Andrei Herasimchuk's latest essay: The complexity principle
In general, the simplest way to think of any interaction within an application is in binary terms. The choice may be yes or no. The choice may be chocolate or not chocolate.
In essence, the user can or cannot perform a certain action, or interact a certain way with the interface.
The nature of this core interaction model gives us a base unit of 2. So, at the most basic level, we can think of complexity as a factor of this binary interaction raised to the number of items present in the interface.
C = 2i
Where "c" is complexity and "i" is equal to the number of items that require interaction.
adding 1 more of anything (item, field, widget, palette, etc.) increases the complexity not by 1 but exponentially. so the goal is not to make the interface as simple as possible but "as complex as it absolutely needs to be."
To emphasize this point he quotes Antoine de Saint-Exupery:
"In anything at all, perfection is finally attained not when there is no longer anything to add, but when there is no longer anything to take away."
Andrei emphasizes that the complexity prionciple does not apply to the amount of data or content (users are adept at sorting through large sets of data, such as in search results) but to the visual presentation of that data or content.
This means knowing that every ornament, typographic change, or color added to the presentation of the data set increases its visual complexity exponentially. This is not to say design should be bare, uninspired or boring. It just means that one should be aware of complexity in their work and resist the urge to overly decorate when it is not somehow reinforcing a certain aspect of the design.
in the comments josh offered another supporting quote:
"The ability to simplify means to elminate the unnecessary so that the necessary may speak"
-Hans Hofmann
there is some great discussion in the comments, expanding the point of this article into emotional/conceptual/qualittative complexity. Andrei continually emphasizes that his essay is specifically aimed at the number of "controls" and these other aspects of complexity would be separate areas of discussion.