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2025 Oct 29

- Carlo Rovelli’s Radical Perspective on Reality

Q&A | VIEW ON WEBSITE

Carlo Rovelli’s Radical Perspective on Reality

By Zack Savitsky

October 29, 2025

The theoretical physicist and best-selling author finds inspiration in politics and philosophy for rethinking space and time.

There is no objective reality, according to Rovelli — only perspectives. “This is very radical, because you can no longer say, ‘This is a list of things in the world, and this is how they are.’”

Jan Jackle for Quanta Magazine

Introduction

Sitting outside a Catholic church on the French Riviera, Carlo Rovelli jutted his head forward and backward, imitating a pigeon trotting by. Pigeons bob their heads, he told me, not only to stabilize their vision but also to gauge distances to objects — compensating for their limited binocular vision. “It’s all perspectival,” he said.

A theoretical physicist affiliated with Aix-Marseille University, Rovelli studies how we perceive reality from our limited vantage point. His research is wide-ranging, running the gamut from quantum information to black holes, and often delves into the history and philosophy of science. In the late 1980s, he helped develop a theory called loop quantum gravity that aims to describe the quantum underpinnings of space and time. A decade later, he proposed a new “relational” interpretation of quantum mechanics, which goes so far as to suggest that there is no objective reality whatsoever, only perspectives on reality — be they a physicist’s or a pigeon’s.

More recently, he’s gained recognition as a best-selling author of popular science books, including Seven Brief Lessons on Physics, which has sold more than 2 million copies worldwide — placing him in a limelight he’s still adjusting to. “I’m very bad at being somewhat famous,” he said. “I’m always getting myself in trouble.” (During my visit, he was fending off criticism from the president of the Italian Physical Society, who accused him of defaming Enrico Fermi as a “bloodthirsty fascist/Nazi.”)

Rovelli’s own perspective on physics is heavily influenced by his rebellious, countercultural youth. A student protestor in an attempted political revolution in Bologna in 1977, Rovelli worked at a subversive left-wing radio station, drafted an illegal manifesto, and was later detained for refusing compulsory military service. Disillusioned by societal norms, “I had a sense that we were confused about how to think about reality around us,” he said. At 69, he remains politically engaged (and often enraged). “Part of me is still an old hippie.”

After the political unrest in Bologna petered out, Rovelli transferred his deep misgivings to the very fabric of reality. He used the same proclivity for challenging traditional ways of thinking to confront long-standing problems in the foundations of physics — not by rejecting established theories, but by embracing a new perspective on them. His approach centers around a radical openness to abandoning intuitions about how the world works.

Video: Carlo Rovelli discusses his research on time and his view that it should not appear in the quantum theory of gravity.

Emily Buder/Quanta Magazine;

Jan Jackle for Quanta Magazine

To confront his own biases, whether about physics or society, Rovelli turns to philosophy. He often publishes on metaphysical topics and advocates for more dialogue between the disciplines. His newest book, published this month in Italian, is a deep dive into the intersection of philosophy and physics, a mash-up he sees as the key to understanding what our existing theories are really telling us.

Quanta visited Rovelli at his home overlooking the cliffs of Cassis. Over a 12-hour conversation, held while we lounged on his patio, strolled around town, and cruised on his 100-year-old sailboat, we discussed religion, war, consciousness, media, love, pigeons and, of course, physics. The interview has been condensed and edited for clarity.

What is your central question, and how did it lead you to study quantum gravity?

My central question has always been: How does the world work? We have two main theories that work incredibly well for different domains: general relativity and quantum mechanics. When I learned about these theories in school, I was impressed by how radical they were. They both challenge very foundational conceptions that we have about the world around us — of space as an empty stage where objects exist, and of time as a steady linear flow. They resonated with this idea I had that if you really want to understand reality, you have to be ready to be radical.

All attempts to disprove quantum mechanics and general relativity have failed. But nevertheless, in this picture, there’s clearly a crack. There are phenomena out there — like objects falling into a black hole — that fall outside the domain of both theories. When you try to put the two theories together, they appear to result in all sorts of contradictions and paradoxes. To me, the interface of these two theories — the problem of quantum gravity — was really this deep, profound gap in our fundamental physical picture of the world.

Jan Jackle for Quanta Magazine

Tell me about the approach you’ve taken to fill that gap: loop quantum gravity.

Loop quantum gravity is a very conservative approach with a very radical consequence. It’s an attempt to say: Let’s take seriously what we’ve learned from general relativity and quantum mechanics all the way through and see where they lead us. There are no extra fields, extra particles, modifications of the Einstein equations, or other hypotheses about nature. It’s just an effort to make coherent what we know so far.

Basically, loop quantum gravity implies that space is not infinitely divisible — it’s made of elementary chunks, which are linked together into loops. The theory is a very simple set of equations, but there’s no time variables and no space variables. Those concepts emerge from the way these quanta of gravity interact and transform. What we call space is the quantity of these loops, and what we call time is how the loops evolve continuously.

How do we account for our common experience of time if it’s not fundamental?

Our experience of time flowing forward is a product of the second law of thermodynamics — the tendency for physical systems to increase in disorder, or what we call entropy. But this only appears fundamental from our perspective. We happen to be beings that are connected to certain macroscopic variables with respect to which entropy is globally moving in one direction.

My intuition is that the overall flow of time really could be like the rotation of the sky every day. It’s a majestic, immense phenomenon, but it’s actually an illusion. This is a totally perspectival understanding of the second law of thermodynamics. It’s real in the same sense that the rotating sky is real, but it’s real only with respect to us.

Jan Jackle for Quanta Magazine

One critique of loop quantum gravity is that it contradicts certain predictions of Einstein, namely that the speed of light is constant for all wavelengths. What do you make of this critique?

The theory has evolved a lot over the last 20 years, and the current version is not incompatible with Einstein’s predictions — the speed of light is indeed constant at all physical wavelengths. That said, there are some things about loop quantum gravity that still need resolving. We’re not sure how the different versions of the theory are equivalent to one another. We have a problem in which particle scattering seems to generate infinite amounts of low-energy radiation. And solving the equations is still a very complicated task that we’re working to simplify.

Our community has wasted a lot of time searching after speculative ideas. What we need instead is to digest the knowledge we already have.

The main shortcoming is the lack of experiments supporting it. However, there’s hope on the horizon. There are some proposals to use loop quantum gravity to make sense of signatures in the cosmic microwave background radiation that’s left over from the Big Bang. And there’s another new idea I’m very excited about: If loop quantum gravity is right, there should exist tiny black holes weighing around 10 micrograms that are long-living and that interact only gravitationally. We’re thinking about ways to detect a background “wind” of these particles. And perhaps these tiny black holes are actually what we call dark matter, a mysterious widespread astronomical phenomenon that we have not yet understood.

