Excellent question! The answer is "No, but I should, shouldn't I," yes okay. (Thanks @logodaedalus.)
My twitter-sized reply was "Sound cool while supporting the puzzles," but I can say more than that.
The keynote for HL's system was the alchemy puzzle in The Dreamhold. The Dreamhold lab had just two ingredients and three actions to take, but it felt like a dense explorable territory.
Dreamhold's principle was that any action you try on a given substance will produce a new and interesting result. And then you can try new actions on that! Obviously this exponential expansion has to be tied off pretty soon. Many of the combinations converge to common outcomes. The tree is only a few steps deep, really. (I think there are twelve possible substances to find.) But it's enough to give a sense of experimentation and discovery.
For HL, I wanted that sense, but bigger. Did I succeed? Heck no! It was an impossible goal. HL has forty-odd starting ingredients and thirty-odd magic words (not to mention other ritual actions, and the environmental influences, and...). Just providing the first step of a dense exploration tree would be... well, somebody might do it, but I wasn't going to.
So I developed HL with a less ambitious principle: you get recipes. When following a recipe, you should always be able to tell a right action from a wrong one. That is, a particular magic word will produce a unique response if you use it at the right time -- different from the response you get if you use it at the wrong time. The differences may be slight, but they're perceptible.
I didn't want to entirely crush the spirit of experimentation. So the second principle was: recipes aren't everything. The opening puzzle demonstrates this, and various later puzzles require you to substitute or invert ritual elements. I set up parallel structures and oppositional structures to make that make sense.
I think everyone agrees that I didn't hit the perfect balance. The game starts you with an off-recipe puzzle, but there's too long an interval before the next one. In between are lots of recipes that you have to follow perfectly; you lose track of the initial lesson. But most players were able to get onto the right track (or jump off the wrong one, if you like).
A followup question was "Did you have alchemical dynamics in mind when making the puzzles?" The answer is... mixed.
(Spoiler warning for the overall game structure, starting here!)
The core arc of HL is the limited supply of four key elements. You need all four for the endgame, and there are intermediate goals which require two or three. So initially you can only accomplish one intermediate goal at a time; then you have to reset.
That was my initial puzzle framework. I wrote that down, and then started complicating it. What ritual needs elements X and Y? Is it the ritual itself which needs those elements, or do I invent a sub-ritual which consumes X and provides a related X2? And so on.
At this point, I was inventing puzzles and alchemical mechanics in parallel. Or rather, I was going back and forth -- every decision on one side firmed up the possibilities on the other side. I needed puzzles whose solutions would seem reasonable; I needed mechanics which would feel like parts of a plausible magical science.
You'll note that I didn't start by creating a complete magical system and then deriving puzzles from it. Nor did I invent a bunch of puzzles and then invent alchemy that could solve them. Neither approach has ever worked for me. So if you're hoping for a complete, consistent model of HL alchemy -- I'm sorry. No such thing exists.
I knew that it couldn't exist, of course. That's one reason that the alchemy is described as being eclectic and syncretic. It fits nicely with the social background, too. The real-life British Empire did steal artifacts from all over the world. I evolved the idea that a magical British Empire would lift occult knowledge from every place they conquered, and jam it all together without regard for consistency or context!
(We assume this made them better at conquering. The game doesn't touch on much history, but references to the "East Empire" imply that they've got a firm grasp on Central Europe, and no doubt the New World as well. If I were a better writer, I'd have built a story about the Navy running into aliens and trying to treat them colonially... oh, well, room for a sequel.)
(There will be no sequel. That was a joke.)
The point is, I could make up whatever alchemical rules I wanted. I tried for a balance -- consistency in some places, chaos in others. I could draw on mythical, mathematical, or religious sources without having to be accurate about any of it. Convenient!
Back to the puzzle construction. As I said, there were a few key resources whose scarcity determined the game arc. Then I invented more resources -- both ingredients and formulae -- which either resulted from or combined with the key ones.
This could itself have created an ever-expanding tree of dependencies. But I constrained it, or at least bent it back on itself, with a third principle: everything in the game should be used at least twice. Ideally, in slightly different ways.
A naive adventure game uses each item exactly once. Indeed, many graphical adventures remove things from your inventory once you've used them successfully. This cuts against your sense of immersion -- not because of the anti-realism, but because you wind up watching the game mechanics rather than the game. An object disappearing (or being checked off) is a better signal of progress than the response of the game world. Text adventures don't have this disappearance convention; nonethless, the player learns to keep track of what's been used and ignore it thereafter.
I would rather teach the player that there's always more to learn. You may think you understand an item, but you still have to keep it in mind for future use. You have to keep everything in the game in mind at all times. This is the underlying challenge.
So I went over and over the list of rituals, looking for singletons. Magic word used only once? Work it into a new ritual. Alchemical potion only solves one puzzle? Invent a new place to use it. This added a richness to the mechanics. Two uses of a reagent imply there must be more; you have the sense that there must be underlying laws to explain it all. This is, as I said, an illusion; but it's a well-supported illusion.
Of course, it added up to a gob-smacking number of puzzles. Fortunately (or perhaps not), I was blessed with a very large list of formulae, resources, and recipes to scatter around the Retort. I could "use up" these extra puzzles as obstacles to various resources. (Thus all the locked cabinets.)
Also, since these puzzles weren't involved in the key resource plotline, it was okay if they had multiple solutions. (Some of the cabinets can be opened two or three ways.)
The final principle of Hadean Lands: involve all the senses. Let me go back to a line that I quoted in 2010, explaining the HL Kickstarter:
"If a witch could teleport (a thing that seems impossible, but I could be wrong), it would involve hours of preparation, rituals, chanting, and filling all the senses with the desired result until the spell would work in a blinding explosion of emotional fulfillment." (Steven Brust, Taltos)
Magic should be a transcendent experience. I tried to describe the effects of your rituals in colors, textures, sounds, scents... even the words that you speak are given synesthetic weight. Not to mention the ineffable air of things going wrong or right (so useful for cueing mistakes).
Of course, an adventure game involves lots of repetition, and nothing wears out faster than a repeated sense of transcendence. (Except maybe humor.) I dodged this problem with HL's PERFORM mechanic. When you PERFORM a known ritual, it doesn't repeat all of the descriptive text; I kept the output bare and mechanical. You're not reading it anyway! You just want to know whether the ritual succeeded. This preserves your sense of involvement with new rituals.
(Admittedly this falls apart when you're failing at a new ritual. That's a somewhat repetitive experience -- inevitably, I think.)
So there are my principles of magic design. I don't suppose I sound like a Hermetic occultist. I hope I do sound like a writer or designer describing his craft, because that's what this is. A lot of fussy details and a clear plan, is all.
Like the man said: writing is the art of causing change in a consenting reader, in accordance with the writer's will. You gotta be pragmatic about that stuff or you'll get nowhere.