Is there a word like "nonversation"?
Do people use this word in daily life? Where can it be used?
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It is not a "word" yet. It could be a word, shortly, if all goes well. It seems it's already being promoted as you can see under User-Submitted Words on Merriam-Webster: #1: Nonversation in Top 10.
Then again, it may never make it to the OED, being "among the millions of 'non words' rejected for inclusion in the Oxford English Dictionary."
You may have created it. I think it has good possibilities. You can use it, for example, when you're straining very hard to talk to someone who doesn't have much of anything to say. When you feel it's pointless to continue, you can say something like this:
"Excuse me, but I was hoping to have a stimulating conversation about warthogs, warlocks, and witches, not a nonversation filled with grunts, groans, and woeful sighs of vacuousness. Can you show me the way to go home? I'm tired and I want to go to bed."