Lifeboat Foundation

When two black holes collide into each other to form a new bigger black hole, they violently roil spacetime around them, sending ripples, called gravitational waves, outward in all directions. Previous studies of black hole collisions modeled the behavior of the gravitational waves using what is known as linear math, which means that the gravitational waves rippling outward did not influence, or interact, with each other. Now, a new analysis has modeled the same collisions in more detail and revealed so-called nonlinear effects.

“Nonlinear effects are what happens when waves on the beach crest and crash,” says Keefe Mitman, a Caltech graduate student who works with Saul Teukolsky (Ph. D. ‘74), the Robinson Professor of Theoretical Astrophysics at Caltech with a joint appointment at Cornell University.

“The waves interact and influence each other rather than ride along by themselves. With something as violent as a black hole merger, we expected these effects but had not seen them in our models until now. New methods for extracting the waveforms from our simulations have made it possible to see the nonlinearities.”

David Hilbert was a great leader and spokesperson for the discipline of mathematics in the early 20th Century. But he was an extremely important and respected mathematician in his own right.

Like so many great German mathematicians before him, Hilbert was another product of the University of Göttingen, at that time the mathematical centre of the world, and he spent most of his working life there. His formative years, though, were spent at the University of Königsberg, where he developed an intense and fruitful scientific exchange with fellow mathematicians Hermann Minkowski and Adolf Hurwitz.

Sociable, democratic and well-loved both as a student and as a teacher, and often seen as bucking the trend of the formal and elitist system of German mathematics, Hilbert’s mathematical genius nevertheless spoke for itself. He has many mathematical terms named after him, including Hilbert space (an infinite dimensional Euclidean space), Hilbert curves, the Hilbert classification and the Hilbert inequality, as well as several theorems, and he gradually established himself as the most famous mathematician of his time.

Andrew Strominger is a theoretical physicist at Harvard. Please support this podcast by checking out our sponsors:
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EPISODE LINKS:
Andrew’s website: https://www.physics.harvard.edu/people/facpages/strominger.
Andrew’s papers:
Soft Hair on Black Holes: https://arxiv.org/abs/1601.00921
Photon Rings Around Warped Black Holes: https://arxiv.org/abs/2211.

Continue reading “Andrew Strominger: Black Holes, Quantum Gravity, and Theoretical Physics | Lex Fridman Podcast #359” »

Session kindly contributed by Silvester Sabathiel in SEMF’s 2021 Numerous Numerosity Workshop: https://semf.org.es/numerosity/

ABSTRACT
With the rise and advances in the field of artificial intelligence, opportunities to understand the finer-grained mechanisms involved in mathematical cognition have increased. A vast scope of related research has been conducted on machine learning systems that learn solving differential equations, algebraic equations and integrals or proofing complex theorems, all for which the preprocessed symbolic representations form the input and output types. However on the search for cognitive mechanisms that match the scope of humans when it comes to generalizability and applicability of mathematical concepts in the external world, a more grounded approach might be required. This involves starting with fundamental mathematical concepts that are earliest acquired in the human development and learning these within an interactive and multimodal environment. In this talk we are going to examine how artificial neural network systems within such a framework provide a controlled setup to discover possible cognitive mechanisms for intuitive numerosity perception or culturally acquired numerical concepts, such as counting. First we review impactful research results from the past, before I present the contributions of the work myself was involved in. Finally we can discuss the upcoming challenges for the field of numerical cognition and where this research journey could evolve to.

Continue reading “Neural Network Models of Mathematical Cognition | Silvester Sabathiel | Numerosity Workshop 2021” »

https://youtube.com/watch?v=4LevUzfdBtw

In this video, I’ll discuss some of the most advanced humanoid robots currently in development and reveal if the future really is bright for Robotics.

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Watch this next video about the Future of Artificial Intelligence (2030 — 10,000 A.D.+): https://youtu.be/cwXnX49Bofk.
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SOURCES:
• Life 3.0: Being Human in the Age of Artificial Intelligence (Max Tegmark): https://amzn.to/3xrU351
• The Future of Humanity (Michio Kaku): https://amzn.to/3Gz8ffA
• The Singularity Is Near: When Humans Transcend Biology (Ray Kurzweil): https://amzn.to/3ftOhXI

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Continue reading “This video explores Artificial Super Intelligence and how it will change the world” »

This video explores Super Intelligent AI and 5 reasons it will be unstoppable. Watch this next video about the Timelapse of Artificial Intelligence (2030 — 10,000 A.D.+): https://youtu.be/cwXnX49Bofk.
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SOURCES:
• https://research.aimultiple.com/artificial-general-intellige…ty-timing/
• https://www.popularmechanics.com/technology/robots/a35267508…-machines/
• https://www.businessinsider.com/mankind-will-not-be-able-to-…g-to-study.
• https://www.analyticsinsight.net/superintelligent-ai-can-we-…-humanity/
• https://www.mpg.de/16231640/0108-bild-computer-scientists-we…s-149835-x.
• https://www.nytimes.com/2019/10/31/opinion/superintelligent-…gence.html.
• https://www.nickbostrom.com/superintelligence.html.
• https://codebots.com/artificial-intelligence/the-3-types-of-…n-possible.
• https://spectrum.ieee.org/super-artificialintelligence.
• https://www.forbes.com/sites/cognitiveworld/2019/06/19/7-typ…f6d649233e.
• https://en.wikipedia.org/wiki/Superintelligence.

Continue reading “Super Intelligent AI: 5 Reasons It Could Destroy Humanity” »

This video covers digital immortality, its required technologies, processes of uploading a mind, its potential impact on society, and more. Watch this next video about the world in 2200: https://bit.ly/3htaWEr.
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CHAPTERS
00:00 Required Technologies.
01:42 The Processes of Uploading a Mind.
03:32 Positive Impacts On Society.
05:34 When Will It Become Possible?
05:53 Is Digital Immortality Potentially Dangerous?

Continue reading “Digital Immortality: When Will We Live Forever?” »

Mathematicians of the era sought a solid foundation for mathematics: a set of basic mathematical facts, or axioms, that was both consistent — never leading to contradictions — and complete, serving as the building blocks of all mathematical truths.

But Gödel’s shocking incompleteness theorems, published when he was just 25, crushed that dream. He proved that any set of axioms you could posit as a possible foundation for math will inevitably be incomplete; there will always be true facts about numbers that cannot be proved by those axioms. He also showed that no candidate set of axioms can ever prove its own consistency.

His incompleteness theorems meant there can be no mathematical theory of everything, no unification of what’s provable and what’s true. What mathematicians can prove depends on their starting assumptions, not on any fundamental ground truth from which all answers spring.