In The Expanse (TV), Series 3, what is The Investigator talking about when he says "Doors and Corners"?

Question

In Season 1's episode "Doors and Corners", the actual Miller talks about how "doors and corners" are where they can get you, and that one on an attack (or in his case, police action) should always be on the lookout for doors and corners. I get that.

The Investigator is played by the same actor as Miller (and is known as "Miller" to Holden when he first appears) and it is strongly implied that Miller's memories or something is absorbed by the protomolecule. Logically, the protomolecule would act like Miller for many reasons. However, The Investigator often talks about "Doors and Corners" to Holden. This is odd because:

1. Holden was not on Thoth station, so presumably didn't hear Miller say that, although that is speculative
2. Doors and corners refers to hidden enemies

Is there any canon explanation to why The Investigator keeps repeating that phrase?

Answer 1

You've asked about the TV show but the books have more and better examples of Miller's use of the "doors and corners" phrase so the books are more illuminating.

Miller does not use the phrase "doors and corners" until the third book, Abaddon's Gate, at which point Miller is The Investigator. The first use of the phrase is:

“Doors and corners,” Miller said. His voice was soft and rough. “I tell you check your doors and corners, and you blow into the middle of the room with your dick hanging out. Lucky sonofabitch. Give you this, though, you’re consistent.”

_{Abaddon's Gate, p. 174}

He gives a better explanation of what he means later:

“You don’t know what’s in here. Doors and corners. Never walk into a crime scene until you know there’s not someone there waiting to put you down. You’ve got to clear the room first..."

_{Abaddon's Gate, p. 235}

Holden still didn't completely understand the meaning by that point, as he later complains to himself that Miller wasn't explicit enough:

Doors and corners, Miller had warned him. The places where you got killed if you weren’t paying attention. Where the ambushes happened. Could have been a little more explicit, Holden thought, and then imagined Miller shrugging apologetically and bursting into a cloud of blue gnats.

_{Abaddon's Gate, p. 410}

Without unnecessarily revealing spoilers, all these warnings are given in the context of humans trying to learn about the protomolecule's creators. The warnings are for Holden specifically as well as the entire human species:

“I keep warning you. Doors and corners, kid. That’s where they get you. Humans are too fucking stupid to listen. Well, you’ll learn your lessons soon enough, and it’s not my job to nursemaid the species through the next steps.”

_{Abaddon's Gate, p. 520}

Holden starts to use the phrase after interacting with The Investigator, and as he and the rest of humanity learn more about the protomolecule's creators (their history, their creations, etc.).

It's also worth noting that Miller's Star Helix partner Dimitri Havelock uses the phrase in the context of police action training after Miller became The Investigator. Havelock did not interact with Miller as The Investigator so evidently Miller taught it to him while the two worked for Star Helix. Havelock's explanation of the phrase is very similar to Miller's:

"We have a natural tendency to see an empty space and think it’s safe. Doors and corners are always dangerous, because you’re moving into something without being sure what’s there. By the time you see the enemy, you’re exposed to them.”

_{Cibola Burn, p. 192}

Answer 2

My Interpretation of that phrase is very close to the second oddity you mention, "Hidden enemies". I believe that is exactly what he was trying to convey. When tackling Doors and corners, you want to Take your time, and check every angle and corner before proceeding into the room, where as rushing in exposes you to the unknown dangers within. This I believe is how the protomolecule(via Millers memories) cryptically explains the concept of the slow zone, by telling him to slow it down to avoid danger.