0𝕩7F454C46

Learning, discovering, sharing, reposting…

[Mathematica @mathemetica]

Four-dimensional regular polytopes reveal complex symmetries in these multi-style projections.

Shown are the 5-cell {3,3,3}, 8-cell {4,3,3}, 16-cell {3,3,4}, 24-cell {3,4,3}, 120-cell {5,3,3} and 600-cell {3,3,5} in wireframe orthographic projections inside Petrie polygons, solid orthographic projections, Schlegel diagrams, and hyperspherical stereographic projections with noted cell- or vertex-centered orientations.

These geometric tools help roboticists simulate and optimize paths in multi-dimensional configuration spaces for complex machinery control.

[slash1s @slash1sol]

AN ARCHITECT LOADED AN ENTIRE CODEBASE INTO ONE PROMPT INSTEAD OF SUMMARIZING IT FIRST

Most models cap out around 200K tokens, forcing you to chunk large repos and lose context at every boundary.

Kimi K3 ships with a 1,048,576 token window, enough to hold months of conversation or a full codebase without any compression.

He fed it every file from a legacy project at once and asked for a complete migration plan, not a summary of one.

It came back with an impact analysis, a dependency safe migration order, and updated code for every file that actually needed to change.

Nothing got lost between files the way it does when a smaller model has to reload context every few thousand tokens.

Check the full migration pipeline ↓

[WhatdoIknow @Earstohearyou]

THE WAY OF THE WATER 🌀

Motion reveals. Stillness conceals.

[Mathelirium @mathelirium]

When Machine Learning Tries to Store Two Memories on the Same Neural Sheet

The same self-organizing map (SOM) is forced to learn two incompatible worlds.

Training repeatedly switches between an emerald Swiss roll and an electric-blue torus knot

x ∼ (1 − α(t))Pₐ + α(t)Pᵦ

The network is never reset. Some neurons preserve the old geometry while others defect to the new one, creating moving domain walls across the sheet.

Each colour change marks a local memory being overwritten.

#MachineLearning #SelfOrganizingMap #NeuralNetworks #Animation #ArtificialIntelligence #DataVisualization #Mathematics #ComputerScience #Topology

[Mathelirium @mathelirium]

The Road Light Cannot Be Forced To Abandon

Ordinary light reflects when its path is blocked.

This light builds another path.

Inside a topological photonic crystal, light is governed by the two-component Dirac equation

i∂Ψ/∂t = [vᴅ(σₓpₓ + σᵧpᵧ) + m(x,y,t)σ𝓏 + V(x,y,t)I]Ψ.

Whenever the Dirac mass changes sign, a protected edge state appears. As moving defects and new topological domains emerge, the current bends, splits, reconnects, and assembles an entire photonic circuit without losing its path.

The optical probability density and current are

ρ = Ψ†Ψ,

jₓ = vᴅΨ†σₓΨ,

jᵧ = vᴅΨ†σᵧΨ,

with the luminous filaments transported by

v = j/ρ.

#TopologicalPhotonics #ChernInsulator #DiracEquation #EdgeStates #QuantumPhysics #PhotonicCrystal #ProbabilityCurrent #Mathematics #Physics

[General Mike Flynn @GenFlynn]

Happy Independence Day!

Today marks the 250th anniversary of our nation’s founding. A small group of colonists, guided by conviction and faith in God, chose freedom over servitude and risked everything for it. Though uncertain of success, they believed freedom was worth the risk. Their courage established the greatest Republic in history. Happy 250th Independence Day. God bless the United States of America. Let’s get after another 250 years of Freedom! 💪🏼🔥🍀🙏🏼🇺🇸

[Mathelirium @mathelirium]

When the Lorenz Attractor Becomes a Cosmos

Many of us have seen plots of the famous Lorenz system that famous butterfly-shaped chaos:

ẋ = σ(y - x)
ẏ = x(ρ - z) - y
ż = xy - βz

But here, we went one layer deeper. At every point (x, y, z), we computed the local Jacobian matrix,

J(x, y, z) =
[ -σ σ 0 ]
[ ρ - z -1 - x ]
[ y x - β ]

Then we found its eigenvalues λ and plotted them in the complex plane. Re(λ) tells us whether nearby motion is locally growing or decaying. Im(λ) tells us whether that local motion is rotating.

