Archive for the ‘mathematics’ category

May 31, 2023

Paraconsistent Logic (Stanford Encyclopedia of Philosophy)

Posted by in category: mathematics

Paraconsistent logic challenges this standard view. A logical consequence relation is said to be paraconsistent if it is not explosive. Thus, if a consequence relation is paraconsistent, then even in circumstances where the available information is inconsistent, the consequence relation does not explode into triviality. Thus, paraconsistent logic accommodates inconsistency in a controlled way that treats inconsistent information as potentially informative.

The prefix ‘para’ in English has two meanings: ‘quasi’ (or ‘similar to, modelled on’) or ‘beyond’. When the term ‘paraconsistent’ was coined by Miró Quesada at the Third Latin America Conference on Mathematical Logic in 1976, he seems to have had the first meaning in mind. Many paraconsistent logicians, however, have taken it to mean the second, which provided different reasons for the development of paraconsistent logic as we will see below.

Paraconsistent logic is defined negatively: any logic is paraconsistent as long as it is not explosive. This means there is no single set of open problems or programs in paraconsistent logic. As such, this entry is not a complete survey of paraconsistent logic. The aim is to describe some philosophically salient features of a diverse field.

May 27, 2023

Cambridge researchers have created a mathematical model for building muscle

Posted by in category: mathematics

Now there’s a mathematical model that could maximize the effectiveness of exercise.

May 27, 2023

Fractons as information storage: Not yet tangible, but close

Posted by in categories: energy, mathematics, quantum physics

Excitations in solids can also be represented mathematically as quasiparticles; for example, lattice vibrations that increase with temperature can be well described as phonons. Mathematically, also quasiparticles can be described that have never been observed in a material before. If such “theoretical” quasiparticles have interesting talents, then it is worth taking a closer look. Take fractons, for example.

Fractons are fractions of spin excitations and are not allowed to possess kinetic energy. As a consequence, they are completely stationary and immobile. This makes fractons new candidates for perfectly secure information storage. Especially since they can be moved under special conditions, namely piggyback on another quasiparticle.

“Fractons have emerged from a mathematical extension of quantum electrodynamics, in which electric fields are treated not as vectors but as tensors—completely detached from real materials,” explains Prof. Dr. Johannes Reuther, at the Freie Universität Berlin and at HZB.

May 22, 2023

Hello, Computer — Sabine Hossenfelder — A.I. going mainstream

Posted by in categories: cosmology, mathematics, media & arts, particle physics, quantum physics, robotics/AI

Perspective from a very-educated layman. Er, laywoman.

This is Hello, Computer, a series of interviews carried out in 2023 at a time when artificial intelligence appears to be going everywhere, all at once.

Continue reading “Hello, Computer — Sabine Hossenfelder — A.I. going mainstream” »

May 20, 2023

Physics: The big questions of our existence in under an hour

Posted by in categories: mathematics, particle physics, space

SABINE HOSSENFELDER: My name is Sabine Hossenfelder. I’m a physicist and Research Fellow at the Frankfurt Institute for Advanced Studies, and I have a book that’s called “Existential Physics: A Scientist’s Guide to Life’s Biggest Questions.”

NARRATOR: Why did you pursue a career in physics?

HOSSENFELDER: I originally studied mathematics, not physics, because I was broadly interested in the question how much can we describe about nature with mathematics? But mathematics is a really big field and I couldn’t make up my mind exactly what to study. And so I decided to focus on that part of mathematics that’s actually good to describe nature and that naturally led me to physics. I was generally trying to make sense of the world and I thought that human interactions, social systems are a pretty hopeless case. There’s no way I’ll ever make sense of them. But simple things like particles or maybe planets and moons, I might be able to work that out. In the foundations of physics, we work with a lot of mathematics and I know from my own experience that it’s really, really hard to learn. And so I think for a lot of people out there, the journal articles that we write in the foundations of physics are just incomprehensible.

May 17, 2023

Curved spacetime in a quantum simulator

Posted by in categories: cosmology, mathematics, particle physics, quantum physics

The theory of relativity works well when you want to explain cosmic-scale phenomena—such as the gravitational waves created when black holes collide. Quantum theory works well when describing particle-scale phenomena—such as the behavior of individual electrons in an atom. But combining the two in a completely satisfactory way has yet to be achieved. The search for a “quantum theory of gravity” is considered one of the significant unsolved tasks of science.

