I’m well aware that there had been so many theories regarding this topic from complicated ones to Oda probably closing his eye for aesthetic reason. But here is my take on it, for me it is simply to enhance his observation haki or even develop future sight. Here’s why:

The Japanese Culture of Tatemae and Honne

Most of us probably know already the concept of Tatemae and Honne in Japanese Culture. Tatemae refers to “white lies” or surface level intention and Honne to true intention. Most Japanese only show Tatemae and not their Honne or true feelings so as not to offend anyone.

Of course these does not only work in everyday life, it is also applied in samurai code. Based on the Legendary Undefeated Samurai Miyamoto Musashi in his book, ‘The Book of Five Rings’. “One must cultivate the intuition in order to ascertain an opponent’s true intention (Honne)”. It was even popularized in the quote and one of his winning strategies:

Even Zoro hinted about it the Fishman Island arc.

Two Types of Visions: Ken and Kan

According to Musashi, a samurai must develop Kan or deeper seeing of things to detect hidden enemies and impending attacks before it happens.

In conclusion:

We know well that Oda likes to resume some concepts from japanese culture and real samurai warriors and since Zoro sucks at direction and observation so probably Mihawk or Zoro himself chose to close it to develop his Kan or (in One Piece world) Observation Haki or even Future Sight. His concept drawing even looks like Date “the one-eyed dragon” Masamune, an undefeated samurai who is known to have supernatural observation and instinct.

*Theory by Dr. Ug P. Usher