Jan 24, 2025 01:52 AM
(This post was last modified: Jan 24, 2025 07:38 PM by C C.)
The jagged, monstrous function that broke calculus
https://www.quantamagazine.org/the-jagge...-20250123/
EXCERPT: . . . The proof demonstrated that calculus could no longer rely on geometric intuition, as its inventors had done. It ushered in a new standard for the subject, one that was rooted in the careful analysis of equations. Mathematicians were forced to follow in Weierstrass’ footsteps, further sharpening their definition of functions, their understanding of the relationship between continuity and differentiability, and their methods for computing derivatives and integrals. This work to standardize calculus has since grown into the field known as analysis; Weierstrass is considered one of its founders.
But his function’s legacy extends far beyond the foundations of calculus and analysis. It revealed that mathematics is full of monsters: impossible-seeming functions, strange objects (it’s one of the earliest examples of a fractal), wild behaviors. “There’s a whole universe of possibilities, and the Weierstrass function is supposed to be opening your eyes to it,” said Philip Gressman (opens a new tab) of the University of Pennsylvania.
It also turned out to have many practical applications. In the early 20th century, physicists wanted to study Brownian motion, the random movement of particles in a liquid or gas. Because this movement is continuous but not smooth — characterized by rapid and infinitely tiny fluctuations — functions like Weierstrass’ were perfect for modeling it. Similarly, such functions have been used to model uncertainty in how people make decisions and take risks, as well as the complicated behavior of financial markets.
Much like Weierstrass himself, the consequences of his function have sometimes been late to bloom. But they’re continuing to shape mathematics and its applications today... (MORE - missing details)
Bacteria found to eat forever chemicals — and even some of their toxic byproducts
https://www.eurekalert.org/news-releases/1071523
INTRO: In the quest to take the “forever” out of “forever chemicals,” bacteria might be our ally. Most remediation of per- and polyfluoroalkyl substances (PFAS) involves adsorbing and trapping them, but certain microbes can actually break apart the strong chemical bonds that allow these chemicals to persist for so long in the environment.
Now, a University at Buffalo-led team has identified a strain of bacteria that can break down and transform at least three types of PFAS, and, perhaps even more crucially, some of the toxic byproducts of the bond-breaking process.
Published in this month’s issue of Science of the Total Environment, the team’s study found that Labrys portucalensis F11 (F11) metabolized over 90% of perfluorooctane sulfonic acid (PFOS) following an exposure period of 100 days. PFOS is one of the most frequently detected and persistent types of PFAS and was designated hazardous by the U.S. Environmental Protection Agency last year.
The F11 bacteria also broke down a substantial portion of two additional types of PFAS after 100 days: 58% of 5:3 fluorotelomer carboxylic acid and 21% of 6:2 fluorotelomer sulfonate... (MORE - details, no ads)
Imagining the physics of George R.R. Martin’s fictional universe
https://publishing.aip.org/publications/...-universe/
PRESS RELEASE: Many science fiction authors try to incorporate scientific principles into their work, but Ian Tregillis, who is a contributing author of the Wild Cards book series when he’s not working as a physicist at Los Alamos National Laboratory, took it one step further: He derived a formula to describe the dynamics of the fictional universe’s viral system.
In independent research published in the American Journal of Physics, from AIP Publishing, Tregillis and George R.R. Martin derive a formula for viral behavior in the Wild Cards universe.
Wild Cards is a science fiction series written by a collection of authors and edited by Martin and Melinda M. Snodgrass. Sitting at over 30 volumes, the books are about an alien virus called the Wild Card that mutates human DNA. Martin is credited as a co-author of the paper, making it his first peer-reviewed physics publication.
The idea to explore the science behind the fictional virus came from a series of blog posts on the Wild Cards website.
“Like any physicist, I started with back-of-the-envelope estimates, but then I went off the deep end. Eventually I suggested, only half-jokingly, that it might be easier to write a genuine physics paper than another blog post,” Tregillis said. “Being a theoretician, I couldn't help but wonder if a simple underlying model might tidy up the canon.”
The formula he derived is a Lagrangian formulation, which considers the different ways a system can evolve. It’s also a fundamental physics principle, which also makes the fictional example a powerful teaching tool.
Tregillis shared that deriving this physical model was a fun but open-ended puzzle. After some trial and error of models based on fractals or thermodynamic analogies, he and Martin settled on the Lagrangian approach.
“We translated the abstract problem of Wild Card viral outcomes into a simple, concrete dynamical system. The time-averaged behavior of this system generates the statistical distribution of outcomes,” he said.
While the Wild Card virus can be modeled by physics, Tregillis emphasized that it isn’t a hard-and-fast rule in the canon.
“Good storytelling is about characters: their wants, needs, obstacles, challenges, and how they interact with their world,” Tregillis said. “The fictional virus is really just an excuse to justify the world of Wild Cards, the characters who inhabit it, and the plot lines that spin out from their actions.”
