I'm used to "pseudo" in academic contexts, where the word/prefix has no connotation at all. It essentially means "not genuine":
I was about to use the word in normal conversation, but I wondered about its connotation outside of academia. I'm glad I withheld, because it seems to be quite negative upon first glance! A quick google for "pseudo" gives plenty of synonyms:
bogus, sham, phony, artificial, mock, ersatz, quasi-, fake, false, spurious, deceptive, misleading, assumed, contrived, affected, insincere;
Those vary from neutral to negative in connotation. Oxford's definition and examples are neutral to negative as well:
pseu·do
adjective
1. Not genuine; sham
2. informal Pretentious or insincere
But that "definition" is one of many I found that is little more than a list of synonyms, and synonyms don't necessary imply connotation. Does colloquial use of "pseudo" inherently carry negative connotation? Or is it context-dependent like in academia?
Colloquially, when used with certain nouns, a negative connotation is obvious. For instance, calling someone "pseudo intellectual," accuses them of only pretending to be intelligent, which implies that they are not actually intelligent.
A positive connotation seems possible, but if the answer to my question is affirmative, then I'm just misusing the word. Say I have a friend who's claiming laziness despite actual hard work and success. I could say to him, "you're only being pseudo incompetent, quit downplaying your achievements!" That sounds strictly positive, but I might just be misusing the word.
Best Answer
Not always, although it often carries a negative connotation.
For example when giving programming advice (eg on Stack Overflow), I'll often provide "pseudo-code". This is code that isn't necessarily written in a particular language, and instead shows the basical structures/logic in a simplified manner. It looks pretty much the same as code, it uses the same words, but it's not actually code.
In this case "pseudo" is "not genuine" in that the code is not written in a particular language, the person I'm talking to couldn't just take what I write verbatim and use it directly.
It's much less common than the "pseudo-science" type of negative connotation, but is still used as you note for pseudo-atoll, pseudo-random etc and is, as you say, context dependent. Typically the context is "It's close enough not to matter for the way I'm using it, but we still need to differentiate it from the 'true' version". It's kind of a "just be aware that this may not be quite what you were expecting, even though it's close" warning.
In general, however, you're right that it usually carries a negative connotation, where it is used to deride something as not being genuine. "Pseudo-science" is the most common I hear, regarding an article which is pretending to be scientific but is really opinion with some statistics tagged on.
One thing to note is that even these neutral variants usually are technically negative in some way: my code still isn't code (so is worse than true code), pseudo-random could technically be potentially predicted.... it's just that in the way they're being used, the fact they aren't genuine isn't significant to the discussion at hand.
The real question, I guess, comes down to "is a lack of authenticity/being genuine always a bad thing" - to which the answer is "no, but it's usually a bad thing"