*sigh*
Investigation is about investigating things, not finding them. See? I can stay play that game too.
Yep, you can. And you are right. Both investigation and perception are about methods, not about goals. The goals are various and complex, and can include finding things, but are not what the skill is about. Investigation is about connecting dots i can see and discerning what's relevant to what's not to what i want. To answer "Who, What, When, Why, Where...".
Both can be used to "find things", but neither is about "finding things" specifically. And have different ways and limitation that have to be applied to them to make the difference matter.
You can perceive the light coming from below what seems to be a wall whether or not you are searching for hidden doors. You are not able to perceive said hidden door if it's well made - it would feel like a wall, taste like a wall, look like a wall. Still, you might think that there's a hidden door there, even if in reality there's just a hole. You need to do one more step - investigate the anomaly - to have some answers. You do not need to roll for it prehaps, as you do not roll to notice you still have your feets and such, as long as there's no need for the roll.
CAN WE PLEASE STOP DISCUSSING THE DEFINITIONS OF PERCEPTION AND INVESTIGATION?
No.
My intention was to point out that it is not consistent to ask for only one of those checks. Instead, any trap must usually include both checks:
I do not agree. If there's nothing to be perceived, then there's no meaning in having a perception check. If the trap is obvious in its working, there's no need for an investigation check. And vice versa.
Also, compounding checks makes failure easier, but nothing prevents a trap to have multiple requirements. I think it just goes against the intention of "simplicity" of 5e.
[*]Trip Wire: The wire is very hard to spot, so the Perception check might be around DC 20. After you have noticed it, it is quite clear that it's a piece of a trap. So investigating it would require a really low DC of 5.
[*]Doorknob triggers trap: The scuffs and wear pattern require advanced deduction to find out this is a trap and how it works. So the Investigation check might be around DC 20. But realizing them is still no auto success, because a character doesn't realize any detail of its surroundings automatically. So it would require a medium DC of 10-15 to perceive those hints, before being able to deduce them via Investigation.
[*]Fiery Trap: The Fiery trap's description speaks of "faint ash marks". Faint means "not obvious". So again, the outcome to spot is uncertain. And that means, it should require a Perception check at first, followed by an Investigation check to deduce those facts to realize, it's a trap.
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I think you are missing the point.
Tripwire: You can always ask for an investigation check if a player wants to know if that particular wire is or not connected to a mechanism, and what that mechanism does. However, in that particular trap, the bare minimal requirement for successfully avoid or negate the trap is spotting the wire. No need to go any deeper: a proficient character knows how to check for tension and disable the trap without caring for any other mechanism - if the trap is a simple tripwire.
Doorknob: You are required an investigation check to notice a particular pattern on the marks on the door. The implication is that the character looking at the door could already see the marks. Perception has already passed, possibly because the difficulty to notice them was so trivial that the marks were simply described into the scene.
Both this examples are in a place where it's underlined the difference between the two skills: Perceiving and Analyzing, exactly as you say, to simply underline the difference. Neither is an actual trap.
This leaves the Fiery one as the apex of contention: Ash and burn marks.
Quite simply for what i see the trap is still a simple one. For me it requires investigation alone because perception passes from "you have no way to perceive this normally" to " it becomes obvious once , while investigating and thus being near the place i'm looking at, i see that the mosaic is not intended to have black in that place and what i thought was dust like the rest is actually ash", neither situation requiring a check. You still need to perceive those things, it just passes from "impossible" to "automatic" once the right situation comes up.
AGAIN: I am not arguing the definition of those skills. I am arguing the point that any trap and any detail which is uncertain to perceive normally requires a Perception check. But these rules handle traps that require deduction (via Investigation) as if any of those details would automatically been perceived. And that is not consistent.
And that's why i think there's no uncertainty at least for these examples. Again, the Fire trap is a thematic one and if we want to go for it the Dm might already have been describing the temple as having a "deep, hot air that smells of coals, dust and ash, with a light whiteish fog that, while not enough to impede vision, gives the whole area some sort of supernatural and eeire feeling", already covering most of the sensorial inputs that perception itself would cover.
Player knowledge vs. character knowledge
It's only a guess, but maybe the real problem is a different: It seems like WotC wants to avoid that details perceived by Perception are automatically interpret by the Players. E.g. a character succeeds on a perception check and the DM tells the player: "Your character spots faint burn marks". I guess, most of the Players would realize, it's a trap and continue acting in great care. So they make the Investigation check for its Character obsolet by deducing informations as a Player. Maybe this is the real reason, why WotC doesn't ask for both checks. But that's not satisfying though.
Regards.
That is not possible. The very same tripwire example falls perfectly in what you say Wotc doesn't want to happen. Again, it's simply impossible to notice those things without inspecting the related surface in detail. Once one does so, the anomaly becomes apparent. Then again a temple with a mosaic with runes on the floor smells like trap even without a perception check ;D