Everyone knows two things about the stegosaurus brain. One of them is an exaggeration and the other one is simply false.

The braincase of specimen CM 106 has been cast, and the cast measures about 64 cubic centimetres.

A walnut kernel is somewhere around 10 to 15 cubic centimetres. So the walnut line undersells the animal by a factor of four or five. It is a good line, and it has been repeated for a century, and it is not a measurement. "No bigger than a dog's" is closer to the truth.

Although — and this cuts the other way — the cast measures the cavity, not the brain. In dinosaurs that are not birds, the brain often filled only about half of it. So the real organ was probably smaller than 64 cc. Nobody can tell you exactly how much smaller.

What is not in doubt is the ratio. Marsh worked it out in 1896: scaled for body size, the brain came to roughly one hundredth that of an alligator. He concluded the animal had "one of the smallest brains of any known land vertebrate", and a century of work has not overturned him.

For scale, that brain was running an animal of about 3.5 tonnes. The most complete stegosaurus ever found — a young adult, about 85% of a skeleton, 5.8 metres long and 2.9 metres tall — has been carefully modelled at 1,560 kilogrammes.

You have heard that the stegosaurus had a second brain in its hips to operate the back half of the animal. It did not. There is no second brain and there never was one.

Here is what is actually there. Over the hips, the canal that carries the spinal cord widens out into a chamber. It is a real feature, and it is big — Marsh estimated it at at least twenty times the volume of the braincase. That is a nineteenth-century plaster estimate and should be held loosely, but the cavity is genuinely large.

The interesting part is that Marsh never called it a second brain. He called it a "posterior brain case" and a "posterior nervous center", which is a description rather than a claim. The two-brains story was built afterwards by other people: German anatomists who wrote about a "sacral brain" governing digestion and reproduction, and a geologist who stated flatly in 1930 that the animal "had two brains". The second brain was invented by Marsh's readers, not by Marsh.

The leading answer is a glycogen body — a fatty, sugar-storing structure that birds have in exactly the same place. A 1991 review of dinosaurs with this kind of enlargement concluded it was the best fit.

But be careful how much weight you put on that. It is an argument from comparing anatomy, not from anything preserved. And here is the awkward bit: nobody knows what a glycogen body does in a living chicken either. So "it was a glycogen body, which did such-and-such" is two guesses stacked on each other.

There is newer work suggesting the equivalent structure in birds may be a balance organ. That is a live alternative, not a settled replacement.

Last thing, and it takes some of the mystique off: a widening of the spinal cord over the hips, serving the back legs and tail, exists in every four-limbed animal. You have one. The stegosaurus's is just unusually roomy.