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Category: mathematics – Page 2

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Continue reading “The Continuum Hypothesis — The Problem that BROKE Mathematics” | >

A standard digital camera used in a car for stuff like emergency braking has a perceptual latency of a hair above 20 milliseconds. That’s just the time needed for a camera to transform the photons hitting its aperture into electrical charges using either CMOS or CCD sensors. It doesn’t count the further milliseconds needed to send that information to an onboard computer or process it there.

A team of MIT researchers figured that if you had a chip that could process photons directly, you could skip the entire digitization step and perform calculations with the photons themselves, which has the potential to be mind-bogglingly faster.

“We’re focused on a very specific metric here, which is latency. We aim for applications where what matters the most is how fast you can produce a solution. That’s why we are interested in systems where we’re able to do all the computations optically,” says Saumil Bandyopadhyay, an MIT researcher. The team implemented a complete deep neural network on a photonic chip, achieving a latency of 410 picoseconds. To put that in perspective, Bandyopadhyay’s chip could process the entire neural net it had onboard around 58 times within a single tick of the 4 GHz clock on a standard CPU.

Instead of sensing photons and processing the results, why not process the photons?

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Anyone who’s ever tried tiling a floor, a backsplash or even an arts-and-crafts project probably knows the emotional frustration of working with pieces whose shapes don’t perfectly complement each other. It turns out, though, that some creatures may actually rely on similar mismatches to create geometric frustrations that result in complex natural structures with remarkable properties, such as protective shells and sturdy yet flexible bones.

Now, researchers at the University of Michigan have developed mathematical models showing one way that nature achieves this. These models, in turn, could help design advanced materials for medical devices, sustainable construction and more.

“Frustration—using these mismatched building blocks—gives rise to wonderful complexity and that complexity can be useful in providing superior material properties,” said Xiaoming Mao, U-M professor of physics and senior author of the new study.

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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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Continue reading “MIND-STUFF: How William Clifford Connected Geometry, Matter, and Mind — VERSADOCO” | >

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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