Refer to this link for part 1.
Okay, now we can continue pondering the implication of the infinite hotel paradox. We will start from the scenario already laid out in part 1 where one pulse of a sleepy guest knocking on the 
neighbour’s door and requesting him to do the same for the room next door. Can we imagine further things from here than accepting that this nightmare will continue forever?
Well, yes. First, we can imagine sound can travel faster than the speed of this wave of sleepy guests moving. With that, we can imagine a wavefront of sound traveling faster than the weary guests and say it decays exponentially. Thus, we can imagine that when the 
starts to knock on the 
‘s door, there are 
number of guests who already realize the situation and start to move too. In practice, the sound velocity is finite but way larger than the speed of the person moving. So the above approximation is relatively feasible. In this situation, the frontwave speed will be the same (which is the speed of the front people moving), but instead of only one person, now we have number of person moving simultaneously. Obviously, this is faster than only one person moving.
Now, instead of relying on one person knocking, say the receptionist will flash a laser from his position which will alert a sensor in each room to ask them to shift one room further. So in this case, the information is carried by the photon instead of sound. Since light has a finite speed we can imagine that there is still time needed for each room to be alerted by 
where 
is the distance of the room from the receptionist. In this scenario, there will be several sleepy guests on the move where the furthest informed guest is determined by the speed of light. It is still a nightmare, but at least it is a collective nightmare than just a single person on the move nightmare.
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