Gary Larson framed the issue best in a famous Far Side cartoon. A Stegosaurus behind a podium addresses an audience of his fellow dinosaurs: "The picture's pretty bleak, gentlemen. ..the world's climates are changing, the mammals are taking over, and we all have a brain about the size of a walnut." (See a list of the 10 smartest dinosaurs.)
For over a century, that quote pretty much summed up popular (and even professional) opinions about dinosaur intelligence. It didn't help that one of the earliest dinosaurs to be dug up and classified (the above-named Stegosaurus, in 1877) had an unusually small brain, about the size of, yes, a walnut. It also didn't help that dinosaurs were long extinct; wiped out by the famine and freezing temperatures of the K/T Extinction 65 million years ago. If only the dinosaurs had been smarter, we like to think, some of them might have found a way to survive!
One Measure of Dinosaur Intelligence: EQ
Since there's no way to travel back in time and give an Iguanodon an IQ test, scientists have developed a new way to evaluate the intelligence of extinct (as well as living) animals. The Encephalization Quotient, or EQ, measures the size of a creature's brain against the size of the rest of its body, and compares this ratio to that of other species of roughly the same size.
Part of what makes us human is the enormous size of our brains compared to our bodies; our EQ is a hefty 5. That may not seem like such a big number, so let's look at the EQs of some other creatures: on this scale, wildebeests weigh in at .68, African elephants at .63, and opossums at .39. As you might expect, monkeys have higher EQs: 1.5 for a red colobus, 2.5 for a capuchin. Dolphins are the only animals on the planet with EQs even close to those of humans; the bottlenose comes in at 3.6. (EQ scales vary considerably; some set human EQ at about 8, with the EQ of other creatures scaled proportionally.)
As you might expect, the EQs of dinosaurs (based on analysis of fossil remains) are spread across the low end of the spectrum. Triceratops weighed in at about .11 on the EQ scale, and it was the class genius compared to lumbering sauropods like Brachiosaurus, which don't even come close to hitting the .1 mark. However, some swift, two-legged dinosaurs post relatively high scores--not quite as smart as modern wildebeests, but not much dumber, either.
How Smart Were Carnivorous Dinosaurs?
One of the tricky aspects of animal intelligence is that, as a rule, a creature only has to be smart enough to prosper in its immediate environment. Since the plant-eating sauropods were so massively dumb, the predators that fed on them only needed to marginally smarter--and most of the relative increase in the brain size of these carnivores can be attributed to their need for better smell, vision and muscular coordination. (For that matter, the reason sauropods were so dumb is that they only had to be marginally smarter than giant ferns!)
However, it's possible to swing the pendulum too far the other way and exaggerate the intelligence of carnivorous dinosaurs. For example, the doorknob-turning, pack-hunting Velociraptors of Jurassic Park are a complete fantasy--if you met a live Velociraptor today, it would probably strike you as slightly dumber than a chicken. You certainly wouldn't be able to teach it tricks, since its EQ wouldn't be in the same ballpark as a dog or cat.
Could Dinosaurs Have Evolved Intelligence?
It's easy, from our present-day perspective, to poke fun at walnut-brained dinosaurs that lived tens of million of years ago. However, you should bear in mind that the proto-humans of 5 or 6 million years ago weren't exactly Einsteins, either--though, as stated above, they were significantly smarter than the other creatures in their ecosystems.
This raises the question: what if at least some dinosaur species had survived the K/T extinction 65 million years ago? Dale Russell, the curator of vertebrate fossils at the National Museum of Canada, has caused a stir with his speculation that Troodon--a human-sized theropod dinosaur about as smart as an opossum--might eventually have evolved a human-sized brain if it had been left to evolve for another few million years.
This is just amusing speculation, of course; for one thing, the whole question of brain size also depends crucially on metabolism. If the dinosaurs were indeed cold-blooded, there's no question that they would have had to evolve a warm-blooded metabolism to proceed on the march to intelligence--and even if they were already warm-blooded, their low EQs meant they had a lot of catching up to do.