After introducing the ideas of tuples, vectors, and points, the book goes on to say:

But looking at (4, -4, 3) and (-4, 4, -3) , it’s impossible to know that one is a point

and the other is a vector. Let’s add a fourth component to these (x, y, z) tuples,

called w , to help us tell them apart. Set w to 1 for points, and 0 for vectors.

Thus, your point becomes (4, -4, 3, 1) , and your vector becomes (-4, 4, -3, 0) .

Now, the choice of 0 or 1 for w probably seems arbitrary just now, but sit

tight! It’ll make more sense when you get to Chapter 3, Matrices, on page 25,

where it turns out to be rather important for multiplying matrices and tuples.

This advice seems misguided to me, as it amounts to using the fourth component as a type code, and not even a symbolic one–you just have to remember that 1.0 in the fourth component means a vector and 0.0 indicates a point. Especially given that this book appears to be aimed towards fairly junior developers, that’s not a practice we should be encouraging.

I agree that it’s necessary to differentiate between vectors and points, and the best way to do it depends largely on the language you’re using. That said, every mainstream language that I know of has a better way to do that than what is suggested here.