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The ultimate Engineering flex is making almost any shape fly.😁 AUREOLE - PVRA TriDisc is our experimental drone concept that replaces spinning propellers with Perimetric Vectoring Ring Arrays (PVRA). We place micro-nozzle belts around tri-lobed ring. These tiny jets push air to generate lift, lateral motion, and rotational control... show more

Mathelirium

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44,691 次观看 • 4 个月前 •via X (Twitter)

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SHAPE-SHIFTING WING COULD REWRITE FLIGHT EFFICIENCY This prototype wing isn’t fixed in place, it’s alive in the air. Its surface can twist, stretch, and adjust camber on the fly, reacting instantly to shifting aerodynamic conditions. Each micro-adjustment trims drag and boosts lift, squeezing every drop of efficiency from takeoff to landing. The payoff is sharper stability, smoother maneuverability, and fuel savings that could ground old designs for good. It’s the kind of tech that makes the sky feel like a smarter place to fly. Source: kaizen.engineered

SHAPE-SHIFTING WING COULD REWRITE FLIGHT EFFICIENCY This prototype wing isn’t fixed in place, it’s alive in the air. Its surface can twist, stretch, and adjust camber on the fly, reacting instantly to shifting aerodynamic conditions. Each micro-adjustment trims drag and boosts lift, squeezing every drop of efficiency from takeoff to landing. The payoff is sharper stability, smoother maneuverability, and fuel savings that could ground old designs for good. It’s the kind of tech that makes the sky feel like a smarter place to fly. Source: kaizen.engineered

Mario Nawfal

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Wolfram Stephen Wolfram might be onto something here😁 WOLFRAM PHYSICS in motion: Two competing feeders and and a predator. Everything here is a hypergraph...including the environment. We visualize a synthetic micro-ecosystem built on computational irreducibility, hypergraph rule-flow & emergent geometry. Inspired by the Wolfram Physics Project's quest for a "Theory of Everything". The full 1750 line python code is available to Gold members on YouTube upon request. Wolfram #WolframPhysics #TheoryOfEverything #ComputationalUniverse

Wolfram Stephen Wolfram might be onto something here😁 WOLFRAM PHYSICS in motion: Two competing feeders and and a predator. Everything here is a hypergraph...including the environment. We visualize a synthetic micro-ecosystem built on computational irreducibility, hypergraph rule-flow & emergent geometry. Inspired by the Wolfram Physics Project's quest for a "Theory of Everything". The full 1750 line python code is available to Gold members on YouTube upon request. Wolfram #WolframPhysics #TheoryOfEverything #ComputationalUniverse

Mathelirium

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The Most Powerful Formula in All of Mathematics. This beast can cover almost any shape you can think of 💪

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Mathelirium

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A Million-Dollar Storm Mathematics Still Cannot Tame. Turbulence matters because it is the default behavior of real fluids once motion becomes strong enough, e.g. air over wings, blood through vessels, weather in the atmosphere, water in oceans, fuel in engines, and flow in pipes and turbines. We can write down the Navier-Stokes equations for all of this, but in 3D one of the deepest open questions is still whether smooth solutions always stay smooth, or can break down in finite time. That is crucial because it asks whether the basic equations of fluid motion remain mathematically under control forever, or can form a true singularity where the theory itself breaks. Solve that and you got yourself a million dollars

A Million-Dollar Storm Mathematics Still Cannot Tame. Turbulence matters because it is the default behavior of real fluids once motion becomes strong enough, e.g. air over wings, blood through vessels, weather in the atmosphere, water in oceans, fuel in engines, and flow in pipes and turbines. We can write down the Navier-Stokes equations for all of this, but in 3D one of the deepest open questions is still whether smooth solutions always stay smooth, or can break down in finite time. That is crucial because it asks whether the basic equations of fluid motion remain mathematically under control forever, or can form a true singularity where the theory itself breaks. Solve that and you got yourself a million dollars

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Do you know how we simulate electromagnetic radiation around real systems like antennas, aircraft, and waveguides? We break the geometry into a mesh, a collection of small elements that lets the solver compute Maxwell’s equations locally instead of attacking the whole shape at once. This makes the simulations practical, fast, and accurate enough to use in real engineering.

