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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: Mathematical and Theoretical 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.

It could hardly be more complicated: tiny particles whir around wildly with extremely high energy, countless interactions occur in the tangled mess of quantum particles, and this results in a state of matter known as “quark-gluon plasma”. Immediately after the Big Bang, the entire universe was in this state; today it is produced by high-energy atomic nucleus collisions, for example at CERN.

Such processes can only be studied using high-performance computers and highly complex computer simulations whose results are difficult to evaluate. Therefore, using artificial intelligence or machine learning for this purpose seems like an obvious idea. Ordinary machine-learning algorithms, however, are not suitable for this task. The mathematical properties of particle physics require a very special structure of neural networks. At TU Wien (Vienna), it has now been shown how neural networks can be successfully used for these challenging tasks in particle physics.

https://youtube.com/watch?v=E1AxVXt2Gv4

Marcus Hutter is a senior research scientist at DeepMind and professor at Australian National University. Throughout his career of research, including with Jürgen Schmidhuber and Shane Legg, he has proposed a lot of interesting ideas in and around the field of artificial general intelligence, including the development of the AIXI model which is a mathematical approach to AGI that incorporates ideas of Kolmogorov complexity, Solomonoff induction, and reinforcement learning.

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Over 240 years ago, famous mathematician Leonhard Euler came up with a question: if six army regiments each have six officers of six different ranks, can they be arranged in a square formation such that no row or column repeats either a rank or regiment?

After searching in vain for a solution, Euler declared the problem impossible – and over a century later, the French mathematician Gaston Tarry proved him right. Then, 60 years after that, when the advent of computers removed the need for laboriously testing every possible combination by hand, the mathematicians Parker, Bose, and Shrikhande proved an even stronger result: not only is the six-by-six square impossible, but it’s the only size of square other than two-by-two that doesn’t have a solution at all.

Many people think that mathematics is a human invention. To this way of thinking, mathematics is like a language: it may describe real things in the world, but it doesn’t “exist” outside the minds of the people who use it.

But the Pythagorean school of thought in ancient Greece held a different view. Its proponents believed reality is fundamentally mathematical. More than 2,000 years later, philosophers and physicists are starting to take this idea seriously.

Continue reading “Humans Didn’t Invent Mathematics, It’s What the World Is Made Of” »

Musk is sounding a familiar alarm. But the math might not add up.

SpaceX CEO Elon Musk is sounding the alarm, as data sparks concern over global population figures.

Numbers like π, e and φ often turn up in unexpected places in science and mathematics. Pascal’s triangle and the Fibonacci sequence also seem inexplicably widespread in nature. Then there’s the Riemann zeta function, a deceptively straightforward function that has perplexed mathematicians since the 19th century. The most famous quandary, the Riemann hypothesis, is perhaps the greatest unsolved question in mathematics, with the Clay Mathematics Institute offering a $1 million prize for a correct proof.

Numbers like π, e and φ often turn up in unexpected places in science and mathematics. Pascal’s triangle and the Fibonacci sequence also seem inexplicably widespread in nature. Then there’s the Riemann zeta function, a deceptively straightforward function that has perplexed mathematicians since the 19th century. The most famous quandary, the Riemann hypothesis, is perhaps the greatest unsolved question in mathematics, with the Clay Mathematics Institute offering a $1 million prize for a correct proof.

UC Santa Barbara physicist Grant Remmen believes he has a new approach for exploring the quirks of the zeta function. He has found an analog that translates many of the function’s important properties into quantum field theory. This means that researchers can now leverage the tools from this field of physics to investigate the enigmatic and oddly ubiquitous zeta function. His work could even lead to a proof of the Riemann hypothesis. Remmen lays out his approach in the journalPhysical Review Letters.

“The Riemann zeta function is this famous and mysterious mathematical function that comes up in number theory all over the place,” said Remmen, a postdoctoral scholar at UCSB’s Kavli Institute for Theoretical Physics. “It’s been studied for over 150 years.”

Tech companies continued to draw criticism for their roles in political and social scandals, most notably when whisteblower and former Facebook employee Frances Haugen testified to lawmakers. Undeterred, Facebook rebranded itself Meta and said it would now focus on building the metaverse. Twitter CEO Jack Dorsey stepped down and likewise changed the name of his company Square to Block in a not-so-subtle nod to the blockchain.

Meanwhile, volatile cryptocurrencies set new records, their prices jumping and crashing on a tweet. NFTs, a once-obscure type of cryptoasset, went on an eye-watering tear as redditors pushed meme stocks skyward. It was also the year of ever-bigger AI. Machine learning models surpassed a trillion parameters, designed computer chips, and tackled practical problems in biology, math, and chemistry. Elsewhere, billionaires went to space, regular folks bought 3D printed houses, fusion power attracted billions in investment, gene editing trials hit their stride, and “flying car” companies hit the New York Stock Exchange.

For this year’s list of fascinating stories in tech and science, we sifted our Saturday posts and selected articles that looked back to where it all began, glanced ahead to what’s coming, or otherwise stood out from the chatter to stand the test of time.