## Archive for the ‘mathematics’ category: Page 63

E verything is Code. Immersive [self-]simulacra. We all are waves on the surface of eternal ocean of pure, vibrant consciousness in motion, self-referential creative divine force expressing oneself in an exhaustible variety of forms and patterns throughout the multiverse of universes. “I am” the Alpha, Theta & Omega – the ultimate self-causation, self-reflection and self-manifestation instantiated by mathematical codes and projective fractal geometry.

In my new volume of The Cybernetic Theory of Mind series – The Omega Singularity: Universal Mind & The Fractal Multiverse – we discuss a number of perspectives on quantum cosmology, computational physics, theosophy and eschatology. How could dimensionality be transcended yet again? What is the fractal multiverse? Is our universe a “metaverse” in a universe up? What is the ultimate destiny of our universe? Why does it matter to us? What is the Omega Singularity?

“The methods used to approach it cover, I would say, the whole of mathematics,” said Andrei Yafaev of University College London.

The new paper begins with one of the most basic but provocative questions in mathematics: When do polynomial equations like x3 + y3 = z3 have integer solutions (solutions in the positive and negative counting numbers)? In 1994, Andrew Wiles solved a version of this question, known as Fermat’s Last Theorem, in one of the great mathematical triumphs of the 20th century.

In the quest to solve Fermat’s Last Theorem and problems like it, mathematicians have developed increasingly abstract theories that spark new questions and conjectures. Two such problems, stated in 1989 and 1995 by Yves André and Frans Oort, respectively, led to what’s now known as the André-Oort conjecture. Instead of asking about integer solutions to polynomial equations, the André-Oort conjecture is about solutions involving far more complicated geometric objects called Shimura varieties.

Imagine if we could use strong electromagnetic fields to manipulate the local properties of spacetime—this could have important ramifications in terms of science and engineering.

Electromagnetism has always been a subtle phenomenon. In the 19th century, scholars thought that electromagnetic waves must propagate in some sort of elusive medium, which was called aether. Later, the aether hypothesis was abandoned, and to this day, the classical theory of electromagnetism does not provide us with a clear answer to the question in which medium electric and magnetic fields propagate in vacuum. On the other hand, the theory of gravitation is rather well understood. General relativity explains that energy and mass tell the spacetime how to curve and spacetime tells masses how to move. Many eminent mathematical physicists have tried to understand electromagnetism directly as a consequence of general relativity. The brilliant mathematician Hermann Weyl had especially interesting theories in this regard. The Serbian inventor Nikola Tesla thought that electromagnetism contains essentially everything in our universe.

“It is what I would call a dippy process,” Richard Feynman later wrote. “Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent.”

Justification came decades later from a seemingly unrelated branch of physics. Researchers studying magnetization discovered that renormalization wasn’t about infinities at all. Instead, it spoke to the universe’s separation into kingdoms of independent sizes, a perspective that guides many corners of physics today.

Renormalization, writes David Tong, a theorist at the University of Cambridge, is “arguably the single most important advance in theoretical physics in the past 50 years.”

Quantum computers could cause unprecedented disruption in both good and bad ways, from cracking the encryption that secures our data to solving some of chemistry’s most intractable puzzles. New research has given us more clarity about when that might happen.

Modern encryption schemes rely on fiendishly difficult math problems that would take even the largest supercomputers centuries to crack. But the unique capabilities of a quantum computer mean that at sufficient size and power these problems become simple, rendering today’s encryption useless.

That’s a big problem for cybersecurity, and it also poses a major challenge for cryptocurrencies, which use cryptographic keys to secure transactions. If someone could crack the underlying encryption scheme used by Bitcoin, for instance, they would be able to falsify these keys and alter transactions to steal coins or carry out other fraudulent activity.

A joint research team from the Hong Kong University of Science and Technology (HKUST) and the University of Tokyo discovered an unusual topological aspect of sodium chloride, commonly known as table salt, which will not only facilitate the understanding of the mechanism behind salt’s dissolution and formation, but may also pave the way for the future design of nanoscale conducting quantum wires.

