I'd totally be down with a book club where the #1 rule was don't talk at book club. The club therefore consists of people willing to sit in the same place at the same time, and read their own books without ever ruining them by discussing them. Relationship interest would be telegraphed by slightly overlapping your cone of personal space onto someone else's, and hoping it doesn't make them panic and flee.

Nothing spoils a potential relationship quite like finding out the other person is a babbling idiot.