To “look askance” is an idiom from meaning “to consider someone or something in a disapproving way.” I first learned it when reading Michael Leja’s eponymous book about late 19th century deception in American art (P.T. Barnum and such).
It also has a meaning in astronomy. One of the problems in astronomy is the limits of the human eyeball–this is the main reason astronomers uses high quality cameras instead of looking through telescopes with their own eyes. Humans have many different receptors in their eyeballs that have evolved for different purposes and good for seeing different things — it’s just like in Jurassic Park. Human peripheral vision, for example, is very good at seeing motion (an ability that has understandably saved a lot of lives!), but very poor at distinguishing detail. To see detail, we have to look at the object or thing directly, which employs the receptors at the center of our eye. For more on this topic, see Margaret Livingstone’s Vision and Art: The Biology of Seeing, or her lecture.
In astronomy, to look askance us to look indirectly at the object one is trying to see in order to employ different receptors and perhaps be able to pick it up. For this reason, very faint objects are often visible if one slowly moves the telescope, making the object appear to move, and therefore respond to peripheral receptors.
To “look askance,” then, is to see something by not looking at it directly, to paradoxically not look at something in order to see it. It is the Medusa strategy, or Perseus strategy. It is a nod to the limits of empiricism.
To see what cannot be seen, one must try to look at it.