Do you know how we simulate electromagnetic radiation around real systems like antennas, aircraft, and waveguides? We break the geometry into a mesh, a collection of small elements that lets the solver compute Maxwell’s equations locally instead of attacking the whole shape at once. This makes the simulations practical, fast, and accurate enough to use in real engineering.

Mathelirium

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#WATCH | Delhi: At the Synergia Conclave, Lieutenant General Vipul Shinghal, AVSM, SM, Deputy Chief of Integrated Defence Staff (Doctrine, Organisation, and Training), says, "...Even when I operate an AI system, I understand how to use it, but I don’t know what manipulation of data is happening... Where we have control and where we are also focusing is that our commanders, who earlier were only dealing with troops and making decisions based on that, are now dealing with algorithms and systems... they must have the ability to question machine outputs... These aspects are being debated worldwide... India itself has recently lost any regulation after the AI summit, and we are part of these discussions. The consensus is hard, but it is building..." He adds, "Meaningful human control is another aspect that is taking shape. Meaningful human control means that commanders must be able to access control meaningfully, and for that, they require 4 inputs or rather 4 levers: sufficient situational awareness... adequate time and information... And the ability to override or intervene... if they understand its limitations, we will be able to, at least in systems of the armed forces and weapons systems, ensure that we use AI for user responsibility. The moral responsibility must remain with the commander, and our conscience must keep that in place... In the Indian context, we have always believed that Shakti must go hand in hand with Dharma, that this force must go hand in hand with righteousness..." (11.03)

#WATCH | Delhi: At the Synergia Conclave, Lieutenant General Vipul Shinghal, AVSM, SM, Deputy Chief of Integrated Defence Staff (Doctrine, Organisation, and Training), says, "...Even when I operate an AI system, I understand how to use it, but I don’t know what manipulation of data is happening... Where we have control and where we are also focusing is that our commanders, who earlier were only dealing with troops and making decisions based on that, are now dealing with algorithms and systems... they must have the ability to question machine outputs... These aspects are being debated worldwide... India itself has recently lost any regulation after the AI summit, and we are part of these discussions. The consensus is hard, but it is building..." He adds, "Meaningful human control is another aspect that is taking shape. Meaningful human control means that commanders must be able to access control meaningfully, and for that, they require 4 inputs or rather 4 levers: sufficient situational awareness... adequate time and information... And the ability to override or intervene... if they understand its limitations, we will be able to, at least in systems of the armed forces and weapons systems, ensure that we use AI for user responsibility. The moral responsibility must remain with the commander, and our conscience must keep that in place... In the Indian context, we have always believed that Shakti must go hand in hand with Dharma, that this force must go hand in hand with righteousness..." (11.03)

ANI

104,382 次观看 • 4 个月前

Erwin Schrödinger’s 1926 equation changed the game by turning Quantum Mechanics into wave dynamics. That move gave Physics a new way to think. Instead of forcing a particle onto one sharp path, it lets a complex wavefunction evolve in time, with its shape and phase holding the structure of the phenomenon. What makes this so striking is that Schrödinger’s equation does not start from vague mystery. It starts from a precise and daring idea The state of a particle is a complex field ψ(x,t), and the dynamics must push ψ forward in a way that preserves total probability.

Erwin Schrödinger’s 1926 equation changed the game by turning Quantum Mechanics into wave dynamics. That move gave Physics a new way to think. Instead of forcing a particle onto one sharp path, it lets a complex wavefunction evolve in time, with its shape and phase holding the structure of the phenomenon. What makes this so striking is that Schrödinger’s equation does not start from vague mystery. It starts from a precise and daring idea The state of a particle is a complex field ψ(x,t), and the dynamics must push ψ forward in a way that preserves total probability.

