Just a commentary or tirade if you want to call it that.
W alphabetically comes before X and not after Z. So a point in 4D space should be (W,X,Y,Z) not (X,Y,Z,W). I know it is nit-picky.
Also, people should get into the habit of saying "four spacial dimensions" or "four dimensions of distance" and not assume that distance is always implied when you say "dimension". I can have four dimensions that have differing units such as energy, charge, mass and time. None of these are "distance". Also, mathematicians often talk about "4D Space" and they are often not talking about Distance Dimensions. They are often sloppy in other ways like omitting operators as in A = 4B + C. They should write A = 4 × B + C. It's one of my gripes about what mathematicians do. This omission makes it impossible to use variable and constant names that are more than one letter long. For example, would A = BC + D be equivalent to A = B × C + D or is BC a variable name? Their laziness is what turned me off to being a math major and the field in general.
My brother once told me a story about a mathematician who committed suicide because he ran out of mathematical symbols to serve as variable names. Programmers have solved that problem by always showing the operators explicitly instead of making them invisible and making every body else guess as to what they mean.
I guess what I am saying is that a lot of confusion comes from being inconsistent with the words we use in our sentences.