Detection will be difficult, but it’s not out of the game. I’m hopeful there will be some experiment that will make the larger community see loop quantum gravity as the natural explanation. It’s far from clear that we cannot account for all of these phenomena using the existing theories that have worked so well for 100 years.

If we are to hold on to our existing theories, what picture do they paint about the nature of reality when taken together?

Rethinking space and time pushed me to view reality in a completely different way — not as a universe made of objects with defined properties, but as a network of interactions. This is the “relational” interpretation of quantum mechanics. In some sense, it’s a continuation of the trend in modern physics that we have seen with general relativity and quantum mechanics — a strong push toward perspectivalism.

We’re used to velocity being relative: The velocity of this table is different with respect to me, with respect to [that pigeon flying] outside, or with respect to the sun. Einstein showed us that time and length are also relative to different observers. Relational quantum mechanics takes this idea a step further. It argues that all properties of an object — its color, location, size, etc. — are in principle only definable in relation to another system. We need to give up the idea that there are material things which we’re describing from the outside. The best way of conceptualizing reality in light of modern science is in terms of the relative information that pieces of nature have about one another.

We can only say how the world looks from our limited, biased perspective. This is very radical, because you can no longer say, “This is a list of things in the world, and this is how they are.” We have to live with this lack of total description over reality.

Jan Jackle for Quanta Magazine

There’s something unsettling about this argument. It seems to undermine the ultimate goal of physics to describe the “true” nature of reality, does it not?

It very much does, but if you look at the history of science, the ultimate goal has been changing constantly. It went from describing the rotation of heavenly bodies to tracking the forces that guide particles to following the evolution of fields in space-time. I think that the problem of science is to figure out the right conceptual scheme to best understand nature as we see it. The relational perspective is rooted in a deep awareness that our knowledge about the world is fundamentally limited and that everything we see is partial. We have a much stronger and more honest way of approaching reality without being attached to this misleading idea of there being an ultimate truth. We must not confuse the knowledge we have with the reality of the world.

If this leaves you with a sense of emptiness about reality, that’s fair. But it’s precisely by knowing that our knowledge is limited that we are able to learn. Between absolute certainty and ignorance there’s all this interesting space in which we live.

You’ve written about how your change in worldview has been guided by philosophers. How do you view the relationship between philosophy and physics?

The disciplines desperately need one another. A philosopher who doesn’t think about science is not willing to engage with the knowledge we have, and that’s just silly. And a scientist who refuses to look at philosophy is trapped in ways of thinking from which there may be an escape. Historically, the relationship between physicists and philosophers has been very strong. All scientific revolutions have been strongly influenced by philosophical ideas. Copernicus, Galileo and Newton were all philosophers themselves. Einstein very explicitly credited his insights to philosophers like Immanuel Kant, Ernst Mach and others. And Erwin Schrödinger was likely influenced by his reading of the Upanishads, the sacred Hindu texts, when he came up with wave mechanics.

Jan Jackle for Quanta Magazine

But lately, the relationship between physicists and philosophers has been at an all-time low. Stephen Hawking famously pronounced that “philosophy is dead,” and Richard Feynman said things like “Philosophers are as good for science as ornithologists are good for birds.” What they don’t realize is that, first, they are doing philosophy by commenting on what it means to do science; and second, their whole view of science is already under the influence of American pragmatism thinking and philosophers like Karl Popper and Thomas Kuhn. What the physics community took away from these philosophers was that science is about picking new ideas out of thin air, developing a theory, and testing whether it’s right or wrong. This gives the false impression that scientific progress comes only in paradigm-shifting insights that overturn previous thinking, and that all new hypotheses are equally probable until falsified. But science is so much more than that. It’s a continuous process of building on past knowledge to refine our perspective.

In my opinion, this closed-mindedness is precisely the problem with modern theoretical physics. We’re undergoing a colossal jump in knowledge that’s forcing us to rethink notions of reality, information, time and space. Our community has wasted a lot of time searching after speculative ideas. What we need instead is to digest the knowledge we already have. And to do that, we need philosophy. Philosophers help us not to find the right answers to given questions, but to find the right questions to better conceptualize reality.

Jan Jackle for Quanta Magazine

In your book Helgoland, you talk about how the Buddhist philosopher Nagarjuna shaped your work. In what way did his texts open your mind?

The core idea of relational quantum mechanics is that when we talk about an object — be it an atom, a person or a galaxy — we are never just referring to the system alone. Rather, we are always referring to the interactions between this system and something else. We can only describe — and in fact understand — a thing as it relates to ourselves, or to our measuring devices.

Related:

1. The Unraveling of Space-Time

2. How to Understand the Universe When You’re Stuck Inside of It

3. What Is Entropy? A Measure of Just How Little We Really Know.

Nagarjuna expresses a very similar idea: that no entity has a proper independent existence — things only exist depending on one another. By renouncing “primary” entities or any “ultimate absolute reality,” we can better make sense of the world in terms of how things manifest themselves to other things.

Relational quantum mechanics uses similar ideas to make sense of all quantum paradoxes in a precise mathematical way. The main idea is to give up questions about how things really are, in absolute terms. It’s just like how Galileo taught us that asking “Is this object really moving?” is meaningless, and Einstein taught us that asking “Are these two events really simultaneous?” is meaningless. The confusion about quantum mechanics, I believe, is generated by asking questions that have no meaning. The answer to the riddle is that there is no riddle.

2025 Oct 27

- Shark Data Suggests Animals Scale Like Geometric Objects

ZOOLOGY | VIEW ON WEBSITE

Shark Data Suggests Animals Scale Like Geometric Objects

By Joanna Thompson

October 27, 2025

Despite their wide variety of sizes, niches and shapes, sharks scale geometrically, pointing to possible fundamental constraints on evolution.

Samantha Mash for Quanta Magazine

Introduction

It’s a universal fact that as any 3D object, from a Platonic sphere to a cell to an elephant, grows outward in all directions, its total surface area will increase more slowly than the space it occupies (its volume). If the object’s geometry and shape remain the same as it gets bigger, then its surface area will increase roughly as fast as its volume to the two-thirds power. For centuries, biologists have wondered if life forms, too, follow this two-thirds scaling law, even though they come in a stunning variety of shapes and sizes. If so, it would suggest that there are underlying constraints fundamental to evolution that might influence how life interacts with the world around it.

