So if I have two designs with the same spaces, why then are you suggesting that because the space is taken up by something wholly unsimilar, that they must be the same because they occupy the same space?
No one is saying they are literally the same. In a part of my post that I quoted, I even said that "No one is saying that the play in the same fashion." I am not entirely sure on the criteria for identity of game rules (when they fall short of being expressed in formally identical ways) but playing in the same way is probably among them.
The point, rather, is that the two mechanics occupy the same space. So that, when a high level PC with no shield or cover survives being attacked by a dozen skilled archers because s/he has so many hp, the relationship between mechanics and fiction is something like when a PC in a fate point game who has no shield or cover survives being attacked by a dozen skilled archers because the player of that PC spends a fate point. In both cases, the narrative established by the mechancis - "A dozen skill archers shot at your PC, and you survived despite your lack of shield and cover" - may stand in need of supplementation in some fashion for it to be clear in the fiction what happened. Did all the archers missed because the gods intervened and turned their aims? Did the PC duck or deflect all the arrows?
Similarly for surving the fall. In both cases, where many hp or expenditure of a fate point results in survival, the fiction as established by the mechanics goes "Your PC jumped over a cliff, and despite falling 100' s/he survived to run away." How did s/he survive? The mechanics on their own - be they hp or fate points - don't tell us.
In some fate point mechanics, it may be incumbent upon the player who wants to spend the point to first stipulate, in the fiction, how his/her PC is surviving: "I spend a fate point to make the archers miss;" or, "I spend a fate point to land on a ledge, or in a pool at the bottom of the cliff." But this is not true of all such systems (eg it is not true in HARP, and is not always true in Burning Wheel). Hit points are more like this second sort of approach: the mechanics don't
require explaining what has happened in the fiction, but leave it open for the table to fill the narrative gap, or not, as the mood and the need take them. (Likewise with 4e powers like pre-errata Come and Get It or Inspiring Word.)
Being in the same spot, or looking similar does not mean they serve the same function, does not mean they work the same way, does not mean ANY of the things you're attempting to prove here.
My gut feel is that, given that "design space" in a game is more-or-less defined in terms of function, proving that two mechanical elements occupy the same space means proving that they serve the same function.
But even if that general claim is false (like I said, it's just a gut feel on my part), my argument that the two mechanics occupy the same functional space is the one stated in [MENTION=6678226]Mattachine[/MENTION]'s original post, plus the post of mine that you quoted, and that I have now reiterated above - like fate points, hit points operate to create a
gap within the fiction that has been established via the mechanics. "That PC was shot by 12 skilled archers, and yet survived? What happened?" "That PC fell 100' down a cliff, yet survived? How?"
Note again that in games with no mechanic in this functional space - like Runequest, or Classic Traveller - this sort of question never arises. If a PC survives the shots of 12 skilled archers or a fall of 100', the mechanics themselves explain how, in the fiction, this stange event occurred: improbably enough, for example, his/her armour deflected all the arrows; improbably enough, for example, the fall only broke his/her legs.
D&D HP may represent a lot of things, and what that represents is up to personal rationalization.
Obviously this characterisation of hit points is not uncontentious. It's at odds with the "hp = meat" school of thought. But I think that school of thought was not so prevalent until 3E (the original AD&D rulebooks had lengthy passages devoted to dispelling it).
It's also at odds with the "hp = dodging" school of thought, which the 3E rulebooks hint at, and which was probably also a fairly popular school of thought in classic D&D play. But that school of thought has always had trouble explaining how hit points work outside of melee (ie outside contexts where a level-dependent dodging ability makes sense).
But that's part of Mattachine's point, I believe: if you want a more process-simulationist game, in which hp
don't lead to gaps within the fiction that have to be retrosectively narrated shut, then you are adopting the same sort of approach to play as a game like RQ or Traveller that has no fate point mechanic. You can treat hp as dodging, and have to use some sort of variant massive damage rule, or wound and vitality systems, or modified coup-de-grace rule, or whatever it might be, to produce "gapless" fiction in which no one survives 12 arrows at point blank range, nor a 100' fall; or you can go the way that I believe Aaron and Triqui are going in this thread, of treating hp as meat - PCs survive 12 arrows at point blank range, and 100' falls, simply because they are tough enough to do so.
The point of the "hit points are a version of fate points" claim (or, to use the language of AD&D, the claim that they represent luck, divine favour etc) is not to elide the obvious differences you note between fate points and hit points, but to draw attention to a way in which hit points can work as written, without the need for new mechanics, but equally without requiring a "hit points = meat" approach.
D&D HP is NOT, in any way shape or form, a stand-in for Fate Points. Fate Points allow the player to adjust a given outcome independent from table mechanics, HP does not do this. HP is not Fate Points.
I don't understand your phrase "independent from table mechanics". Fate points are part of the mechanics used at any given table. In a game like HeroWars/Quest, they are integral to action resolution - the action resolution mechanics cannot be stated without reference to "bumping" via Hero Point expenditure.
It's a given that, unlike fate points, hit points don't require a player choice to expend them. It's as if the button saying "Do you want to spend a fate point to avert that consequence for your PC?" was switched permanently to ON.
It's a given that, unlike fate points in (say) HARP (but not in, say, HeroWars/Quest), the action resolution mechanic in D&D can't be stated without reference to hit points.
The mechanics are not identical. They don't play the same way. But they serve the same function: of ensuring PC survival, by creating gaps within the fiction established by the mechanics. Although the situation
seems to be one of certain death,
something - the mechanics on their own don't tell us what - has occurred which resulted in the PC's survival.
(To use some jargon: both fate points and (under this interpretation) hit points are "fortune in the middle" mechanics.)