[nsonha]

Compressing does help it. To trained eyes a couple of lines is easier to read and less ambiguous than one or 2 pages of English explanation, which is hard to follow for both trained and untrained eyes if you're gonna encouter a bunch of them while reading a proof.

[prox]

To me it seems language can also be interpreted as more ambiguous, where as well defined symbols and notation are far more rigorous in definition and use.

[foerbert]

Except you have instances of misuse of those well-defined symbols and notations. Without any accompanying language it can be very difficult to not only determine that there is an error, but then also figure out how to fix it.

And other times in some fields there is a lack of well-defined symbols and notations. I don't recall the specifics, but in game theory there is some notation that is ambiguous. There are two methods or forms of representation, and the field is split on which version the notation stands for. It's also frequently not mentioned explicitly in papers, so you have to dig around a bit to see if you can find a usage that makes the meaning clear.

I don't know why we can't just have both.

[nsonha]

my main argument is that humans only have so much sort term memory so compression is crucial for readability. Reading a proof is different than reading a book because you have to retain the whole thing with details in your mind not just vague ideas.

[foerbert]

I find myself completely unable to understand that. I suspect we use very different methods. Notation doesn't stay with me once my eyes move past it. The notation is merely there to inform me of what is happening, and as long as I understand the meaning it doesn't matter if it was one symbol or a whole paragraph.