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Forget the “trampoline” analogy; it’s a 2D lie. Gravity isn’t a pull. It’s the metric deformation of a 4D manifold. Every mass is just a localized curvature gradient forcing the geodesics of spacetime to converge. You’re not “falling.” You’re simply following the path of least resistance through a warped... show more

Cosmos Archive

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18,117 次观看 • 4 个月前 •via X (Twitter)

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Ever Heard of a Metric in Differential Geometry? How About a Geodesic? These two ideas are central to how Mathematics and Physics describe Spacetime. A metric is how a surface measures distance and angle. A geodesic is the path that counts as "straight" after that measuring rule is chosen. Once the metric changes from point to point, straightness is no longer something you judge by eye. On a curved surface, the shortest paths are geodesics. They are chosen by the metric. Take a surface written as r(x,y) = (x, y, f(x,y)) Its metric is gᵢⱼ = ∂ᵢr · ∂ⱼr A geodesic q(t) = (x(t), y(t)) obeys q̈ᵏ + Γᵏᵢⱼ q̇ᶦq̇ʲ = 0 where Γᵏᵢⱼ are the Christoffel symbols of the surface metric. Launch many almost-parallel paths. At the start, they look like a clean beam until curvature takes over. Some paths focus, others separate and some slide around ridges. The surface is essentially the rulebook for motion. The shortest path is local. The geometry remembers everything. #DifferentialGeometry #Geodesics #RiemannianGeometry #MathematicalPhysics #Curvature #TensorCalculus #AppliedMathematics #Geometry #ScienceAnimation

Ever Heard of a Metric in Differential Geometry? How About a Geodesic? These two ideas are central to how Mathematics and Physics describe Spacetime. A metric is how a surface measures distance and angle. A geodesic is the path that counts as "straight" after that measuring rule is chosen. Once the metric changes from point to point, straightness is no longer something you judge by eye. On a curved surface, the shortest paths are geodesics. They are chosen by the metric. Take a surface written as r(x,y) = (x, y, f(x,y)) Its metric is gᵢⱼ = ∂ᵢr · ∂ⱼr A geodesic q(t) = (x(t), y(t)) obeys q̈ᵏ + Γᵏᵢⱼ q̇ᶦq̇ʲ = 0 where Γᵏᵢⱼ are the Christoffel symbols of the surface metric. Launch many almost-parallel paths. At the start, they look like a clean beam until curvature takes over. Some paths focus, others separate and some slide around ridges. The surface is essentially the rulebook for motion. The shortest path is local. The geometry remembers everything. #DifferentialGeometry #Geodesics #RiemannianGeometry #MathematicalPhysics #Curvature #TensorCalculus #AppliedMathematics #Geometry #ScienceAnimation

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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.

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.

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🌀🌌 What if gravity isn’t really a force? Einstein’s general relativity gives us a radically different picture: mass and energy curve the fabric of spacetime, and objects follow paths shaped by that geometry. Even light bends when passing through strongly curved spacetime. In this view, planets aren’t simply being “pulled” by the Sun they’re moving through curved spacetime created by its mass. Gravity may be less like an invisible force… and more like the geometry of the universe itself. 🕳️✨

🌀🌌 What if gravity isn’t really a force? Einstein’s general relativity gives us a radically different picture: mass and energy curve the fabric of spacetime, and objects follow paths shaped by that geometry. Even light bends when passing through strongly curved spacetime. In this view, planets aren’t simply being “pulled” by the Sun they’re moving through curved spacetime created by its mass. Gravity may be less like an invisible force… and more like the geometry of the universe itself. 🕳️✨

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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

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

What you’re seeing is a Riemannian Manifold—the mathematical "skeleton" of our universe. While most see a grid, physicists see the secret language of gravity and curved space-time. The transformation you see at 0:32 is a total "glitch" in the logic of a flat world, but it’s exactly how the fabric of existence behaves when it meets mass. In our daily lives, we assume a straight line is the shortest distance between two points, but in a Riemannian world, "straight" is an illusion. This visual captures the moment where geometry transcends the 3rd dimension, twisting and folding back on itself in a way that would make Euclidean logic shatter. It is the same mind-bending curvature that governs everything from the orbit of planets to the way light bends around a black hole.

