Something I see a lot that I think blocks understanding is “the dimensions”, “the 3rd dimension”, “the 4th dimension”, etc. This is wrong.
Dimensionality is a property of something. It is a number which describes some aspect of a thing. As others have said, it corresponds to the number of “independent directions” needed to describe a thing, but these directions need not be uniquely definable in any way, and most certainly you cannot say “this is the first one, this is the second one”, etc.
As a small example, just as you can say North and East are two independent directions on a map, you can also say South and North North East are as well; either of these facts on their own imply that a map is at least two dimensional. The fact that you cannot find a third independent direction means a map is two dimensional.
Something I see a lot that I think blocks understanding is “the dimensions”, “the 3rd dimension”, “the 4th dimension”, etc. This is wrong.
Dimensionality is a property of something. It is a number which describes some aspect of a thing. As others have said, it corresponds to the number of “independent directions” needed to describe a thing, but these directions need not be uniquely definable in any way, and most certainly you cannot say “this is the first one, this is the second one”, etc.
As a small example, just as you can say North and East are two independent directions on a map, you can also say South and North North East are as well; either of these facts on their own imply that a map is at least two dimensional. The fact that you cannot find a third independent direction means a map is two dimensional.