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Public Recantation: An Object Can Be A Model of Itself

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.

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