In my case it's simple: I don't take much of it anywhere nearly as seriously as some of you and can't for the life of me understand why anyone would.
Have you ever written fiction, aside from gaming? The GM is discovering or realizing (or I suppose composing) what's in the world in the same way a free-writing novelist does, approximately. GMing feels different to me than writing fiction did (note the past tense--I quickly ran out of things to say as a writer) but it's the closest thing in my experience I can point to. It feels a lot like discovery--at least one writer I respect has compared it to being a paleontologist on a dig, and that makes sense to me, though it wasn't exactly my experience of it.See, this is where I get stuck. The world doesn't exist, so how is the GM discovering or realising things about it?
This is possible in mathematics - ie 2+2 = 4 even if someone hasn't noticed yet.
But how is it possible to discover that Elminster is wearing red rather than blue stockings other than by having someone make that up?
GMing that way, I mean, would feel more like reading a book. I mean, playing a TRPG isn't a lot like reading a book, and neither really is GMing one. I guess that your description feels more ... rote, than my experience of it is. Like writing from an outline (something I've never, ever been much good at).I don't see why.
I've often posted that one important aspect of RPGing is that players declare actions for their PCs that oblige the GM to narrate more stuff. What do we see? is a paradigm example but there are many others.
That is very different from reading a book, but it is still playing to discover the GM's conception of the fiction.
Again, this is where I get stuck. There is nothing that is being modelled. Not in any literal sense. When the player says I check out Elminster's legs. What colour are his stockings? the GM isn't deriving an answer from a model in the way that a weather forecaster might try to. The GM is making a decision.
This seems to be a sticking point. As far as I can tell, you seem unwilling to discuss play from the starting point that someone has to make up the imaginary stuff.
I'm sure you understand how words work. You can say something that is true in two different ways. One neutral and one highly offensive. I very much doubt that you fail to understand how "playing to discover the DM's notes." is pejorative.Why not?
This is how crosswords work. This is how escape rooms work. This is how Call of Cthuhlu modules work. This is how Tomb of Horrors work. This is how Christopher Tolkien has made his living. Many of those are regarded as fun pursuits by a non-trivial number of people. The notion that it's pejorative to actually describe how puzzles work in the context of a RPG is strange to me.
The world does exist in our thoughts. It just doesn't have an independent existence or an existence outside of it.See, this is where I get stuck. The world doesn't exist, so how is the GM discovering or realising things about it?
This is possible in mathematics - ie 2+2 = 4 even if someone hasn't noticed yet.
But how is it possible to discover that Elminster is wearing red rather than blue stockings other than by having someone make that up?
To use your Elminster example: The GM hasn't considered the color of his stockings, until asked. I'm not going argue that the answer isn't a decision, but it doesn't feel like one--any more than describing a character in fiction does, most of the time.
I think this is where our respective ways of thinking about (and possibly experiencing) what happens at a TRPG table are different enough that bridging the gap is difficult.
I think this is an example where we can probably talk meaningfully about the point of the GM's notes, how they contribute to play, and how player's learning what they say factors into that.Most of the good GMs I've been around have written up things because they wanted the players to find out about them.
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In my instance, I enjoy being asked specific questions about my setting--I have a number to answer before a session tomorrow night, and I'm expecting to have a good deal of fun doing so; but the questions are relevant to PC goals, so very much in service of PCs' dramatics needs, IMO.
This is an interesting point, but I don't think I agree with it. At least not fully.If the intended purpose of play is to change the setting, there needs to be some definition of what the setting is before the change.
This assertion seems pretty blatantly contradicted by not only the number of GM's actively looking for advice online discussions on how to improve, including here on ENWorld, Reddit, Discord, and other forums, but also the sheer number of GMing Advice videos on YouTube. There are a LOT of D&D content creators on YouTube who mostly cater their content to GMs, new and veterans alike. On the whole, Generation Y and Z are the main players of D&D, and they have long been using YouTube as a general resource for instructional material.There's a difference between a) actively wanting to improve and b) naturally improving through simple experience without any conscious effort involved. Most people are quite happy with b) and many see a) as overkill and all too often - rightly - equate it with wanting to be "the best".

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.