What you’re seeing is a Riemannian Manifold—the mathematical "skeleton" of our universe. While most see a grid, physicists see the secret language of gravity and curved space-time. The transformation you see at 0:32 is a total "glitch" in the logic of a flat world, but it’s exactly how the fabric of existence behaves when it meets mass. In our daily lives, we assume a straight line is the shortest distance between two points, but in a Riemannian world, "straight" is an illusion. This visual captures the moment where geometry transcends the 3rd dimension, twisting and folding back on itself in a way that would make Euclidean logic shatter. It is the same mind-bending curvature that governs everything from the orbit of planets to the way light bends around a black hole.

Mathematica

28,564 次观看 • 4 个月前

If you’re an engineer, physicist, or CS person and you’ve been telling yourself that Pure Mathematics is optional, and you’re anywhere between an ambitious undergrad and a beginning PhD, gravity is usually where that story ends. Not because mathematicians are trying to show off, but because the basic object in the theory is Spacetime, and Spacetime is already a pure mathematical structure. It’s a Manifold with Topology built in. Sure you can get pretty far by memorising formulas, but at some point you realise you’re no longer reading the theory, you’re just reciting it. In 2015, during the 100th anniversary of general relativity and the International Year of Light, the Scientific Organizing Committee released a central set of 24 lectures by Frederic P. Schuller. The series is titled: A thorough introduction to the theory of general relativity. It builds the subject carefully from first principles, step by step, across 24 self-contained lectures. #GeneralRelativity #Spacetime #MathematicalPhysics #DifferentialGeometry #PhysicsEducation #Relativity

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Kyle Kulinski: “It’s now the least cool thing in the world to be a Republican. It’s not edgy, it’s not interesting, it’s not contrarian, it’s not fun. You are a fucking loser asshole who is sadistic. To be in MAGA or even a Republican, you’re just a sadist. You’re basically advertising to the world: I have a low IQ, I’m unintelligent, I’m a dipshit”

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Marco Foster

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Parliament has just decriminalised abortion up to the point of birth. A baby at 9 months is not a cluster of cells. It’s a human life. We now live in a country where that life can be legally ended with no consequences. This isn’t progress. It’s the legalisation of murder. Liberalism has gone mad.

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Ben Habib

114,560 次观看 • 1 年前

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Welcome to MycoDAO, a groundbreaking initiative where science, technology, and the power of the people converge to harness the untapped potential of #mushrooms. #MycoDAO isn’t just a DAO; it’s a revolution, democratizing fungal research and redefining how we tackle global challenges.

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Mathematics is often gatekept as a series of "spells" to be memorized, but Terence Tao reminds us that the true power lies in the process, not just the proof. If you’re only following the recipe, you aren’t doing math—you’re just practicing alchemy. Real math is the art of deconstruction; it’s the systematic breakdown of chaos into digestible, logical structures. Stop fearing the deviation. The "sorcery" ends where understanding begins.

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22,574 次观看 • 4 个月前

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What’s infuriating isn’t the theft—it’s the total absence of shame. Not a flicker of guilt or a trace of reflection. Just the arrogance of someone who feels entitled to lie, cheat, and steal—like a moral Groundhog Day with no hope of redemption.

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Jayant Bhandari

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Stephen A. to the WNBA: “It’s too damn late” “If your rules were more finite and clear, you wouldn’t have to have a meeting of team presidents and general managers. You’re the commissioner. You should already know. We literally are living in a society where there has to be a debate involving a collective bargaining agreement that explicitly states that the league is for women. If you’re not a woman, you’re not eligible. It’s simple and plain. What’s the complication? The complication is that our society has devolved to a point where we’re not clear what defines a woman… What about the WNBA? We will not be used as political pawns. When you gonna wake the hell up?”

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126,192 次观看 • 17 天前