Relative vs absolute
This:
Relative: x = y * 3
(The value of x is relative to the value of y) — Leontiskos
applies to what I said here:
You could say something changes in relation to something else, but that relation is defined in absolute terms. — Matt Thomas
I would say that x = y * 3 describes the natures of x and y in terms of each other. However, I don't think it is true to describe it as statement of relativity. I am more of the opinion that the terms relative and absolute are pretty much redundant. So, I would describe the two examples you gave as equally absolute and relative, and equally neither. X = 5 describes the natures of x and 5 in terms of each other, just how the other example does for y and the other x. At the same time, they both the examples are saying that each side of the equations are not just equal, but the same. Saying that there is fundamentally no difference between the two, that they are two ways of saying the same thing, that x
is y * 3. In this way, they can't really be seen as providing comparisons, or description of a relation between two things, if fundamentally each side of the equation is referring to exactly the same thing. As far as I know, there are infinite solutions to the second example you gave. But, in any example that fits the conditions of that equation would provide a very absolute comparison between the value for x and the value for y. It is really arbitrary in this case to make a distinction between numbers defining a value and letters not. For example, if we are to look at the first equation you gave, we could define another variable that is perfectly logical within the boundaries that equation defines. We could say y = 2.5. Then that equation could be re-written as x = 2y. What I'm getting at is that real numbers also only provide a comparison. None of them mean anything in isolation. They only appear to mean anything because of the rules that define how they relate to each other, their relative values. For example, 2 is defined by being 1 bigger than 1, or being double 1. And you can represent how two numbers relate to each other, their relative values, in whichever way you like. However, this is the only thing that gives numbers meaning to us. We only know the value of one number because we know the value of another. Nothing has value in isolation. The value of one thing implies the value of another, because it is dependent of the value of that other.
I guess I'm more inclined to side with the idea of relativity, but this is due to the language that I don't really have a choice but to use. But I tried to show here that all you can really show is equivalence or non-equivalence, and that there is no intermediate. I'm not happy to support the idea of relativity though, because it implies the idea of absolutes, which I tried to show as illogical. Of course I can't support an idea that requires another that I consider illogical.