Who says it's a mathematical operation? Who says it's random? It's you, and the only reason you believe it is because everyone else does too (ad populum is a logical fallacy, though it doesn't make something less pluasible). And by the way, random is a bullshit word, anyway -- "It was caused by randomness." Go figure that one out. Additionally, absolutely every single definition of anything is essentially a theory of it; we live in a world of theories whether you like it or not. This includes operational definitions which are the basis for knowing what the hell it is you want to measure in the first place. When you say you want "results," you are asking for the results of what happens when one piece of reality (us) tries to measure some other piece of reality, without taking into account the entire system in which we both inhabit. But, without understanding the 'theory of theories,' (aka Universe) you are simply asking for results to pile atop a nonexistent foundation.
Fortunately, the things that help us learn about the 'theory of theories' are self-evident. The 'results' you are looking for are an indirect route to knowledge whereas direct experience is, well, a direct route to knowledge. "What one can prove, he does not know. What one knows, he cannot prove." ~ Me
On a side note, I wasn't trying to form a rebuttal. I was following up on the 'double slit experiment' because it was mentioned by someone else.
What part of a miner's work is "random"? All the possible nonces in a work are tested (2^32). The work is simply a merkle root, which is generated from hashes of pending transactions. Do the transactions appear randomly out of thin air? No, they come from people who send transactions. There's nothing random about any of that, everything is deterministic.
And before you argue some random point about chaos theory or double slit experiment, this thread is about affecting the result of mining in a controlled way. It doesn't matter if your breath can affect the merkle root that you get, it only matters if it can make the merkle root have a higher probability of containing a valid nonce.