Category theory lets you jump from the category of topological spaces to this other category. You can use something called a functor to translate your two topological spaces into vector spaces, for example. If you then find that the dimensions of the vector spaces are different — something that’s much easier to measure — then… Continue reading Where Does Meaning Live in a Sentence? Math Might Tell Us.
Category: Quantum Stuff
‘Paraparticles’ Would Be a Third Kingdom of Quantum Particle
When you swap two paraparticles, these hidden properties change in tandem. As an analogy, imagine that these properties are colors. Start with two paraparticles, one that’s internally red and another that’s internally blue. When they swap places, rather than keeping these colors, they both change in corresponding ways, as prescribed by the mathematics of the… Continue reading ‘Paraparticles’ Would Be a Third Kingdom of Quantum Particle
Earth’s Mysterious Inner Core Is Changing Shape
February 11, 2025 2 min read Earth’s Mysterious Inner Core Is Changing Shape Earth’s core is transforming, which could affect the length of our 24-hour day, Earth’s magnetic field, and more By Alexandra Witze & Nature magazine Earth’s inner core was long considered to be completely solid, but research has shown that it can be… Continue reading Earth’s Mysterious Inner Core Is Changing Shape
The High Cost of Quantum Randomness Is Dropping
Nothing is certain in the quantum realm. A particle, for example, can exist in multiple quantum states simultaneously. The same goes for a quantum bit, or qubit — the basic unit of information used in quantum computing. The act of measurement causes these objects to collapse into a single state, and usually the best you… Continue reading The High Cost of Quantum Randomness Is Dropping
A New Proof Smooths Out the Math of Melting
For any closed, compact surface — that is, a surface that is finite in diameter and has a distinct inside and outside — mean curvature flow is destined to lead to a singularity. (For a simple sphere, this singularity is the final point the surface shrinks to.) “We have this flow that is supposed to… Continue reading A New Proof Smooths Out the Math of Melting
Why Everything in the Universe Turns More Complex
“I had got disillusioned with the state of the art of looking for life on other worlds,” Wong said. “I thought it was too narrowly constrained to life as we know it here on Earth, but life elsewhere may take a completely different evolutionary trajectory. So how do we abstract far enough away from life… Continue reading Why Everything in the Universe Turns More Complex
Trump Spending Freeze on Rural Electric Co-ops Could Raise Energy Costs
CLIMATEWIRE | Billions of dollars for rural electric cooperatives are stuck in limbo as the Department of Agriculture continues the Trump administration’s funding freeze, despite federal court orders. The Empowering Rural America program — also known as New ERA, a $9.7 billion grant and loan program created by the Inflation Reduction Act — has been… Continue reading Trump Spending Freeze on Rural Electric Co-ops Could Raise Energy Costs
What Is the True Promise of Quantum Computing?
Quantum computing promises unprecedented speed, but in practice, it’s proven remarkably difficult to find important questions that quantum machines can solve faster than classical ones. One of the most notable demonstrations of this came from Ewin Tang, who rose to prominence in the field as a teenager. When quantum algorithms had in principle cracked the… Continue reading What Is the True Promise of Quantum Computing?
How a Problem About Pigeons Powers Complexity Theory
By January 2020, Papadimitriou had been thinking about the pigeonhole principle for 30 years. So he was surprised when a playful conversation with a frequent collaborator led them to a simple twist on the principle that they’d never considered: What if there are fewer pigeons than holes? In that case, any arrangement of pigeons must… Continue reading How a Problem About Pigeons Powers Complexity Theory
Why Private Forecasting Companies Can’t Replace the National Weather Service
The following essay is reprinted with permission from The Conversation, an online publication covering the latest research. When a hurricane or tornado starts to form, your local weather forecasters can quickly pull up maps tracking its movement and showing where it’s headed. But have you ever wondered where they get all that information? The forecasts… Continue reading Why Private Forecasting Companies Can’t Replace the National Weather Service