正在加载视频...

视频加载失败

返回首页

This isn't VFX visual effects...it's actual freakin physics! 🤯🤩🤗🙌🏾 You're watching the physics of space and matter coevolve...a small window into the kind of world Wolfram Physics Wolfram predicts. Every ripple, collision, and shimmer you see is a causal event in a living hypergraph. Space itself is an active...

mathelirium's profile picture

Mathelirium

11,577 subscribers

20,090 次观看 • 10 个月前 •via X (Twitter)

LIVE

Anya Rossi• Live Now

Private livecam show

0 条评论

暂无评论

原始帖子的评论将显示在这里

相关视频

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
2:00

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

99,636 次观看 • 10 个月前

The Dance of Three Masses on a Warped Spacetime Fabric Newtonian Gravity says masses attract one another through force. General Relativity changes the picture by treating gravity as geometry itself, where matter shapes Spacetime, and motion follows that evolving curved structure. In a three-body system, the bodies are not just pulling on each other. They are moving through a geometric landscape that shifts as the mass arrangement changes.
0:59

The Dance of Three Masses on a Warped Spacetime Fabric Newtonian Gravity says masses attract one another through force. General Relativity changes the picture by treating gravity as geometry itself, where matter shapes Spacetime, and motion follows that evolving curved structure. In a three-body system, the bodies are not just pulling on each other. They are moving through a geometric landscape that shifts as the mass arrangement changes.

Mathelirium

10,806 次观看 • 4 个月前

You're watching spacetime in motion...two spinning black holes orbit, twist, and merge, dragging the very geometry of the universe into a luminous storm. Their union births a single remnant that fires smoke-wreathed jet as gravitational waves ring the cosmic fabric itself. 🤩😍 #Math #Physics #Astrophysics #SciArt #MathArt
1:00

You're watching spacetime in motion...two spinning black holes orbit, twist, and merge, dragging the very geometry of the universe into a luminous storm. Their union births a single remnant that fires smoke-wreathed jet as gravitational waves ring the cosmic fabric itself. 🤩😍 #Math #Physics #Astrophysics #SciArt #MathArt

Mathelirium

42,647 次观看 • 9 个月前

Can Spacetime Move Faster Than Light? In 1994, Miguel Alcubierre proposed a strange solution to Einstein’s field equations: A Spacetime geometry where a compact region could be transported without the object inside locally breaking the speed of light. The idea is not that a ship accelerates through space faster than light. The local interior remains comparatively calm. The violent part is the surrounding geometry. Space contracts in front of the bubble, expands behind it, and forms a moving transport shell that carries the interior region forward. A simplified form of the Alcubierre metric is ds² = −dt² + [dx − vₛ f(rₛ)dt]² + dy² + dz² where f(rₛ) shapes the warp bubble and vₛ describes the motion of its centre. The physics is still highly speculative, especially because the original construction requires exotic stress-energy, but the mathematical idea is powerful. #GeneralRelativity #AlcubierreDrive #WarpDrive #Spacetime #EinsteinEquations #Relativity #Physics #Astrophysics #Cosmology
0:56

Can Spacetime Move Faster Than Light? In 1994, Miguel Alcubierre proposed a strange solution to Einstein’s field equations: A Spacetime geometry where a compact region could be transported without the object inside locally breaking the speed of light. The idea is not that a ship accelerates through space faster than light. The local interior remains comparatively calm. The violent part is the surrounding geometry. Space contracts in front of the bubble, expands behind it, and forms a moving transport shell that carries the interior region forward. A simplified form of the Alcubierre metric is ds² = −dt² + [dx − vₛ f(rₛ)dt]² + dy² + dz² where f(rₛ) shapes the warp bubble and vₛ describes the motion of its centre. The physics is still highly speculative, especially because the original construction requires exotic stress-energy, but the mathematical idea is powerful. #GeneralRelativity #AlcubierreDrive #WarpDrive #Spacetime #EinsteinEquations #Relativity #Physics #Astrophysics #Cosmology

