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Category: mathematics

What if the key to the universe was discovered over a century ago—and then forgotten?

In the late 19th century, a young math prodigy named William Clifford proposed a radical idea: that reality itself is woven from the same fabric as the mind. Long before Einstein, long before quantum theory, Clifford envisioned a world where matter, consciousness, and geometry are one.

His ideas were largely overlooked, seen as too speculative for the science of his time. Today, they look like the missing blueprint for a true Theory of Everything.

Is Clifford’s path one that science is only now catching up to?

Based on the original research by idb.kniganews “Clifford’s Path”

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A recent study published in ACM Transactions on the Web by researchers at Queen Mary University of London sheds new light on one of the most significant collapses in cryptocurrency history: the crash of the TerraUSD stablecoin and its sister token, LUNA. The research team uncovered evidence of suspicious, large-scale trading activity that may point to a coordinated effort to destabilize the ecosystem, triggering a rapid $3.5 billion loss in market value.

Led by Dr. Richard Clegg, the study uses temporal multilayer graph analysis, an advanced method for tracking dynamic and interconnected systems over time. By applying this technique to transaction data from the Ethereum blockchain, the researchers were able to trace complex relationships between cryptocurrencies and pinpoint how TerraUSD was systematically undermined through a series of calculated trades.

Stablecoins like TerraUSD are designed to maintain a steady value, typically pegged to a fiat currency like the US dollar. However, in May 2022, TerraUSD and its sister currency, LUNA, experienced a catastrophic collapse. Dr. Clegg’s research sheds light on how this happened, uncovering evidence of a coordinated attack by traders who were betting against the system, a practice known as “shorting.”

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Nietzsche’s intuition about time’s nature likely emerged from his engagement with contemporary scientific thought, particularly the work of Johann Friedrich Herbart and Roger Joseph Boscovich, whose atomistic theories influenced Nietzsche’s conception of force and matter (Small, 2001). Additionally, Nietzsche’s reading of Heinrich Czolbe and Otto Caspari exposed him to cyclical cosmological theories that were precursors to modern conceptions of cosmological cycles.

More compelling than these historical influences, however, is the philosophical insight Nietzsche demonstrated in recognizing that a truly eternal cosmos with finite configurations must contain repetition. This insight, while not formulated in the mathematical language of relativity, nevertheless grasped a fundamental consequence of infinite time and finite states — one that would later be encoded in physical theory.

The convergence between Nietzsche’s eternal recurrence and modern physics becomes even more significant when we recognize similar conceptions in numerous cultural and religious traditions. This suggests a perennial human intuition about time’s nature that transcends historical and cultural boundaries.

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“I give you God’s view,” said Toby Cubitt, a physicist turned computer scientist at University College London and part of the vanguard of the current charge into the unknowable, and “you still can’t predict what it’s going to do.”

Eva Miranda, a mathematician at the Polytechnic University of Catalonia (UPC) in Spain, calls undecidability a “next-level chaotic thing.”

Undecidability means that certain questions simply cannot be answered. It’s an unfamiliar message for physicists, but it’s one that mathematicians and computer scientists know well. More than a century ago, they rigorously established that there are mathematical questions that can never be answered, true statements that can never be proved. Now physicists are connecting those unknowable mathematical systems with an increasing number of physical ones and thereby beginning to map out the hard boundary of knowability in their field as well.

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In a new study published in ACM Transactions on the Web, researchers from Queen Mary University of London have unveiled the intricate mechanisms behind one of the most dramatic collapses in the cryptocurrency world: the downfall of the TerraUSD stablecoin and its associated currency, LUNA. Using advanced mathematical techniques and cutting-edge software, the team has identified suspicious trading patterns that suggest a coordinated attack on the ecosystem, leading to a catastrophic loss of $3.5 billion in value virtually overnight.

The study, led by Dr. Richard Clegg and his team, employs temporal multilayer graph analysis—a sophisticated method for examining complex, interconnected systems over time. This approach allowed the researchers to map the relationships between different cryptocurrencies traded on the Ethereum blockchain, revealing how the TerraUSD stablecoin was destabilized by a series of deliberate, large-scale trades.

Stablecoins like TerraUSD are designed to maintain a steady value, typically pegged to a fiat currency like the US dollar. However, in May 2022, TerraUSD and its sister currency, LUNA, experienced a catastrophic collapse. Dr. Clegg’s research sheds light on how this happened, uncovering evidence of a coordinated attack by traders who were betting against the system, a practice known as “shorting.”

Read more | >

Monash University researchers have extended Descartes’ Circle Theorem by finding a general equation for any number of tangent circles, using advanced mathematical tools inspired by physics. A centuries-old geometric puzzle dating back to the 17th century has finally been solved by mathematicians

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Whether extra dimensions prove to be physical realities or useful mathematical constructs, they have already transformed our understanding of the universe. They have forced us to reconsider fundamental assumptions about space, time, and the nature of physical law. And they remind us that reality may be far richer and more complex than our everyday experience suggests — that beyond the familiar dimensions of length, width, height, and time, there may exist entire realms waiting to be discovered and, perhaps one day, explored.

The theoretical physicist John Wheeler once remarked that “we live on an island of knowledge surrounded by an ocean of ignorance.” Our exploration of extra dimensions extends the shoreline of that island, pushing into uncharted waters with the tools of mathematics, experiment, and imagination. Though we may never set foot in the fifth dimension or beyond, the very act of reaching toward these hidden aspects of reality expands our perspective and deepens our understanding of the cosmos we call home.

As we continue this grand scientific adventure, we carry forward the legacy of those who first dared to imagine worlds beyond our immediate perception — from the mathematicians who developed the language of higher-dimensional geometry to the physicists who incorporated these concepts into our most fundamental theories. Their vision, coupled with rigorous analysis and experimental testing, illuminates a path toward an ever more complete understanding of the universe in all its dimensions.

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Network models provide a flexible way of representing objects and their multifaceted relationships. Deriving a network entails mapping hidden structures in inevitably noisy data—a critical task known as reconstruction. Now Gang Yan and Jia-Jie Qin of Tongji University in China have provided a mathematical proof showing what makes some networks easier to reconstruct than others [1].

Complex systems in biology, physics, and social sciences tend to involve a vast number of interacting entities. In a network model, these entities are represented by nodes, linked by connections weighted to describe the strength of each interaction. Yan and Qin took an empirical dataset and used a statistical inference method to calculate the likelihood that any pair of nodes is directly linked. Then, based on the true positive and false positive rates of these inferred connections, they analyzed the fidelity of the reconstructed networks. They found that the most faithful reconstructions are obtained with systems for which the number of connections per node varies most widely across the network. Yan and Qin saw the same tendency when they tested their model on synthetic and real networks, including metabolic networks, plant-pollinator webs, and power grids.

With the rapid increase in available data across research areas, network reconstruction has become an important tool for studying complex systems. Yan and Qin say their new result both solves the problem of what complex systems can be easily mapped into a network and provides a solid foundation for developing methods of doing so.

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Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the first room, and it’s dark, completely dark. One stumbles around bumping into the furniture, and gradually, you learn where each piece of furniture is, and finally, after six months or so, you find the light switch. You turn it on, and suddenly, it’s all illuminated. You can see exactly where you were.

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