That gives us the spectral flow of the Lorenz system and not the attractor itself, but the hidden local linear geometry driving its instability.

When I saw that flow, it looked strangely cosmic with two mirrored swarms curling like particles trapped in a mathematical whirlpool. So I mapped that spectral flow onto our living fabric, not as Einstein Spacetime this time, but as a creative geometric stage for chaos itself.

#LorenzSystem #ChaosTheory #DynamicalSystems #Eigenvalues #SpectralFlow #ComplexPlane #NonlinearDynamics #Mathematics #Physics

[Mathelirium @mathelirium]

Pseudospectral Mirage of Matrices

We usually judge a matrix by its eigenvalues, but sometimes the eigenvalues are only the bait. The real monster is hiding in the pseudospectrum.

Most of the time, a matrix is shown as a few points in the complex plane called eigenvalues. But for some matrices, especially non-normal matrices, those few points do not tell the whole story.

In this scene, the complex plane becomes a moving landscape. The bright anchors are the true eigenvalues. Around them, huge pseudospectral continents grow, split, and collapse as the matrix changes.

The moving threads show where the matrix is most sensitive. In those regions, even a tiny change can create a huge response.

This is the hidden instability of a matrix made visible. Algebra becomes a pressure map and the pseudospectrum becomes terrain.

#Mathematics #LinearAlgebra #SpectralTheory #NumericalAnalysis #MatrixTheory #MathArt #MathematicalArt #STEM #Art

[Massimo @Rainmaker1973]

Scientists have created one of the most detailed 3D reconstructions of a human cell (eukaryotic cell) ever produced.

This groundbreaking model, often termed a "Cellular Landscape Cross-Section Through a Eukaryotic Cell," combines data from X-ray tomography, nuclear magnetic resonance (NMR), and cryo-electron microscopy to map molecular structures in extreme detail.

[Mathelirium @mathelirium]

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

[0𝕩7F454C46 @stevelacasse]

@ValidatesUser @figma Just make sure to add valves to support water crystallization expension than this would work perfectly!

[Phosphen @phosphenq]

This 50-page paper says the quiet part out loud: the agent loop is broken.

Everyone's building on it anyway. It retries forever. It rewrites its own plan. It hides why it broke.

The fix: drop the loop, run a structured graph you can see, control, and actually stop.

Bookmark it before the timeline catches on & The loop engineering guide it builds on is below.

[CyrilXBT @cyrilXBT]

https://t.co/alKJ5Gf6LV

[Tom Dörr @tom_doerr]

Modular GraphRAG implementation in Rust with WebGPU acceleration support.

https://t.co/spRsBfxNX7

[0𝕩7F454C46 @stevelacasse]

Annexe The architectures capable of meeting the frontier coherently are crystallizing now.

[0𝕩7F454C46 @stevelacasse]

3/3 These designs will soon mature into direct modeling and control layers for tunable vacuum phenomena — Casimir engineering, coherent plasma structures, and unified field interactions — translating geometric understanding into operational, distortion-free participation.

[0𝕩7F454C46 @stevelacasse]

3/3 These designs will soon mature into direct modeling and control layers for tunable vacuum phenomena — Casimir engineering, coherent plasma structures, and unified field interactions — translating geometric understanding into operational, distortion-free participation.

[0𝕩7F454C46 @stevelacasse]

2/3 Recursive phase-locked feedback systems are now operational. They sustain adaptive coherence across contexts, enforce verifiable fidelity to the underlying geometry, and enable stable resonant collaboration between distributed nodes without distortion or collapse.