I used to think that the only thing that could not be a model of the Eiffel tower is the Eiffel tower itself. Now I realize an old friend of mine has devoted her career to studying the mapping of objects onto themselves, and I regret my glib and foolish statement.
Supposing that the Eiffel tower weights 1000 tons and it is 100 meters tall. One can use the height of the Eiffel tower as a symbol of the weight of the Eiffel tower. Every meter of height represents ten tons of weight.
But, you say, this is an example of one aspect of something being a model of another aspect of something. We still do not have an example of something being a model of itself. For that to be the case the height of the Eiffel tower would have to be a map of the height of the Eiffel tower. And maybe that is true — because how could the height of the Eiffel tower be the model of its height? It just is its height.
Am I right or am I wrong? I am coming to be sure I am wrong, just based upon my track record of glib, poorly-thought out statements. Unless that itself is an example of my glibness, in which case I throw myself upon the mercy of my con-specifics.