It is a sunny day in Moscow. I am participating in an excellent meeting on Disaster Medicine. While sitting at the breakfast table eating red caviar and sturgeon, somebody started to talk of the scarce value attributed to qualitative research since it cannot be statistically evaluated. I do not recall the unfortunate statement I made that induced Dr. Birnbaum to say, “You are going to write a paper for our journal on this topic.” I did not know what to reply and thus started the day in a very troubled mood. In a status of “reverie” (almost dozing) during a presentation in the morning session, a title spontaneously presented itself for what I still do not know I am going to write—Can You Average Cheshire Cat Smiles? Perhaps the further development of this free writing will explain the title or will serve to float, as if a koan, for our meditation and interpretation.