Thinking intuitively about higher dimensionality in physics

See this laundry pile? Looks just like our universe.
Here, have another.
See it now? It’s got three dimensions and all.
But look again.
The shirts and towels? They’re not truly three-dimensional. They’re really crinkled and interlocked two-dimensional surfaces.
These surfaces aren’t real, after all. It’s really one-dimensional yarn, knotted up tightly.
You ok?
Have another.
I see it clearly now. It’s everything at once, one-two-three dimensional. It just depends on how closely you look at it.
Amazing, don’t you think? What if our universe was just like that?

Another way to think about this is to imagine becoming an ant, or a giant on a whim. What to a human might be a thick pipe (3-dimensional) might be to an ant a curved field (2-dimensional, and to a giant, a thin toothpick (1-dimensional). All are true, relative to the observer.