"Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover."
Math isn't behind everything, and not everything can be explained with math. But it happens that the things that are mathematical turn out to also be quite useful.
Math isn't behind everything, and not everything can be explained with math.
Without myself making any claim about whether maths is or isn't behind everything....
that we may only be able to discover mathematical properties does not itself justify saying that "Math isn't behind everything, and not everything can be explained with math."
Can you give me any examples? I'm curious.
So now you say: Could you give me an example of such a real number that we can not write down?
Answer: No such example can be given because even e or pi or any other real number constructed by an equation is given by just inventing new (countable many) symbols (like π) or by writing down an algorithm which consists of countable many symbols.
So to answer your question: There could be problems that can not be explained by math but in the same way you might not even be able express/name/describe the problem.
Sure, i may not write an answer, when thinking from an algebraic perspective, but i sure can answer it from a logical or sets perspective.
Perhaps the answer is an empty set?
The answert to what is the empty set?
Thst this is a question without any answer can be quantified as a logical equation. The question might not have an answer that is a number, but has a superseding answer thst it is not logically consistent.
Is clearly: No, I can not.
But the answer to the question "Are there real numbers that can not be written down in _any_ way" is clearly: yes. If the question is understood as "Is the set of reals bigger than the set of naturals?".
So there are cases in which the answer to "can you give me x?" != "is there an x?".
So back to you original question:
> > not everything can be explained with math > Can you give me any examples? I'm curious.
I guess nobody might be able to give you any examples but they could still exist.
Not true. Most real numbers cannot be constructed at all [1] [2]. There is some interest in replacing the mathematics of real numbers with computable numbers, but this adds additional complexity to analysis (requiring a computable modulus of convergence).
Only coutable many real numbers can be given by name (like pi) or by an algorithm. But there are still many more numbers left which you can not name/point to/give as example.
Why? There's no way to know why. Just downvotes. Maybe someone thinks math explains physics, which explains [...], which explains dreams. Maybe that's not it at all. Who knows?
I can only speak for myself here, but silly downvotes are the primary reason I'm disengaged with this otherwise really great site.
It's just an incredibly flexible tool.
Are there ways of understanding things in a non-mathematical - meaning non-cognitive - way? Is there something greater than Turing Completeness?
Such an idea is silly because we're using reason to fathom the answer.
When we encounter some sort of alien cognition out there which is beyond the bounds of math, it either will be understandable and expand our mathematical vocabulary as we seek to formalize it...
Or it will look just like gibberish and passed off as 'too chaotic, or too self-referential', or some other unfathomable quality.