Mathelirium

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In Calculus of Variations, we give up the idea of only optimizing values and start optimizing geometries instead. The unknown is not a single x. It is a whole curve/surface y(x). The object you are minimizing is usually not a simple formula that you can guess. It is an integral that judges the whole shape. In our first lecture, we discuss the famous Brachistochrone problem. You choose two points, turn on gravity and ask a question which almost sounds too simple...which track will allow a bead to move from A to B in the minimum time? At your first attempt, your instinct will lead you astray. It is not the straight line. It is not the drop hard then cruise sketch either. The winner turns out to be a cycloid...the curve a point on a rolling circle traces. The track is the moving character in the animation. We begin with a flawed curve, perform gradient descent in curve-space, and observe the geometry change frame by frame as T[y] collapses to the brachistochrone. Please see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

In Calculus of Variations, we give up the idea of only optimizing values and start optimizing geometries instead. The unknown is not a single x. It is a whole curve/surface y(x). The object you are minimizing is usually not a simple formula that you can guess. It is an integral that judges the whole shape. In our first lecture, we discuss the famous Brachistochrone problem. You choose two points, turn on gravity and ask a question which almost sounds too simple...which track will allow a bead to move from A to B in the minimum time? At your first attempt, your instinct will lead you astray. It is not the straight line. It is not the drop hard then cruise sketch either. The winner turns out to be a cycloid...the curve a point on a rolling circle traces. The track is the moving character in the animation. We begin with a flawed curve, perform gradient descent in curve-space, and observe the geometry change frame by frame as T[y] collapses to the brachistochrone. Please see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

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Gravity makes things orbit...but what happens when the mass distribution itself is rotating and dragging phase space into resonances and chaos? In this scene we follow tens of thousands of stars in a toy barred galaxy: a flat disc with a central mass and a rotating bar of extra density that is not rigid, but wobbling, swaying, and breathing in strength over time. The stars start on almost circular orbits in a calm ring, but as the bar turns and its pattern speed and strength modulate, they feel a time-dependent gravitational shove that nudges some onto resonant tracks. 🤩😍 #Mathelirium #Astrophysics #GalacticDynamics #BarredGalaxy #PhaseSpace #HamiltonianChaos #OrbitalResonance

Mathelirium

152,143 次观看 • 7 个月前

Why Are Some People Still Taking String Theory Seriously? String theory is controversial, but it is still one of the few ideas that tries to describe Quantum Physics and Gravity in one picture. This animation points to one of its best-known ideas: Holography. What happens on the boundary helps determine what happens in the interior, so the edge seems to shape the bulk.

Why Are Some People Still Taking String Theory Seriously? String theory is controversial, but it is still one of the few ideas that tries to describe Quantum Physics and Gravity in one picture. This animation points to one of its best-known ideas: Holography. What happens on the boundary helps determine what happens in the interior, so the edge seems to shape the bulk.

Mathelirium

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FLIGHT STATS 🥩🚀 - 33G's max acceleration - Mach 2.6 - 8.5km - Meat internal temp reached 105C / 221F Yaw/pitch/roll control worked great! At low speed and low air pressure we get a little oscillation, starting on the roll axis and progressing to pitch/yaw. A little more detail in the modeling should fix that. Cross range at apogee was about 230m from the launch point with lateral velocity less than 2m/s! HUGE win for my goal with pitch/yaw control: reducing recovery dispersion. The rocket is in awesome shape, I think it should fly again! Maybe as a second stage to a much higher altitude so we can nail down attitude control in the upper atmosphere.

FLIGHT STATS 🥩🚀 - 33G's max acceleration - Mach 2.6 - 8.5km - Meat internal temp reached 105C / 221F Yaw/pitch/roll control worked great! At low speed and low air pressure we get a little oscillation, starting on the roll axis and progressing to pitch/yaw. A little more detail in the modeling should fix that. Cross range at apogee was about 230m from the launch point with lateral velocity less than 2m/s! HUGE win for my goal with pitch/yaw control: reducing recovery dispersion. The rocket is in awesome shape, I think it should fly again! Maybe as a second stage to a much higher altitude so we can nail down attitude control in the upper atmosphere.

