Archive for the ‘mathematics’ category: Page 4

Aug 31, 2020

Mathematicians Report New Discovery About the Dodecahedron

Posted by in category: mathematics

Three mathematicians have resolved a fundamental question about straight paths on the 12-sided Platonic solid.

Aug 28, 2020

Superluminal Motion-Assisted 4-Dimensional Light-in-Flight Imaging

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

Abstract: Advances in high speed imaging techniques have opened new possibilities for capturing ultrafast phenomena such as light propagation in air or through media. Capturing light-in-flight in 3-dimensional xyt-space has been reported based on various types of imaging systems, whereas reconstruction of light-in-flight information in the fourth dimension z has been a challenge. We demonstrate the first 4-dimensional light-in-flight imaging based on the observation of a superluminal motion captured by a new time-gated megapixel single-photon avalanche diode camera. A high resolution light-in-flight video is generated with no laser scanning, camera translation, interpolation, nor dark noise subtraction. A machine learning technique is applied to analyze the measured spatio-temporal data set. A theoretical formula is introduced to perform least-square regression, and extra-dimensional information is recovered without prior knowledge. The algorithm relies on the mathematical formulation equivalent to the superluminal motion in astrophysics, which is scaled by a factor of a quadrillionth. The reconstructed light-in-flight trajectory shows a good agreement with the actual geometry of the light path. Our approach could potentially provide novel functionalities to high speed imaging applications such as non-line-of-sight imaging and time-resolved optical tomography.

Aug 27, 2020

How Close Are Computers to Automating Mathematical Reasoning?

Posted by in categories: mathematics, robotics/AI

AI tools are shaping next-generation theorem provers, and with them the relationship between math and machine.

Aug 25, 2020

I am creating mathematical meme magic art for future advanced artificial intelligence to enjoy alongside cosmopolitan intellectuals

Posted by in categories: mathematics, robotics/AI

Aug 19, 2020

Google Will Solve Your Kids’ Math Homework. That’s a Good Thing

Posted by in categories: biotech/medical, mathematics

Google has announced a new technology, powered by an acquisition called Socratic, that will let students take photos of their math homework in order to get the solutions. Google says it wants the Lens-powered technology to help parents and caretakers who are homeschooling, likely for the first time, as a result of the global COVID-19 pandemic.

Aug 19, 2020

Mathematicians Solve Part of the Weirdest Open Problem Ever

Posted by in category: mathematics

Two mathematicians say they’ve untangled the first part of Paul Erdos’s famously thorny and unproven conjecture. In a new paper they’ve uploaded to arXiv and submitted to journals, mathematicians Thomas Bloom and Olof Sisask say they’ve jumped the first hurdle in the Erdos conjecture. If this is true, the next generation of researchers could start from that point with the first part finished and in hand.

➗ You love numbers. So do we. Let’s nerd out over numbers together.

Aug 19, 2020

From sociology of quantification to ethics of quantification

Posted by in categories: ethics, information science, mathematics

Quantifications are produced by several disciplinary houses in a myriad of different styles. The concerns about unethical use of algorithms, unintended consequences of metrics, as well as the warning about statistical and mathematical malpractices are all part of a general malaise, symptoms of our tight addiction to quantification. What problems are shared by all these instances of quantification? After reviewing existing concerns about different domains, the present perspective article illustrates the need and the urgency for an encompassing ethics of quantification. The difficulties to discipline the existing regime of numerification are addressed; obstacles and lock-ins are identified. Finally, indications for policies for different actors are suggested.

Aug 17, 2020

Gearing for the 20/20 Vision of Our Cybernetic Future — The Syntellect Hypothesis, Expanded Edition | Press Release

Posted by in categories: computing, cosmology, engineering, information science, mathematics, nanotechnology, neuroscience, quantum physics, singularity

“A neuron in the human brain can never equate the human mind, but this analogy doesn’t hold true for a digital mind, by virtue of its mathematical structure, it may – through evolutionary progression and provided there are no insurmountable evolvability constraints – transcend to the higher-order Syntellect. A mind is a web of patterns fully integrated as a coherent intelligent system; it is a self-generating, self-reflective, self-governing network of sentient components… that evolves, as a rule, by propagating through dimensionality and ascension to ever-higher hierarchical levels of emergent complexity. In this book, the Syntellect emergence is hypothesized to be the next meta-system transition, developmental stage for the human mind – becoming one global mind – that would constitute the quintessence of the looming Cybernetic Singularity.” –Alex M. Vikoulov, The Syntellect Hypothesis…ss-release


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Aug 11, 2020

Time-reversal of an unknown quantum state

Posted by in categories: computing, engineering, information science, mathematics, quantum physics

Physicists have long sought to understand the irreversibility of the surrounding world and have credited its emergence to the time-symmetric, fundamental laws of physics. According to quantum mechanics, the final irreversibility of conceptual time reversal requires extremely intricate and implausible scenarios that are unlikely to spontaneously occur in nature. Physicists had previously shown that while time-reversibility is exponentially improbable in a natural environment—it is possible to design an algorithm to artificially reverse a time arrow to a known or given state within an IBM quantum computer. However, this version of the reversed arrow-of-time only embraced a known quantum state and is therefore compared to the quantum version of pressing rewind on a video to “reverse the flow of time.”

In a new report now published in Communications Physics, Physicists A.V. Lebedev and V.M. Vinokur and colleagues in materials, physics and advanced engineering in the U.S. and Russia, built on their previous work to develop a technical method to reverse the temporal evolution of an arbitrary unknown . The technical work will open new routes for general universal algorithms to send the temporal evolution of an arbitrary system backward in time. This work only outlined the mathematical process of time reversal without experimental implementations.

Aug 5, 2020

The mathematician who helped to reshape physics

Posted by in categories: mathematics, physics

Barry Simon linked a phenomenon that had shocked physicists to topology, the branch of mathematics that studies shapes.

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