Recently, researchers used CT scans and digital tools to calculate the surface areas and volumes of an ancient and diverse animal lineage: sharks. The team’s analysis, published in Royal Society Open Science, included more than 50 shark species and provides some of the best empirical evidence to date for some kind of firm scaling rule in zoology. As with a sphere, the surface area and body mass of sharks do indeed follow a two-thirds scaling law, the team found. If this holds true in other animal groups, it probably reflects underlying rules of heat exchange, metabolism or development that constrain evolution.

If you’re looking for an animal group in which to study biological scaling, it’s hard to do better than sharks, according to Joel Gayford, a shark biologist at James Cook University in Australia who led the new study. They share an overall form, but come in many sizes, occupy a plethora of niches, and have huge variations in body shape. In his research into sharks’ morphological evolution, Gayford noticed what appeared to be scaling relationships between their body parts, such as the sizes of their fins. It made him wonder whether there might be more fundamental rules constraining the forms that sharks can take.

However, he could find little high-quality research into scaling in large animals. Research in single cells has uncovered many deviations from expected rules; rare studies in smaller animals such as insects and snakes have found some evidence for two-thirds scaling. But few studies included larger animals, and most of those were conducted decades ago. Plus, Gayford found that existing animal scaling data was somewhat messy. Due to technological limitations in the 19th and 20th centuries, attempts to accurately measure animals’ surface area and volume were “error-prone and also kind of ethically questionable,” he said.

Joel Gayford (pictured with a goblin shark) created 3D models of more than 50 shark species of various sizes and shapes to find out if they scale geometrically.

Dr. Yi-Kai Tea

He wasn’t the only one who thought so. “One of the big limitations — especially if you read these early biology studies — is, like, how do you measure the surface area of a cow?” said Brian Enquist, an evolutionary biologist at the University of Arizona who was not involved in the study.

Until recently, options were limited. Researchers could run a measuring wheel across an animal’s hide and mark out units in chalk, or skin the creature and measure its surface area by hand. To calculate its volume, they could drop the animal into a water-filled tub and see how much liquid it displaced; some went one step further and poured water directly into freshly liberated pelts.

Gayford’s team had significantly more advanced technology available. They measured the surface area and volume of 54 different shark species, ranging from a nine-inch pygmy shark, one of the world’s smallest, to a whale shark, the largest living fish. But rather than skinning them, they took CT scans of high-quality museum specimens to create detailed virtual reconstructions. For those species too large to fit in a CT scanner, they used photogrammetry software, which stitches together many photos of an object’s surface to create a 3D model. (In one case, the object in question was a 37-foot-long whale shark that lives at the Georgia Aquarium.) They then loaded the models into 3D processing software called Blender, which was originally developed for rendering objects in video games. To calculate a shark’s surface area, Gayford just had to click a button.

Mark Belan/Quanta Magazine; Source: Joel Harrison Gayford

In addition to reflecting a huge range of animal sizes, the dataset also represented sharks that fill a variety of ecological niches, from reef dwellers to bottom feeders to open-ocean predators. They came in “a ton of different unique morphologies,” Gayford said, including several oblong-faced hammerhead species; the common thresher, whose tail fin is nearly as long as the rest of its body; and the flat and frilly wobbegong, along with your more standard shark-shaped sharks. And while most sharks are cold-blooded, or ectothermic, a few species (including great whites) can generate their own heat. Gayford’s team included one of these regionally endothermic sharks — the thresher — in the dataset.

Despite this diversity of size, shape, lifestyle and metabolism, the sharks fit the two-thirds scaling rule almost perfectly. “They showed there’s not a lot of variability in it, so that’s really cool,” Enquist said.

The analysis suggests that this two-thirds scaling rule could be universal for animals. To be certain, more research is needed in other animal groups — including terrestrial animals, which can have complex external geometries such as feathers and hair, and warm-blooded, or endothermic, animals such as mammals and birds. To that end, Gayford’s team is collecting more data; he hopes other researchers will further test biological scaling in the animals they study.

Sharks are an incredibly old and diverse group of species, encompassing many sizes, shapes, habitats and lifestyles, including (from top to bottom) the whale shark, scalloped hammerhead, tassled wobbegong and zebra shark.

From top to bottom: Guillen Photo; Kris Mikael Krister; Simon Pierce; Leonard Low

Sharks are an incredibly old and diverse group of species, encompassing many sizes, shapes, habitats and lifestyles, including (clockwise from top left) the whale shark, scalloped hammerhead, zebra shark and tassled wobbegong.

Clockwise from top left: Guillen Photo; Kris Mikael Krister; Simon Pierce; Leonard Low

However, the surface area measurements could still be considered incomplete because they only include the sharks’ external features. Even though structures such as gills are tucked away inside animals’ bodies, their surfaces are actually external from a topological perspective, said Karl Niklas, an emeritus professor of biomechanics at Cornell University. If the researchers had analyzed the sharks’ gills as well, Niklas speculated that they would have found a scaling ratio closer to three-fourths. Still, the consistency of the numbers across many different shark species suggests the rule is not incidental. “We’ve got to think of this as some kind of reflection of adaptive evolution,” Niklas said.

The scientists aren’t certain what fundamental mechanisms could be limiting sharks and other animals’ sizes and shapes, but they have hypotheses. One involves tissue allocation during early growth. To visualize this, imagine a developing animal as a ball of clay. “There’s only so many ways you can stretch out the clay to make different shapes without incurring energetic costs,” Gayford said. In that case, the scaling relationship is significant to the embryo, and it goes on to limit the potential forms the adult organism can take.

Related:

1. The ‘Elegant’ Math Model That Could Help Rescue Coral Reefs

2. Ancient Turing Pattern Builds Feathers, Hair — and Now, Shark Skin

3. Random Search Wired Into Animals May Help Them Hunt

Alternatively, the ratio could reflect a fundamental constraint on heat exchange. In animals, which can absorb external heat and generate it through metabolism or movement, a scaling principle in which surface area grows more slowly than volume would create an insulating effect as you move from small species to larger ones. “Surface area to volume is really important for heat exchange,” said Van Savage, a computational biologist at the University of California, Los Angeles who was not involved in the study. This may explain why Arctic species tend to be large and bulky, while those living in tropical climates can be svelte: A bigger body is harder to cool down than a smaller one. This applies even to ectothermic animals, which may need to hold on to heat as they move between warm and cool environments — for example, when whale sharks dive into deeper, colder water.