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Not only does our company believe in the Second Amendment, but we also believe in freedom of expression protected by the First Amendment. We love the United States. There is no other place in the world that shares the liberties that we cherish here on a daily basis; our products revolve around a concept that, in many other nations, is completely abolished for civilian ownership. A nation of freedom is what we have strived to be since conception, and a free nation should recognize that the burning of any flag is a protected form of free speech.

Not only does our company believe in the Second Amendment, but we also believe in freedom of expression protected by the First Amendment. We love the United States. There is no other place in the world that shares the liberties that we cherish here on a daily basis; our products revolve around a concept that, in many other nations, is completely abolished for civilian ownership. A nation of freedom is what we have strived to be since conception, and a free nation should recognize that the burning of any flag is a protected form of free speech.

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Theoretical Physicist Dr. Lara Anderson: "Our 3 dimensional universe is expanding in to a 4th dimension" "Early 20th-century physics revealed our universe has more dimensions than we can see, and string theory suggests they shape everything from particles to reality itself." "The universe is not only stranger than we suppose, but stranger than we can suppose." This insight from physicist Arthur Eddington captures how extra dimensions, compactified in complex shapes like Calabi-Yau manifolds, remain hidden yet influence the fundamental laws we observe. These dimensions aren't sci-fi portals. They're tiny, folded geometries woven into the fabric of spacetime, enabling string theory to unify quantum mechanics and gravity while explaining unseen aspects like dark matter. Consciousness may even connect to these deeper structures in ways physics is only beginning to explore. Mind bending science that challenges everything we think we know about existence. What if the reality we perceive is just a slice of something far richer?

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Reminder that if every Armenian left Artsakh and Azerbaijan had full control, there still wouldn't be peace with AZ. Aliyev on "Western AZ" (the parts of Armenia AZ regularly attacks): "Present-day Armenia is our land; we need to develop a concept of returning to Western AZ."

Lindsey Snell

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Dropping the CapCut Video Studio Behind the Scene Series: Episode 1 - Getting Started. When people first start creating with AI, it often begins with a blank screen. A loose idea, a fleeting visual, something you can almost see but not fully shape yet. In this episode, we will follow how creators getting start to shape their story with Video Studio. How an idea is framed, how direction is set, and how the first decisions shape everything that follows. If you’ve ever wondered how to start strong and turn a rough idea into something real, this is something you don’t want to miss.

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In just a few months, we've closed the gap from 21 points to 5 points in the polls. We can end political corruption. We can control AI so it works for humanity, not the oligarchs. We can have Medicare-for-all and lower the cost of living. But to do any of that, we have to change the leadership and direction of the Democratic Party, and our campaign is the only one willing to speak that truth. San Franciscans agree, and that's why we're surging. Sign up to volunteer at This is our chance.

In just a few months, we've closed the gap from 21 points to 5 points in the polls. We can end political corruption. We can control AI so it works for humanity, not the oligarchs. We can have Medicare-for-all and lower the cost of living. But to do any of that, we have to change the leadership and direction of the Democratic Party, and our campaign is the only one willing to speak that truth. San Franciscans agree, and that's why we're surging. Sign up to volunteer at This is our chance.

Saikat Chakrabarti for Congress

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We often hear that Machine Learning models learn patterns in data. But what does that actually look like in Geometry? If you dropped a little elastic mesh into a cloud of points and let it learn, how would it fold itself to match the shape of the data? In this scene we watch a Self-Organizing Map (SOM), a simple unsupervised neural model, learn the shape of a 3D datasets l, one static and the other dynamic. On top of this, we lay down a square grid of neurons whose weights live in the same plane. At the start, this grid is just a flat net floating across the cloud. It knows nothing about the structure underneath. Learning is a repeated game: Pick a random data point, find the neuron whose weight is closest, and then nudge that neuron and its neighbours toward the point. Do this again and again, while slowly shrinking how far the neighbourhood influence spreads. Python code is available for Subscribers. #MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML

