Jeff Cassman

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.

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

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

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

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