The vertical self is the part of you that is connected to all-of-it. It is the part of you that isn't concerned with the world, opinions, competition, who is superior to who, using people, and such.
It is like a tree: striving to grow taller, to reach the stars, doing what is challenging and yet causes pleasure and satisfaction.
It relates to the lower, the horizontal self and the horizontal plane with mild amusement and curiosity, much like one would look at interesting bugs...
The position of this relationship, the vantage point is that of the Watcher or the Observer. It might also be called the Witness.
When you live from your vertical Self, then all-of-it is the witness of your life, so you don't NEED another, although you can connect and enjoy being with another, but you don't need them.