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On irrational downvoting my post: If you hate somebody, the object of hate can harm you by presenting you some true information that you by hate will consider false. (It seems this way I probably unintentionally killed Russia, because I hold priority on ordered semigroup actions (OSA) and if anyone can research OSA and Russia cannot, Russia is weaker than others.)
I present an updated version of my text:
"but then never mention cartesian products again", "You then don't define a relation" - fixed.
I am about arbitrary relations on variables , not only binary ones.
"usually discuss dependency over things called "random variables"" - I know, but there is simpler non-stochastic case, that I discuss in the beginning of my article.
"How does a relation express a law of physics?" - addressed.
"I don't think you know the formal definition of what it means for a random variable X to depend on a random variable Y" - it is . I did study probability and statistics in a university.
I did address all your complaints, they are too many. If you don't understand me, it does not make me wrong. We could have a Zoom or Google Meet call where I would explain what I mean, and you would help me to make it understandable.
In this article I also express my thoughts on faster-than-light communication and time travel.
I understood sum threshold attack long time ago (at least as pertaining to sum-threshold attack to aposteriori probabilities, as in the case of the Frog court), except that I didn't produce a name for this. I understood that it can be applied in court, in communication, etc. So, I knew most of this without knowing (or maybe just without remembering) the name.
I call you to make a next step. This step requires a certain courage because it looks like an attack to the science (but not as a sum threshold attack, this seems to be a single point of failure):
I think we should (try) and make the next step: Conclude from sum threshold attack that the scientific method is wrong, because (so it seems for me, I never tried to prove it formally) it can produce incorrect results under sum threshold attack. I call you fellow thinkers to try to check if scientific method is resilient to sum threshold attack or no.
I mean that Science is based on Bayesian inference and Bayesian inference is liable to sum threshold attack: Repeat a million times an experiment that produces P(E|H) where E is 10% possible in the case of H meaning energy conservation law and consider every instance of the experiment as a separate evidence. Then we have "proved" no energy conservation.
How to avoid such a misuse of science? I don't really know, but I suspect that we need to take into account basic principles of the scientist that he is not going to give up ("faith"). That reminds me religious faith, and I, probably, has drawn the argument from my study of religion. But after the argument is presented this way, it is purely scientific. We need stability (faith?) against the attack, don't we?
If no, we certainly should nevertheless keep doing scientific research, but we should develop a new method differing from the scientific method by resilience to sum threshold attacks.
I always thought that counter-factual means some message that is not conforming to reality. Was my personal understanding of semantics of this word wrong? Or maybe, your definition and my intuitive understanding can be reconciled? Isn't counter-factual as contrary to past decisions a special case of counter-factual as not conforming to reality? If yes, can the word be used in both senses, dependently on a context?