I think it’s funny to think of mathematics as a universal language because all of formal logic is built on the assumption that binary truth values are grounded in reality, but I believe that has yet to be proven. All of human communication functions based on an assumed shared context.
If I say I have an apple, and you say you have an apple, humans would say that together we have two apples but in reality we each have an estimated collection of matter that shares nothing physically in common with the other. Maybe other intelligent life forms don’t make the same assumptions that we do that lead to the statement that there are two “apples,” and maybe mathematics isn’t universal.
I guess I mean to say that formal logic and mathematics are not grounded in reality, but are grounded in the way that a human brain perceives reality.
First of all, there has been a lot of research into what the minimal set of assumptions you need is to reproduce what we consider “basic math” and also what happens if you tweak those assumptions.
Second of all, the main goal for science and the type of math we use for science is to effectively model the world we live in.
Any aliens that live in the same universe are subject to the same physics, and any civilization advanced enough to detect our messages will know some basic universal facts about the world, and those facts are what we hope to use as the basis for starting communication.
Yeah you’re right, the main goal of science and the math we use for science is to model the universe. That model is completely subjective. The more we learn about the universe, the more the model changes. The way we learn is limited by our 5 senses and our mental models for the immediate universe around us.
That model is something of a language itself, and if a language is subjectively limited then I don’t think it can be universal
The model we currently have for the universe goes well beyond anything we could learn with our natural senses and the way we intuitively think about the world because of those senses.
It’s true that we keep refining our models and it’s very possible that an alien would have slightly different models, but at the end of the day, we are trying to describe the same universe and those models are going to overlap a lot because of that.
