rule of trees. Their analysis of 16th century Islamic architecture, Japanese paintings from the Edo period, and 20th century European art showed fractal scaling between 1.5 and 2.5. However, when they analyzed an abstract tree painting by Piet Mondrian, they found it exhibited fractal scaling of 3, before mathematicians had formulated Murray’s Law, even though Mondrian’s tree did not feature explicit branching.

The findings intrigued physicist Richard Taylor of the University of Oregon, whose work over the last 20 years includes analyzing fractal patterns in the paintings of Jackson Pollock. “In particular, I thought the extension to Mondrian’s ‘trees’ was impressive,” he told Ars earlier this year. “I like that it establishes a connection between abstract and representational forms. It makes me wonder what would happen if the same idea were to be applied to Pollock’s poured branchings.”

Taylor himself published a 2022 paper about climate change and how nature’s stress-reducing fractals might disappear in the future. “If we are pessimistic for a moment, and assume that climate change will inevitably impact nature’s fractals, then our only future source of fractal aesthetics will be through art, design and architecture,” he said. “This brings a very practical element to studies like [this].”

DOI: arXiv, 2024. 10.48550/arXiv.2402.13520 (About DOIs).

IDing George Washington’s descendants

Portrait of George Washington

A DNA study identified descendants of George Washington from unmarked remains. Credit: Public domain

DNA profiling is an incredibly useful tool in forensics, but the most common method—short tandem repeat (STR) analysis—typically doesn’t work when remains are especially degraded, especially if said remains have been preserved with embalming methods using formaldehyde. This includes the remains of US service members who died in such past conflicts as World War II, Korea, Vietnam, and the Cold War. That’s why scientists at the Armed Forces Medical Examiner System’s identification lab at the Dover Air Force Base have developed new DNA sequencing technologies.

They used those methods to identify the previously unmarked remains of descendants of George Washington, according to a March paper published in the journal iScience. The team tested three sets of remains and compared the results with those of a known living descendant, using methods for assessing paternal and maternal relationships, as well as a new method for next-generation sequencing data involving some 95,000 single-nucleotide polymorphisms (SNPs) in order to better predict more distant ancestry. The combined data confirmed that the remains belonged to Washington’s descendants and the new method should help do the same for the remains of as-yet-unidentified service members.

In related news, in July, forensic scientists successfully used descendant DNA to identify a victim of the 1921 Tulsa massacre in Oklahoma City, buried in a mass grave containing more than a hundred victims. C.L. Daniel was a World War I veteran, still in his 20s when he was killed. More than 120 such graves have been found since 2020, with DNA collected from around 30 sets of remains, but this is the first time those remains have been directly linked to the massacre. There are at least 17 other victims in the grave where Daniel’s remains were found.

DOI: iScience, 2024. 10.1016/j.isci.2024.109353 (About DOIs).

Spidey-inspired web-slinging tech

stream of liquid silk quickly turns to a strong fiber that sticks to and lifts objects

stream of liquid silk quickly turns to a strong fiber that sticks to and lifts objects. Credit: Marco Lo Presti et al., 2024

Over the years, researchers in Tufts University’s Silklab have come up with all kinds of ingenious bio-inspired uses for the sticky fibers found in silk moth cocoons: adhesive glues, printable sensors, edible coatings, and light-collecting materials for solar cells, to name a few. Their latest innovation is a web-slinging technology inspired by Spider-Man’s ability to shoot webbing from his wrists, described in an October paper published in the journal Advanced Functional Materials.

Coauthor Marco Lo Presti was cleaning glassware with acetone in the lab one day when he noticed something that looked a lot like webbing forming on the bottom of a glass. He realized this could be the key to better replicating spider threads for the purpose of shooting the fibers from a device like Spider-Man—something actual spiders don’t do. (They spin the silk, find a surface, and draw out lines of silk to build webs.)

The team boiled silk moth cocoons in a solution to break them down into proteins called fibroin. The fibroin was then extruded through bore needles into a stream. Spiking the fibroin solution with just the right additives will cause it to solidify into fiber once it comes into contact with air. For the web-slinging technology, they added dopamine to the fibroin solution and then shot it through a needle in which the solution was surrounded by a layer of acetone, which triggered solidification.

The acetone quickly evaporated, leaving just the webbing attached to whatever object it happened it hit. The team tested the resulting fibers and found they could lift a steel bolt, a tube floating on water, a partially buried scalpel and a wooden block—all from as far away as 12 centimeters. Sure, natural spider silk is still about 1000 times stronger than these fibers, but it’s still a significant step forward that paves the way for future novel technological applications.

DOI: Advanced Functional Materials, 2024. 10.1002/adfm.202414219

Solving a mystery of a 12th century supernova

Pa 30 is the supernova remnant of SN 1181.

Pa 30 is the supernova remnant of SN 1181. Credit: unWISE (D. Lang)/CC BY-SA 4.0

In 1181, astronomers in China and Japan recorded the appearance of a “guest star” that shone as bright as Saturn and was visible in the sky for six months. We now know it was a supernova (SN1181), one of only five such known events occurring in our Milky Way. Astronomers got a closer look at the remnant of that supernova and have determined the nature of strange filaments resembling dandelion petals that emanate from a “zombie star” at its center, according to an October paper published in The Astrophysical Journal Letters.

The Chinese and Japanese astronomers only recorded an approximate location for the unusual sighting, and for centuries no one managed to make a confirmed identification of a likely remnant from that supernova. Then, in 2021, astronomers measured the speed of expansion of a nebula known as Pa 30, which enabled them to determine its age: around 1,000 years, roughly coinciding with the recorded appearance of SN1181. PA 30 is an unusual remnant because of its zombie star—most likely itself a remnant of the original white dwarf that produced the supernova.

