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Category: mathematics – Page 4

DNA origami vaccine rivals mRNA shots while being easier to store and manufacture

The COVID-19 pandemic brought messenger RNA (mRNA) vaccines to the forefront of global health care. After their clinical trial stages, the first COVID-19 mRNA vaccine was administered on 8 December 2020 and mathematical models suggest that mRNA vaccines prevented at least 14.4 million deaths from COVID-19 in the first year alone.

Their extraordinary effectiveness in having softened the blow of the disease has led to the development of mRNA vaccines to also combat other infectious pathogens.

Clinical trials for influenza virus, Respiratory Syncytial Virus (RSV), HIV, Zika, Epstein-Barr virus, and tuberculosis bacteria are all on the way. Importantly, however, COVID-19 research has revealed shortcomings of mRNA vaccines that highlight the need for different approaches.

Engineers Create Unusual Magnetic Material That Behaves Like Graphene

Researchers at the University of Illinois have discovered a surprising mathematical connection between two areas of condensed-matter physics that were long considered separate. The electronic and magnetic behavior of two-dimensional materials both hold significant promise for future technologies.

The Simulation Argument Was Never Actually Debunked — And The Math Is Getting Worse

In 2017, headlines around the world declared the simulation hypothesis dead. Physicists had debunked it, the articles said. We could all move on. There was one problem. The paper they cited never mentioned the simulation hypothesis. The debunking was invented by journalists who never read the research. And in the years since, the actual physics has gotten significantly worse.

This documentary follows that physics all the way down.

We begin with what really happened in 2017 — the Ringel-Kovrizhin paper, what it actually proved, and Scott Aaronson’s correction that nobody shared. Then we examine Nick Bostrom’s original 2003 trilemma, the real math behind it, and why two decades of attacks from Sean Carroll, Lisa Randall, and Sabine Hossenfelder have failed to break it. Every critique concedes something. Every attempted kill shot narrows the escape routes.

From there, we trace the physics of information through three remarkable lives. Konrad Zuse, who built the first programmable computer in his parents’ living room during the bombing of Berlin, then proposed in 1967 that the universe itself is a computation — and was ignored. John Archibald Wheeler, who lost his brother in World War Two and spent the rest of his life asking whether reality is built from information, condensing it into three words that changed physics: \.

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Philip Kitcher — Philosophy of Reductionism & Emergence

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Can biology be explained entirely in terms of chemistry and then physics? If so, that’s “reductionism.” Or are there “emergent” properties at higher levels of the hierarchy of life that cannot be explained by properties at lower or more basic levels?

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Philip Stuart Kitcher is a British philosopher who is the John Dewey Professor Emeritus of philosophy at Columbia University. He specialises in the philosophy of science, the philosophy of biology, the philosophy of mathematics, and more recently pragmatism.

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Closer To Truth, hosted by Robert Lawrence Kuhn and directed by Peter Getzels, presents the world’s greatest thinkers exploring humanity’s deepest questions. Discover fundamental issues of existence. Engage new and diverse ways of thinking. Appreciate intense debates. Share your own opinions. Seek your own answers.

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Making mini-lightning in a block of plastic

Lightning formation and the conditions triggering it have long been shrouded in a cloud of mystery, but new research led by Penn State scientists is lifting the fog. Using mathematical calculations, the researchers have discovered that lightning-like discharge doesn’t require a storm cloud—it could be made inside everyday material on a lab bench. The study is published in the journal Physical Review Letters.

“We applied the same exact models that we use for lightning research but shrank down the scale to slightly larger than a deck of cards,” said Victor Pasko, professor of electrical engineering at Penn State and lead author on the paper. “We calculated that when supplied with a high-powered electron source, lightning can be triggered in everyday insulating materials like glass, acrylic and quartz.”

The team used detailed numerical simulations to show that lightning-like radiation bursts could form inside small solid blocks, under conditions achievable in the lab. The work, if proven experimentally, could have implications for more compact and potentially safer X-ray sources in doctors’ offices and security checkpoints, the researchers said. The primary benefit, however, would be to enable the study of a powerful natural phenomenon on a lab bench.

Mysteries of Math and the Langlands Program — Episode 1

The first in a series of 4 lectures by Edward Frenkel filmed at MSRI, Berkeley and broadcast on the Japanese TV channel NHK in the Fall of 2015 in the “Luminous Classroom” series. The lectures went from elementary topics such as Pythagoras theorem, prime numbers and symmetries to Fermat’s last theorem and the general Langlands conjectures, and to the recent work connecting the Langlands Program to Quantum Physics. Even though the Intro is in Japanese, the lecture itself is in English.

On the number of digital pictures Let’s switch from Go positions to digital pictures

There is an art project to display every possible picture. The project admits this will take a long time, because there are many possible pictures. But how many? We will assume the very common color model known as True Color, in which each pixel can be one of 224 ≅ 17 million distinct colors. The digital camera shown below left has 12 million pixels. We’ll also consider much smaller pictures: the array below middle, with 300 pixels, and the array below right with just 12 pixels. Shown are some of the possible pictures:

12,000,000 pixels 300 pixels 12 pixels.

Quiz: Which of these produces a number of pictures similar to the number of atoms in the universe?

Answer: An array of n pixels produces (17 million)n different pictures. (17 million)12 ≅ 1,086, so the tiny 12-pixel array produces a million times more pictures than the number of atoms in the universe!

How about the 300 pixel array? It can produce 102,167 pictures. You may think the number of atoms in the universe is big, but that’s just peanuts to the number of pictures in a 300-pixel array. And 12M pixels? 1,086,696,638 pictures. Fuggedaboutit!

So the number of possible pictures is really, really, really big. And the number of atoms in the universe is looking relatively small, at least as a number of combinations.

On counting combinations People often underestimate the number of combinations of things. I think there are two main reasons: Combinations of things are multiplicative, while collections of things are additive. If you see a line of 6 people, it is easy to visualize a line of 60 people—it is ten times longer. But even if you know that there are 720 different orderings (permutations) in which those 6 people can line up, there is no way you can visualize the number of orderings for 60 people, because it is—you guessed it—larger than the number of atoms in the universe. Big numbers are hard. Even with simple collections of things, it takes practice to get a real intuition for the difference between 6 million and 6 billion people. When it comes to combinations, growth is faster and therefore intuition fails earlier. Authors are sloppy. Doug Smith reports that the New York Times confused “million” and “billion” over a dozen times per year; other sources also make similar mistakes. See the book by Unix co-creator Brian Kernighan for more on this. So beware, and be sure to use some simple math to augment your intuition when dealing with combinations.

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