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Archive for the ‘mathematics’ category: Page 60

Feb 21, 2023

David Hilbert — The Foundations of Geometry

Posted by in categories: mathematics, space

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.

Feb 21, 2023

Andrew Strominger: Black Holes, Quantum Gravity, and Theoretical Physics | Lex Fridman Podcast #359

Posted by in categories: alien life, mathematics, military, particle physics, quantum physics

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” »

Feb 20, 2023

Neural Network Models of Mathematical Cognition | Silvester Sabathiel | Numerosity Workshop 2021

Posted by in categories: information science, mathematics, robotics/AI

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.

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Feb 20, 2023

The Most Realistic Humanoid Robots In The World: How Will Artificial Intelligence Affect Our Future?

Posted by in categories: business, mathematics, robotics/AI, space

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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Feb 20, 2023

This video explores Artificial Super Intelligence and how it will change the world

Posted by in categories: augmented reality, bioengineering, biological, genetics, mathematics, Ray Kurzweil, robotics/AI, singularity, transhumanism

Watch this next video about the Future of Artificial Intelligence (2030 — 10,000 A.D.+): https://youtu.be/cwXnX49Bofk.
► Udacity: Up To 75% Off All Courses (Biggest Discount Ever): https://bit.ly/3j9pIRZ
► Brilliant: Learn Science And Math Interactively (20% Off): https://bit.ly/3HAznLL
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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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Feb 20, 2023

Super Intelligent AI: 5 Reasons It Could Destroy Humanity

Posted by in categories: mathematics, robotics/AI

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.
► Support This Channel: https://www.patreon.com/futurebusinesstech.
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► Jasper AI: Write 5x Faster With Artificial Intelligence: https://bit.ly/3MIPSYp.

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.

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Feb 20, 2023

Digital Immortality: When Will We Live Forever?

Posted by in categories: biological, life extension, mathematics, Ray Kurzweil, robotics/AI, singularity

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?

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Feb 18, 2023

How Gödel’s Proof Works

Posted by in category: mathematics

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.

Feb 18, 2023

AI and the Transformation of the Human Spirit

Posted by in categories: business, economics, employment, encryption, mathematics, robotics/AI, transportation

A second problem is the risk of technological job loss. This is not a new worry; people have been complaining about it since the loom, and the arguments surrounding it have become stylized: critics are Luddites who hate progress. Whither the chandlers, the lamplighters, the hansom cabbies? When technology closes one door, it opens another, and the flow of human energy and talent is simply redirected. As Joseph Schumpeter famously said, it is all just part of the creative destruction of capitalism. Even the looming prospect of self-driving trucks putting 3.5 million US truck drivers out of a job is business as usual. Unemployed truckers can just learn to code instead, right?

Those familiar replies make sense only if there are always things left for people to do, jobs that can’t be automated or done by computers. Now AI is coming for the knowledge economy as well, and the domain of humans-only jobs is dwindling absolutely, not merely morphing into something new. The truckers can learn to code, and when AI takes that over, coders can… do something or other. On the other hand, while technological unemployment may be long-term, its problematicity might be short-term. If our AI future is genuinely as unpredictable and as revolutionary as I suspect, then even the sort of economic system we will have in that future is unknown.

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Feb 18, 2023

New multi-policy-based annealer for solving real-world combinatorial optimization problems

Posted by in categories: finance, mathematics, policy, robotics/AI

A fully-connected annealer extendable to a multi-chip system and featuring a multi-policy mechanism has been designed by Tokyo Tech researchers to solve a broad class of combinatorial optimization (CO) problems relevant to real-world scenarios quickly and efficiently. Named Amorphica, the annealer has the ability to fine-tune parameters according to a specific target CO problem and has potential applications in logistics, finance, machine learning, and so on.

The has grown accustomed to an efficient delivery of goods right at our doorsteps. But did you know that realizing such an efficiency requires solving a mathematical problem, namely what is the best possible route between all the destinations? Known as the “traveling salesman problem,” this belongs to a class of mathematical problems known as “combinatorial optimization” (CO) problems.

As the number of destinations increases, the number of possible routes grows exponentially, and a brute force method based on exhaustive search for the best route becomes impractical. Instead, an approach called “annealing computation” is adopted to find the best route quickly without an exhaustive search.

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