The study offers insight into the mathematical limits of evolution, and could help identify fundamental mechanisms that limit life’s topology. But calculating how organisms scale has practical value as well. It can help veterinarians figure out how much anesthesia to administer to a cat versus a Great Dane, for example, or help doctors determine drug dosages for infants versus adults.

For Gayford, it highlights the need for continued empirical studies of biological scaling. “It’s really important that people actually test these laws,” he said. “Because often they’re just kind of assumed to be correct.”

2025 Oct 24

- First Shape Found That Can’t Pass Through Itself

GEOMETRY | VIEW ON WEBSITE

First Shape Found That Can’t Pass Through Itself

By Erica Klarreich

October 24, 2025

After more than three centuries, a geometry problem that originated with a royal bet has been solved.

The Platonic solids that have six, eight, 12 and 20 sides can pass through themselves.

David Renshaw

Introduction

Imagine you’re holding two equal-size dice. Is it possible to bore a tunnel through one die that’s big enough for the other to slide through?

Perhaps your instinct is to say “Surely not!” If so, you’re not alone. In the late 1600s, an unidentified person placed a bet to that effect with Prince Rupert of the Rhine. Rupert — a nephew of Charles I of England who commanded the Royalist forces in the English Civil War — spent his sunset years studying metallurgy and glassmaking in his laboratory at Windsor Castle.

Rupert won the bet. The mathematician John Wallis, recounting the story in 1693, didn’t say whether Rupert wrote a proof or bored a hole through an actual cube. But Wallis himself proved mathematically that, if you drill a straight tunnel in the direction of one of the cube’s inner diagonals, it can be made wide enough to allow another cube through. It’s a tight squeeze: If you make the second cube just 4% larger, it will no longer fit.

It’s natural to wonder which other shapes have this property. “I think of this problem as being quite canonical,” said Tom Murphy, a software engineer at Google who has explored the question extensively in his free time. It “would have gotten rediscovered and rediscovered — aliens would have come to this one.”

Tip a cube on its corner, and another can pass through.

Mark Belan/Quanta Magazine

The full menagerie of shapes is too diverse to get a handle on, so mathematicians tend to focus on convex polyhedra: shapes, like the cube, that have flat sides and no protrusions or indentations. When such a shape is much wider in some directions than others, it’s usually easy to find a straight tunnel that will allow another copy of the shape to pass through. But many famous convex polyhedra — for instance the dodecahedron, or the truncated icosahedron, the shape that forms a soccer ball — are highly symmetric and difficult to analyze. Among these, “for hundreds of years we only knew of the cube,” said Jakob Steininger, a mathematician at Statistics Austria, Austria’s federal statistics organization.

Then, in 1968, Christoph Scriba proved that the tetrahedron and octahedron also have the “Rupert property,” as mathematicians now call it. And in a burst of activity over the past decade, professional mathematicians and hobbyists have found Rupert tunnels through many of the most widely studied convex polyhedra, including the dodecahedron, icosahedron and soccer ball.

The Rupert property appeared to be so widespread that mathematicians conjectured a general rule: Every convex polyhedron will have the Rupert property. No one could find one that didn’t — until now.

The Noperthedron. To date, it’s the only shape proved to not have Rupert’s property.

In a paper posted online in August, Steininger and Sergey Yurkevich — a researcher at A&R Tech, an Austrian transportation systems company — describe a shape with 90 vertices and 152 faces that they’ve named the Noperthedron (after “Nopert,” a coinage by Murphy that combines “Rupert” and “nope”). Steininger and Yurkevich proved that no matter how you bore a straight tunnel through a Noperthedron, a second Noperthedron cannot fit through.

The proof required a mix of theoretical advances and massive computer calculations, and relies on a delicate property of the Noperthedron’s vertices. “It’s a miracle that it works,” Steininger said.

Passing Through the Shadows

To see how one cube can pass through another, imagine holding a cube over a table and examining its shadow (assuming it’s illuminated from above). If you hold the cube in the standard position, the shadow is a square. But if you point one of the corners directly upward, the shadow is a regular hexagon.

In 1693, Wallis showed that the square shadow fits inside the hexagon, leaving a thin margin. That means that if you point a cube’s corner upward, you can bore a vertical tunnel that’s big enough for a second cube to pass through. About a century later, Pieter Nieuwland showed that a different orientation casts an even better shadow — one that can accommodate a cube more than 6% larger than the cube with the tunnel.

Mark Belan/Quanta Magazine

Every subsequent analysis of more complicated shapes has relied on this process of turning the shape in different directions and looking for one shadow that fits inside another. With the aid of computers, mathematicians have found Rupert passages through a wide variety of shapes. Some are incredibly tight fits — for instance, the passage in a “triakis tetrahedron” has a margin that’s only about 0.000002 times the length of the shape’s radius. “The world of mixing computation and discrete geometry has flowered to make these kinds of calculations possible,” said Joseph O’Rourke, an emeritus professor at Smith College.

Researchers who have written algorithms to find Rupert passages have noticed a curious dichotomy: For any given convex polyhedron, the algorithm seems to either find a passage almost immediately, or not find one at all. In the past five years, mathematicians have accumulated a small collection of holdout shapes for which no passage has been found.

“I’ve had my desktop churn for two weeks on trying the rhombicosidodecahedron,” said Benjamin Grimmer, an applied mathematician at Johns Hopkins University, referring to a solid made of 62 regular triangles, squares and pentagons. “That one just seems to resist any attempt.”

The rhombicosidodecahedron is a leading Nopert candidate.

But such resistance doesn’t prove that a shape is a Nopert. There are infinitely many ways to orient a shape, and a computer can only check finitely many. Researchers don’t know whether the holdouts are true Noperts or just shapes whose Rupert passages are hard to find.

What they do know is that candidate Noperts are incredibly rare. Starting last year, Murphy began to construct hundreds of millions of shapes. These include random polyhedra, polyhedra whose vertices lie on a sphere, polyhedra with special symmetries, and polyhedra in which he moved one vertex to intentionally mess up a previous Rupert passage. His algorithm easily found Rupert tunnels for nearly every one.

The contrast between these quick results and the stubbornness of the Nopert holdouts made some mathematicians suspect that true Noperts do exist. But until August, all they had were suspicions.

No Passage

Steininger, now 30, and Yurkevich, 29, have been friends since they participated together as teenagers in mathematics Olympiad competitions. Even though both eventually left academia (after a doctorate for Yurkevich and a master’s for Steininger), they have continued to explore unsolved problems together.

“We just had pizza three hours ago, and we talked about math almost the whole time,” Steininger told Quanta. “That’s what we do.”

