Mathematics IS an actual language. And if both me and the interlocutor know the exact same concepts described, these scriblings are understandable, as opposed to spoken languages, laced with species-specific concepts and ambiguities.
That's my point. You DON'T know the concepts being described, because you don't know what symbols or combinations of symbols are being used to describe what concept or in what context the concept applies. You don't know if you're looking at an alien sigma notation, an equivalency, a logarithm, a derivative, a second derivative, a linear function, an addition statement, or something else entirely that human mathematics has never heard of (alien equivalent of FORTRAN, perhaps).
If you don't know ahead of time what type of concept is being described, translating a mathematical system is out of the question. If you know that ahead of time it gets alot easier, but
this is also true of a written language.
You really do have trouble grasping this concept, do you?
The wave function DOES reflect the particle's objective state! You see, the particle does occupy simultaneously more positions in space, etc
No it doesn't. Famously demonstrated in the example of Schrodinger's Cat, formalized by Heisenberg's Uncertainty principle: you cannot know both the velocity and the position of a particle, but both quantities exist even if you can't measure them. QM gets around this by measuring it as a wave function, which works only because the PROBABILITY of a particle being in any particular state is calculable, and therefore partly predictable.
In other words (extreme simplification) a wave function states "one in six chance of having state A, five in six of State B." While this is logically correct, it doesn't actually tell you whether a particular particle in a particular time and place actually IS in State A. QM works as well as it does precisely because nobody ever needs to know something like that.
on the quantum level, that's how physics works.
Strictly speaking, that's how mathematics works. It is not, however, how NATURE works. A particle can only have one defined state at a time; probabilities find expression in the aggregate of behaviors, but they do not manifest in individual particles the way wave functions do.
Hence what it means to say "Schrodinger's Cat is alive/Shrodinger's Cat is dead." Nature requires that the particle either decayed or it didn't; it cannot do BOTH, even if the wave function says otherwise.
A perusal of any grammar book will reveal that the 'rules of spelling' are anything but self-consistent
I'm not sure you understand what "self consistent means."
Let's clear this up: I open my college grammar book and I find that the word "adjective" is spelled the same way throughout the entire book. No matter how many other grammar books I open, "adjective" always has the same spelling, with that ridiculous silent C in the middle of it.
The silent C is an arbitrary and illogical construction. But since it is a construction that is consistent throughout the english-speaking world, we call this "self-consistency." Which is to say the system of spelling and grammar is consistent within itself; it does not need to be consistent with
anything else.
Since the language is built on an internal logical framework that is consistent and knowable (and apparently analyzable, given the existence of grammar books you alluded to earlier) then it is also translatable to someone who knows nothing at all about it. All you have to do is provide a linguistic primer: a basic set of bare-bones concepts that an intelligent person can use to extract meaning from another larger sample of literature. This is precisely why the Rosetta Stone was so useful in translating ancient Egyptian texts; without a similar mathematical rosetta stone, Earth's mathematicians are equally clueless.
? Really? The wave function expresses the 'fuzzy' state of a quantum particle and it DOES actually reflect the particle's objective state; the concept is hard to swallow for some humans, it contradicts those expectations I mentioned, but it describes the physical universe - and this is why, despite contradicting 'common sense' aka subjective expectations, it is part of mathematics. Aliens would know the exact same concept and would use it in their mathematics in the same relations.
