Indoors, in indirect light, it looks like really dark taupe creme, or a dark grey creme, or a greyed plum creme. Definitely not purple. Definitely not a shimmer.
Indoors, in more direct light, a very small amount of purple shimmer peeks out.
Outside, in direct sun, if one holds one's fingers at certain angles, pink AND purple shimmer show up.
I don't have anything quite like this in my stash, but that didn't stop me from doing comparisons. I'd read Paradoxal described as Essie Demure Vixen's darker sister, so I included that in the lineup, thinking I might layer it with something, but that didn't work out.
Passionate Kiss is a dark purple shimmer (and shows that, even indoors), but it lacks the pink highlights and murkiness of base color that Paradoxal has. Ki is more shimmery, and the duochromey-ness of it means it sometimes is closer in color to Paradoxal and sometimes farther away. YDKJ is not really anything like Paradoxal, but it might be a good place to start a franken because it does have that dark cool-toned taupe tone.
All in all, I'm happy I got Paradoxal, even though it was pricey. I can see myself wearing it a lot this fall. I might have to carry around a powerful lamp with me to show off the shimmer, though.