Another common definition refers to the clarity or sharpness of an image on a display screen. Good resolutions are clearly defined.
One definition of resolution is new to me: the act or process of resolving or separating into constituent or elementary parts. That definition can strengthen my resolutions; I can break my goals into elementary, achievable parts. Smart.
My favorite definition of 'resolution' relates to music. There it means the progression of a voice part or the harmony as a whole from dissonance to consonance. One legendary story about resolution is that Wolfgang Mozart's dad would wake him up in the morning by playing a chord progression on the piano without resolving it; Mozart could not bear to leave the progression unfinished and would get up to play the resolution. Disharmony is that disquieting.
Maybe the most inspired definition of resolution is this: a reduction to a simpler form. Can I simplify?
Resolutions: solutions, sometimes a second or subsequent effort, made with fortitude, clarity, and defined steps that lead to consonance and simplicity. Got it.