Above is one of my own drawings with a bit of "mystery" to it. I wasn't consciously trying to make it look "mysterious" as I drew it, but I thought of it as an intriguing scene (that's why I decided to draw it in the first place).
As many have pointed out and artists have known probably since the first one started scratching with a stick in the dirt (but, I think, not enough artists realize, or remember), if we can see at once all that's there and everything that's going on in a picture, there is no "mystery" to pull us in and keep us there - We look, we see it all, we may even love it, but then we leave it behind and move on to something else because there's nothing in it we need to look at again in order to understand it. ("Been there, Seen that.")
Artwork that has an element of mystery evokes curiosity and maybe even a little excitement - It makes a viewer pause. That's not all it does, though. A "mystery" unlocks the viewer's imagination, makes him or her want to stick around and try to figure things out.
Mystery is just one element the artist can use, but it can be very important as it is likely to trigger a phase in which the viewer becomes engaged with the artwork - exploring, thinking, making connections, seeing things that aren't seen right away (or that aren't really "seen" at all, but are suggested). If an artist is really trying to "say something" with his or her art, it behooves him/her to keep the viewer's attention and interest and engagement long enough so that substantial communication, on different levels, can take place.
Certainly, something that we can't quite make out startles us, gives us a feeling of excitement (you never know what might be lurking in something you can't see clearly), challenges us to figure it out. There is little left on this planet that hasn't been discovered, displayed under bright lights, dissected, judged, and forever tamed (and made into something to sell); it's delightful to find something that really makes us wonder about it.
But adding an element of mystery isn't just a "trick" to get people's attention. It is a gift to the viewer. Mystery is something we all need in our lives -- it makes us feel alive, as if we are actively in collaboration with the artist (it takes two to do this dance), and aware of our inner selves and some of the odd bits of knowledge and wisdom we didn't know lay within us. Also, there's that "thrill" mentioned earlier (a thrill now and then is fun).
An artist presents a mystery by not making everything that's going on in a picture obvious at first glance (or maybe even after a long search - maybe the viewer has to use their imagination and cannot really "know" even after long contemplation). One thing about a mystery - Every person will come up with his or her own unique version of the "solution" as they do their contemplating (or else will give up and not come up with anything).
"Mystery magnifies danger, as a fog the sun, the hand that warned Belshazzar derived its horrifying effect from the want of a body." -- Charles Caleb Colton (1780 - 1832)
"A day spent without the sight or sound of beauty, the contemplation of mystery, or the search of truth or perfection is a poverty-stricken day; and a succession of such days is fatal to human life." -- Lewis Mumford (1895-1990).
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