Tech-abstinence is the next big status symbol. Sustained focus without the need to check your phone. Immunity to brainrot. Total detachment from the algorithmic overlords.
Most people are already too far gone.
Hey algorithm, I want to connect with people who love:
📕 Books
📚 Research
🎓 Education
📖 Studying
📝 Scholarship
🔬 Science
💻 Technology
📖 Academia
📊 Analysis
🖋️ Writing
📰 Publications
📓 Journals
NASA just dropped a jaw-dropping animation that squeezes twenty-two confirmed black holes into a single frame, each one lurking inside its own X-ray binary system. These aren’t random monsters; they’re real, catalogued beasts like Cygnus X-1, GRS 1915+105, and V404 Cygni, all scaled to the same size so you can finally compare the cosmic heavyweights side by side. Watch closely and you’ll see the black holes (shown as dark spheres) calmly orbiting their companion stars that glow white-hot from the hellish radiation. The accretion disks blaze in furious orange and yellow, twisted maelstroms of superheated gas spiraling toward oblivion. Every frame is a violent ballet: matter gets ripped from the donor star, forms a glowing ring, then vanishes forever past the event horizon. To make the show visible to human eyes, NASA cranked the orbital speeds up by roughly 22,000 times; what you’re seeing as seconds actually unfolds over weeks, months, or years in real time. Some pairs whirl around each other in just a few hours; others take lazy days to complete a single lap. A few systems flare like paparazzi cameras when the black hole suddenly gorges on extra material. The whole scene feels like a cosmic nightclub where the darkest guests throw the wildest parties. In under a minute, you witness feasts, flares, and gravitational dances that would take lifetimes to observe naturally; proof that even the most patient universe can be edited into pure adrenaline.
100 years ago, in November 1925, Erwin Schrödinger attended a colloquium in Zürich where Louis de Broglie’s bold idea was being discussed: that every moving particle carries a wave-like nature.
After the talk, a colleague made a casual remark if matter behaves like a wave, shouldn’t there be a wave equation for it? For most people, it was a fleeting comment. For Schrödinger, it became an obsession.
By late December, Schrödinger wrote to Wilhelm Wien admitting he was struggling with a new atomic theory, even joking: “If only I knew more mathematics!” Yet he remained optimistic, convinced that if he could solve the problem, “it will be very beautiful.”
He was not the only one wrestling with the new quantum world. Around the same time, the great mathematician David Hilbert remarked, “Physics is much too hard for physicists,” capturing the difficulty of the era.
The breakthrough arrived quickly. On 27 January 1926, Schrödinger submitted the first of four papers titled Quantization as an Eigenvalue Problem. In it, he introduced the wave equation that now bears his name and solved the hydrogen atom with it, offering the first coherent picture of atomic structure.
Meanwhile, Wolfgang Pauli, using the matrix mechanics developed by Werner Heisenberg, Max Born, and Pascual Jordan, had already derived the hydrogen spectrum. Soon, Schrödinger proved that wave mechanics and matrix mechanics were mathematically equivalent two languages describing the same quantum reality.
By mid-1926, Schrödinger had applied wave mechanics to the harmonic oscillator, the diatomic molecule, the Stark effect in hydrogen, and the processes of absorption, emission, and scattering. What began as a struggle became one of the most productive bursts of creativity in the history of physics.
A century later, this moment reminds us of something timeless: great scientific revolutions are built not on certainty, but on persistence and the belief that something beautiful lies beyond the struggle.
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...a simple unsupervised neural model...learn the shape of a two-dimensional dataset arranged in a spiral arm. 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.
#MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML
The geodesic equation describes a particle's motion under the influence of gravity in general relativity. It defines the straightest possible path (a geodesic) in curved spacetime.