Mathelirium

37,986 次观看 • 2 个月前

String Theory is one of the few frameworks that tries to describe Quantum Physics and Gravity in the same mathematical language. In this animation, the glowing loop is the string, the shifting color along it represent its quantum vibration modes, and the surrounding fabric is a proxy for Spacetime responding. When you quantize a string, one of its vibration modes behaves like a graviton. So, geometry shows up as part of the same quantum system. #StringTheory #QuantumGravity #GeneralRelativity #QuantumPhysics #TheoreticalPhysics #PhysicsVisualization
1:00

String Theory is one of the few frameworks that tries to describe Quantum Physics and Gravity in the same mathematical language. In this animation, the glowing loop is the string, the shifting color along it represent its quantum vibration modes, and the surrounding fabric is a proxy for Spacetime responding. When you quantize a string, one of its vibration modes behaves like a graviton. So, geometry shows up as part of the same quantum system. #StringTheory #QuantumGravity #GeneralRelativity #QuantumPhysics #TheoreticalPhysics #PhysicsVisualization

Mathelirium

42,172 次观看 • 6 个月前

A Black Hole Can Be Dragged Through Spacetime A Black Hole does not have to sit still. Einstein’s equations allow a stranger possibility... a Black Hole that accelerates. This is the C-metric, an exact solution of General Relativity describing an accelerating Black Hole. The Black Hole accelerates because the geometry of Spacetime says it must. The C-metric is one of those exact solutions that reminds us how wild General Relativity really is. Gravity is not just attraction, and Spacetime is not just a stage. Sometimes the stage itself contains the force. #Astrophysics #GeneralRelativity #Einstein #CMetric #BlackHole #CosmicStrings #Spacetime #Cosmology #Mathematics #Physics
0:59

A Black Hole Can Be Dragged Through Spacetime A Black Hole does not have to sit still. Einstein’s equations allow a stranger possibility... a Black Hole that accelerates. This is the C-metric, an exact solution of General Relativity describing an accelerating Black Hole. The Black Hole accelerates because the geometry of Spacetime says it must. The C-metric is one of those exact solutions that reminds us how wild General Relativity really is. Gravity is not just attraction, and Spacetime is not just a stage. Sometimes the stage itself contains the force. #Astrophysics #GeneralRelativity #Einstein #CMetric #BlackHole #CosmicStrings #Spacetime #Cosmology #Mathematics #Physics

Mathelirium

789,561 次观看 • 2 个月前

Why String Theory Won't Die The string theory idea refuses to die because it's one of the few frameworks that forces a quantum object and spacetime geometry into the same picture. In the render, a closed string isn’t just a loop doing pretty vibrations. Its internal phase pattern is a quantum degree of freedom, shown as color. At the same time, its motion stirs ripples in the surrounding metric, shown as the fabric below. One object, two roles. A wave-like state living on the string, and a curvature-like response spreading through the background. You can literally watch quantum stuff and gravity stuff talk to each other in the same scene. #StringTheory #Physics #QuantumMechanics #GeneralRelativity #MathematicalPhysics #SciComm
1:00

Why String Theory Won't Die The string theory idea refuses to die because it's one of the few frameworks that forces a quantum object and spacetime geometry into the same picture. In the render, a closed string isn’t just a loop doing pretty vibrations. Its internal phase pattern is a quantum degree of freedom, shown as color. At the same time, its motion stirs ripples in the surrounding metric, shown as the fabric below. One object, two roles. A wave-like state living on the string, and a curvature-like response spreading through the background. You can literally watch quantum stuff and gravity stuff talk to each other in the same scene. #StringTheory #Physics #QuantumMechanics #GeneralRelativity #MathematicalPhysics #SciComm

Mathelirium

13,657 次观看 • 7 个月前

The Chinese Physicist Who Turned Force Into Geometry In 1954, Chinese physicist Chen-Ning Yang, together with Robert Mills, introduced a new idea that changed modern physics: Maybe a force is not just something that pushes or pulls. Maybe a force can come from geometry. In Yang-Mills Theory, every point in space carries a hidden internal direction. As you move through space, that direction can twist. If you go around a closed loop and the direction does not return exactly the same, the field has curvature. That curvature is what we see as force. In this animation, the glowing surface shows where the gauge field is strongest. The changing colours show how the hidden internal direction varies across space. The moving rectangular loops are Wilson loops. They travel through the field and measure how much the internal direction changes after completing a closed path. The key equation behind the scene is Fₓᵧ = ∂ₓAᵧ - ∂ᵧAₓ + Aₓ × Aᵧ. The final term, Aₓ × Aᵧ, is the special part. It means the field can interact with itself. That self-interaction is one reason Yang-Mills theory became one of the foundations of particle physics. #China #ChinesePhysics #YangMills #GaugeTheory #QuantumFieldTheory #NonAbelianGeometry #WilsonLoops #ModernPhysics #STEM
0:30