Five years ago, the pair happened upon a YouTube video of one cube passing through another, and they were instantly smitten. They developed an algorithm to search for Rupert tunnels and soon became convinced that some shapes were Noperts. In a 2021 paper, they conjectured that the rhombicosidodecahedron is not Rupert. Their work, which preceded Murphy’s and Grimmer’s recent explorations, was, “I think, the first to conjecture that there might be solids that don’t have this property,” Steininger said.

If you want to prove that a shape is a Nopert, you must rule out Rupert tunnels for every possible orientation of the two shapes. Each orientation can be written down as a collection of rotation angles. This collection of angles can then be represented as a point in a higher-dimensional “parameter space.”

Sergey Yurkevich (left) and Jakob Steininger, friends since their teenage years, enjoy working on math problems together, even though neither has remained in academia.

Florentina Stadlbauer; Courtesy of Jakob Steininger

Suppose you choose an orientation for your two shapes, and the computer tells you that the second shadow sticks out past the border of the first shadow. This rules out one point in the parameter space.

But you may be able to rule out much more than a single point. If the second shadow sticks out significantly, it would require a big change to move it inside the first shadow. In other words, you can rule out not just your initial orientation but also “nearby” orientations — an entire block of points in the parameter space. Steininger and Yurkevich came up with a result they called their global theorem, which quantifies precisely how large a block you can rule out in these cases. By testing many different points, you can potentially rule out block after block in the parameter space.

If these blocks cover the entire parameter space, you’ll have proved that your shape is a Nopert. But the size of each block depends on how far the second shadow sticks out beyond the first, and sometimes it doesn’t stick out very far. For instance, suppose you start with the two shapes in exactly the same position, and then you slightly rotate the second shape. Its shadow will at most stick out just a tiny bit past the first shadow, so the global theorem will only rule out a tiny box. These boxes are too small to cover the whole parameter space, leaving the possibility that some point you’ve missed might correspond to a Rupert tunnel.

I think of this problem as being quite canonical.… Aliens would have come to this one.

Tom Murphy

To deal with these small reorientations, the pair came up with a complement to their global theorem that they called the local theorem. This result deals with cases where you can find three vertices (or corner points) on the boundary of the original shadow that satisfy some special requirements. For instance, if you connect those three vertices to form a triangle, it must contain the shadow’s center point. The researchers showed that if these requirements are met, then any small reorientation of the shape will create a shadow that pushes at least one of the three vertices further outward. So the new shadow can’t lie inside the original shadow, meaning it doesn’t create a Rupert tunnel.

If your shape casts a shadow that lacks three appropriate vertices, the local theorem won’t apply. And all the previously identified Nopert candidates have at least one shadow with this problem. Steininger and Yurkevich sifted through a database of hundreds of the most symmetric and beautiful convex polyhedra, but they couldn’t find any shape whose shadows all worked. So they decided to generate a suitable shape themselves.

They developed an algorithm to construct shapes and test them for the three-vertices property. Eventually, the algorithm produced the Noperthedron, which is made of 150 triangles and two regular 15-sided polygons. It looks like a rotund crystal vase with a wide base and top; one fan of the work has already 3D-printed a copy to use as a pencil holder.

Prince Rupert of the Rhine, a 17th-century army officer, naval commander, colonial governor and gentleman scientist, won a bet about whether it’s possible to pass a cube through another.

Peter Lely

Steininger and Yurkevich then divided the parameter space of orientations into approximately 18 million tiny blocks, and tested the center point of each block to see if its corresponding orientation produced a Rupert passage. None of them did. Next, the researchers showed that each block satisfied either the local or global theorem, allowing them to rule out the entire block. Since these blocks fill out the entire parameter space, this meant that there is no Rupert passage through the Noperthedron.

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The “natural conjecture has been proved false,” O’Rourke said.

It remains to be seen whether mathematicians can use the new method to generate other Noperts, or if they can find a different local theorem that can handle candidates like the rhombicosidodecahedron. But now that mathematicians know that Noperts do exist, “we’re on sound footing to study other shapes,” Murphy said.

Murphy, who like Steininger and Yurkevich has been exploring the question for its own sake, independent of his day job, feels a kinship across the centuries with Prince Rupert. “I like that he chose to use his retirement to do math and science in his castle,” he said.

Meanwhile, Steininger and Yurkevich are on the lookout for new questions to tackle. “We’re just humble mathematicians — we love working on such problems,” Steininger said. “We’ll keep doing that.”

2025 Oct 22

- The Game Theory of How Algorithms Can Drive Up Prices

GAME THEORY | VIEW ON WEBSITE

The Game Theory of How Algorithms Can Drive Up Prices

By Ben Brubaker

October 22, 2025

Recent findings reveal that even simple pricing algorithms can make things more expensive.

Nash Weerasekera for Quanta Magazine

Introduction

Imagine a town with two widget merchants. Customers prefer cheaper widgets, so the merchants must compete to set the lowest price. Unhappy with their meager profits, they meet one night in a smoke-filled tavern to discuss a secret plan: If they raise prices together instead of competing, they can both make more money. But that kind of intentional price-fixing, called collusion, has long been illegal. The widget merchants decide not to risk it, and everyone else gets to enjoy cheap widgets.

For well over a century, U.S. law has followed this basic template: Ban those backroom deals, and fair prices should be maintained. These days, it’s not so simple. Across broad swaths of the economy, sellers increasingly rely on computer programs called learning algorithms, which repeatedly adjust prices in response to new data about the state of the market. These are often much simpler than the “deep learning” algorithms that power modern artificial intelligence, but they can still be prone to unexpected behavior.

So how can regulators ensure that algorithms set fair prices? Their traditional approach won’t work, as it relies on finding explicit collusion. “The algorithms definitely are not having drinks with each other,” said Aaron Roth, a computer scientist at the University of Pennsylvania.

Yet a widely cited 2019 paper showed that algorithms could learn to collude tacitly, even when they weren’t programmed to do so. A team of researchers pitted two copies of a simple learning algorithm against each other in a simulated market, then let them explore different strategies for increasing their profits. Over time, each algorithm learned through trial and error to retaliate when the other cut prices — dropping its own price by some huge, disproportionate amount. The end result was high prices, backed up by mutual threat of a price war.

Aaron Roth suspects that the pitfalls of algorithmic pricing may not have a simple solution. “The message of our paper is it’s hard to figure out what to rule out,” he said.

