In it we read of Christina, a woman who has lost all sense of proprioception. She learns to puppeteer her own body; if she is not looking at a limb, she has no internal sense of what it was doing.

A nightmare scenario for anyone, but one that sounds oddly familiar to gamers.
Proprioception is what we aim to replicate, albeit distantly, when we talk about "body awareness" in games--to look down and see your body is the most basic feedback for a body we cannot sense.
I want to use this as a way to look more generally at the sense of immersion, of being embodied in the avatar, and how FPS games are limited in this respect. Before we talk about any design changes or solutions, we need to understand the problems.
We'll never be able to capture full proprioception (nor would we likely want to), but that same sense of "being there" is critical to immersion. Lack of proprioception is much of the difficulty for new players to grasp FPS controls, given the relative dearth of sensory feedback, and why even experienced players may become injured or killed in the world in a way that seems "unfair."
If FPS players ever feel as though they're a walking refrigerator box in the game instead of a person, it's because they are. Many games refine hit detection for the purpose of assigning damage, but collision-wise most player characters really are just ambulatory refrigerator boxes with a small view slit and a gun, and games are designed to suit.

This box-and-gun model has implications that have shaped and limited FPS games more than we might care to admit. First we'll talk about the player's field of view, then basic collision in the world and scaling issues, and finally a little bit of what this means for the game space and interactivity.
You may recall the furor over "true widescreen" shortly after Bioshock's release. Without getting into that fairly snarled topic of debate, it's worth noting that it was all over a few degrees of field of view. With the standing box-and-gun model for the player in FPS games, the player's field of view (FOV) is a critical window to the world outside the refrigerator box.
In reality we enjoy 140 degrees of binocular vision, where the overlap between the two eyes' vision gives us depth perception, as well as an additional 40 degrees of peripheral FOV.
Stepping inside the refrigerator box gives us monocular (i.e. non-depth perceptive) vision limited to about 90 degrees, and typically far lower, all with no periphery. (A move to third person would expand our practical FOV as well dramatically improve our body awareness, but with other far-ranging costs and implications to the game design, so we'll talk about that later.)
What makes this so troublesome is that maximizing player FOV in order to play the game effectively--situational awareness and target acquisition and so on--can run contrary to other design imperatives.

FOV 75 and FOV 90 on HL2: The Lost Coast. The man appears more distant at 90, even though we are standing face to face. Note that the crowbar remains the same, as it is rendered separately to prevent distortion.
A well known case is that of Half-Life 2. Evolving from the player's fondness for the non-player characters in HL1, Valve spent a great deal of time and effort modeling, animating, and voicing NPCs like Alyx and Barney, characters that would make up the emotional core of the experience.
They quickly found that their wide-angle FOV, ideal for fighting enemies in the world, made these friendly characters appear farther away then they would have liked, even when standing face to face (or face to box). HL2 shipped with a standard FOV set to 75 degrees instead of 90, with a special case that opened it up to 85 degrees during vehicle driving sequences.
Bethesda Softworks would take a different approach to the same problem for The Elder Scrolls IV:Oblivion and then later Fallout 3. They retained a higher, more "distancing" FOV, and chose to dynamically zoom in on any NPC in the world that the player talks to to simulate the desired visual intimacy.
In addition to the relative perceptual difficulties related to FOV and characters in the world, higher FOVs introduce distortion, given from projecting a spherical perspective onto a flat screen. While this can be cleverly incorporated into the game, as with playing the alien perspective Aliens Vs. Predator with a very high "fisheye" type FOV, it's a problem for weapons in first person.
And when you're a refrigerator box with a hole cut out, the gun you hold in your hands is a central visual hallmark, your primary (and often only) agency in the world.
At higher FOVs, the gun in hand begins to distort along with the world, its apparent distance from you potentially more disconcerting than the apparent distance to NPCs. That the gun is often rendered separately from the world may ameliorate this, but alienate the player in other ways, furthering his or her apparent separation from the world. They're already a firm proprioceptive barrier away from the game already; any additional layers between the player and the world become prohibitive.
But this is enough to sketch out the myriad of issues associated with the first person perspective and FOV; I'd like to talk about the box out in the gameworld.
People understand that their avatar is clumsier than themselves, and that with practice a player is able to overcome or compensate for most shortcomings. This means they're nominally past thinking about the refrigerator box, but the box is always there. Often we can feel it, more often if the gameworld has not been scrupulously designed to accomodate the problem.
What I mean is that with level design there's a tricky balance between visual scale and player scale. The immersed player forgets that he is a refrigerator box, yet the world still need be scaled to accomodate his generous girth.
A friend of mine and fellow level designer Drew Risch taught me the simple, fundamental rule for good playspace in an FPS: keep it wide.
It's relatively simple to establish scale for all buildings, objects, and characters in a game to correspond with reality, but real world scale is unbearable for a refrigerator box to negotiate, even if the box itself is the relative dimensions of a person. You're a box, a box with only a small hole out the front with which to engage the world, so allowances must be made. Despite being a box you must be made to feel the hero, and heroes don't have to carefully negotiate kitchen furniture like the morbidly obese.
To that end the gameworld must be carefully widened, ballooned to allow the passage of this refrigerator box player and his often as-clumsy-if-not-clumsier AI compatriots.
The trick is to make this work mechanically, while still visually keeping the world in the ballpark of reality. It won't match, not if the world is truly wide enough for the player to move around comfortably, but these discrepancies can be carefully masked. In HL2, the corners of the Gordon-box can get the player stuck neatly into right angles of tight spaces such as elevators--level designers place invisible wedges in corners to prevent exactly this.
(In third person these sorts of issues are even more pronounced, though in different form; replay the beginning of Max Payne 2 and observe a world necessarily warped to accomodate Max's bullet-dodging antics and follow camera.)

We begin to see clearly why information systems, usually delivered via some sort of heads-up display (HUD) become so critical to helping the player over such considerable handicaps. The player has a narrow FOV and no proprioception, so environmental cues of sight and sound (plus a little rumble, if on a console) are all he or she is going to get.
Detailed sound design with corresponding sensitization of the player that these sound cues mean something (like the dry snapping sound of a bullet passing close by) can help close to gap left by so many missing senses, but won't fix everything. Which is why damage indicators and the like are now considered standard, as there is simply too much critical feedback the player needs to survive.
But I feel as though we've opened many doors without much sense to how we might approach a solution or a change from the problems these issues present.
At this point, what I want to impress upon you is that the player character is a refrigerator box with a hole cut in it and a gun sticking out, and so long as he remains such--a mute, verb-poor box, murdering everything in his path only to pause occasionally to flail at an oversized green-lit button or watch a mandatory cutscene--FPS games will likely remain the dim spectacle that they've been for years. There certainly is hope, but there's also a lot of dead weight carried from sequel to sequel that ought to be reconsidered.
But I'm getting ahead of myself and betraying more ambition than I care to for a first entry.
Next time, we'll talk about methods to overcome these seemingly crippling limitations, and explore other design issues present with the status quo.
Summary of embedded links:
The Man Who Mistook His Wife For A Hat on Amazon.com
Excerpt from The Man Who Mistook His Wife For A Hat, "The Disembodied Lady."
Wikipedia entry for Proprioception
Wikipedia entry for field of view
Valve Developer Wiki on FOV in HL2
Excerpt of Max Payne 2 playthrough on youtube