The Chinese Physicist Who Turned Force Into Geometry In 1954, Chinese physicist Chen-Ning Yang, together with Robert Mills, introduced a new idea that changed modern physics: Maybe a force is not just something that pushes or pulls. Maybe a force can come from geometry. In Yang-Mills Theory, every point in space carries a hidden internal direction. As you move through space, that direction can twist. If you go around a closed loop and the direction does not return exactly the same, the field has curvature. That curvature is what we see as force. In this animation, the glowing surface shows where the gauge field is strongest. The changing colours show how the hidden internal direction varies across space. The moving rectangular loops are Wilson loops. They travel through the field and measure how much the internal direction changes after completing a closed path. The key equation behind the scene is Fₓᵧ = ∂ₓAᵧ - ∂ᵧAₓ + Aₓ × Aᵧ. The final term, Aₓ × Aᵧ, is the special part. It means the field can interact with itself. That self-interaction is one reason Yang-Mills theory became one of the foundations of particle physics. #China #ChinesePhysics #YangMills #GaugeTheory #QuantumFieldTheory #NonAbelianGeometry #WilsonLoops #ModernPhysics #STEM

Mathelirium

83,635 次观看 • 2 个月前

The Elusive Concept of Time - Part II Pulsar Timing The first scene showed you Time as a local rate...clocks nearer the hole run slower, light gets redshifted, and spin drags the geometry around. This follow-up keeps the same idea, but turns it into a timing experiment. Instead of watching a clock face, we watch a receiver compare what arrives versus what flat space would predict. In the animation, the three small orange dots are the pulsars...orbiting emitters that flash regularly (in their own proper time). The larger white dot is the receiver sitting off to the side, and the little dark nub next to it is a tiny craft/antenna marker to make it feel like an instrument, not a star. When a pulsar lines up behind the hole relative to the receiver, the arrival times jump, because curved spacetime added extra delay and bent the path. #Physics #GeneralRelativity #PulsarTiming #BlackHoles #FrameDragging #Spacetime #Astrophysics #Time
1:00

The Elusive Concept of Time - Part II Pulsar Timing The first scene showed you Time as a local rate...clocks nearer the hole run slower, light gets redshifted, and spin drags the geometry around. This follow-up keeps the same idea, but turns it into a timing experiment. Instead of watching a clock face, we watch a receiver compare what arrives versus what flat space would predict. In the animation, the three small orange dots are the pulsars...orbiting emitters that flash regularly (in their own proper time). The larger white dot is the receiver sitting off to the side, and the little dark nub next to it is a tiny craft/antenna marker to make it feel like an instrument, not a star. When a pulsar lines up behind the hole relative to the receiver, the arrival times jump, because curved spacetime added extra delay and bent the path. #Physics #GeneralRelativity #PulsarTiming #BlackHoles #FrameDragging #Spacetime #Astrophysics #Time

Mathelirium

55,826 次观看 • 7 个月前

The Non-Traversable Bridge Einstein Found Inside Gravity Einstein’s equations not only describe gravity as a force but as the shape of Spacetime as well. In 1935, Einstein and Rosen found that the Schwarzschild solution could be written in a way that reveals something astonishing: Two separate exterior regions of Spacetime joined by a bridge-like throat Rᵤᵥ = 0 This became known as the Einstein-Rosen Bridge. It is often called a Wormhole, but the classical Einstein-Rosen bridge is not a science-fiction tunnel. In the standard Schwarzschild geometry, it is non-traversable. The throat does not remain open long enough for ordinary travel from one region to the other. Its real power is mathematical. It shows that General Relativity is not merely about objects moving through space. The theory allows Spacetime to have global structure such as different regions, horizons, extensions, and hidden connections that are not visible from one local patch alone. The Einstein-Rosen bridge is one of the earliest glimpses of that deeper idea. Gravity is geometry. And sometimes, geometry has two worlds joined by a throat. #Astrophysics #GeneralRelativity #Einstein #BlackHole #Spacetime #Cosmology #Gravity #Wormhole #Mathematics #Physics
0:56

