So, in the puzzle I mentioned before, whereas the the change in understanding, ΔU, would have been quite large, since it was a big leap to go from strange symbols to the latin alphabet in disguise. Had I not remembered something similar on the TV, that would have been the case, and assuming that the time we took to figure out the puzzle, T, would have been fairly small, then we would have had a great time and the puzzle would have been a success. Personally I think it's a great puzzle, feel free to use it! (obviously I don't need to give permission, if someone puts a DnD puzzle up on the web then they've no right to keep it from anyone)
However, because I did figure it out so quickly, my leap in understanding was very small, the ΔU was only me going from 'Ooh,those look like letters with bits missing' to 'those missing bits are the on the other sheet, obviously.' So the puzzle was a failure. Whereas T was very small, the ΔU was so insignificant compared to what it might be that the puzzle became a disappointment.
The other side to this was nicely demonstrated earlier on in our adventure, where our DM threw another really cool puzzle at us. We walked into a room in which we needed to find an old man, for some weird prophecy stuff. In the room, there was a carpet, some images of faces along the walls and three doors (or four, including the one we came through). We figured that this was going to be some kind of maze, so to mark the exit Torrin stuck a dagger in the door we had come through.
However, after inspecting the room, we found two things: that there was a trapdoor under the carpet, and, more interestingly, that in the door opposite us was a point of a dagger sticking through from the other side. After some investigation, we confirmed our suspicion that the doors each lead to their respective opposites (think Portal, with each pair of doors being a set of portals) and that if we opened the trapdoor then we could see down though the ceiling at ourselves, after a hidden trapdoor opened up in the ceiling as we opened the one on the floor.
We tried everything. We went in and out of the doors, cast spells, looked at the images on the walls, tried tricking the system (thank you to Portal for helping us figure out how the physics of it might work) and eventually were on the edge of giving up. However, our pixie decided to fly up through the ceiling for some reason that I can't remember (possibly just to make sure we had tested each opening) at which point we discovered that the hole in the ceiling did not actually send us through out of the floor.
After getting everyone up to the room above, we found the old man behind another door, although at this point I was wondering how we were going to escape. As Vale shut after coming out he opened it again, hopeful that it might get us out of here on the second try. Unfortunately not, said our DM:
It's the same room, it doesn't change on this side
The key was to shut the door while in the room with the old man, then open it from inside to escape. If our DM hadn't chosen his words as carefully, it's pretty likely that we would have headed back down into the room below and gotten very stuck. So, he reduced T (remember that?) in order to make sure that the puzzle was successful (and it was). It wasn't perfect, as the real ΔU arrived before we really tried solving the puzzle (so, at a small value of T, making it very satisfactory), when we realised the connections between the doors, which was the enjoyable moment. After getting no closer to the solution for a while (big T by the end of the interaction) then it became far less enjoyable, but was worth it for the ΔU we had in learning about the mechanics of the room.
So perhaps puzzles aren't the only thing you can apply the theory to, and when you do then the ΔU doesn't necessarily need to be the solution. I think that keeping this in mind is important when designing adventures, as that's where the true enjoyment of DnD comes from for me, in finding out about the world and in being surprised. Players need that to stay engaged, and making sure that their change in understanding ΔU is as big as possible at all times and that the time it takes T for them to learn stays small, I think that a decent campaign should be able to grow...
Christ, that was a wall of text. I assume this sounds like the ramblings o a madman. I'll proof-read it at some point when I'm not so sleepy. I'm also worried that I sound like I want to sound like I know what I'm talking about and stuff, and that I'm coming off as pretentious. This isn't a foolproof way of creating adventures but I think it's a fascinating idea, so thanks to Zach Weinersmith for getting me thinking.