Tensors generalize vectors as lists and matrices as grids into higher-order arrays like 3D cubes.
Comparisons include a vector as a list, a matrix as a grid, and a 3-tensor as a cube, along with the stress tensor σij on a cube featuring arrows for components like σ11 and σ23, the product derivative rule, the Riemann curvature tensor R(u,v)w = ∇u ∇_v w − ∇_v ∇_u w − ∇[u,v]w, quantum superposition 1/√2(|00⟩ + |11⟩), and algebraic operations like the tensor product.
It is used to analyze internal forces and deformations in engineering materials and to describe the geometry of spacetime under gravity in general relativity.
These kings, queens, and jacks were hand-painted in the southern Netherlands in 1475. Today, they're the only complete deck of playing cards surviving from the 15th century.
The hearts, diamonds, spades, and clubs found in today's French-suited decks are absent here. Instead, the four suits are represented by hunting-related gear: hunting horns, dog collars, hound tethers, and nooses used for suspending birds or small game from a belt.
These cards aren't ordinary examples printed on cardboard. Drawn with pen and ink on pasteboard composed of four layers of paper, they're finished with opaque paint, translucent paint layers, and gold and silver leaf.
On the face cards, red ochre, azurite blue, lead-tin yellow, and other medieval pigments were applied with a level of craftsmanship akin to illuminated manuscripts.
There are three known luxury hand-painted European playing card decks surviving from the Late Middle Ages: the Stuttgart Cards, the Ambras Court Hunting Cards, and the Cloisters deck. Among these three, only the Cloisters deck is complete with all 52 cards. The others have been preserved as incomplete sets.
In 1978, the Amsterdam-based antiquarian Harrie Kenter bought these cards for $2,800 at a Paris auction, where they were described in the catalog as an incomplete 16th-century tarot deck.
Kenter suspected that the cards might be older than their catalog description. The watermarks on the paper, the painting style, and the figures' short jackets, hair cropped above the ears, and pointed shoes helped date the deck to the 1470-1480 period.
Five years later, on December 6, 1983, the deck was sold to the Metropolitan Museum of Art for $143,000 through Sotheby’s in London. Today, it's housed in The Met Cloisters collection, in Gallery 13.
Because works on paper are sensitive to light, all 52 cards of the deck generally aren't displayed at the same time. Most of the time, only a small selection is on view to the public.
Introducing Claude Sonnet 5, our most agentic Sonnet yet.
It makes plans, uses tools like browsers and terminals, and runs autonomously at a level that just a few months ago required larger and more expensive models.
Owl of Athena tetradrachm. The word drachma means 'a handful.' Before money was invented, six iron spits were as much as a single hand could hold - and that handful of spits was called a 'drachma.'
Tetradrachms displaying the little owl, Greek letters for Athens, an olive twig, and crescent moon were minted after about 500 BC.
The Crisis in the Humanities Is Not About Money: "Critical theory did not merely politicize scholarship. It made scholarship easier to produce" (anyone could get a dissertation out of showing that some work was really an instrument of oppression). Abraham Wyner cites a phenomenon I've long noticed: for an academic movement to get traction, it has to give grad students & junior scholars something to do. Chomsky dominated linguistics in part because he revised his theory every decade or so, sending linguists scrambling to reanalyze every construction in the new theory's terms. In the 80s and 90s neural networks spawned hundreds of papers called "A Connectionist Model of X," followed by the cognitive neuroscience revolution in which anyone could get a thesis out of sticking people in a magnet while they did some familiar experimental task. https://t.co/gguNcI0DFm
Introducing a limited preview of GPT-5.6 Sol, our next generation frontier model, as well as GPT-5.6 Terra, a balanced model for efficient, everyday work, and GPT-5.6 Luna, a fast and affordable model for high-volume work.
https://t.co/OoM83SyISN
The Rhind Mathematical Papyrus is the oldest manuscript written in algebra and trigonometry, dating back to 3,550 years ago.
It shows that the Egyptians used first-order equations, geometric series and a second-order algebraic equation, related to the Pythagorean theorem a² + b² = c²
It also describes how to obtain an approximation of π accurate to within less than 1% and one of the earliest attempts at squaring the circle.
Mohenjo-Daro, in the Indus Valley, still holds mysteries, but archaeologists got a bit of new illumination studying its massive walls. It was occupied earlier than previously thought, around 2700 B.C.—making it one of the world’s oldest metropolises.
https://t.co/nIo5spTqjg
Google’s Tensor Processing Unit (TPU) uses the systolic array architecture - an idea from 1978 - to accelerate matrix multiplication with far less memory movement. Fun to build a small scale version on an FPGA. Links to original paper and TPU design: