This reminds me of a discussion I once contributed to in an AI research lab, which I got to participate through a Research Experiences for Undergrads program.

This reminds me of a discussion I once contributed to in an AI research lab, which I got to participate through a Research Experiences for Undergrads program. The topic was genetic programming and someone casually mentioned picking a genome (code) at random. They seemed to assume that would create an initially flat distribution. Whoa hold up there, I said, you can't assume that. They asked, what did I mean? I told them that both the way the "random" genome bits are picked and the way the genome bits are interpreted (fitness function) changes the distribution. For example, if the genome bits are picked as a random integer between 0 and 2^n-1, but the fitness function is a popcount of 1 bits, then the distribution will be hill shaped for the same reason that a 7 is more likely to be rolled with two dice than a 2 or 12. Out of the researchers and undergrads there, I think about half nodded their heads as soon as I pointed it out, and the other half struggled to understand or accept the idea that interpretation could affect probability distribution, no matter how much exposition or supporting arguments I gave. I didn't know about the water/wine paradox then, I wish I had. But now I wonder if part of the water/wine paradox (the fact it is even considered a paradox) has to do with that bi-modal distribution I saw between people who understood that interpretation affects probability distribution and those who could or would not accept that.