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Archive for the ‘mathematics’ category

Apr 25, 2024

The universe’s repeated rebirth and dying, controversial claim by Nobel Prize Winner

Posted by in categories: cosmology, mathematics, physics

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.

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Apr 25, 2024

What Was There Before the Big Bang? 3 Good Hypotheses!

Posted by in categories: cosmology, mathematics, security

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Apr 25, 2024

Institute for Extinction Risk Shuts Down: What We Know

Posted by in categories: computing, existential risks, mathematics

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.

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Apr 22, 2024

Mathematicians Marvel at ‘Crazy’ Cuts Through Four Dimensions

Posted by in category: mathematics

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.

Apr 19, 2024

Selective language modeling: New method allows for better models with less data

Posted by in categories: mathematics, transportation

👉 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.

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Apr 19, 2024

Research reveals a surprising topological reversal in quantum systems

Posted by in categories: mathematics, quantum physics

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.

Apr 19, 2024

Chaos: The real problem with quantum mechanics

Posted by in categories: mathematics, quantum physics, space

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.

Apr 19, 2024

How Chaos Control Is Changing The World

Posted by in categories: mathematics, quantum physics, robotics/AI

Try out my quantum mechanics course (and many others on math and science) on Brilliant using the link https://brilliant.org/sabine. You can get started for free, and the first 200 will get 20% off the annual premium subscription.

Physicists have known that it’s possible to control chaotic systems without just making them even more chaotic since the 1990s. But in the past 10 years this field has really exploded thanks to machine learning.

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Apr 18, 2024

Never-Before-Seen Quantum Hybrid State Discovered on Arsenic Surface

Posted by in categories: mathematics, particle physics, quantum physics

Physicists have just found something no one expected, lurking on the surface of an arsenic crystal.

While undertaking a study of quantum topology – the wave-like behavior of particles combined with the mathematics of geometry – a team found a strange hybrid of two quantum states, each describing a different means of current.

“This finding was completely unexpected,” says physicist M. Zahid Hasan of Princeton University. “Nobody predicted it in theory before its observation.”

Apr 17, 2024

The Closest We Have to a Theory of Everything

Posted by in categories: mathematics, quantum physics

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. In the diagram at 4 minutes 30 seconds, the labels for h_1 and h_2 are mixed up. Sorry about that! Subscribe to my weekly science newsletter: https://sabinehossenfelder.com/ Everything I am talking about here is standard material of undergrad physics textbooks. My personal favorite is good old Goldstein https://en.wikipedia.org/wiki/Classic… On variational principles more specifically I quite like this textbook: https://link.springer.com/book/10.100… You can support me on Patreon: / sabine 0:00 Intro 0:45 Optimization 1:35 Shortest Path 3:20 Least Time 5:36 Least Action 10:27 Quantum Mechanics 11:53 Sponsor Message.

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