I am creating a game where the player has to discover things in order to continue to advance in the game. In most games, there is a limited set of combinations and incorrect combinations which usually provide some kind of clue or result output. For example, you need a combination to open a door or some mechansim to get you to the next part of the game. In this idea, the next part of the game isn't necessarily obvious, and since it deals with "outer space", it deals with a branch of physics that is "my" fiction, so there no context in which somebody might be aware that there might be something available to discover. That means I have to provide hints. While I could say something like "congratulations you have acheived X, now it's time to think about Y." I want to create mechanism that is much more subtle so that the player looking for the ultimate challenge has to poke around a bit before they discover the answer. One mechanism I thought about was to have a dream sequence in the opening video that eluded to the existance of the various technologies the player will eventually discover. Is that a good approach, or is there anything that could use that is more subtle; to maximize the difficulty and the enjoyment at discovering the answer?

The dream sequence idea seems similar to Prince of Persia and might work, but the concept as a whole doesn't seem to be a player friendly approach for allowing the player to advance. Personally, I think players can become extremely frustrated and impatient if they don't have any clue as to how to progress in the game. Main plot sequences should be fairly obvious. Easter eggs, side quests, and secrets are another matter. I have no problem as a gamer if their are bonus aspects to the game that require unusual tactics and more time to acquire.

A similar approach to what you described, but staged, was used (and worked well, imho) by Bioware in Knights of the Old Republic. Upon reaching a new planet, the player would have a dream sequence that identified the general location of the next goal. He then had the opportunity to talk to a certain crew member and discuss the dream and what it means. Thus you had visual and textual information about your overall goal. Granted, it was only a hint and some visual candy.

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but the concept as a whole doesn't seem to be a player friendly approach for allowing the player to advance

Unless the game is sort of a puzzle/adventure game and the point of the game IS discovering how to advance.

The dream sequence could work fine, but is also overused and a little silly. It's very hard to come up with ideas without knowing anything about your world or physics.

Some hints could be given through a trial and error. When the player tries something and it doesn't work, the character lead the players thoughts "X didn't work, I need something a little more Y, maybe something a little like Z"

Another way of giving hints is in the environment itself. Maybe you are following in someone elses path and they have left you clues. Thinking with outer space, maybe there can be a constellation that leads the player to the next planet, and the character can make it obvious that "it looks like there could be a message in the sky", or something similar.

Essentially the player needs to discover how to exceed the speed of light. Actually there are several ways, each yeilding a different speed. If they combine some of the discoveries, they can go even faster, do different things ...

They start out in an environment where knowledge of these abilities have been lost, but they have the mechanism to discover though an experimental lab with different things which would help them discover new technologies.

The idea is to have an open ended technology tree, or at least one where the technologies are not in a tree where the player simply says "allocate X research units to this discovery" then some number of cycle later the games says "congratulations you've discovered Y".

The experimental lab is where they will need to be in order to discover many advanced concept besides the speed of light; such as weapons, shields, communications, etc.

Sounds like a very interesting game. So essentially, you DO have a technology tree, it's just hidden from the player, and instead of being able to just wait for reasearch to be done to get the next tree item, you have to play minigames/puzzles which both guide your research progression as well as move research along? I remember the game Utopia had invisible research, it was exciting to get a new technology because you didn't know what techs were available. I also loved sending spies over the mountains and hearing reports about what the aliens were doing (but never seeing them!)

I am getting a picture of something that might be similar to those csi games, except less linear. Where you have different tools that you can use on artifacts and samples that give you different clues about the strange physics of your world. The clues can be what these tools readings reveal. The other part of the game can be collecting samples and artifacts, as your technology gets better and you can travel further away from your homeworld :) Sounds cool.

I see the lab work as being similar to alchemy in some rpg games (like oblivion), where you mix one ingredient with another and it keeps track of all the combinations you've tried. And also, you can have the stuff like in csi where you can examine a piece of evidence and use tools on it like uncovering fingerprints etc. You could also have samples/artifacts that fit together, but you have to rotate them and move them around to see if they fit, rather than just "use x on y -> looks like they fit together!".

If you haven't already played Riven, then do so. It is, IMHO, the peak of the adventure genre and absolutely masters the art of subtle hints. I will give you spoiler as an example. In the game there is an island (island A) that can only be reached by drawbridges from two different island. One of these bridges can only be raised/lowered from the island A, the other can only be controlled from the far side of the bridge. The bridge that cannot be controlled from the central island starts up. The player, naturally, tries to climb up the bridge(the bridges tilt up from the side farthest away from Island A) and get ontop of a building on Island A(which you can see stuff ontop of it).This is impossible becuase of there being a gap between the roof and the bridge. However, the bridge that can be controlled from Island A(which starts down), if raised, will provide a ramp onto the roof.

The point is that since one bridge starts down, and the player must walk all the way about on a side route to get to the side across from Island A, it needs a clue that you should walk up it. This clue is shown in a similiar object(the other bridge) which invites you quite obviously to climb up it.

These are the types of clues that are really good. Ones that use similiar objects, symbols, ideas, etc. to convey an idea of how to use something else.

The lab sounds like a very interesting concept. Maybe you'd want to add some randomness effect to it, otherwise it would not have much replayability - someone who already knows what he has to do in your lab to get some technology will find the game very tedious the second or third time around. Not a problem if you are not really aiming for replayability but instead at a unique first experience, but something to keep in mind maybe.

This game has no technology tree, per se, as the ability to create a light-speed capable engine is possible at the beginning of the game. The trick to achieving light-speed is the combination of components to produce more powerful designs.

The game is a simulator, so introducing technology at different points in the game will result in different outcomes.

Replayability comes in the form of creating a more formitable opponent in terms of either technological might, AI intellience, numbers of enemies, etc., with the recognition that the first few times through the game the "big powerful" technology will like not be discovered, unless they bought a hint book. Further, having all the technology may not be enough against an adaptive AI. This is where things like strategy play a big part.