Courtesy of Aaron Roth

Implicit threats like this also underpin many cases of human collusion. So if you want to guarantee fair prices, why not just require sellers to use algorithms that are inherently incapable of expressing threats?

In a recent paper, Roth and four other computer scientists showed why this may not be enough. They proved that even seemingly benign algorithms that optimize for their own profit can sometimes yield bad outcomes for buyers. “You can still get high prices in ways that kind of look reasonable from the outside,” said Natalie Collina, a graduate student working with Roth who co-authored the new study.

Researchers don’t all agree on the implications of the finding — a lot hinges on how you define “reasonable.” But it reveals how subtle the questions around algorithmic pricing can get, and how hard it may be to regulate.

“Without some notion of a threat or an agreement, it’s very hard for a regulator to come in and say, ‘These prices feel wrong,’” said Mallesh Pai, an economist at Rice University. “That’s one reason why I think this paper is important.”

No Regrets

The recent paper studies algorithmic pricing through the lens of game theory, an interdisciplinary field at the border of economics and computer science that analyzes the mathematics of strategic competitions. It’s one way to explore the failures of pricing algorithms in a controlled setting.

“What we’re trying to do is create collusion in the lab,” said Joseph Harrington, a University of Pennsylvania economist who wrote an influential review paper on regulating algorithmic collusion and was not involved in the new research. “Once we do so, we want to figure out how to destroy collusion.”

Natalie Collina and her colleagues discovered that high prices can arise in unexpected ways.

Nandan Tumu

To understand the key ideas, it helps to start with the simple game of rock-paper-scissors. A learning algorithm, in this context, can be any strategy that a player uses to choose a move in each round based on data from previous rounds. Players might try out different strategies over the course of the game. But if they’re playing well, they’ll ultimately converge to a state that game theorists call equilibrium. In equilibrium, each player’s strategy is the best possible response to the other’s strategy, so neither player has an incentive to change.

In rock-paper-scissors, the ideal strategy is simple: You should play a random move each round, choosing all three possibilities equally often. Learning algorithms shine if one player takes a different approach. In that case, choosing moves based on previous rounds can help the other player win more often than if they just played randomly.

Suppose, for instance, that after many rounds you realize that your opponent, a geologist, chose rock more than 50% of the time. If you’d played paper every round, you would have won more often. Game theorists refer to this painful realization as regret.

Researchers have devised simple learning algorithms that are always guaranteed to leave you with zero regret. Slightly more sophisticated learning algorithms called “no-swap-regret” algorithms also guarantee that whatever your opponent did, you couldn’t have done better by swapping all instances of any move with any other move (say, by playing paper every time you actually played scissors). In 2000, game theorists proved that if you pit two no-swap-regret algorithms against each other in any game, they’ll end up in a specific kind of equilibrium — one that would be the optimal equilibrium if they only played a single round. That’s an attractive property, because single-round games are much simpler than multi-round ones. In particular, threats don’t work because players can’t follow through.

One way to have regret is just to be kind of dumb. Historically, that hasn’t been illegal.

Aaron Roth, University of Pennsylvania

In a 2024 paper, Jason Hartline, a computer scientist at Northwestern University, and two graduate students translated the classic results from the 2000 paper to a model of a competitive market, where players can set new prices every round. In that context, the results implied that dueling no-swap-regret algorithms would always end up with competitive prices when they reached equilibrium. Collusion was impossible.

However, no-swap-regret algorithms aren’t the only pricing game strategies in the world of online marketplaces. So what happens when a no-swap-regret algorithm faces a different benign-looking opponent?

The Price Is Wrong

According to game theorists, the best strategy to play against a no-swap-regret algorithm is simple: Start with a specific probability for each possible move, and then choose one move at random every round, no matter what your opponent does. The ideal assignment of probabilities for this “nonresponsive” approach depends on the specific game you’re playing.

In the summer of 2024, Collina and her colleague Eshwar Arunachaleswaran set out to find those optimal probabilities for a two-player pricing game. They found that the best strategy assigned strikingly high probabilities to very high prices, along with lower probabilities for a wide range of lower prices. If you’re playing against a no-swap-regret algorithm, this strange strategy will maximize your profit. “To me, it was a complete surprise,” Arunachaleswaran said.

Eshwar Arunachaleswaran and Collina obtained their result while exploring the best responses to well-behaved pricing algorithms.

Paritosh Verma

Nonresponsive strategies look superficially innocuous. They can’t convey threats, because they don’t react to their opponents’ moves at all. But they can coax learning algorithms to raise their prices, and then reap profits by occasionally undercutting their competitors.

At first, Collina and Arunachaleswaran thought that this artificial scenario wasn’t relevant to the real world. Surely the player using the no-swap-regret algorithm would switch to a different algorithm after realizing that their competitor was profiting at their expense.

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But as they studied the problem further and discussed it with Roth and two other colleagues, they realized their intuition was wrong. The two players in their scenario were already in a state of equilibrium. Their profits were nearly equal, and both were as high as possible as long as neither player switched to a different algorithm. Neither player would have an incentive to change strategy, so buyers would be stuck with high prices. What’s more, the precise probabilities weren’t that important. Many different choices led to high prices when pitted against a no-swap-regret algorithm. It’s an outcome you’d expect from collusion, but without any collusive behavior in sight.

It Pays To Be Dumb

So, what can regulators do? Roth admits he doesn’t have an answer. It wouldn’t make sense to ban no-swap-regret algorithms: If everyone uses one, prices will fall. But a simple nonresponsive strategy might be a natural choice for a seller on an online marketplace like Amazon, even if it carries the risk of regret.

“One way to have regret is just to be kind of dumb,” Roth said. “Historically, that hasn’t been illegal.”

As Hartline sees it, the problem of algorithmic collusion has a simple solution: Ban all pricing algorithms except the no-swap-regret algorithms that game theorists have long favored. There may be practical ways to do this: In their 2024 work, Hartline and his colleagues devised a method for checking if an algorithm has a no-swap-regret property without looking at its code.

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Hartline acknowledged that his preferred solution wouldn’t prevent all bad outcomes when no-swap-regret algorithms compete with humans. But he argued that scenarios like the one in Roth’s paper aren’t cases of algorithmic collusion.

“Collusion is a two-way thing,” he said. “It fundamentally must be the case that there are actions a single player can do to not collude.”

Either way, the new work still leaves many open questions about how algorithmic pricing can go wrong in the real world.

“We still don’t understand nearly as much as we want,” Pai said. “It’s an important question for our time.”

2025 Oct 20

- How Soon Will the Seas Rise?

EARTH SCIENCE | VIEW ON WEBSITE

How Soon Will the Seas Rise?

