High-dimensional mathematics underpins fundamental physics, computation, and many aspects of modern life.

Intuitively, we can picture a one-dimensional entity, eternally restricted to walking an infinite line, or a two-dimensional being resigned to life on a flat plane. We do not have to picture three-dimensional beings, as that is how we experience our universe.

Yet, the computational power driving the modern world thrives in abstract spaces of five, 10, or even thousands of dimensions. How does high-dimensional mathematics allow us to process and interpret information, and reveal hidden patterns that govern everything from our biology to artificial intelligence?

This week at the HLFF Blog, Ben Skuse explores that exact question. Read more here: HLFF Blog

Image caption: From left to right, depiction of one-, two- and three-dimensional beings. This image was created with the assistance of Google Gemini.