[the_af]

Haha, I never understood why the point-free (aka "pointless") form in Haskell actually is the form that requires lots of "."!

[tome]

"Points" means something like "elements". When you write

    \x -> f (g x)

you are defining a function that explicitly specifies how each "point" `x` is to be mapped. When you write

    f . g

you don't mention any point. You are abstracting away from the notion of point. That's why it's "point free".