The Non-Traversable Bridge Einstein Found Inside Gravity Einstein’s equations not only describe gravity as a force but as the shape of Spacetime as well. In 1935, Einstein and Rosen found that the Schwarzschild solution could be written in a way that reveals something astonishing: Two separate exterior regions of Spacetime joined by a bridge-like throat Rᵤᵥ = 0 This became known as the Einstein-Rosen Bridge. It is often called a Wormhole, but the classical Einstein-Rosen bridge is not a science-fiction tunnel. In the standard Schwarzschild geometry, it is non-traversable. The throat does not remain open long enough for ordinary travel from one region to the other. Its real power is mathematical. It shows that General Relativity is not merely about objects moving through space. The theory allows Spacetime to have global structure such as different regions, horizons, extensions, and hidden connections that are not visible from one local patch alone. The Einstein-Rosen bridge is one of the earliest glimpses of that deeper idea. Gravity is geometry. And sometimes, geometry has two worlds joined by a throat. #Astrophysics #GeneralRelativity #Einstein #BlackHole #Spacetime #Cosmology #Gravity #Wormhole #Mathematics #Physics

Mathelirium

91,291 次观看 • 2 个月前

What Happens When a Black Hole Does More Than Fall? In General Relativity, a rotating Black Hole is described by the Kerr Metric. Its spin does something strange to spacetime... it drags the geometry around with it. The horizon sits at r₊ = M + √(M² - a²) but outside it there is another surface, the Ergosphere, r_E(θ) = M + √(M² - a²cos²θ) Inside that region, Spacetime is being swept around so strongly that remaining still is no longer possible. Every particle, every light thread, every local observer is forced to rotate with the geometry. For this scene, the C-metric acceleration remains alive in the background and the Black Hole still moves through the fabric, pulled along an axial defect. But the main event is Kerr frame dragging. The fabric twists. The Ergosphere breathes. Light paths shear into spirals. Particles that try to cross the region get carried around before falling inward. #GeneralRelativity #BlackHole #KerrMetric #FrameDragging #Ergosphere #Spacetime #EinsteinEquations #Astrophysics #Physics
0:57

What Happens When a Black Hole Does More Than Fall? In General Relativity, a rotating Black Hole is described by the Kerr Metric. Its spin does something strange to spacetime... it drags the geometry around with it. The horizon sits at r₊ = M + √(M² - a²) but outside it there is another surface, the Ergosphere, r_E(θ) = M + √(M² - a²cos²θ) Inside that region, Spacetime is being swept around so strongly that remaining still is no longer possible. Every particle, every light thread, every local observer is forced to rotate with the geometry. For this scene, the C-metric acceleration remains alive in the background and the Black Hole still moves through the fabric, pulled along an axial defect. But the main event is Kerr frame dragging. The fabric twists. The Ergosphere breathes. Light paths shear into spirals. Particles that try to cross the region get carried around before falling inward. #GeneralRelativity #BlackHole #KerrMetric #FrameDragging #Ergosphere #Spacetime #EinsteinEquations #Astrophysics #Physics

Mathelirium

27,112 次观看 • 1 个月前

Phase Space Is the Real Stage of Dynamics. So, Stop Watching the Object and Watch the State. Ordinary Space tells you where something is. Phase Space tells you what state it is in. Position alone is not enough because you also need the variable that tells you where the system is trying to go. In the animation, the left panel shows the particle moving in Ordinary Space, while the right panel shows the same system as a moving point in Phase Space. For one degree of freedom, the state is (x, p) and as time evolves, that state traces a trajectory t ↦ (x(t), p(t)) Instead of thinking of a differential equation as just a formula, Phase Space lets you see it as a flow on the space of states. For this lecture we use ẋ = p ṗ = x − x³ with Hamiltonian H(x,p) = 0.5 p² + 0.25 x⁴ − 0.5 x² #PhaseSpace #DynamicalSystems #NonlinearDynamics #HamiltonianMechanics #Mathematics
0:30

