In spite of what some people insisted twenty years ago, Neanderthals are not members of our species. They are Homo neanderthalensis and we are Homo sapiens. We are closely related but different species, not different races of the same species. Thousands of years in chilly overcast Europe selected for lots of Neanderthal characteristics similar to those of modern White humans, but now that we are able to compare actual Neanderthal DNA to ours, we find that these similarities are derived altogether differently. Neanderthals used entirely different DNA for their red hair than we use for ours.
Neanderthals' DNA differs from ours by 27.2 gene substitutions. Chimpanzees' DNA differs from ours by 55.0 gene substitutions. This means that Neanderthals were half as distantly related to us as chimpanzees. In spite of how much graphic representations such as Popeye look like humans to us, we would not have been inclined to breed with the Neanderthals we chanced upon, because they were simply too different.
If one is lucky enough to compare actual Neanderthal skulls to those of humans, he sees that Neanderthals had brow ridges and rounded chins, all right, but he also sees that Neanderthals had huge eye sockets and a ballooned-out cranium in back, called an occipital bun. Casual observers seem to miss this, but to me this strongly suggests that Neanderthals were nocturnal. Nocturnal animals have larger eyes and enlarged visual areas of the brain which the bun would have housed.
Neanderthal fossils have an exceptional amount of healed fractures. When I was a crazy kid, we had a sport. We'd go out into the pasture where the cattle were bedded down in the moonlight to pick out a cow, jump astride her and see how long we could hang on when she got to her feet. Is this how Neanderthals hunted wooly mammoths?
Neanderthals showed up in Europe about 200,000 years ago and persisted until 28,000-24,000 years ago. We showed up about 35,000 years ago and warily shared the same habitat with them, for anywhere from 7,000 to 11,000 years. That's a long time to avoid running into them in the shadows. We've only farmed and had towns for what, 8,000 years?
24,000 years is an awfully long time ago, but do you reckon that the troll under the bridge is some sort of ancient cultural memory? Is that why trolls are supposed to turn to stone in daylight? What do you think?