Islands of Dirtiness
For the majority of this talk, we assume that the
placement of objects is entirely random. Thinking back, this
assumption is partially flawed. While it is true that most
object can be randomly distributed throughout a room, in
most cases, objects are left in very particular areas that I
will call an Island of dirtiness. Consider clothes for
example. While it is true that clothes may go anywhere
inside a room, in many cases, people naturally gather all
the dirty clothes and put them in a single pile. In another
example, dirty dishes, while it is true that dirty dishes
may be place anywhere throughout a house, they tend to be
left only in certain areas where either dirty dishes are
cleaned or where food is eaten. Throughout a common
household, there are numerous examples of said Islands of
dirtiness. Outside of these islands, the area is relatively
tidy, inside these islands however, there area may start to
resemble the random nature of the ping-pong problem
discussed in the first section.