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Category: mathematics

Bell-bottoms today, miniskirts tomorrow: Math reveals fashion’s 20-year cycle

Fashion insiders and beauty magazines have long cited the “20-year-rule”—the idea that clothing trends often resurface every two decades. According to Northwestern University scientists, that observation isn’t just anecdotal. It’s a mathematical reality.

In a new study, the Northwestern team developed a new mathematical model showing that fashion trends tend to cycle roughly every 20 years. By analyzing roughly 37,000 images of women’s clothing spanning from 1869 to today, the team found that styles rise in popularity, fall out of favor and then eventually experience renewal. Along with supporting common perceptions about the life cycles of fads, the researchers say these results could help explain how new ideas spread in society.

The study’s lead author, Emma Zajdela, will present these findings on Tuesday, March 17, at the American Physical Society (APS) Global Physics Summit in Denver. Her talk, “Back in Fashion: Modeling the Cyclical Dynamics of Trends,” is part of the session “Statistical Physics of Networks and Complex Society Systems.”

💡 We talk about the past as if it’s gone forever — erased, unreachable, finished

But according to Richard Feynman and the laws of physics, that intuition is deeply misleading.

At the fundamental level, the equations that describe reality don’t care which way time flows. The same mathematics behind Quantum Electrodynamics — the most precisely tested theory in science — work just as well forward in time as they do backward.

In this video, we explore why the past may not be as “gone” as it feels.

🎥 *In this video, we explore:*
→ Why the laws of physics don’t distinguish past from future
→ How particles can be treated as moving backward in time in calculations
→ What time symmetry really means — and what it doesn’t
→ Why our experience of time is not fundamental
→ How Feynman explained time without mysticism.

This isn’t philosophy or speculation.
This is how physicists actually calculate the universe.

📚 *Based on the work of:*

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Consciousness is the hidden architecture behind fundamental and quantum physics

Physics and phenomenology are usually taken to inhabit different worlds. Physics aims at a description of objective reality in mathematical terms. Phenomenology—the philosophical movement inaugurated by Edmund Husserl—is an a priori investigation into consciousness and into the ways things appear in experience. Physics deals with equations, invariants, and symmetries, aiming to represent reality minus observers; phenomenology seems to concern precisely what physics leaves out: subjectivity, consciousness, meaning. If the two meet at all, it is only in polite, but ultimately inconsequential, interdisciplinary dialogue.

My claim is that this picture is mistaken. Physics does not stand outside phenomenology. It presupposes the very structures phenomenology seeks to analyse—above all, the structured correlation between subject and object through which objectivity first becomes intelligible. The task, therefore, is not to unite two distant domains, but to recognize a relation that has been there from the beginning.

To make this more tangible, consider what physics means by objectivity. Contrary to the image sometimes promoted in popular science—objectivity as detachment from all observers—in spacetime physics, objectivity is defined by invariance across observers. A physical description is deemed objective if it holds regardless of the coordinate frame in which it is expressed.

THOR AI solves a 100-year-old physics problem in seconds

A new AI framework called THOR is transforming how scientists calculate the behavior of atoms inside materials. Instead of relying on slow simulations that take weeks of supercomputer time, the system uses tensor network mathematics and machine-learning models to solve the problem directly. The approach can compute key thermodynamic properties hundreds of times faster while preserving accuracy. Researchers say this could accelerate discoveries in materials science, physics, and chemistry.

Mathematicians find one pi formula to rule them all

From the article:

“Each equation [for calculating π ] seemed unrelated to the others. But in late 2025, a team of seven AI researchers at the Technion–Israel Institute of Technology found a previously unknown mathematical structure underlying hundreds of pi formulas, including those of Archimedes, Euler and Ramanujan. “It’s not every day that you get to cite Archimedes,” says Ph.D. student Michael Shalyt, part of the team. The structure, called a conservative matrix field, or CMF, acts as a kind of mathematical common ancestor, showing how formulas that look nothing alike turn out to be different expressions of the same underlying object.”

