“We are planning to build our own model, made in Germany!”
- but the data you will be training it on, where most of it is hosted?
“Ohhhhh, well, Ich habe nicht darüber nachgedacht.”
This is our quantum memory under construction: a rack of steel and about a hundred optical fibres (100km of total length).
When fully populated, we'll store 1000s of photonic qubits in each of these. These memories, built from ultra-stable optical fibre and ultra-low-loss large optical switches, reduce the overall footprint of our useful quantum computer by 1000x.
On this day June 10 in 1854, Bernhard Riemann delivered his historic habilitation lecture at the University of Göttingen:
“On the Hypotheses which lie at the Foundations of Geometry.”
In one lecture, he introduced Riemannian geometry, curved manifolds, and the foundations of modern differential geometry; ideas that would later shape Einstein’s theory of relativity.
Gauss (one of his examiners) selected this topic from three options Riemann proposed. The lecture introduced Riemannian geometry, including the concept of n-dimensional manifolds and curvature (now central to the Riemann curvature tensor).
It laid foundational ideas for non-Euclidean geometries and curved space, which later became essential to Einstein's general theory of relativity (about 60 years later).
The work was not published until 1868 (after Riemann's death), but it is considered one of the most influential papers in the history of mathematics.
Hardcover color versions of my books Linear Algebra Done Right and Measure, Integration & Real Analysis are on sale for $42 each (30% off) at
https://t.co/cEObSlJtdj
and
https://t.co/2Xf6PGH5NR.
Use coupon code SNSUM30 at checkout to get this price. Sale price valid until 27 June 2026.
Hold my hand?
In this Hubble view, two galaxies known collectively as NGC 5331 are seen just beginning to "link" their spiral arms.
This galactic interaction is unfolding about 450 million light-years away, in the constellation Virgo.
Read more: https://t.co/V0qJECHPZ7
The bundle projection π₁ from the total space (the upper grid surface) onto the base space P₂ (the lower disk with polar coordinates).
The vertical line illustrates how each fiber in the total space maps straight down to its image in the base. This setup captures the twisting and non-orientable geometry typical of bundles over the real projective plane.
In practice, fiber bundle models like this help physicists describe gauge fields in quantum field theory and enable engineers to simulate complex geometries in robotics and computer vision.
@paulg If e^x represents model’s revenue then…, but if that’s true and everyone will use it, big AI’s revenue will drop by 50% which will force them to charge more… (since that will cool the heat currently allows them to lose that much).
Wow, what an exciting guest list for the upcoming season of @QuantaMagazine’s The Joy of Why podcast. Can’t wait to learn from @stevenstrogatz and @JannaLevin’s smart and engaging interviews. https://t.co/rlviH2p9zK
@QualiaQuanta Our perception of aesthetics is most likely wrong as it relies on a collapsed view into 3D. We develop aesthetics around shadows and reflections.
This Maqam Awshar, is barely mentioned in the Classical Arabic music literature, today I learn (from my Iranian-Canadian teacher) that is it almost identical to the Persian Segah Maqam, whilst transitioning to Bayati and Hijaz. Masterpiece.
https://t.co/MlDqgGAsad
The way algebra & geometry are interwoven at n dimensions is mind blowing. Adding on top of that Riesz representation and showing how to cook pure calculus in a linear kitchen (projection) is shocking.
Studying section 6C in Linear Algebra Done Right by Sheldon Axler gives me pleasure, joy and fascination at a psychedelic experience level. That’s not a joke!
I would’ve never imagine mathematics can elevates one’s spirit to those heights.
Thank you @stevenstrogatz 🙏
“Made in China” is becoming “made by China”—all over the world. Faced with higher Western tariffs and weak demand at home, many Chinese factories are moving abroad, making everything from appliances to cars everywhere from North America to Eastern Europe. https://t.co/CIxfnrZ4Ub
The feed at @X became such a mess in the last day or two that I suspect @nikitabier is on vacation and there is not one to watch the kids as they’re playing with the feed’s knobs.