Hitchcockian 'doubling'

Alfred Hitchcock's films often included complex examples of "doubling", where two characters would have a symbiotic effect upon each other, often being two parts of a larger reality. One can mention the two Charlies in Shadow of a Doubt, Guy and Bruno in Strangers on a Train, Jeff and Thorwald in Rear Window, Roger O. (for nothing) Thornhill and “Kaplan” in North by Northwest, and others.

There have been discussions on the Raising Arizona board about a similar connection between H.I. and Leonard Smalls, in that in many ways the former created the latter out of his own subconscious. There is much to say about that reading, and it’s interesting to see how the motif exists in other films they’ve made. I don’t want to push the matter by making absurd claims for every character pair, but there is a case to be made for:

Barton and Charlie in Barton Fink
Sidney J. Mussburger and his proxy in The Hudsucker Proxy
Larry and his brother in A Serious Man

The last example isn't always mentioned, but central, I feel, to the film. Both are lost souls, using mathematics in a useless search for certainty, only one brother works in a socially accepted (and paying) manner, while the other works outside the pale. It seems that seeing Larry and Uncle Arthur as two sides of the same character, in the thematic sense of the word, is central to the film.

Listen to the river sing sweet songs
to rock my soul