In fact the person who found the block has no control over it either.
It was only one single hash they did that found the block, out of the 8.6 * 10^16 hashes they do every day per 1THs they have.
Yeah a 1PH miner does almost 10^20 hashes a day.
Currently, it is expected on average that 1 single random hash in almost 10^21 will find a block.
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It's probably more relevant to look at it terms of a comparison:
Someone sent my neighbour a letter. I want to find out who did, so I can reward them for doing that.
No, that's called invasion of privacy, or being a stalker, and frowned upon for good reason.
I bet you didn't read this part of my post:
Some decisions miners make are reflected in the blocks they solve.Or perhaps you don't believe that's true. However, Slush mined both
https://blockchain.info/block-height/414056 and
https://blockchain.info/block-height/414072 which have different version numbers. The difference in version numbers is a result of the owners of the machines having made some decisions which differ. If I have $1,000,000 that I want to use to encourage people to use one of those versions instead of the other, then I DO need to know who solved the block. I could rely on the pool operator to tell me, but in the spirit of bitcoin, I'd like to do it in a way that I can verify.
I understand that the creeps who want more control over others frown upon the person-to-person communications that support bitcoin as well as widespread sharing of occulted information, both of which are slowly destroying the oppression on which those parasites live, but that only makes such behavior more attractive to me.
I trust that you now understand me better, so perhaps you can help me improve my writing. Is there something in my initial post that I could have written to make what you didn't understand any clearer?
Thanks!