I Think My Head Is Broken

To illustrate this I want to describe what happened in the two minutes since a coworker posted the following on our internal messaging system:

[S]ome builders have arrived to put a wall in my room

Atomic Thoughts

The first thing I thought was: before they begin there is one room, when they are complete there are two. Does this transition occur according to some continuous function, that is at some point do you have 1.3 and 0.7 rooms? This seem absurd, clearly you still have one room just with a major obstacle somewhere near the middle. However if we analyse this thought further we can clearly see that there is some point, say the new wall is half the height of the room, when it seems more logical to describe the areas as two separate spaces. This is more akin to the phase transitions we normally see when for example water goes from liquid to gas, it is clearly boiling. That is there is a defined moment when you can say 1 room has become 2.

Really?

Then I thought, well topologically speaking, even with doors, you can shrink the dimensions of each wall while preserving the topology of the interior of the building effectively making it one room with wierd pillars and some difficulty getting upstairs (though the upstairs rooms will still have floors).

What?

So by building a wall to make two rooms you really just make the one room harder to walk around. And yet that makes life easier. Hmmmmm I think my head is broken.