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.

What is a space-filling curve capable of doing in terms of dimensions?

• Creating a 4D space from a 3D space

• Labeling every point in 3D space with one coordinate

• Filling up 2D space using a 3D curve

• Filling up 3D space using a 2D curve

Why is it difficult to definitively say we live in three-dimensional space?

• Because we lack the technology to measure dimensions

• Because dimensions are a theoretical concept

• Because we can only perceive two dimensions

• Because space can be represented with fewer dimensions

What method is suggested to test the dimensionality of space?

• Observing the behavior of light

• Analyzing the movement of planets

• Calculating the speed of sound

• Measuring the diffusion of gas

In a one-dimensional space, how do volume and radius relate?

• Volume and radius are the same up to a factor

• Volume is radius cubed

• Volume is radius squared

• Volume is radius to the fourth power

What does the diffusion of gas in 3D space demonstrate?

• That gas does not spread in 3D

• That gas spreads faster in 2D

• That volume is radius squared

• That volume is radius cubed