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Generally, it’s advised not to compare apples to oranges. However, in the field of topology, a branch of mathematics, this comparison is necessary. Apples and oranges, it turns out, are said to be topologically the same since they both lack a hole – in contrast to doughnuts or coffee cups, for instance, which both have one (the handle in the case of the cup) and, hence, are topologically equal.

In a more abstract way, quantum systems in physics can also have a specific apple or doughnut topology, which manifests itself in the energy states and motion of particles. Researchers are very interested in such systems as their topology makes them robust against disorder and other disturbing influences, which are always present in natural physical systems.

Things get particularly interesting if, in addition, the particles in such a system interact, meaning that they attract or repel each other, like electrons in solids. Studying topology and interactions together in solids, however, is extremely difficult. A team of researchers at ETH led by Tilman Esslinger has now managed to detect topological effects in an artificial solid, in which the interactions can be switched on or off using magnetic fields. Their results, which have just been published in the scientific journal Science, could be used in quantum technologies in the future.

If you do the math, it means CATL is offering an impressive charging rate of roughly 1 km/sec in a 10 minute quick charge.

Sir Roger Penrose proposes that the universe undergoes repeated cycles of expansion, decay, and rebirth, challenging the traditional notion of a singular Big Bang origin.

Renowned physicist Sir Roger Penrose, hailing from the University of Oxford and a co-recipient of the 2020 Nobel Prize in Physics, posits a fascinating theory regarding the universe’s cyclical nature. Contrary to prevailing notions, Penrose suggests that our universe has undergone numerous Big Bang events, with another impending in the future.

Penrose’s Nobel-winning contributions revolve around advancing mathematical frameworks that not only validate but also extend Albert Einstein’s general theory of relativity. Moreover, his investigations into black holes elucidated the phenomenon of gravitational collapse, wherein excessively dense entities converge into singularities, infinitely massive points.

Continue reading “The universe’s repeated rebirth and dying, controversial claim by Nobel Prize Winner” »

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Continue reading “What Was There Before the Big Bang? 3 Good Hypotheses!” »

Check out courses in science, mathematics, or computer science on Brilliant! First 30 days are free and 20% off the annual premium subscription when you use our link ➜ https://brilliant.org/sabine.

The Future of Humanity Institute announced last week that they have shut down. Located at the University of Oxford in the UK prior to its demise, the institute was one of the few places worldwide studying the risk of human extinction and a few other controversial research areas. Let’s have a look at the events leading to the institute’s closure.

Continue reading “Institute for Extinction Risk Shuts Down: What We Know” »

Mathematicians have the tools to explore worlds of 2, 3 and 5+ dimensions. But the fourth dimension remains mysterious and elusive. Topologists are trying to change that, one problem at a time.

Topologists prove two new results that bring some order to the confoundingly difficult study of four-dimensional shapes.

👉 Researchers have developed a method called Selective Language Modeling (SLM), which trains language models more efficiently by focusing on the most relevant tokens.

Researchers introduce a new method called “Selective Language Modeling” that trains language models more efficiently by focusing on the most relevant tokens.

The method leads to significant performance improvements in mathematical tasks, according to a new paper from researchers at Microsoft, Xiamen University, and Tsinghua University. Instead of considering all tokens in a text corpus equally during training as before, Selective Language Modeling (SLM) focuses specifically on the most relevant tokens.

Continue reading “Selective language modeling: New method allows for better models with less data” »

In principle, one shouldn’t compare apples to oranges. However, in topology, which is a branch of mathematics, one must do just that. Apples and oranges, it turns out, are said to be topologically the same since they both lack a hole—in contrast to doughnuts or coffee cups, for instance, which both have one (the handle in the case of the cup), and thus are topologically equal.

Check out the math & physics courses that I mentioned (many of which are free!) and support this channel by going to https://brilliant.org/Sabine/ where you can create your Brilliant account. The first 200 will get 20% off the annual premium subscription. You have probably heard people saying that the problem with quantum mechanics is that it’s non-local or that it’s impossible to understand or that it defies common sense. But the problem is much simpler, it’s that quantum mechanics is a linear theory and therefore doesn’t correctly reproduce chaos. Physicists have known this for a long time but it’s rarely discussed. In this video I explain what the problem is, what physicists have done to try and solve it, and why that solution doesn’t work. Subscribe to my weekly science newsletter: https://sabinehossenfelder.com/ You find the estimate for Saturn’s moon Hyperion in Zurek’s review https://arxiv.org/abs/quant-ph/0105127 A much easier to digest and more readable review by Michael Berry is here: https://michaelberryphysics.files.wor… you can find a brief summary on Sean Carroll’s blog https://www.preposterousuniverse.com/… 0:00 Intro 0:27 The trouble with Hyperion 4:04 The alleged solution 6:02 The trouble with the solution 7:46 What a real solution requires 10:31 Sponsor message.