Heinlein uses the phrase the whichness of what in The Door Into Summer, Podkayne of Mars, and Red Planet. It is a description of the nothings that we sometimes delve into at great depth and deep satisfaction when friends stay up talking to the wee hours. (Or create deep discussions in blog comments that go on for days.)
I googled it today and found very little. The Whichness of the Whatness is a song that Fred Astaire sang in the 1920s by Lloyd Daly. It is the kind of wordplay that would have appealed to Astaire, I think. My conclusion is that whichness of whatness may have been an obscure catch phrase used around the turn of the century. If I had to guess, I’d say it was a college thing, limited to one or two campuses. I have never heard it used in conversation.
It is a great unused title. There are a few blogs that use it, but if I ever have a collection of short stories, I think that I may title it The Whichness of What. (I still like Channeling Murray Leinster, though.)