A mixture of AI and algorithms uncovered a hidden structure spanning 2,000 years of equations for pi.

By Lyndie Chiou edited by Clara Moskowitz.

The Singularity Needs a Navigator

In 2013, physicist Alex Wissner-Gross published a single equation for intelligence in [ITALIC] Physical Review Letters [/ITALIC]: # F = T∇Sτ

The force of an intelligent system equals its temperature — computational capacity, raw horsepower — multiplied by the gradient of its future option-space. Intelligence is not a mysterious property of carbon-based brains.

It is a physical force: the tendency of any sufficiently energetic system to maximize the number of future states accessible to it.

The equation was elegant. Correct. And incomplete.

It describes the force. It does not describe the geometry of the space through which that force navigates.

A gradient without a metric is a direction without distance — it tells the system where to push but not what distortion it will encounter on the way there.

We spent three years building the geometry. We tested it across 69 billion simulations. What we found changes everything. ## The Missing Geometry — From Force to Navigation.

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3 Questions: On the future of AI and the mathematical and physical sciences

Curiosity-driven research has long sparked technological transformations. A century ago, curiosity about atoms led to quantum mechanics, and eventually the transistor at the heart of modern computing. Conversely, the steam engine was a practical breakthrough, but it took fundamental research in thermodynamics to fully harness its power.

Today, artificial intelligence and science find themselves at a similar inflection point. The current AI revolution has been fueled by decades of research in the mathematical and physical sciences (MPS), which provided the challenging problems, datasets, and insights that made modern AI possible. The 2024 Nobel Prizes in physics and chemistry, recognizing foundational AI methods rooted in physics and AI applications for protein design, made this connection impossible to miss.

In 2025, MIT hosted a Workshop on the Future of AI+MPS, funded by the National Science Foundation with support from the MIT School of Science and the MIT departments of Physics, Chemistry, and Mathematics. The workshop brought together leading AI and science researchers to chart how the MPS domains can best capitalize on — and contribute to — the future of AI. Now a white paper, with recommendations for funding agencies, institutions, and researchers, has been published in Machine Learning: Science and Technology. In this interview, Jesse Thaler, MIT professor of physics and chair of the workshop, describes key themes and how MIT is positioning itself to lead in AI and science.

Fundamental constraints to the logic of living systems

Excellent review in which Solé et al. explore how physical/mathematical constraints may determine what subset of biological systems could theoretically evolve in the universe. Lots of fascinating ideas applying concepts like Turing machines, cellular automata, McCulloch-Pitts networks, energy minimization, and phase transitions to multiscale biological and evolutionary phenomena!

I found the description of how parasites almost inevitably emerge and drive increased biodiversity in computational models of evolution particularly fascinating. Interestingly, I recall this idea was featured in the Hyperion Cantos novels during an explanation of the history of artificial intelligence in their fictional universe!

Abstract. It has been argued that the historical nature of evolution makes it a highly path-dependent process. Under this view, the outcome of evolutionary dynamics could have resulted in organisms with different forms and functions. At the same time, there is ample evidence that convergence and constraints strongly limit the domain of the potential design principles that evolution can achieve. Are these limitations relevant in shaping the fabric of the possible? Here, we argue that fundamental constraints are associated with the logic of living matter. We illustrate this idea by considering the thermodynamic properties of living systems, the linear nature of molecular information, the cellular nature of the building blocks of life, multicellularity and development, the threshold nature of computations in cognitive systems and the discrete nature of the architecture of ecosystems. In all these examples, we present available evidence and suggest potential avenues towards a well-defined theoretical formulation.

World’s most advanced supercomputers decode nuclear reactor turbulence

At Argonne National Laboratory, researchers are trading in old-school approximations for raw supercomputing power, proving that the secret to a safer carbon-free future lies in mastering the math of chaos.

Researchers are advancing nuclear safety by using high-performance computing to model turbulent flow — the chaotic movement of fluids and gases that governs heat transfer and gas mixing within a reactor.

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