Phase Space Is the Real Stage of Dynamics. So, Stop Watching the Object and Watch the State. Ordinary Space tells you where something is. Phase Space tells you what state it is in. Position alone is not enough because you also need the variable that tells you where the system is trying to go. In the animation, the left panel shows the particle moving in Ordinary Space, while the right panel shows the same system as a moving point in Phase Space. For one degree of freedom, the state is (x, p) and as time evolves, that state traces a trajectory t ↦ (x(t), p(t)) Instead of thinking of a differential equation as just a formula, Phase Space lets you see it as a flow on the space of states. For this lecture we use ẋ = p ṗ = x − x³ with Hamiltonian H(x,p) = 0.5 p² + 0.25 x⁴ − 0.5 x² #PhaseSpace #DynamicalSystems #NonlinearDynamics #HamiltonianMechanics #Mathematics

Mathelirium

30,457 次观看 • 5 个月前

Sharing our computer vision system design for TRON: Ares. We approached these shots from the perspective of the machine. The frame becomes a field of observation. Every pixel is potential information waiting to be interpreted. The process begins by squarepacking the live action plates, dividing the image into a computational lattice. Once the grid exists, the system begins to read. Targets emerge. Motion vectors form. Signals ripple through layers of analysis. Inside these overlays lives the source code of the system itself. Streams of logic, fragments of instruction, the internal language of the machine. At times the imagery dissolves directly into that code, as if the world itself is being rewritten from within. Visual information collapses into structure, then reconstructs again as data. Scanning pulses move across the frame. Timers react. Coordinates lock. Each layer is part of a larger ecosystem of perception, constantly processing, evaluating, and iterating. The goal was maximum detail and living systems. Interfaces that breathe, think, and evolve in real time.
1:44

Sharing our computer vision system design for TRON: Ares. We approached these shots from the perspective of the machine. The frame becomes a field of observation. Every pixel is potential information waiting to be interpreted. The process begins by squarepacking the live action plates, dividing the image into a computational lattice. Once the grid exists, the system begins to read. Targets emerge. Motion vectors form. Signals ripple through layers of analysis. Inside these overlays lives the source code of the system itself. Streams of logic, fragments of instruction, the internal language of the machine. At times the imagery dissolves directly into that code, as if the world itself is being rewritten from within. Visual information collapses into structure, then reconstructs again as data. Scanning pulses move across the frame. Timers react. Coordinates lock. Each layer is part of a larger ecosystem of perception, constantly processing, evaluating, and iterating. The goal was maximum detail and living systems. Interfaces that breathe, think, and evolve in real time.

GMUNK

37,625 次观看 • 5 个月前

An intense pulse of laser light enters a plasma and what follows is almost unbelievable. The laser pushes plasma electron aside, carving out a charged cavity. As the plasma rushes back, it creates an electric wake that can trap and accelerate another bunch of electrons. This is known as Laser Wakefield Acceleration (LWFA) and is being explored for future accelerator Physics. For this animation, we used a reduced particle-in-cell (PIC) method, coupling particle motion to the self-consistent plasma field on a computational mesh.
0:40

An intense pulse of laser light enters a plasma and what follows is almost unbelievable. The laser pushes plasma electron aside, carving out a charged cavity. As the plasma rushes back, it creates an electric wake that can trap and accelerate another bunch of electrons. This is known as Laser Wakefield Acceleration (LWFA) and is being explored for future accelerator Physics. For this animation, we used a reduced particle-in-cell (PIC) method, coupling particle motion to the self-consistent plasma field on a computational mesh.

