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The goal of this encounter is to see which of these strange things would cross the finish line first, granted that they both in some way know about the conditions of the race and strive to win. The dwarf is placed one hundred yards away, facing the incorrect direction. The rotting wooden door is attached to an archway that sits directly in front of the finish line. All the door must do to succeed is rot off of its hinges, AND fall in the correct direction to win. The dwarven torso man has an amulet that allows him to, once per week, travel exactly half of the distance to his desired location via levitation. The movement takes the entire week (thus the first day 50 yards = 7 days, second 25 yards = 7 days). Also, this dwarf has no need for food or drink. His requirement for sleep is negated by the fact that he floats really slowly and can sleep while he moves. The Torso of the dwarf is missing all key components of movement, unless you count his head and neck. Because of this, he could easily be diagnosed as suffering from deep depression. So much so, that he often become unmotivated to act or think on any given day. This means that even though his amulet can take him a fairly long way toward his goal of winning the race, he may not even use it half of the time, and even if he does he may not realize that no matter how many times he does use it he will never reach his destination.
A two way ANOVAW was calculated to determine the point of significance between the studies with the following results: A (depressions effect on movement) P < .01, B (depressions effect on cognition) P < .023, AxB (interaction between the variables) P < .017.
Setting: Demi plane of the fallen child of a forgotten god. The magic that was used to create this plane was one of love and admiration. Although the god who created it has long since been forgotten, the plane persists ever green and lush with flowers. In that way the weather is relatively constant at a "just right" comfortable temperature (82 degrees F). The wind appears like clock work to rustle the leaves gently every few hours, or if the occupants begin to feel too warm (whichever comes first). The wind never breaks the speed of a light breeze in random directions (.02 mph).
The time of day depends on the disposition of the fallen child, and thus cannot be changed (constant 4:30 pm if calculated through similarity to that of the city Berlin on Earth).
The door was magically crafted out of fresh pine wood 100 years ago and is not magically sustained.
Thus I conclude that there is but one good question to ask at this point: "Who would win in a race, a magically sustained dwarf torso who suffers from deep and significantly hindering (P< .01, .023, .017) depression and the rotting door that stands in the doorway just before the finish line (if the door fell the correct direction it would cross the finish line)?

The door wins. The torso will actually never reach the finish line, and the door, even if it falls the wrong direction, will eventually decompose and the occasional light wind will blow fragments of the door over the finish line, eventually. Meanwhile the dwarf will literally never cross the finish line.

The dwarf. Even with only a movable head, the dwarf will dig its chin into the ground and pull itself forward, eventually crossing the line. Depressed dwarves are angry dwarves, and its rage will carry it along. That, and its spite at whatever made it an unmoving torso.

If the dwarf can only ever move up to a maximum of half the distance to the finish line... doesn't that mean he can never actually reach it? Isn't that a paradox of distance, or something?? The door wins, when the wind blows its decayed bits across that final goal. Once this is accomplished the door can find some peace knowing it did something worth something at the end of its existence. Through a cruel trick of fate, the lifeless torso must bear witness to this final jest on its being. For it is in a race it can never win. Alas the gods are fickle indeed.

odd.. Cheyne is the only person to realize both A: the dwarf is sentient and B: that the dwarf has other, unconventional as they may be, forms of movement. (angry chin flopping motion)

The dwarf is capable of crossing the finish line, it is just high improbable that it will happen any time soon.

thank you Cheyne for being both thorough and of a similar mindset as I am.

Nope.

is the proper debate etiquette to reply, "yahuh!"
The paradox only applies to the most likely courses of action, the dwarf can still use his angry/sad chin, which is not subject to the paradox. Thus, it is possible, however unlikely, that he may indeed cross the finish line.

not to beat a dead horse
but the paradox only holds if the target location is the door.
He could move to a place 2x the distance from the point of the finish and pass the finish line in 7 days.

Don't let fundamental laws of mathematics solidify as conceptual absolutes. Reality is the coming together of the "truths" of mathematics et al and systems of life. o.O (those terms are vague and I am sad as a result)