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 $V$, 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 $P\left(X|Y\right)\ne Y$. 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.

Based on your previous posts (and other posts like this), I suspect this might not get any comments explaining the downvotes. So I'll explain the reason for my downvote, which you may find helpful:

I don't see any ideas. You start with a really weird, hard-to-read, and I think wrong definition of a Cartesian product, but then never mention cartesian products again. You then don't define a relation, but I'm guessing that you meant a relation to be a subset of V x V. But then your definition of dependency doesn't make sense. We usually discuss dependency over things called "random variables" (which are not actual variables in the sense that you're using them), and it's hard to find a charitable interpretation of what you could possibly mean in a way that makes sense.

The next section is a bunch of vague ramblings that make no effort to be coherent. How does a relation express a law of physics? What are the variables? How the heck are you getting boundary conditions into a relation? These are not rhetorical questions: I was trying to find a charitable interpretation to make any of these concepts make sense but I couldn't.

For future posts I think you should:

1. Take the time to properly understand the concepts you want to talk about. 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, and I suspect you might not even know what a random variable is.

2. Properly flesh out your ideas instead of bringing up a bunch of vague concepts and hoping the reader can flesh them out for you. Definitely don't publish anything that has things like "what are consequences???" in there: if you're creating a theory you should obviously be the one to define everything.

3. Make sure each line actually follows from the line before it. You can use an AI to help you here: give it your draft and ask if every line convincingly follows from the prior assumptions.

In this article I also express my thoughts on faster-than-light communication and time travel.