May 23, 2025 05:41 PM
A theory of everything will never work at all scales
https://iai.tv/articles/a-theory-of-ever..._auid=2020
INTRO: Physicists have long hoped to discover a single, all-encompassing theory of everything that would unlock the secrets of the universe. But, as LMU Munich philosopher of science, Stephan Hartmann, argues, a new picture is emerging—one where no single framework reigns supreme. Effective field theories are transforming how we understand science itself. Rather than reducing everything to fundamental laws, they offer a patchwork of powerful, scale-sensitive models that reflect the layered structure of reality. What, if the most reliable truths are not universal, but local, scale-dependent and context-dependent?
EXCERPTS: Instead of aiming for a single final theory, physics increasingly resembles a tower of theories: one for atoms, another for nuclei, another for quarks. Each level is largely autonomous, yet still connected to the levels above and below. This layered structure is made precise by renormalization group methods, which help us understand how a system’s behavior changes as we shift from one scale to another. You can think of these methods as a kind of theoretical zoom lens: as we zoom out, the fine-grained details blur, and broad, stable patterns come into focus.
[...] The layered structure of scientific theories complicates the traditional picture of reductionism. While higher-level theories can sometimes be derived from lower-level ones, the process is rarely straightforward—and even when it succeeds, the resulting derivation may obscure more than it reveals.
[...] What effective field theories ultimately support, then, is not a wholesale rejection of reductionism, but a more pragmatic and flexible picture of scientific explanation. Understanding emerges from models that are tractable, context-sensitive, and responsive to the structures that matter at a given scale.
In this sense, emergence becomes central to how science makes sense of the world. Phenomena such as fluid flow, superconductivity, or magnetism don’t fully reveal themselves at the micro-level. They become intelligible only through higher-level models that capture patterns irreducible to the underlying mechanics.
[...] If effective field theories are so useful, do we need a theory of everything? Many physicists now say no. As Harvard physicist Howard Georgi once quipped: “Who knows? Who cares?” For him, the point is not whether a final theory exists, but whether it's useful. This marks a shift from metaphysical ambition to methodological humility... (MORE - missing details)
Graduate Student Solves Classic Problem About the Limits of Addition
https://www.quantamagazine.org/graduate-...-20250522/
INTRO: The simplest ideas in mathematics can also be the most perplexing.
Take addition. It’s a straightforward operation: One of the first mathematical truths we learn is that 1 plus 1 equals 2. But mathematicians still have many unanswered questions about the kinds of patterns that addition can give rise to. “This is one of the most basic things you can do,” said Benjamin Bedert, a graduate student at the University of Oxford. “Somehow, it’s still very mysterious in a lot of ways.”
In probing this mystery, mathematicians also hope to understand the limits of addition’s power. Since the early 20th century, they’ve been studying the nature of “sum-free” sets — sets of numbers in which no two numbers in the set will add to a third. For instance, add any two odd numbers and you’ll get an even number. The set of odd numbers is therefore sum-free.
In a 1965 paper, the prolific mathematician Paul Erdős asked a simple question about how common sum-free sets are. But for decades, progress on the problem was negligible.
“It’s a very basic-sounding thing that we had shockingly little understanding of,” said Julian Sahasrabudhe, a mathematician at the University of Cambridge.
Until this February. Sixty years after Erdős posed his problem, Bedert solved it. He showed that in any set composed of integers — the positive and negative counting numbers — there’s a large subset of numbers that must be sum-free. His proof reaches into the depths of mathematics, honing techniques from disparate fields to uncover hidden structure not just in sum-free sets, but in all sorts of other settings.
“It’s a fantastic achievement,” Sahasrabudhe said... (MORE - details)
https://iai.tv/articles/a-theory-of-ever..._auid=2020
INTRO: Physicists have long hoped to discover a single, all-encompassing theory of everything that would unlock the secrets of the universe. But, as LMU Munich philosopher of science, Stephan Hartmann, argues, a new picture is emerging—one where no single framework reigns supreme. Effective field theories are transforming how we understand science itself. Rather than reducing everything to fundamental laws, they offer a patchwork of powerful, scale-sensitive models that reflect the layered structure of reality. What, if the most reliable truths are not universal, but local, scale-dependent and context-dependent?
EXCERPTS: Instead of aiming for a single final theory, physics increasingly resembles a tower of theories: one for atoms, another for nuclei, another for quarks. Each level is largely autonomous, yet still connected to the levels above and below. This layered structure is made precise by renormalization group methods, which help us understand how a system’s behavior changes as we shift from one scale to another. You can think of these methods as a kind of theoretical zoom lens: as we zoom out, the fine-grained details blur, and broad, stable patterns come into focus.
[...] The layered structure of scientific theories complicates the traditional picture of reductionism. While higher-level theories can sometimes be derived from lower-level ones, the process is rarely straightforward—and even when it succeeds, the resulting derivation may obscure more than it reveals.
[...] What effective field theories ultimately support, then, is not a wholesale rejection of reductionism, but a more pragmatic and flexible picture of scientific explanation. Understanding emerges from models that are tractable, context-sensitive, and responsive to the structures that matter at a given scale.
In this sense, emergence becomes central to how science makes sense of the world. Phenomena such as fluid flow, superconductivity, or magnetism don’t fully reveal themselves at the micro-level. They become intelligible only through higher-level models that capture patterns irreducible to the underlying mechanics.
[...] If effective field theories are so useful, do we need a theory of everything? Many physicists now say no. As Harvard physicist Howard Georgi once quipped: “Who knows? Who cares?” For him, the point is not whether a final theory exists, but whether it's useful. This marks a shift from metaphysical ambition to methodological humility... (MORE - missing details)
Graduate Student Solves Classic Problem About the Limits of Addition
https://www.quantamagazine.org/graduate-...-20250522/
INTRO: The simplest ideas in mathematics can also be the most perplexing.
Take addition. It’s a straightforward operation: One of the first mathematical truths we learn is that 1 plus 1 equals 2. But mathematicians still have many unanswered questions about the kinds of patterns that addition can give rise to. “This is one of the most basic things you can do,” said Benjamin Bedert, a graduate student at the University of Oxford. “Somehow, it’s still very mysterious in a lot of ways.”
In probing this mystery, mathematicians also hope to understand the limits of addition’s power. Since the early 20th century, they’ve been studying the nature of “sum-free” sets — sets of numbers in which no two numbers in the set will add to a third. For instance, add any two odd numbers and you’ll get an even number. The set of odd numbers is therefore sum-free.
In a 1965 paper, the prolific mathematician Paul Erdős asked a simple question about how common sum-free sets are. But for decades, progress on the problem was negligible.
“It’s a very basic-sounding thing that we had shockingly little understanding of,” said Julian Sahasrabudhe, a mathematician at the University of Cambridge.
Until this February. Sixty years after Erdős posed his problem, Bedert solved it. He showed that in any set composed of integers — the positive and negative counting numbers — there’s a large subset of numbers that must be sum-free. His proof reaches into the depths of mathematics, honing techniques from disparate fields to uncover hidden structure not just in sum-free sets, but in all sorts of other settings.
“It’s a fantastic achievement,” Sahasrabudhe said... (MORE - details)