Mathelirium

35,400 次观看 • 8 天前

When Light Becomes Heavy Enough to Trap Itself Can light collapse into a black hole? In General Relativity, light is not weightless in the geometric sense. It has energy, it carries momentum, and energy curves Spacetime. A Vaidya-type collapse describes a mass that grows because radiation is falling inward. The mathematics is the same brutal idea behind Einstein’s equation Gᵤᵥ = 8πTᵤᵥ If the stress-energy Tᵤᵥ is made from radiation, then light itself becomes a source of curvature. As more radiation falls inward, the mass aspect grows, the Spacetime fabric tightens, and a clean black horizon appears where escaping paths begin to fail. #GeneralRelativity #EinsteinEquations #BlackHole #Spacetime #Astrophysics #TheoreticalPhysics #Light #Mathematics #Science
0:55

When Light Becomes Heavy Enough to Trap Itself Can light collapse into a black hole? In General Relativity, light is not weightless in the geometric sense. It has energy, it carries momentum, and energy curves Spacetime. A Vaidya-type collapse describes a mass that grows because radiation is falling inward. The mathematics is the same brutal idea behind Einstein’s equation Gᵤᵥ = 8πTᵤᵥ If the stress-energy Tᵤᵥ is made from radiation, then light itself becomes a source of curvature. As more radiation falls inward, the mass aspect grows, the Spacetime fabric tightens, and a clean black horizon appears where escaping paths begin to fail. #GeneralRelativity #EinsteinEquations #BlackHole #Spacetime #Astrophysics #TheoreticalPhysics #Light #Mathematics #Science

Mathelirium

27,760 次观看 • 2 个月前

Ever feel like you've worked hard, learned a lot, yet the leap to innovative originality still feels out of reach? Pure Mathematics is the solution! Pure Mathematics feels optional until you reach areas where the central objects are mathematical structures and not just equations. In Physics, gravity does this because General Relativity is a theory of Spacetime itself...a Topological Manifold. In Engineering it shows up in Optimization when you need to know what assumptions make a method stable, fast or even correct. In Computer Science, it shows up when you stop treating Algorithms as black boxes and start asking WHY they behave the way they do, especially when they surprise you.
2:46

Ever feel like you've worked hard, learned a lot, yet the leap to innovative originality still feels out of reach? Pure Mathematics is the solution! Pure Mathematics feels optional until you reach areas where the central objects are mathematical structures and not just equations. In Physics, gravity does this because General Relativity is a theory of Spacetime itself...a Topological Manifold. In Engineering it shows up in Optimization when you need to know what assumptions make a method stable, fast or even correct. In Computer Science, it shows up when you stop treating Algorithms as black boxes and start asking WHY they behave the way they do, especially when they surprise you.

Mathelirium

19,011 次观看 • 6 个月前

Calculus of Variations is what happens when you stop optimizing values and start optimizing geometries. The unknown isn’t a single x...it’s a whole curve y(x). And the thing you’re minimizing usually isn’t a formula you can eyeball...it’s an integral that judges the entire shape. For our first lecture, we look at the famous Brachistochrone problem. Fix two points, switch on gravity, and ask a question that sounds too simple...which track gets a bead from A to B in the least time? Your intuition will betray you on the first try. It’s not the straight line. It’s not the drop hard then cruise sketch either. The winner is a cycloid...the curve traced by a point on a rolling circle. In the animation, the track is the moving character. We start with an imperfect curve, run gradient descent in curve-space, and watch the geometry reshape frame by frame as T[y] collapses until it locks into the brachistochrone. Pls see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics
0:29

Calculus of Variations is what happens when you stop optimizing values and start optimizing geometries. The unknown isn’t a single x...it’s a whole curve y(x). And the thing you’re minimizing usually isn’t a formula you can eyeball...it’s an integral that judges the entire shape. For our first lecture, we look at the famous Brachistochrone problem. Fix two points, switch on gravity, and ask a question that sounds too simple...which track gets a bead from A to B in the least time? Your intuition will betray you on the first try. It’s not the straight line. It’s not the drop hard then cruise sketch either. The winner is a cycloid...the curve traced by a point on a rolling circle. In the animation, the track is the moving character. We start with an imperfect curve, run gradient descent in curve-space, and watch the geometry reshape frame by frame as T[y] collapses until it locks into the brachistochrone. Pls see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