- - - - - - -
The article “Ergodic Lagrangian dynamics in a superhero universe” is authored by Ian Tregillis and George R.R. Martin. It will appear in the American Journal of Physics on Jan. 23, 2025 (DOI: 10.1119/5.0228859). After that date, it can be accessed at https://doi.org/10.1119/5.0228859
https://www.quantamagazine.org/the-jagge...-20250123/
EXCERPT: . . . The proof demonstrated that calculus could no longer rely on geometric intuition, as its inventors had done. It ushered in a new standard for the subject, one that was rooted in the careful analysis of equations. Mathematicians were forced to follow in Weierstrass’ footsteps, further sharpening their definition of functions, their understanding of the relationship between continuity and differentiability, and their methods for computing derivatives and integrals. This work to standardize calculus has since grown into the field known as analysis; Weierstrass is considered one of its founders.
But his function’s legacy extends far beyond the foundations of calculus and analysis. It revealed that mathematics is full of monsters: impossible-seeming functions, strange objects (it’s one of the earliest examples of a fractal), wild behaviors. “There’s a whole universe of possibilities, and the Weierstrass function is supposed to be opening your eyes to it,” said Philip Gressman (opens a new tab) of the University of Pennsylvania.
It also turned out to have many practical applications. In the early 20th century, physicists wanted to study Brownian motion, the random movement of particles in a liquid or gas. Because this movement is continuous but not smooth — characterized by rapid and infinitely tiny fluctuations — functions like Weierstrass’ were perfect for modeling it. Similarly, such functions have been used to model uncertainty in how people make decisions and take risks, as well as the complicated behavior of financial markets.
Much like Weierstrass himself, the consequences of his function have sometimes been late to bloom. But they’re continuing to shape mathematics and its applications today... (MORE - missing details)
Bacteria found to eat forever chemicals — and even some of their toxic byproducts
https://www.eurekalert.org/news-releases/1071523
INTRO: In the quest to take the “forever” out of “forever chemicals,” bacteria might be our ally. Most remediation of per- and polyfluoroalkyl substances (PFAS) involves adsorbing and trapping them, but certain microbes can actually break apart the strong chemical bonds that allow these chemicals to persist for so long in the environment.
Now, a University at Buffalo-led team has identified a strain of bacteria that can break down and transform at least three types of PFAS, and, perhaps even more crucially, some of the toxic byproducts of the bond-breaking process.
Published in this month’s issue of Science of the Total Environment, the team’s study found that Labrys portucalensis F11 (F11) metabolized over 90% of perfluorooctane sulfonic acid (PFOS) following an exposure period of 100 days. PFOS is one of the most frequently detected and persistent types of PFAS and was designated hazardous by the U.S. Environmental Protection Agency last year.
The F11 bacteria also broke down a substantial portion of two additional types of PFAS after 100 days: 58% of 5:3 fluorotelomer carboxylic acid and 21% of 6:2 fluorotelomer sulfonate... (MORE - details, no ads)
Imagining the physics of George R.R. Martin’s fictional universe
https://publishing.aip.org/publications/...-universe/
PRESS RELEASE: Many science fiction authors try to incorporate scientific principles into their work, but Ian Tregillis, who is a contributing author of the Wild Cards book series when he’s not working as a physicist at Los Alamos National Laboratory, took it one step further: He derived a formula to describe the dynamics of the fictional universe’s viral system.
In independent research published in the American Journal of Physics, from AIP Publishing, Tregillis and George R.R. Martin derive a formula for viral behavior in the Wild Cards universe.
Wild Cards is a science fiction series written by a collection of authors and edited by Martin and Melinda M. Snodgrass. Sitting at over 30 volumes, the books are about an alien virus called the Wild Card that mutates human DNA. Martin is credited as a co-author of the paper, making it his first peer-reviewed physics publication.
The idea to explore the science behind the fictional virus came from a series of blog posts on the Wild Cards website.
“Like any physicist, I started with back-of-the-envelope estimates, but then I went off the deep end. Eventually I suggested, only half-jokingly, that it might be easier to write a genuine physics paper than another blog post,” Tregillis said. “Being a theoretician, I couldn't help but wonder if a simple underlying model might tidy up the canon.”
The formula he derived is a Lagrangian formulation, which considers the different ways a system can evolve. It’s also a fundamental physics principle, which also makes the fictional example a powerful teaching tool.
Tregillis shared that deriving this physical model was a fun but open-ended puzzle. After some trial and error of models based on fractals or thermodynamic analogies, he and Martin settled on the Lagrangian approach.
“We translated the abstract problem of Wild Card viral outcomes into a simple, concrete dynamical system. The time-averaged behavior of this system generates the statistical distribution of outcomes,” he said.
While the Wild Card virus can be modeled by physics, Tregillis emphasized that it isn’t a hard-and-fast rule in the canon.
“Good storytelling is about characters: their wants, needs, obstacles, challenges, and how they interact with their world,” Tregillis said. “The fictional virus is really just an excuse to justify the world of Wild Cards, the characters who inhabit it, and the plot lines that spin out from their actions.”
- - - - - - -
The article “Ergodic Lagrangian dynamics in a superhero universe” is authored by Ian Tregillis and George R.R. Martin. It will appear in the American Journal of Physics on Jan. 23, 2025 (DOI: 10.1119/5.0228859). After that date, it can be accessed at https://doi.org/10.1119/5.0228859