"Know Yourself" -> Master your Spirit aka Conquerors Haki
"Know the World" -> The World is Imu, yeah? So perhaps, something related to Omen powers?
Sommers also talked about how Omen powers are the perfect counterpart to Conquerors Haki this chapter.
And Mihawk clearly has some connection to the Celestial Dragons.
Maki/Omen is indeed our first guess when we think of knowing the world, especially when we see how Imu is presented & how He talked about that power, but I feel unsure about Sommers Words, because even Imu couldn't fully block Gaban's CoC Attack,
If Shanks or Roger were there, They wouldn't have taken any damage, their CoC & Gaban's would have cancelled each other out or just had an insane clash, but Imu was clearly struggling to block, and it doesn't matter if He was trying hard or not, because supposedly Omen counters CoC, similar to how lightning can't hurt Luffy's rubber or how Darkness absorbs fire or almost anything else,
Also, Joy Boy clearly knows about Maki, and yet He gave Emet a rope of Haoshoku Haki, so I don't think it's entirely true that Omen counters Haoshoku Haki, I think Maki is opposite of CoC because it's fueled by Submission rather than Dominance,
So while CoC allows you to dominate others & weaken them & make you submit, Maki in turn weaponizes & turns that submission into Power, that's why it's considered a counter, but it's not like a higher level than CoC.
Know the world imo is understanding where Haki actually comes from, as this might seem like a plot twist, but I'm pretty convinced that it doesn't come from people, it's only quantified by them.