Mathelirium

106,981 次观看 • 8 个月前

A White Hole is a Black Hole Running Backward A Black Hole is famous because it lets things fall in, but never lets them come back out. A White Hole is the time-reversed version of that idea. In the full Schwarzschild solution of General Relativity, the Black-Hole region and the White-Hole region appear as two different causal parts of the same exact geometry. Outside the horizon, the metric is the usual Schwarzschild metric ds² = -(1 - 2M/r)dt² + (1 - 2M/r)⁻¹dr² + r²dΩ². The horizon sits at rₛ = 2M, using G = c = 1. For an ordinary Black Hope, future-directed paths can cross this surface inward. Once they do, they cannot return to the outside universe. For a White Hole, the arrow is reversed and particles and light can come out from the horizon, but outside observers cannot enter it. No one has observed a physical White Hole. It may be an ideal solution rather than an object that nature actually forms. But as Mathematics, it is one of the strangest lessons of General Relativity: The equations allow a horizon that throws the universe outward. #WhiteHoles #GeneralRelativity #Schwarzschild #Spacetime #BlackHoles #Cosmology #Physics #Mathematics #Astrophysics #Astronomy
0:56

A White Hole is a Black Hole Running Backward A Black Hole is famous because it lets things fall in, but never lets them come back out. A White Hole is the time-reversed version of that idea. In the full Schwarzschild solution of General Relativity, the Black-Hole region and the White-Hole region appear as two different causal parts of the same exact geometry. Outside the horizon, the metric is the usual Schwarzschild metric ds² = -(1 - 2M/r)dt² + (1 - 2M/r)⁻¹dr² + r²dΩ². The horizon sits at rₛ = 2M, using G = c = 1. For an ordinary Black Hope, future-directed paths can cross this surface inward. Once they do, they cannot return to the outside universe. For a White Hole, the arrow is reversed and particles and light can come out from the horizon, but outside observers cannot enter it. No one has observed a physical White Hole. It may be an ideal solution rather than an object that nature actually forms. But as Mathematics, it is one of the strangest lessons of General Relativity: The equations allow a horizon that throws the universe outward. #WhiteHoles #GeneralRelativity #Schwarzschild #Spacetime #BlackHoles #Cosmology #Physics #Mathematics #Astrophysics #Astronomy

Mathelirium

44,259 次观看 • 2 个月前

Why the character movement in my custom game engine felt janky and how I fixed it. In a game engine, most often, a character moves using the physics engine. Meaning, the player is not just a coordinate in space but a physical body. It has velocity, it handles collisions, and it interacts with the world. Now, as you might know, physics engines need stability. If you run them at variable framerates, things start breaking. Objects phase through walls or fly off into space because the math becomes unpredictable. This is why most game engines lock their physics loop to a 60Hz fixed rate. But here’s the problem: If you have a high-end system, you don't want to limit it at 60 FPS. That's a waste of good hardware. Now, that said, if the GPU is rendering at 144 FPS but the player's position (physics driven) only updates 60 times a second, it creates a micro-stutter that ruins the "smooth" feel of the game. A good way to fix this is to treat the character as two separate things: 1. The Physics Body (Invisible part): This is the "real" character. It lives in the 60Hz physics world, it moves the player and handles collisions. 2. The Visual Model and Camera (Visible part): This is what the player actually sees. It doesn't care about collisions, its only job is to look nice and smooth at whatever framerate the GPU is pushing. Once you have this separation, you can use interpolation to keep them in sync. Every time the physics clock ticks, you save the previous position of the invisible body before moving it to the new one. Between those ticks, calculate how far we are between the last physics update and the next one. By using this to drive the visible parts of the game, the stutters disappear. The physics loop stays fixed behind the scenes, while the visuals slide smoothly between the snapshots. Example: - Right after a tick: blend_weight= 0.0 (The visual model stays at the old physics position). - Halfway to the next: blend_weight= 0.5 (The visual model slides to the middle point). - Just before the next: blend_weight= 0.9 (The visual model is almost at the new physics position). Pro-Tip A critical mistake I made initially, and one many devs make, is parenting the camera and visible parts directly to the player body. If you do this, the camera inherits the discrete 60Hz physics movement by default. In that setup, interpolation won't work because the camera is "stuck" to the physics clock. For this fix to work you must decouple the camera and visuals from the body and move them separately. Player movement processing in Detis Engine: - fixed_process: Physics runs at 60Hz. Handles collisions and raw movement. - process: Variable rate. Mainly used for player input caching in the player case. - late_process: Variable rate. Handles interpolated camera movement after physics and everything else is done being processed. - render. Submits the final interpolated transforms to the GPU. The test environment in the video is running on an old 2070-based laptop. Hopefully the video compression won't introduce any stutter... I’m sharing this in hopes it helps a fellow dev. Cheers.
0:23

