the horizontal self is your worldly self, in the world, of the world, completely dependent for everything on the world, on others, on the culture, other people's knowledge, other people's opinions, other people's money.
This self is the periphery of you, it connects with the world with the mind, the senses, the emotions, the story... while your insides suffer.
None of your work gets done, no satisfaction, no fulfillment, no sense of self... puppet on a string.
The rule of the horizontal plane where the horizontal self plays is competition, comparison, one having power over the other, superiority, inferiority, using people, and such. Not pretty.
99% of people are on this plane, the horizontal plane 99% of their lives.