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Category: mathematics – Page 5

For centuries, the I-Ching, or Book of Changes, has fascinated scholars, mystics, and seekers alike. It is often considered a mere divination tool, a mystical means of interpreting the world through the casting of hexagrams.

But what if the I-Ching is something more? What if it operates as a structured probability space, exhibiting patterns and behaviors reminiscent of quantum mechanics?

Our latest research suggests that the I-Ching might not be a random oracle but instead a system governed by deep mathematical structures.

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Quantum physics, space documentary, and the fabric of reality—these are not just abstract ideas but the keys to unlocking the mysteries of existence. What is reality? Is it an illusion, a simulation, or something far beyond our comprehension? In this mind-expanding documentary, we explore the very fabric of the universe, from the bizarre behavior of quantum mechanics to the cosmic forces shaping space and time.

The universe is a grand puzzle, and science has only begun to unravel its secrets. Quantum physics reveals a world where particles exist in multiple states at once, where time behaves unpredictably, and where observation itself shapes reality. But how does this strange quantum realm connect to the vast expanse of space? Is the fabric of reality woven with unseen forces that govern everything, from black holes to the flow of time itself?

This space documentary takes you on a journey through the cutting-edge theories that challenge our understanding of the cosmos. Could our universe be a hologram? Is time an illusion? Do parallel realities exist beyond our perception? With stunning visuals, expert insights, and mind-bending concepts, we push the boundaries of what we know about existence.

🔔 Subscribe for more deep-space documentaries and quantum mysteries!
📢 Share your thoughts in the comments—what do you think reality truly is?

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Laser diodes are semiconductors that generate light and amplify it using repeated reflection or “optical feedback.” Once the light has achieved desirable optical gain, laser diodes release it as powerful laser beams.

Photonic crystal surface-emitting lasers (PCSELs) are advanced where the optical gain is typically distributed laterally to the propagating light within a photonic crystal (PC) structure. They differ from traditional lasers by separating gain, feedback, and emission functions, offering scalable single-mode power and innovative designs. This leads to enhanced performance and new application possibilities.

In a paper that was published in the IEEE Journal of Selected Topics in Quantum Electronics on 20 November 2024, researchers have developed a method to numerically simulate the interaction of light waves within PCSELs.

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A theoretical particle that travels faster than light, the tachyon has long intrigued physicists and fueled decades of speculation. Initially conceived as a possible solution to quantum and relativity paradoxes, tachyons remain purely hypothetical. Despite the lack of experimental evidence, they continue to serve as a thought-provoking concept in modern physics.

A recent study by an international team of researchers has reignited interest in tachyons, suggesting they might be possible within the framework of Einstein’s special theory of relativity. This bold claim challenges conventional understandings of causality and time, raising fundamental questions about the structure of reality. If confirmed, it could lead to a radical shift in how scientists perceive the limits of physical laws.

Physicist Gerald Feinberg introduced the idea of tachyons in 1962, proposing that such particles could always travel faster than light without ever slowing down to subluminal speeds. His argument was based on the concept of imaginary mass, a theoretical construct involving the square root of a negative number. This allowed for the mathematical possibility of faster-than-light motion without explicitly violating relativity.

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A new mathematical model sheds light on how the brain processes different cues, such as sights and sounds, during decision making. The findings from Princeton neuroscientists may one day improve how brain circuits go awry in neurological disorders, such as Alzheimer’s, and could help artificial brains, like Alexa or self-driving car technology, more helpful.

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A team of researchers at Google’s DeepMind project, reports that its AlphaGeometry2 AI performed at a gold-medal level when tasked with solving problems that were given to high school students participating in the International Mathematical Olympiad (IMO) over the past 25 years. In their paper posted on the arXiv preprint server, the team gives an overview of AlphaGeometry2 and its scores when solving IMO problems.

Prior research has suggested that AI that can solve geometry problems could lead to more sophisticated apps because they require both a high level of reasoning ability and an ability to choose from possible steps in working toward a solution to a problem.

To that end, the team at DeepMind has been working on developing increasingly sophisticated geometry-solving apps. Its first iteration was released last January and was called AlphaGeometry; its second iteration is called AlphaGeometry2.

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An AI system developed by Google DeepMind, Google’s leading AI research lab, appears to have surpassed the average gold medalist in solving geometry problems in an international mathematics competition.

The system, called AlphaGeometry2, is an improved version of a system, AlphaGeometry, that DeepMind released last January. In a newly published study, the DeepMind researchers behind AlphaGeometry2 claim their AI can solve 84% of all geometry problems over the last 25 years in the International Mathematical Olympiad (IMO), a math contest for high school students.

Why does DeepMind care about a high-school-level math competition? Well, the lab thinks the key to more capable AI might lie in discovering new ways to solve challenging geometry problems — specifically Euclidean geometry problems.

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For over 2,000 years, mathematicians believed a purely trigonometric proof of Pythagoras’ theorem was impossible. But two high school students from Louisiana may have just changed that. Their unexpected discovery has sparked debate among experts—and could reshape how we understand geometry.

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Hamilton-Jacobi (HJ) reachability is a rigorous mathematical framework that enables robots to simultaneously detect unsafe states and generate actions that prevent future failures. While in theory, HJ reachability can synthesize safe controllers for nonlinear systems and nonconvex constraints.

In practice, it has been limited to hand-engineered collision

Avoidance constraints modeled via low-dimensional state-space representations and first-principles dynamics. In this work, our goal is to generalize safe robot controllers to prevent failures that are hard—if not impossible—to write down by hand, but can be intuitively identified from high-dimensional observations:

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In today’s AI news, Google launched its much-anticipated new flagship AI model, Gemini 2.0 Pro Experimental, on Wednesday. The announcement was part of a series of other AI model releases. The company is also making its reasoning model, Gemini 2.0 Flash Thinking, available in the Gemini app.

In other advancements, LinkedIn is testing a new job-hunting tool that uses a custom large language model to comb through huge quantities of data to help people find prospective roles. The company believes that artificial intelligence will help users unearth new roles they might have missed in the typical search process.

S Deep Research feature, which can autonomously browse the web and create research reports. ‘ + s up from hitting $50 million ARR, or the yearly value of last month s case for why they are the best positioned to take over TikTok And, in this episode, a16z Partner Marc Andrusko chats with Mastercard’s Chief AI and Data Officer Greg Ulrich about Mastercard’s long history of using AI, the opportunities (and potential risks) associated with integrating generative AI into fraud detection, determining what tech to employ based on use cases, and the best advice he’s ever gotten.

Then, power your AI transformation with an insightful keynote from Scott Guthrie, Executive Vice President, Cloud + AI Group at Microsoft, and other industry experts. Watch this keynote presentation from NYC stop on Microsoft’s AI Tour.

We close out with this insightful discussion with Malcolm Gladwell and Ric Lewis, SVP of Infrastructure at IBM. Learn how hardware capabilities enable the matrix math behind large language models and how AI is transforming industries—from banking to your local coffee shop.

Thats all for today, but AI is moving fast — like, comment, and subscribe for more AI news! Please vote for me in the Entrepreneur of Impact Competition today! Thank you for supporting my partners and I — it’s how I keep Neural News Network free.

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