What is a Dimension (In 3D... and 2D... and 1D)

The video explores the concept of living in three dimensions, questioning how we know our space is 3D. It introduces the idea of space-filling curves, which can label every point in 3D space with one coordinate, challenging our perception of dimensionality. The video then discusses testing dimensionality by observing gas diffusion, where the relationship between volume and radius differs across dimensions. Ultimately, it concludes that while we perceive space as 3D, determining dimensions is complex.

Why is the diffusion of gas relevant to understanding the dimensions we live in?

What conclusion can be drawn about the nature of dimensions based on the behavior of gas?