By Evan Howell

October 20, 2025

The uniquely vulnerable West Antarctic Ice Sheet holds enough water to raise global sea levels by 5 meters. But when that will happen — and how fast — is anything but settled.

One theory says that a chain reaction of toppling ice cliffs could dramatically hasten the timeline of global sea-level rise.

RMNunes/iStock

Introduction

In May 2014, NASA announced at a press conference that a portion of the West Antarctic Ice Sheet appeared to have reached a point of irreversible retreat. Glaciers flowing toward the sea at the periphery of the 2-kilometer-thick sheet of ice were losing ice faster than snowfall could replenish them, causing their edges to recede inland. With that, the question was no longer whether the West Antarctic Ice Sheet would disappear, but when. When those glaciers go, sea levels will rise by more than a meter, inundating land currently inhabited by 230 million people. And that would be just the first act before the collapse of the entire ice sheet, which could raise seas 5 meters and redraw the world’s coastlines.

At the time, scientists assumed that the loss of those glaciers would unfold over centuries. But in 2016, a bombshell study in Nature concluded that crumbling ice cliffs could trigger a runaway process of retreat, dramatically hastening the timeline. The Intergovernmental Panel on Climate Change (IPCC) took notice, establishing a sobering new worst-case scenario: By 2100, meltwater from Antarctica, Greenland and mountain glaciers combined with the thermal expansion of seawater could raise global sea levels by over 2 meters. And that would only be the beginning. If greenhouse gas emissions continue unabated, seas would rise a staggering 15 meters by 2300.

However, not all scientists are convinced by the runaway scenario. Thus, a tension has emerged over how long we have until West Antarctica’s huge glaciers vanish. If their retreat unfolds over centuries, humanity may have time to adapt. But if rapid destabilization begins in the coming decades through the controversial runaway process, the consequences could outpace our ability to respond. Scientists warn that major population centers — New York City, New Orleans, Miami and Houston — may not be ready.

“We’ve definitely not ruled this out,” said Karen Alley, a glaciologist at the University of Manitoba whose research supports the possibility of the runaway process. “But I’m not ready to say it’s going to happen soon. I’m also not going to say it can’t happen, either.”

For millennia, humanity has flourished along the shore, unaware that we were living in a geological fluke — an unusual spell of low seas. The oceans will return, but how soon? What does the science say about how ice sheets retreat, and therefore, about the future of our ports, our homes, and the billions who live near the coast?

Grounded by the Sea

In 1978, John Mercer, an eccentric glaciologist at Ohio State University who allegedly conducted fieldwork nude, was among the first to predict that global warming threatened the West Antarctic Ice Sheet. He based his theory on the ice sheet’s uniquely precarious relationship with the sea.

Bigger than Alaska and Texas combined, West Antarctica is split from the eastern half of the continent by the Transantarctic Mountains, whose peaks are buried to their chins in ice. Unlike in East Antarctica (and Greenland), where most ice rests on land high above the water, in West Antarctica the ice sheet has settled into a bowl-shaped depression deep below sea level, with seawater lapping at its edges. This makes West Antarctica’s ice sheet the most vulnerable to collapse.

A heaping dome of ice, the ice sheet flows outward under its own weight through tentaclelike glaciers. But the glaciers don’t stop at the shoreline; instead, colossal floating plates of ice hundreds of meters thick extend over the sea. These “ice shelves” float like giant rafts, tethered by drag forces and contact with underwater rises and ridges. They buttress the glaciers against an inexorable gravitational draw toward the sea.

Mark Belan/Quanta Magazine

The critical frontline of the ice sheet’s vulnerability is the “grounding line,” where ice transitions from resting on the seafloor to floating as an ice shelf. As the relatively warm sea works its way below the protective shelves, it thins them from below, shifting the grounding line inland. The floating shelves fragment and break away. The upstream glaciers, now without their buttressing support, flow faster toward the sea. Meanwhile, seawater intrudes like an advancing army toward thicker ice, which rests on bedrock that slopes inward toward the bowl-like center of the continent.

“There’s a very serious message here,” said Hilmar Gudmundsson, a glaciologist at Northumbria University: As the grounding line marches inland toward ever-thicker ice in a process called marine ice sheet instability, “you will have a very sharp increase in global sea level, and it will happen very quickly.”

In 2002, scientists got a live view of how that process may play out. The Larsen B ice shelf, a floating mass off the Antarctic Peninsula roughly the size of Rhode Island, broke apart in just over a month, stunning scientists. Pooling surface meltwater had forced open cracks — a process called hydrofracturing — which splintered the shelf, the only barrier for the glaciers behind it. The glaciers began flowing seaward up to eight times faster. One of these, Crane Glacier, lost its cliff edge in a series of collapses over the course of 2003, causing it to shrink rapidly. What if something similar happened to far larger glaciers on the coast of West Antarctica, like Thwaites and Pine Island?

In 2002, scientists watched with amazement as the Larsen B ice shelf collapsed in just over a month. At the start of this series of NASA satellite images, pools of meltwater that contributed to the fracturing of the ice shelf are visible as parallel blue lines. The shelf soon disintegrated into a blue-tinged mélange of slush and icebergs. This ice debris field largely melted the following summer and began to drift away with the currents.

NASA Earth Observatory

In the years that followed, studies of ancient shorelines revealed a stunning sensitivity in the Earth system: It appeared that epochs only slightly warmer than today featured seas 6 to 9 meters above present-day levels.

In response, glaciologists Robert DeConto and David Pollard developed a bold new theory of ice sheet collapse. They created a computer simulation based on Larsen B’s breakup and Greenland’s calving glaciers that was also calibrated to the geologic past — projecting future melt that matched expectations derived from ancient sea levels.

Their 2016 study outlined a scenario of almost unimaginably quick ice loss and sea-level rise. In a process called marine ice cliff instability (MICI), cliffs taller than 90 meters at the edges of glaciers become unstable and collapse, exposing ever-thicker ice in a chain reaction that accelerates retreat. The model suggested that ice from Antarctica alone — before any additions from Greenland, mountain glaciers or thermal expansion — could raise the seas by more than a meter by 2100.

In a 2021 update that incorporated additional factors into the simulations, DeConto and colleagues revised that estimate sharply downward, projecting less than 40 centimeters of sea-level rise by the century’s end under high-emission scenarios. Yet even as the numbers have shifted, DeConto remains convinced of the MICI concept. “It’s founded on super basic physical and glaciological principles that are pretty undeniable,” he said.

