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Category: mathematics – Page 129

At the south pole of Jupiter lurks a striking sight—even for a gas giant planet covered in colorful bands that sports a red spot larger than the earth. Down near the south pole of the planet, mostly hidden from the prying eyes of humans, is a collection of swirling storms arranged in an unusually geometric pattern.

Since they were first spotted by NASA’s Juno space probe in 2019, the storms have presented something of a mystery to scientists. The storms are analogous to hurricanes on Earth. However, on our planet, hurricanes do not gather themselves at the poles and twirl around each other in the shape of a pentagon or hexagon, as do Jupiter’s curious storms.

Now, a research team working in the lab of Andy Ingersoll, Caltech professor of planetary science, has discovered why Jupiter’s storms behave so strangely. They did so using math derived from a proof written by Lord Kelvin, a British mathematical physicist and engineer, nearly 150 years ago.

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Microsoft has made several quirky and useful apps that can help you with daily problems and its new app seeks to help you with math.

Microsoft Math Solver — available on both iOS and Android — can solve various math problems including quadratic equations, calculus, and statistics. The app can also show graphs for the equation to enhance your understanding of the subject.

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Does human consciousness exist separate from matter, or is it embodied in the body –a critical player in anything that has to do with mind? “We are not thinking machines that feel; rather, we are feeling machines that think.” answers neuroscientist Antonio Damasio, who pioneered the field of embodied consciousness –the bodily origins of our sense of self. “We may smile and the dog may wag the tail, but in essence,” he says. “we have a set program and those programs are similar across individuals in the species. There is no such thing as a disembodied mind.”

Consciousness is considered by leading scientists as the central unsolved mystery of the 21st Century: “I have a much easier time imagining how we understand the Big Bang than I have imagining how we can understand consciousness,” says Edward Witten, theoretical physicist at the Institute for Advanced Study in Princeton, New Jersey who has been compared to Isaac Newton and Einstein about the phenomena that has been described as assuming the role spacetime did before Einstein invented his theory of relativity.

Some scientists have asked how can we be sure that the source of consciousness lies within our bodies at all? One popular, if mystical, idea, writes astrophysicist Paul Davies in The Demon in the Machine, “is that flashes of mathematical inspiration can occur by the mathematician’s mind somehow ‘breaking through’ into a Platonic realm of mathematical forms and relationships that not only lies beyond the brain but beyond space and time altogether.”

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In the sixties of the previous century, the science of Cybernetics emerged, which its founder Norbert Wiener defined as “the scientific study of control and communication in the animal and the machine.” Whereas the cyberneticists perhaps saw everything in the organic world too much as a machine type of regulatory network, the paradigm swapped to its mirror image, wherein everything in the natural world became seen as an organic neural network. Indeed, self-regulating networks appear to be ubiquitous: From the subatomic organization of atoms to the atomic organization of molecules, macromolecules, cells and organisms, everywhere the equivalent of neural networks appears to be present.

#EvolutionaryCybernetics #CyberneticTheoryofMind #PhilosophyofMind #QuantumTheory #cybernetics #evolution #consciousness

“At a deep level all things in our Universe are ineffably interdependent and interconnected, as we are part of the Matryoshka-like mathematical object of emergent levels of complexity where consciousness pervades all levels.” –Alex M. Vikoulov, The Syntellect Hypothesis.

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In a delightful alignment of astronomy and mathematics, scientists at MIT and elsewhere have discovered a “pi Earth”—an Earth-sized planet that zips around its star every 3.14 days, in an orbit reminiscent of the universal mathematics constant.

The researchers discovered signals of the planet in data taken in 2017 by the NASA Kepler Space Telescope’s K2 mission. By zeroing in on the system earlier this year with SPECULOOS, a network of ground-based telescopes, the team confirmed that the signals were of a planet orbiting its star. And indeed, the planet appears to still be circling its star today, with a pi-like period, every 3.14 days.

“The planet moves like clockwork,” says Prajwal Niraula, a graduate student in MIT’s Department of Earth, Atmospheric and Planetary Sciences (EAPS), who is the lead author of a paper published today in the Astronomical Journal, titled: “π Earth: a 3.14-day Earth-sized Planet from K2’s Kitchen Served Warm by the SPECULOOS Team.”

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When a virus invades your cells, it changes your body. But in the process, the pathogen changes its shape, too. A new mathematical model predicts the points on the virus that allow this shape-shifting to occur, revealing a new way to find potential drug and vaccine targets. The unique math-based approach has already identified potential targets in the coronavirus that causes COVID-19.

Outlined in April in the Journal of Computational Biology, the strategy predicts protein sites on viruses that stash energy—important spots that drugs could disable. In a rare feat, the work proceeds from pure mathematics, says study author and mathematician Robert Penner of the Institute of Advanced Scientific Studies in France. “There’s precious little pure math in biology,” he adds. The paper’s predictions face a long road before they can be verified experimentally, says John Yin, who studies viruses at the University of Wisconsin–Madison and was not involved in the research. But he agrees that Penner’s approach has potential. “He’s coming at this from a mathematician’s point of view—but a very scientifically informed mathematician,” Yin says. “So that’s highly rare.”

Penner’s method takes advantage of the fact that certain viral proteins alter their shape dramatically when viruses breach cells, and this transformation depends on unstable features. (A stable protein site, by definition, resists change.) By identifying “high free energy sites”—areas on a viral protein that store lots of energy—Penner realized he could spot likely “spring” points that mediate this change in shape. He calls such high-energy spots exotic sites. Finding them required some complex math.

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While the future of the clean energy proposal remains uncertain, the majority of Americans have been reading from the same page regarding what needs to be done: Dramatically cutting down the country’s reliance on fossil fuels over the next two decades is critical to lowering greenhouse gas (GHG) emissions and address climate change, with six in 10 U.S. adults saying they would favor policies with this energy goal. Thankfully, scientists have been researching alternative energy solutions like wind and solar power for decades, including lesser-known sources that may seem a little unusual or even downright ridiculous and unrealistic.

You can chalk up harvesting energy from blackholes to the latter category.

Fifty years ago, British mathematical physicist, Roger Penrose, proposed a seemingly absurd idea how an alien society (or future humans) could harvest energy from a rotating black hole by dropping an object just outside its sphere of influence also known as the ergosphere where it could gain negative energy. Since then, nobody has been able to verify the viability of this seemingly bizarre idea— that is until now.

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San Francisco-based AI research laboratory OpenAI has added another member to its popular GPT (Generative Pre-trained Transformer) family. In a new paper, OpenAI researchers introduce GPT-f, an automated prover and proof assistant for the Metamath formalization language.

While artificial neural networks have made considerable advances in computer vision, natural language processing, robotics and so on, OpenAI believes they also have potential in the relatively underexplored area of reasoning tasks. The new research explores this potential by applying a transformer language model to automated theorem proving.

Automated theorem proving tends to require general and flexible reasoning to efficiently check the correctness of proofs. This makes it an appealing domain for checking the reasoning capabilities of language models and for the study of reasoning in general. The ability to verify proofs also helps researchers as it enables the automatic generation of new problems that can be used as training data.

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