Do I, as someone with an advanced degree in pure mathematics, need to weigh in on the What Is 2+2, Can Anyone Really Say For Sure debate? Is this where we are as a society?

Apparently this is where we are as a society!!!!

I could, I thought that it would make any difference at all, talk at some length about the role of axioms in formal logic, Godel's Incompleteness Theorem, and non-Euclidean geometries. But I teach often-abstract concepts to students who are very practical - more practical than me

I spent a decade teaching computer graphics to developers in training. We spent a week on projective geometry, a system in which there are no parallel lines. Pairs of lines we think of as parallel intersect in this system, at what we call points at infinity.

This confused and disturbed my students. I explained, in not so many words, that in math you can make up whatever rules you want as long as they don't fuck shit up. Most rules you try to make up, alas, fuck shit up. Points at infinity turn out not to, and in fact are useful.

Redefining any of 2, +, =, and 4 - and this is what is happening here - fucks shit up. It fucks up not only just about all math you will ever want to do (including COUNTING THINGS), it fucks up any attempt to communicate basic information about quantities with other humans.

This is why non-Euclidean geometries are rich branches of mathematics, whereas nonstandard definitions of the numbers we teach in kindergarten and the operations and relations we teach in grade one are not.

I realize that the great 2+2 debate is a stand-in for a broader political point, which I am deliberately eliding specifically because my position on that is as follows: if your politics require you to pretend to be a fucking moron, YOU NEED NEW POLITICS.

Ditto if your epistimology and the vocabulary attached to it prevent you from communicating basic ideas about the material world with 99.999% of other humans. That doesn't make you smart, it makes someone who NEEDS BETTER HOBBIES.