How does one "carry Zen every minute" as mentioned in the Koan below?

Merely suggesting that there is no "one" to "carry Zen" does not change one's mental habbits.

Every-Minute Zen

Zen students are with their masters at least ten years before they presume to teach others. Nan-in was visited by Tenno, who, having passed his apprenticeship, had become a teacher. The day happened to be rainy, so Tenno wore wooden clogs and carried an umbrella. After greeting him Nan-in remarked: "I suppose you left your wodden clogs in the vestibule. I want to know if your umbrella is on the right or left side of the clogs."

Tenno, confused, had no instant answer. He realized that he was unable to carry his Zen every minute. He became Nan-in's pupil, and he studied six more years to accomplish his every-minute Zen.

(http://deoxy.org/koan/35)

When Yunyan was sweeping, Douwu said "Too busy"

Yunyan said "You should know when there's one who isn't busy"

Douwu said "If so, there's a second moon"

Yunyan held up the broom and said "Which moon is this?"

(http://zen.thetao.info/perceive/koan.htm)

So what's going on here? Is Douwu merely denying the self-reference ("You should know")?

Just before Ninakawa passed away the Zen master Ikkyu visited him. "Shall I lead you on?" Ikkyu asked.

Ninakawa replied: "I came here alone and I go alone. What help could you be to me?"

Ikkyu answered: "If you think you really come and go, that is your delusion. Let me show you the path on which there is no coming and no going."

With his words, Ikkyu had revealed the path so clearly that Ninakawa smilled and passed away.

Ikkyu seems to be suggesting that there is a self that is not 'subject to'. And nothing is the only thing that is not subject-to.

But if it really isn't there (if there is no self), Zen's utility reduces to a conceptual understanding: "there is no self". Something that 'one' may have a glimpse of in meditation. But generally one continues living one's life as if there was.

Does realization = not taking possession ("selfing" & valuating)? ...for what reason?

Also, unless I'm getting something wrong (which I probably am), this all seems useless [to "me"]. I'd rather learn about mathematical theorems and axioms (the Great Truths). Or better yet, find a real way to boost the ego and/or happiness ;).