How can I conceptualize an array with more than three dimensions?

Question

I just learned about arrays but can't conceptualize arrays with more than three dimensions.

Answer 1

Imagine the following:

• Letters on the line of a book
• Lines on a page of a book
• Pages of the book
• Books in a bookshelf
• A room full of bookshelves
• House full of rooms
• A street with a number of houses
• A town with streets
• A Country with towns
• A planet with countries
• A universe full of planets
• And finally, a big array of universes.

Viola, a 12 dimensional array.

Answer 2

Imagine a series of 3-dimensional cubes, one after another.

You can also think of it as a single 3D cube evolving over discrete intervals of time.

I find these helpful if you want a mental model that fits into the usual spatial (plus time) system, i.e. something whose dimensions you can visualize all at once in the physical world.