This is partly because the mathematics in this field is highly complicated. At the same time, it is tough to perform suitable experiments: One would have to create situations in which phenomena of both the relativity theory play an important role, for example, a spacetime curved by heavy masses, and at the same time, become visible, for example the dual particle and wave nature of light.

At the TU Wien in Vienna, Austria, a new approach has now been developed for this purpose: A so-called “quantum simulator” is used to get to the bottom of such questions: Instead of directly investigating the system of interest (namely quantum particles in curved spacetime), one creates a “” from which one can then learn something about the system of actual interest by analogy. The researchers have now shown that this quantum simulator works excellently.

May 16, 2023

Supercomputing simulations spot electron orbital signatures

Posted by in categories: information science, mathematics, particle physics, quantum physics, supercomputing

Something not musk:

No one will ever be able to see a purely mathematical construct such as a perfect sphere. But now, scientists using supercomputer simulations and atomic resolution microscopes have imaged the signatures of electron orbitals, which are defined by mathematical equations of quantum mechanics and predict where an atom’s electron is most likely to be.

Scientists at UT Austin, Princeton University, and ExxonMobil have directly observed the signatures of electron orbitals in two different transition-metal atoms, iron (Fe) and cobalt (Co) present in metal-phthalocyanines. Those signatures are apparent in the forces measured by atomic force microscopes, which often reflect the underlying orbitals and can be so interpreted.

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May 15, 2023

Powering AI On Mobile Devices Requires New Math And Qualcomm Is Pioneering It

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

The feature image you see above was generated by an AI text-to-image rendering model called Stable Diffusion typically runs in the cloud via a web browser, and is driven by data center servers with big power budgets and a ton of silicon horsepower. However, the image above was generated by Stable Diffusion running on a smartphone, without a connection to that cloud data center and running in airplane mode, with no connectivity whatsoever. And the AI model rendering it was powered by a Qualcomm Snapdragon 8 Gen 2 mobile chip on a device that operates at under 7 watts or so.

It took Stable Diffusion only a few short phrases and 14.47 seconds to render this image.

This is an example of a 540p pixel input resolution image being scaled up to 4K resolution, which results in much cleaner lines, sharper textures, and a better overall experience. Though Qualcomm has a non-algorithmic version of this available today, called Snapdragon GSR, someday in the future, mobile enthusiast gamers are going to be treated to even better levels of image quality without sacrificing battery life and with even higher frame rates.

Continue reading “Powering AI On Mobile Devices Requires New Math And Qualcomm Is Pioneering It” »

May 11, 2023

Physicists create long-sought topological quantum states

Posted by in categories: computing, mathematics, particle physics, quantum physics

The exotic particles are called non-Abelian anyons, or nonabelions for short, and their Borromean rings exist only as information inside the quantum computer. But their linking properties could help to make quantum computers less error-prone, or more ‘fault-tolerant’ — a key step to making them outperform even the best conventional computers. The results, revealed in a preprint on 9 May1, were obtained on a machine at Quantinuum, a quantum-computing company in Broomfield, Colorado, that formed as the result of a merger between the quantum computing unit of Honeywell and a start-up firm based in Cambridge, UK.

“This is the credible path to fault-tolerant quantum computing,” says Tony Uttley, Quantinuum’s president and chief operating officer.

Other researchers are less optimistic about the virtual nonabelions’ potential to revolutionize quantum computing, but creating them is seen as an achievement in itself. “There is enormous mathematical beauty in this type of physical system, and it’s incredible to see them realized for the first time, after a long time,” says Steven Simon, a theoretical physicist at the University of Oxford, UK.

May 7, 2023

A “Window Into Evolution” — Mathematicians Uncover Universal Explanatory Framework

Posted by in categories: biological, evolution, mathematics

Mathematicians have uncovered a universal explanatory framework that provides a “window into evolution.” This framework explains how molecules interact with each other in adapting to changing conditions while still maintaining tight control over essential properties that are crucial for survival.

According to Dr. Araujo from the QUT School of Mathematical Sciences, the research results provide a blueprint for the creation of signaling networks that are capable of adapting across all life forms and for the design of synthetic biological systems.

“Our study considers a process called robust perfect adaptation (RPA) whereby biological systems, from individual cells to entire organisms, maintain important molecules within narrow concentration ranges despite continually being bombarded with disturbances to the system,” Dr. Araujo said.

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