One thing may be more complex than another because there are more things that must be considered, more 'dials to fiddle with' if you will. However, even this over-simplifies the situation.

DonaldNorman mentioned in TheDesignOfEverydayThings the example of a refrigerator/freezer with two dials. But instead of the dials controlling:
	* freezer temperature
	* fridge temperature
they controlled:
	* how often the compressor runs
	* what proportion of cold air is vented into the freezer vs. into the fridge

In the first setup, the dials work the way humans would normally think about fridges. In the second setup, the dials work the way fridges are actually constructed (or at least how ''this'' fridge was constructed).

Now the question is: Which of these setups is more complex? I can think of 3 possible answers.
	1. In each situation, there are two dials, two variables to control, so they are equally complex. This is EssentialDifficulty.
	1. In the first situation, it takes less mental effort, less trial-and-error to get the fridge to work the way you'd expect. Therefore, the second situation is more complex. This is AccidentalDifficulty.
	1. In the second situation, it takes less engineering effort to make the controls operate the fridge, the design of the fridge is simpler. Therefore, the first situation is more complex. This too is AccidentalDifficulty.

The point is that actual dials do not map directly to human or to machine. The same number of dials can make a situation more or less complex, depending on what the dials control and which side of the equation you're on. Furthermore, MoreDials doesn't necessarily make something ''actually'' more complex if the overall EssentialDifficulty is the same. This is not to make light of AccidentalDifficulty. After all, difficulty is difficulty. Just be aware that MoreDials does not necessarily directly relate to more complexity/difficulty.
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How about some other dials?

	* how long my milk will stay fresh
	* how long it will take for my ice cream to freeze

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So what was the UserStory for controlling the unit?  Was it "I want to easily set the temperature in the freezer and the fridge compartments" or was it "I want to easily write the code to control the cooling" ? --PeteHardie
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HP printers these days seem to have 2 buttom and 2 LEDs.  One of the buttons is usually power, and I think the other is usually page feed.  One LED indicates that power is on, and the other usually indicates status. But once the LEDs start blinking their little coded messages to tell you something is happening out of the ordinary, suddenly the meaning of all of the buttons has changed?  Which one cancels the job, which one will cause the printer to try again?  That is a case of FewerDials being just as big of a problem.
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See OoHasMoreDials