Comment by nyrikki

The one place that I think the previous discussion lost something important, at least to me with functions.

The popular lens is the porcupine concept when infinite dimensions for functions is often more effective when thought of as around 8:00 in this video.

https://youtu.be/q8gng_2gn70

While that video obviously is not fancy, it will help with building an intuition about fixed points.

Explaining how the dimensions are points needed to describe a functions in a plane and not as much about orthogonal dimensions.

Specifically with fixed points and non-expansive mappings.

Hopefully this helps someone build intuitions.