We often hear that Machine Learning models learn patterns in data. But what does that actually look like in Geometry? If you dropped a little elastic mesh into a cloud of points and let it learn, how would it fold itself to match the shape of the data? In this scene we watch a Self-Organizing Map (SOM), a simple unsupervised neural model, learn the shape of a 3D datasets l, one static and the other dynamic. On top of this, we lay down a square grid of neurons whose weights live in the same plane. At the start, this grid is just a flat net floating across the cloud. It knows nothing about the structure underneath. Learning is a repeated game: Pick a random data point, find the neuron whose weight is closest, and then nudge that neuron and its neighbours toward the point. Do this again and again, while slowly shrinking how far the neighbourhood influence spreads. Python code is available for Subscribers. #MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML

Mathelirium

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Garry Kasparov Garry Kasparov at the Free Russia Forum: Russia's future is being decided not in Russia, but in Ukraine. From the very beginning of the full-scale invasion, our slogan has been "Victory for Ukraine and freedom for Russia," in such order. We are not dreamers of some concept of a beautiful Russia of the future. We are trying to do what we can. We do not overestimate our strength, but we know exactly what we can do. And we know where our place is. Our place today is in this war alongside Ukraine, which is defending not only its independence, not only its state and national integrity, but also all of Europe and the entire free world. It is the shield of the free world against the advance of the forces of tyranny. We are with Ukraine, which must prevail and save the free world from this invasion.

Garry Kasparov Garry Kasparov at the Free Russia Forum: Russia's future is being decided not in Russia, but in Ukraine. From the very beginning of the full-scale invasion, our slogan has been "Victory for Ukraine and freedom for Russia," in such order. We are not dreamers of some concept of a beautiful Russia of the future. We are trying to do what we can. We do not overestimate our strength, but we know exactly what we can do. And we know where our place is. Our place today is in this war alongside Ukraine, which is defending not only its independence, not only its state and national integrity, but also all of Europe and the entire free world. It is the shield of the free world against the advance of the forces of tyranny. We are with Ukraine, which must prevail and save the free world from this invasion.

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165,592 次观看 • 5 个月前

How do you give a humanoid the general motion capability? Not just single motions, but all motion? Introducing SONIC, our new work on supersizing motion tracking for natural humanoid control. We argue that motion tracking is the scalable foundation task for humanoids. So we "supersized" it: 9k+ GPU hours and 100M+ motion frames. But tracking alone is not enough; we show how to make a useful control system out of it: - Universal Kinematic Planner: Enables game-like gamepad control and high-level teleoperation, just like controlling a character in a game. - VR Full-Body Teleop: Direct, real-time whole-body control by a human wearing a VR headset. - VR Keypoint Teleop: Control the upper body (hands/head) while our planner handles robust locomotion automatically. - VLA Integration: We connect this motion tracker to autonomous Visual-Language-Action (VLA) models for autonomous task execution! We use a Universal Token Space to UNIFY this command space, turning our robust tracker into a general-purpose, programmable humanoid brain. This is the generalist "System 1" for humanoids. 🚀 Project: #Humanoids #Robotics #AI #FoundationModels #NVIDIAResearch 🧠🔥

How do you give a humanoid the general motion capability? Not just single motions, but all motion? Introducing SONIC, our new work on supersizing motion tracking for natural humanoid control. We argue that motion tracking is the scalable foundation task for humanoids. So we "supersized" it: 9k+ GPU hours and 100M+ motion frames. But tracking alone is not enough; we show how to make a useful control system out of it: - Universal Kinematic Planner: Enables game-like gamepad control and high-level teleoperation, just like controlling a character in a game. - VR Full-Body Teleop: Direct, real-time whole-body control by a human wearing a VR headset. - VR Keypoint Teleop: Control the upper body (hands/head) while our planner handles robust locomotion automatically. - VLA Integration: We connect this motion tracker to autonomous Visual-Language-Action (VLA) models for autonomous task execution! We use a Universal Token Space to UNIFY this command space, turning our robust tracker into a general-purpose, programmable humanoid brain. This is the generalist "System 1" for humanoids. 🚀 Project: #Humanoids #Robotics #AI #FoundationModels #NVIDIAResearch 🧠🔥

Zhengyi “Zen” Luo

62,040 次观看 • 8 个月前