In a large, rectangular art gallery room, a performance art piece is being conducted by three performers named Lakshmi, Dmitri, and Joao. Each performer is standing at a different corner of the room, with Lakshmi at the northeast corner, Dmitri at the southeast corner, and Joao at the northwest corner. The southwest corner remains empty. In the center of the room stands a large opaque cube-shaped sculpture that is as tall as an average adult, effectively blocking direct line of sight across the room's diagonal lines.

The performance involves the participants moving around the room along the walls while wearing distinctively colored hats that are visible above the sculpture if they are standing up. Lakshmi has a vivid red hat, Dmitri sports a bright blue hat, and Joao wears a striking yellow hat. 

As part of the performance, Lakshmi starts moving along the eastern wall toward the southern corner at a walking pace, and simultaneously Dmitri begins to walk at the same pace along the southern wall towards the western corner. Joao remains stationary at his corner. From the perspective of Joao, who cannot move from his position but can turn his head in any direction, the question arises: in what order and which colored hats can Joao see move across the two visible corners of the sculpture, and what might he infer about the performers' movements given his limited perspective?
Joao, situated in the northwest corner of the room, has his vision obstructed by the central sculpture when trying to look directly across the diagonal to the southeast corner where Dmitri started. Similarly, the northeast corner, where Lakshmi began, is obscured by the sculpture when Joao attempts to peer diagonally across to that corner. However, he has an unobstructed view of the eastern and southern walls, where Lakshmi and Dmitri are walking toward the southern and western corners, respectively.

As Lakshmi starts moving southward along the eastern wall, her red hat will become visible to Joao as soon as she steps beyond the sculpture's eastern edge from his point of view. She will continue to be in his line of sight until she reaches the southeast corner, at which point the sculpture will once again block Joao's view of her as she turns and moves along the southern wall.

Concurrently, Dmitri, traveling westward along the southern wall with his blue hat, will initially be out of Joao's line of sight due to the sculpture. Only when Dmitri passes the sculpture's southern edge will his blue hat come into Joao's vision. Dmitri's blue hat will remain visible to Joao as he makes his way to the western corner, but eventually, Dmitri will turn the corner and move out of sight along the western wall.

Therefore, Joao will first observe the red hat of Lakshmi passing by the visible eastern corner of the sculpture. Next, after a brief period when Lakshmi's red hat disappears behind the southeastern edge of the sculpture, Dmitri's blue hat will come into view as he passes the visible southern corner of the sculpture. The order of visibility from Joao's perspective is, therefore: Lakshmi's red hat followed by Dmitri's blue hat.

Based on these observations, Joao can infer several things about their movements. Since Joao sees Lakshmi's red hat before he sees Dmitri's blue hat, he can deduce that Lakshmi has already crossed the eastern edge of the sculpture and that Dmitri took slightly longer to reach the southern edge visible to Joao, implying that he was farther away from that point than Lakshmi was from hers at the start. Furthermore, Joao knows that once the hats disappear from his line of sight, they have either reached a corner or are walking along a wall that is obscured by the sculpture from his standpoint. He can also infer that while he can't see either performer, they are continuing to move along the walls parallel to the ones he observed them on, as per the performance's premise.