@gav @karna @genmaicha Once again gav is an untutored math genius and I agree with him

"a variance is the mean of [SQUARED] differences of a set of numbers from their mean" is fine. An expert will understand that 'mean' is defined as an expectation and usually calculated as an integral, 'set' should specify the probability measure, etc. Covariance is just when the data is higher-dimensional, so the 'squared differences' must also live in a higher-dimensional space.

I have not heard of "mean" implying "finite state space" even to the layperson. Most high school calc classes ask students to calculate "averages" or "means" with integrals

Objection: "but the encyclopedia is trying to give the most general definition, useful to professionals, not just one special case known a century ago"

Is there a general definition, though, which is not essentially that? Specifying the method of calculation (taking integrals) or interpretation or purpose or generalizations (covariance) does not belong in a formal definition.

BTW, this is the main problem with the excessively long """definition""" of the page https://en.wikipedia.org/wiki/Coefficient_of_determination#Definitions , where the authors lump in interpretations and relationships with other concepts. These things do not belong in a (ideally, short) definition.

Objection: "but there are multiple definitions of R2, and this causes issues in stats literature!"

The multiple definitions have to do with how the phrase "variance of the data" is defined (e.g. centered or uncentered, that is, whether you subtract off the mean). This is not addressed in the article at all

The problem with the spinor article https://en.wikipedia.org/wiki/Spinor is that it is trying too hard to be accessible to *nonexperts*, and ends up being too wordy for experts and too vague for the layperson. How many paragraphs does it take to get to "a spinor is a representation of the spin group [or, if you like, some clifford algebra]"? Someone who can't understand these words or look them up will not understand the article anyways. And if you lead with a clear definition, at least the layperson knows what to look up (I think this is gav's point).

If you dig around in wikipedia talk pages, you see that even terms like "unit vector" and "SO(3)" are deleted from articles in an effort to get them approved as 'featured articles.' The idea is that to be a featured article, it must be accessible to a broad audience. But replacing jargon with vague circumlocutions just makes things worse for the layperson *and* the expert. This is the shittiest thing about science wikipedia

The articles which are truly written "primarily for professionals" as you (karna) are saying, I feel are actually great and have none of the issues that gav is complaining about. I just wish that was more of them. Often these articles are more niche, rated "low-importance", and are thus unmolested by wikipedia super-editors and their WIKI: policies