Archive for the ‘mathematics’ category: Page 36

Without satellite navigation, rockets can’t navigate to the moon without ground control, which is costly, cumbersome, and requires a lot of math.

In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is “closed”, returning to its starting point. This possibility was first discovered by Willem Jacob van Stockum in 1937[1] and later confirmed by Kurt Gödel in 1949,[2] who discovered a solution to the equations of general relativity (GR) allowing CTCs known as the Gödel metric; and since then other GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes.

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What is the Drake Equation? We are talking about The Odds of ALIEN LIFE.
Is there life out there in the Universe?
How are the chances to find Extraterrestrial life?

Greg Yang is a mathematician and AI researcher at Microsoft Research who for the past several years has done incredibly original theoretical work in the understanding of large artificial neural networks. Greg received his bachelors in mathematics from Harvard University in 2018 and while there won the Hoopes prize for best undergraduate thesis. He also received an Honorable Mention for the Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student in 2018 and was an invited speaker at the International Congress of Chinese Mathematicians in 2019.

In this episode, we get a sample of Greg’s work, which goes under the name “Tensor Programs” and currently spans five highly technical papers. The route chosen to compress Tensor Programs into the scope of a conversational video is to place its main concepts under the umbrella of one larger, central, and time-tested idea: that of taking a large N limit. This occurs most famously in the Law of Large Numbers and the Central Limit Theorem, which then play a fundamental role in the branch of mathematics known as Random Matrix Theory (RMT). We review this foundational material and then show how Tensor Programs (TP) generalizes this classical work, offering new proofs of RMT. We conclude with the applications of Tensor Programs to a (rare!) rigorous theory of neural networks.

As science fiction would have you believe, you can’t really go to “another dimension.” Dimensions are more about how we see the world. But some things point to not just one, but two dimensions of time, according to one expert. If it were true, the theory could fix the biggest problem in physics, which is that quantum mechanics and general relativity don’t agree with each other.

Itzhak Bars from the University of Southern California in Los Angeles says that’s the case. Up, down, left, right, forward, back, and space-time are the normal three dimensions. In Bars’s theory, time is not a straight line. Instead, it is a curved 2D plane that is woven into all of these dimensions and more.

Dr. Bars has been working on “two-time physics” for more than ten years. All of this started when he started to wonder what time has to do with gravity and other forces. Even though the idea of more dimensions sounds strange, more and more physicists are thinking about it because it could help create the “theory of everything” or “unified theory of physics” that everyone wants. This would put all of the basic forces of the universe into a single, simple math equation.

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Irina Rish is a world-renowned professor of computer science and operations research at the Université de Montréal and a core member of the prestigious Mila organisation. She is a Canada CIFAR AI Chair and the Canadian Excellence Research Chair in Autonomous AI. Irina holds an MSc and PhD in AI from the University of California, Irvine as well as an MSc in Applied Mathematics from the Moscow Gubkin Institute. Her research focuses on machine learning, neural data analysis, and neuroscience-inspired AI. In particular, she is exploring continual lifelong learning, optimization algorithms for deep neural networks, sparse modelling and probabilistic inference, dialog generation, biologically plausible reinforcement learning, and dynamical systems approaches to brain imaging analysis. Prof. Rish holds 64 patents, has published over 80 research papers, several book chapters, three edited books, and a monograph on Sparse Modelling. She has served as a Senior Area Chair for NeurIPS and ICML. Irina’s research is focussed on taking us closer to the holy grail of Artificial General Intelligence. She continues to push the boundaries of machine learning, continually striving to make advancements in neuroscience-inspired AI.

If you know anything about special relativity then you probably know that how fast you’re moving has an impact on how quickly time passes for you. What physics gives rise to this effect? Do you need to know some complicated mathematics in order to understand it?

It turns out that this effect, known as “time dilation”, can be very easily derived for a special kind of clock: a light clock. In this video, I consider a light clock moving through space and show how the postulates of special relativity entail that this moving clock runs slow.

On nights and weekends, Justin Gilmer attacked an old question in pure math using the tools of information theory.

Logic gates in biology can be set up to lead to timing important biological events. How is this done?

Edit: at 4:00, not all pathways make use of this motif. This is just one way timing can happen in biology.

We may think we invented mathematics but we actually only discover it. It’s the immaterial underpinning of material nature.

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