There is a whole variety of advanced materials in our daily life, and many gadgets and technology are created through the assembly of different materials. Cellphones, for example, adopted a combination of many different substances—glass for the monitor, aluminum alloy for the frame, and metals like gold, silver and copper for their internal wiring. But nature has its own genius way of ‘cooking’ different properties into one wonder material, or what is known as ‘topological material’.

Topology, as a mathematical concept, studies what aspects of an object are robust under a smooth deformation. For instance, we can squeeze, stretch, or twist a T-shirt, but the number its openings would still be four so long as we do not tear it apart. The discovery of topological phases of matter, highlighted by the 2016 Nobel Prize in Physics, suggests that certain quantum materials are inherently a combination of electrical insulators and conductors. This could necessitate a conducting boundary even when the bulk of the material is insulating. Such materials are neither classified as a metal nor an insulator, but a natural assembly of the two.

A Lancaster physicist has proposed a radical solution to the question of how a charged particle, such as an electron, responded to its own electromagnetic field.

This question has challenged physicists for over 100 years but mathematical physicist Dr. Jonathan Gratus has suggested an alternative approach — published in the Journal of Physics A — with controversial implications.

It is well established that if a point charge accelerates it produces electromagnetic radiation. This radiation has both energy and momentum, which must come from somewhere. It is usually assumed that they come from the energy and momentum of the charged particle, damping the motion.

If you are a scientist, willing to share your science with curious teens, consider joining Lecturers Without Borders!

Established by three scientists, Luibov Tupikina, Athanasia Nikolau, and Clara Delphin Zemp, and high school teacher Mikhail Khotyakov, Lecturers Without Borders (LeWiBo) is an international volunteer grassroots organization that brings together enthusiastic science researchers and science-minded teens. LeWiBo founders noticed that scientists tend to travel a lot – for fieldwork, conferences, or lecturing – and realized scientists could be a great source of knowledge and inspiration to local schools. To this end, they asked scientists to volunteer for talks and workshops. The first lecture, delivered in Nepal in 2017 by two researchers, a mathematician and a climatologist, was a great success. In the next couple of years, LeWiBo volunteers presented at schools in Russia and Belarus; Indonesia and Uganda; India and Nepal. Then, the pandemic forced everything into the digital realm, bringing together scientists and schools across the globe. I met with two of LeWiBo’s co-founders, physicist Athanasia Nikolaou and math teacher Mikhail Khotyakov, as well as their coordinator, Anastasia Mityagina, to talk about their offerings and future plans.

Julia Brodsky: So, how many people volunteer for LeWiBo at this time?

Almost anytime physicists announce that they’ve discovered a new particle, whether it’s the Higgs boson or the recently bagged double-charm tetraquark, what they’ve actually spotted is a small bump rising from an otherwise smooth curve on a plot. Such a bump is the unmistakable signature of “resonance,” one of the most ubiquitous phenomena in nature.

Resonance underlies aspects of the world as diverse as music, nuclear fusion in dying stars, and even the very existence of subatomic particles. Here’s how the same effect manifests in such varied settings, from everyday life down to the smallest scales.

In its simplest form, resonance occurs when an object experiences an oscillating force that’s close to one of its “natural” frequencies, at which it easily oscillates. That objects have natural frequencies “is one of the bedrock properties of both math and the universe,” said Matt Strassler, a particle physicist affiliated with Harvard University who is writing a book about the Higgs boson. A playground swing is one familiar example: “Knock something like that around, and it will always pick out its resonant frequency automatically,” Strassler said. Or flick a wineglass and the rim will vibrate a few hundred times per second, producing a characteristic tone as the vibrations transfer to the surrounding air.

‘’The Weak Gravity Conjecture holds that in a theory of quantum gravity, any gauge force must mediate interactions stronger than gravity for some particles. This statement has surprisingly deep and extensive connections to many different areas of physics and mathematics. Several variations on the basic conjecture have been proposed, including statements that are much stronger but are nonetheless satisfied by all known consistent quantum gravity theories. We review these relat… See more.

The Weak Gravity Conjecture holds that in a theory of quantum gravity, any.

Gauge force must mediate interactions stronger than gravity for some particles.

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