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40d:Dwarven physics
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Dwarven physics is the study of how matter interacts with other matter within the world of Dwarf Fortress. Scholars of traditional Newtonian physics should note that Dwarven physics may or may not correspond with traditional Physics.
It is also worthy of mention that Dwarven physics is a highly complex subject, and thus only be approached by extremely intelligent, extremely curious, or extremely insane individuals.
Overview
Those familiar with traditional physics will recognize the following equation:
E = mc2
This equation, read from left to right, says: "Energy is equal to mass times the speed of light squared."
The following equation is known as the Dwarven Equation of Everything, and is the Dwarven adaption of the above:
E 
mc2
From left to right, it says: "Energy may or may not equal mass times the speed of light squared." Needless to say, there is a small amount of ambiguity when dealing with Dwarven physics.
The Dwarven method
The Dwarven method is a rubric by which experiments in Dwarf Fortress are conducted, but should not be confused with the Scientific method. Although the rigidity of the Dwarven method is disputed, the majority of important Dwarven experiments follow the Method. The Dwarven method consists of the following general guidelines:
Sample size
Again, those familiar with traditional science may recognize the phrase, where it normally means, "The more the better." However, in Dwarven experiments, it means, "The bigger the better. For instance, a 500-meter magma fall is preferable to a 50-meter one. Now, if you had two 500-meter magma falls...
Repeatability
This is whether or not the experiment can be repeated, and if so, under what conditions. If there are few or no restrictions on repeatability, and your experiment receives the same results every time, it will likely be accepted as Dwarven fact. On the other hand, if said experiment can only be reproduced at infrequent or unpredictable intervals, and you were the only one to witness it, and you forgot to take a screenshot, and the experiment can only take place on your computer, and you mysteriously misplaced the savegame, your experiment will likely be dismissed as pointless drivel.
Dwarven factor
This factor is the approximate relative value of the prodigiousness of an experiment. Values must be real numbers, more specifically subsets of the Integer family. In layman's terms, the Dwarven factor is how awesome an experiment is. Keep in mind that the D-factor is relative, and thus intended to be compared with other values.
For instance, a cannon that shoots water may have a D-factor value of 100. However, if this cannon was constructed completely out of Adamantine, or if it was modified to shoot Magma instead, the D-factor may increase to several thousand, depending on the amount of magma used.
Note that a graph of the Dwarven factor may, and often will, asymptote. Vertical asymptotes are often seen when the D-factor of one experiment is just greater than that of another experiment.
Let us say that a hypothetical Player A constructed a catapult that hurls legendary Hammerdwarves at invaders, but Player B constructed a nearly identical catapult, except that it throws Zombie carp at invaders. Let us also say that the Zombie carp catapult has an assigned D-factor of 1,500. Both catapults ultimately accomplish the same task, (in this case, the complete annihilation of the invaders) but due to the inherent superiority of Zombie carp to hammerdwarves, (and everything else except Ironblood himself, booze, and magma) the Zombie carp catapult must have a higher D-factor than the other one. In this case, the D-factor graph of Catapult A will likely have an asymptote at 1,500. For those of you who aren't so calculus-savvy, this means that the D-factor of the "A" catapult will be approxamitely equal to 1,499.999999999, but will never reach 1,500.
Lastly, there is a direct correlation between the Dwarven factor and Sample size. Simply put, the bigger, the more Dwarvenly.
The Dwarven status quo
The Dwarven index is strikingly similar to the concept of entropy. Although it involves chaos, the Index is more related with the innate stupidity of dwarves. A rough example of entropy is if a dwarf is given two decisions, and it is completely uncertain which one he will choose. (The concept of entropy relates loosely to the Dwarven Equation of Everything.)
Even though it is similar to the concept of Entropy, the Dwarven index may produce different results, hence the differentiation between the two. The Dwarven index states, in a nutshell, that when a dwarf is faced with a decision he or she will make the wrong decision approximately 99.7% of the time. This could range from something minor like taking the long route to the kitchen, or to something like building a wall from the wrong side, getting stuck alone with a siege, dying a gory death, and sending the entirety of your fort into a massive tantrum spiral as the invaders split their sides laughing. While entropy will produce the wrong decision roughly 50% of the time, the Dwarven index will produce the wrong decision 99.7% of the time.
Summary of the Dwarven status quo
Dwarves are stupid.
Discrepancies between Dwarven and traditional physics
The following entries are items that are possible in Dwarf Fortress, but impossible otherwise.
Dwarven perpetual motion device
As the name implies, this is a device that continuously generates power. Specifically, it generates power by building a water wheel in a waterfall, then using said waterfall to power a screw pump. The screw pump is used to pump water back to its original Z-level and recycle it through the waterfall. Somehow, the device consistiently generates a surplus of rotational energy.
Quantum garbage dumps
Perhaps the most common Dwarven anomaly, this is simply a 1x1 garbage dump zone, with massive amounts of items (usually stone) all contained in a single tile. The practicality is obvious, where else are you going to put all that stone?
Matter annihilation
Another common method of garbage disposal. Items and creatures in DF can be "annihilated" by placing them under a drawbridge, and lowering the bridge. This is an example where the Dwarven Equation of Everything states that energy is not equal to mass times the speed of light squared. If the opposite was true, players would witness a massive explosion and a corresponding drop in FPS rate whenever an item was annihilated.