This latest study relied on data collected by Caltech’s Keck Cosmic Web Imager, a spectrograph at the Keck Observatory in Hawaii. One of the unique features of this instrument is that it can measure the motion of matter in a supernova and use that data to create something akin to a 3D movie of the explosion. The authors were able to create such a 3D map of P 30 and calculated that the zombie star’s filaments have ballistic motion, moving at approximately 1,000 kilometers per second.

Nor has that velocity changed since the explosion, enabling them to date that event almost exactly to 1181. And the findings raised fresh questions—namely, the ejected filament material is asymmetrical—which is unusual for a supernova remnant. The authors suggest that asymmetry may originate with the initial explosion.

There’s also a weird inner gap around the zombie star. Both will be the focus of further research.

DOI: Astrophysical Journal Letters, 2024. 10.3847/2041-8213/ad713b (About DOIs).

Reviving a “lost” 16th century score

manuscript page of Aberdeen Breviary : Volume 1 or 'Pars Hiemalis'

Fragment of music from The Aberdeen Breviary: Volume 1 Credit: National Library of Scotland /CC BY 4.0

Never underestimate the importance of marginalia in old manuscripts. Scholars from the University of Edinburgh and KU Leuven in Belgium can attest to that, having discovered a fragment of “lost” music from 16th-century pre-Reformation Scotland in a collection of worship texts. The team was even able to reconstruct the fragment and record it to get a sense of what music sounded like from that period in northeast Scotland, as detailed in a December paper published in the journal Music and Letters.

King James IV of Scotland commissioned the printing of several copies of The Aberdeen Breviary—a collection of prayers, hymns, readings, and psalms for daily worship—so that his subjects wouldn’t have to import such texts from England or Europe. One 1510 copy, known as the “Glamis copy,” is currently housed in the National Library of Scotland in Edinburgh. It was while examining handwritten annotations in this copy that the authors discovered the musical fragment on a page bound into the book—so it hadn’t been slipped between the pages at a later date.

The team figured out the piece was polyphonic, and then realized it was the tenor part from a harmonization for three or four voices of the hymn “Cultor Dei,” typically sung at night during Lent. (You can listen to a recording of the reconstructed composition here.) The authors also traced some of the history of this copy of The Aberdeen Breviary, including its use at one point by a rural chaplain at Aberdeen Cathedral, before a Scottish Catholic acquired it as a family heirloom.

“Identifying a piece of music is a real ‘Eureka’ moment for musicologists,” said coauthor David Coney of Edinburgh College of Art. “Better still, the fact that our tenor part is a harmony to a well-known melody means we can reconstruct the other missing parts. As a result, from just one line of music scrawled on a blank page, we can hear a hymn that had lain silent for nearly five centuries, a small but precious artifact of Scotland’s musical and religious traditions.”

DOI: Music and Letters, 2024. 10.1093/ml/gcae076 (About DOIs).

Photo of Jennifer Ouellette

Jennifer is a senior reporter at Ars Technica with a particular focus on where science meets culture, covering everything from physics and related interdisciplinary topics to her favorite films and TV series. Jennifer lives in Baltimore with her spouse, physicist Sean M. Carroll, and their two cats, Ariel and Caliban.

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the-physics-of-ugly-christmas-sweaters

The physics of ugly Christmas sweaters

In 2018, a team of French physicists developed a rudimentary mathematical model to describe the deformation of a common type of knit. Their work was inspired when co-author Frédéric Lechenault watched his pregnant wife knitting baby booties and blankets, and he noted how the items would return to their original shape even after being stretched. With a few colleagues, he was able to boil the mechanics down to a few simple equations, adaptable to different stitch patterns. It all comes down to three factors: the “bendiness” of the yarn, the length of the yarn, and how many crossing points are in each stitch.

A simpler stitch

A simplified model of how yarns interact

A simplified model of how yarns interact Credit: J. Crassous/University of Rennes

One of the co-authors of that 2018 paper, Samuel Poincloux of Aoyama Gakuin University in Japan, also co-authored this latest study with two other colleagues, Jérôme Crassous (University of Rennes in France) and Audrey Steinberger (University of Lyon). This time around, Poincloux was interested in the knotty problem of predicting the rest shape of a knitted fabric, given the yarn’s length by stitch—an open question dating back at least to a 1959 paper.

It’s the complex geometry of all the friction-producing contact zones between the slender elastic fibers that makes such a system too difficult to model precisely, because the contact zones can rotate or change shape as the fabric moves. Poincloux and his cohorts came up with their own more simplified model.

The team performed experiments with a Jersey stitch knit (aka a stockinette), a widely used and simple knit consisting of a single yarn (in this case, a nylon thread) forming interlocked loops. They also ran numerical simulations modeled on discrete elastic rods coupled with dry contacts with a specific friction coefficient to form meshes.

The results: Even when there were no external stresses applied to the fabric, the friction between the threads served as a stabilizing factor. And there was no single form of equilibrium for a knitted sweater’s resting shape; rather, there were multiple metastable states that were dependent on the fabric’s history—the different ways it had been folded, stretched, or rumpled. In short, “Knitted fabrics do not have a unique shape when no forces are applied, contrary to the relatively common belief in textile literature,” said Crassous.

DOI: Physical Review Letters, 2024. 10.1103/PhysRevLett.133.248201 (About DOIs).

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