The DMG has rules for turning a level 12 standard into a level 20 standard, and the math is pretty trivial. I didn't see rules for turning a minion into a standard, or vice versa.
This is a well-known strategy, which appeals to some. You simply generate a minion which is 8 levels higher than your standard. They have exactly the same XP value. Its very easy to create a minion, it will take 2 minutes, tops. You can give it a simple power that is reminiscent of what the standard does, and maybe some kind of a special property that is evocative too. There's a billion minions out there to work from.
I would note that this isn't the only equivalency in XP value, a level 1 solo is the same XP as a level 6 elite, a level 10 standard, and a level 18 minion. So your level 3 young white dragon is a level 8 elite young white dragon, is a level 12 standard young white dragon, and a level 20 minion young white dragon. At level 6 you meet 2, at level 10, 5, at level 16 20 of them, and each of those encounters is (theoretically at least) an identically medium tough encounter, more or less. You can rationalize it quite well, for level 1 PCs the young white is a threat equal to a whole party. By level 6 it takes 2 of them to be threatening, etc.
This technique has been discussed quite heavily in various 4e threads here and elsewhere for years.
The weird thing is that, it never occurred to me when I was running the game that changing the levels or grades of any of the monsters should be a thing, aside from giving a couple of extra levels to an orc in order to represent a more-experienced orc; but the idea that a level 5 solo could be re-statted as a level 10 elite or level 20 minion is something that I would consider to be quintessential of 4E, just from these message boards. Following my own definition from before, if I saw a new game which actually included rules for that, I would immediately assume that they were copying 4E.
Yup! 4e certainly proposes that 'numbers are not the world' just a convenient gamist tool to make an RPG possible and fun.
As for why I would even want to run an encounter full of level 12 enemies against a level 20 party, it's because that's how I would traditionally show that the party is getting stronger. If you're level 12, and you struggle to beat level 12 enemies, then walking all over them when you're level 20 is a very intuitive way to demonstrate how much more powerful you are.
Right, and you COULD do that. I mean it isn't impossible. I really would usually make it an SC though. However, I recall once using some goblins against a level 7 party. There were a LOT of them, enough to make the XP budget a viable level 7 encounter, but the monsters were obviously pretty anemic. It actually WAS fun, but I think that was just good fortune. It definitely did produce the feeling you are talking about, the players were a little scared at first to see 25 foes, but then they laid in and it got to be fun. They actually did get hit back pretty good though. I seem to recall the rogue even went down at least once.
To contrast, if you're level 12 and you struggle to beat level 12 enemies, but then you get to level 20 and you struggle to beat level 20 enemies, it still just feels like you're struggling. (One of my early disappointments with 4E was realizing that my amazing hero character basically couldn't beat a standard orc in a fight; and it felt like a hollow victory to cleave my way through two minions with one swing, since I knew that they were explicitly designed to be easy for me to kill.)
The healing surge mechanic succeeded at what it was intended to do, which was (along with encounter powers) to ensure that nobody was out for the whole day after a single fight went south; (and also to make it so that nobody was forced to play a healer, and I guess also to prevent you from abusing wands or potions).
Right, it was a pretty neat concept.
It does assume that you want the PCs at full power in every fight, though, which can be somewhat limiting in the way you run the game. And it also assumes that you're going to have enough encounters in a day for the limit on healing surges to be meaningful, which can also be pretty limiting. Granted, there are still an infinite number of games that you can play within those parameters, but there was a bit of a learning curve involved, and not everybody was able to (or wanted to) make the transition.
Well, OK, fair enough. 4e is more tricky if you want to string things out and have just a very few encounters. Of course you could just make them VERY strong, at some point they will become dangerous even if its just one encounter in a 'day'. Or you could change the recovery rule somewhat, maybe in "harsh conditions" a rest isn't enough to get back all your HS. Maybe even not many at all, like 1. I've done all of these things too at different times.
However I have also come to think about stories in RPGs in a really different way from what Gygax established as sort of the baseline that D&D seems to still follow. That is, consider how a lot of movies work. The whole plot takes place in 1 day, or something. Does it matter really what the time frames are? I mean, in the end its just moving around from scene to scene and encountering the action as the plot happens. In a lot of stories it isn't even clear what sort of time is passing. It was the whole 'time is a key part of the campaign' stuff that Gary propounded, and all the very structured time-based resource game play that he loved so much that beat it into people's heads that we had to have 'work days' and keep track of time. Its still pretty amazing to me just how strong Gary's hold is over most of the RPG world, even 10 years after he left us.