Dans le domaine de la data, le prochain grand défi consiste à viser l'expertise, en particulier dans les fondements et les connaissances mathématiques avancées.
On 19th May 2026, Mr. Yawo Edem AKPEMADO, Chargé d’Affaires/Head of Mission, exchanged with Representatives of “Jindal Steel Limited”, at the High Commission of Togo in India, on the opportunities and benefits of partnership with Togo in key sectors, namely mining, energy and railway infrastructure.
3 new models from @xai's Grok creative stack are live on OpenRouter:
• Grok Imagine Image Quality: photoreal image generation and editing
• Grok Imagine Video: short clips from text, image, or reference
• Grok Voice TTS 1.0: 5 voices across 20+ languages
More on each below 🧵
Yann LeCun says that within a year to 18 months, we'll have a general method for training hierarchical world models
These models would learn from video and real-world data, then help plan actions in robotics, healthcare, and other areas
"then scale them toward a universal world model"
The Math Paradox That Will Break Your Brain: Gabriel’s Horn
Imagine a 3D object that stretches on forever, giving it an infinite surface area, yet somehow it only holds a finite amount of space inside.
Sounds completely impossible, right?
Welcome to one of the most famous and mind-bending concepts in geometry!
Here is how you make it: take a curve that steadily slopes downward, getting closer and closer to a flat line without ever actually touching it.
Now, spin that curve around to create a 3D funnel shape. As it stretches out into infinity, the spout gets infinitely thin.
The Painter's Paradox
Because the volume inside is limited, you could theoretically fill the entire horn with a specific, measurable number of paint buckets.
However, because the surface area goes on forever, that exact same amount of paint wouldn't be enough to paint the walls of the horn!
How can you fill a container with paint, but not have enough paint to coat its sides?
It defies all real-world logic!
The Secret Behind the Magic.
The answer lies in how fast the shape shrinks as it stretches out into the distance.
The width of the funnel shrinks so rapidly that the total volume gets capped at a specific maximum amountit gets so impossibly thin, so fast, that it barely adds any new space inside.
However, the outside boundary of that shape doesn't shrink quite fast enough.
If you keep adding up the surface area as the horn stretches into infinity, the total just keeps growing and growing without end.
Math doesn't just describe the universe sometimes, it completely shatters our intuition!