Why the character movement in my custom game engine felt janky and how I fixed it. In a game engine, most often, a character moves using the physics engine. Meaning, the player is not just a coordinate in space but a physical body. It has velocity, it handles collisions, and it interacts with the world. Now, as you might know, physics engines need stability. If you run them at variable framerates, things start breaking. Objects phase through walls or fly off into space because the math becomes unpredictable. This is why most game engines lock their physics loop to a 60Hz fixed rate. But here’s the problem: If you have a high-end system, you don't want to limit it at 60 FPS. That's a waste of good hardware. Now, that said, if the GPU is rendering at 144 FPS but the player's position (physics driven) only updates 60 times a second, it creates a micro-stutter that ruins the "smooth" feel of the game. A good way to fix this is to treat the character as two separate things: 1. The Physics Body (Invisible part): This is the "real" character. It lives in the 60Hz physics world, it moves the player and handles collisions. 2. The Visual Model and Camera (Visible part): This is what the player actually sees. It doesn't care about collisions, its only job is to look nice and smooth at whatever framerate the GPU is pushing. Once you have this separation, you can use interpolation to keep them in sync. Every time the physics clock ticks, you save the previous position of the invisible body before moving it to the new one. Between those ticks, calculate how far we are between the last physics update and the next one. By using this to drive the visible parts of the game, the stutters disappear. The physics loop stays fixed behind the scenes, while the visuals slide smoothly between the snapshots. Example: - Right after a tick: blend_weight= 0.0 (The visual model stays at the old physics position). - Halfway to the next: blend_weight= 0.5 (The visual model slides to the middle point). - Just before the next: blend_weight= 0.9 (The visual model is almost at the new physics position). Pro-Tip A critical mistake I made initially, and one many devs make, is parenting the camera and visible parts directly to the player body. If you do this, the camera inherits the discrete 60Hz physics movement by default. In that setup, interpolation won't work because the camera is "stuck" to the physics clock. For this fix to work you must decouple the camera and visuals from the body and move them separately. Player movement processing in Detis Engine: - fixed_process: Physics runs at 60Hz. Handles collisions and raw movement. - process: Variable rate. Mainly used for player input caching in the player case. - late_process: Variable rate. Handles interpolated camera movement after physics and everything else is done being processed. - render. Submits the final interpolated transforms to the GPU. The test environment in the video is running on an old 2070-based laptop. Hopefully the video compression won't introduce any stutter... I’m sharing this in hopes it helps a fellow dev. Cheers.

Ioannis Koukourakis

48,703 次观看 • 8 个月前

Have You Ever Heard of Molecular Communication Systems? Instead of using radio waves or light, molecular communications send information carefully through released chemical particles. A transmitter emits molecules into a medium, the channel reshapes that signal through diffusion, flow, and randomness. The receiver reads the message from the molecules that arrive and bind. It is communication theory at microscopic scale, where physics, probability and biology all become part of the channel. Some applications you may know: Targeted drug delivery inside the body, microscopic health monitoring with nanosensors, and lab-on-a-chip.
0:48

Have You Ever Heard of Molecular Communication Systems? Instead of using radio waves or light, molecular communications send information carefully through released chemical particles. A transmitter emits molecules into a medium, the channel reshapes that signal through diffusion, flow, and randomness. The receiver reads the message from the molecules that arrive and bind. It is communication theory at microscopic scale, where physics, probability and biology all become part of the channel. Some applications you may know: Targeted drug delivery inside the body, microscopic health monitoring with nanosensors, and lab-on-a-chip.

Mathelirium

19,452 次观看 • 5 个月前