Mechanisms to Slow Retreat

After the 2016 study, the scientific community set out to test whether towering ice cliffs really could undergo runaway collapse. Many soon found reasons for doubt.

Few dispute the basic physics: If ice shelves like Larsen B collapse quickly and expose tall-enough cliffs on the glaciers behind them, those cliffs will indeed buckle under their own weight. “There’s a reason why skyscrapers are only so tall,” said Jeremy Bassis, a glaciologist and expert in fracture mechanics at the University of Michigan. However, critics argue that runaway cliff collapse hasn’t been seen in nature, and there might be good reasons why not.

“Yes, ice breaks off if you expose tall cliffs, but you have two stabilizing factors,” said Mathieu Morlighem, a glaciologist at Dartmouth College who led a 2024 study that identified these factors. First, as newly exposed glacier cliffs topple, the ice behind stretches and thins. As this happens, rapidly, “your ice cliff is going to be less of a tall cliff,” Morlighem said. Second, the flowing glacier brings more ice forward to replace what breaks off, slowing the cliff’s inland retreat and making a chain reaction of cliff toppling less likely.

The Thwaites ice shelf in West Antarctica is the floating extension of the Thwaites Glacier, which drains a large portion of the West Antarctic Ice Sheet. The ice shelf is thinning due to melting by warm ocean water below.

NASA

Another study challenging the MICI scenario noted that breaking ice also tends to form a mélange, a dense, jumbled slurry of icebergs and sea ice. This frozen slurry can act as a retaining wall, at least temporarily stabilizing the cliffs against collapse.

The bedrock beneath the ice might also be a key player. “The solid Earth is having much bigger impacts on our understanding of sea-level change than we ever expected,” said Frederick Richards, a geodynamicist at Imperial College London. Scientists have long recognized that when glaciers melt, the land rebounds like a mattress relieved of weight. But this rebound has been mostly dismissed as too sluggish to matter for several centuries. Now, high-precision GPS and other geophysical data reveal rebound occurring over decades, even years.

Whether that’s good or bad depends on how quickly ice retreats. If it goes at a modest clip, the bedrock lifts the ice, reducing the amount of water that can lap away at it. But if retreat happens quickly enough through something like runaway cliff collapse, the Earth can’t keep up. A 2024 study showed that the bedrock still rises, but in that scenario it pushes meltwater into the ocean. “You’re actually getting more sea-level rise,” Richards said. “You’re pushing all this water out of a bowl underneath West Antarctica and into the global ocean system.”

Earth’s restlessness also affects models of ancient sea-level rise. In a 2023 study, Richards and colleagues found that Australia’s 3-million-year-old Pliocene shorelines had ridden the slow heave and sigh of Earth’s mantle, and that accounting for that vertical motion resulted in lower estimates for ancient sea levels. This matters, according to Richards, because the revised record is a better match for more conservative ice retreat models. “Hold on, guys,” he said. “We have to be a little bit careful. [Ancient] sea-level estimates might be overestimates, and therefore we might be overestimating how sensitive the ice sheets are.”

DeConto points to the Larsen B breakup and the crumbling of Greenland’s Jakobshavn Glacier as evidence to the contrary. Once Larsen B stopped holding back the Crane Glacier, he says, ice began breaking away faster than the glacier could replenish it. That is “really strong evidence that fracture can outpace flow.”

From Past to Future

“When I started my career, the question was whether Antarctica was growing or shrinking,” said Ted Scambos, a glaciologist at the University of Colorado, Boulder. The IPCC long held that the ice sheet would remain relatively stable through the 21st century, on the logic that rising temperatures would bring more snow, offsetting melt.

That assumption collapsed along with Larsen B in the early 2000s, and scientists soon came to a consensus that ice loss was well underway. Satellite observations revealed that glaciers along the Amundsen Sea, including Pine Island and Thwaites, were flowing faster than in previous decades. The ice sheet was not in balance. By the time NASA called the 2014 press conference, it was clear that many of West Antarctica’s enormous glaciers had been retreating steadily since the 1990s.

The aftermath of Hurricane Florence in Myrtle Beach, South Carolina in 2018. Worldwide, some 230 million people live less than a meter above sea level, and 1 billion people are within 10 meters of sea level.

National Guard/Alamy

“It was the first time we had enough observations to say, hey, look, these grounding lines have been retreating year after year,” said Morlighem, a co-author on one of the studies presented at the press conference. This steady loss signaled that the glaciers would inevitably disappear. “In theory, if we turn off melt, we can stop it,” he noted. “But there’s absolutely zero chance we can do that.”

While the conversation has centered on how the sea will lap away at the ice shelves, some scientists are increasingly concerned about what’s happening up top, as warming air melts the ice sheet’s surface. Nicholas Golledge, a glaciologist at Victoria University of Wellington, sees West Antarctica today as transitioning to the status of Greenland: Most of Greenland’s marine-vulnerable ice has already vanished, and surface melt dominates. That process, Golledge believes, may soon play a bigger role in Antarctica than most models assume.

Pooling meltwater, for example, contributed to the Larsen B collapse. As the water trickles into crevasses, it lubricates the bedrock and sediments below, making everything more slippery. The Columbia University glaciologist Jonny Kingslake says these processes are oversimplified or omitted in numerical simulations. “If you ignore hydrology change, you are underestimating retreat,” he said.

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Indeed, a 2020 study found that meltwater trickling into Antarctica’s ice shelves could infiltrate cracks and force them open, a precursor to marine ice cliff instability that DeConto and colleagues envisioned.

Depending on future emissions, the IPCC now projects an average sea-level rise of half a meter to 1 meter by 2100, a total that includes all melt sources and the expansion of warming water. The MICI process, if correct, could accelerate Antarctica’s contribution enough to double that overall rise. “There’s deep uncertainty around some of these processes,” said Robert Kopp, a climate scientist and science policy expert at Rutgers University. “The one thing we do know is that the more carbon dioxide we put into the atmosphere, the greater the risk.”

In Bassis’ view, “Whether it’s with marine ice cliff instability or marine ice sheet instability, it’s a bit of a distraction. By 2100, we will be talking about a coastline radically different than what I grew up with.”

Table of Contents

Quanta Magazine: 2025 Oct 29

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Carlo Rovelli’s Radical Perspective on Reality

2025 Oct 27

Shark Data Suggests Animals Scale Like Geometric Objects

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First Shape Found That Can’t Pass Through Itself

2025 Oct 22

The Game Theory of How Algorithms Can Drive Up Prices

2025 Oct 20

How Soon Will the Seas Rise?