Since cats first got their adorable claws into us about 9,500 years ago, humans have had a love affair with felines.

Today more than 80 million cats reside in U.S. homes, with an estimated three cats for every dog on the planet. Yet there's still a lot we don't know about our feline friends—including what they think of their owners.

John Bradshaw is a cat-behavior expert at the University of Bristol and the author of the new book Cat Sense. After observing pet cats for several years, he's come to an intriguing conclusion: They don't really understand us the way dogs do.

Bradshaw recently shared some of his insights with National Geographic.

How did you get into cat behavior?

For the first 20 years of my career I studied olfactory [smell] behavior in invertebrates. I've always been fascinated by this other world that animals live in—primarily of odor, which is dogs' primary sense. So in the early 1980s I started working on dog behavior. [Later] I very quickly became fascinated with cats, and what their idea of the world is compared to the one we have.

What do you do in your research?

A lot of observation—watching groups of cats to see how they interact with one another and deducing their social structure. [I watch] cats in colonies that are free-ranging, and in animal shelters where quite a number will be housed together—you get interesting dynamics [when new cats are introduced].

I've also done slightly more manipulative things, such as studying the way cats play with toys, or testing cat [behaviors] at different times of the day. [I also observe] relationships with owners, interviewing them and giving them questionnaires to find out how they perceive their cats.

Why did you conclude that cats don't "get us" the way dogs do?

There's been a lot of research with dogs and how dogs interact with people. [It's] become very clear that dogs perceive us as being different than themselves: As soon as they see a human, they change their behavior. The way a dog plays with a human is completely different from [the way it plays] with a dog.

We've yet to discover anything about cat behavior that suggests they have a separate box they put us in when they're socializing with us. They obviously know we're bigger than them, but they don't seem to have adapted their social behavior much. Putting their tails up in the air, rubbing around our legs, and sitting beside us and grooming us are exactly what cats do to each other.

I've read articles where you've said cats think of us as big, stupid cats. Is that accurate?

No. In the book [I say] that cats behave toward us in a way that's indistinguishable from [how] they would act toward other cats. They do think we're clumsy: Not many cats trip over people, but we trip over cats.

But I don't think they think of us as being dumb and stupid, since cats don't rub on another cat that's inferior to them.

Can we discover what cats really think about us?

More research needs to be done. [It's] not an area that's received sufficient attention. [Cats are] not wild animals, so ecologists [might think], 'Well they're not really animals at all.'

What has been most surprising to you in your research?

How stressed a lot of pet cats can be without their owners realizing it, and how much it affects the quality of their mental lives and their health. Cats don't [always] get on with other cats, [and people don't realize] how much that can stress them out. Other than routine visits, the most common reason cats are taken to vets is because of a wound sustained in a fight with another cat.

[More cats are mysteriously getting] dermatitis and cystitis [inflammation of the bladder] and it's becoming abundantly clear that these medical problems are made worse by psychological stress. [For instance], inflammation of the bladder wall is linked to stress hormones in the blood.

One solution is to examine the cat's social lifestyle, instead of pumping it full of drugs. [For example, that could mean making sure] two cats that [don't get along] live at opposite ends of the house. Quite often the whole problem goes away.

I have a few questions from cat owners on Facebook. First, why might a cat yowl when it's by itself in a room?

Cats learn specifically how their owners react when they make particular noises. So if the cat thinks, 'I want to get my owner from the other room,' it works to vocalize. They use straightforward learning.

Why do some cats treat one human member of the household differently?

They're much smarter than we give them credit for: They learn what works with what person. They know if [one member of the family] is prone to get up at 4 a.m. and give them some treats.

Why do cats knead us?

They are using behavior that they would use toward their mother—all the behavior they show toward us is derived in some way from the mother-kitten relationship. The kitten learns to raise its tail, rub on its mother, and knead and purr. Grooming is what mothers do back to kittens.

So they're using bits of behavior already in their repertoire to communicate with us. There aren't very many behaviors—maybe half a dozen.

Can you train cats?

Yes. Cats can learn what they're not supposed to do. If your cat has developed a habit [of jumping up on the kitchen table], there are limited ways to prevent it.

You could use a spring-loaded toy, so when a cat jumps up on something, the toy goes bang and up in the air—the cat doesn't like that and jumps down. Another reasonably benign [strategy] is to use a child's water pistol. But make sure the cat doesn't realize you've got it. Cats don't forgive, and once they realize a person is causing them anxiety or hurt, they keep away.

What do you want owners to know about their cats?

Acknowledge that cats are sociable animals to a point, but not sociable to the extent that dogs are. A lot of people who have one cat decide they would like to have another cat, thinking two cats are twice as much fun. But the cats may not see it that way.

The simple message I would like to get across is if you do want to have more than one cat, go about it in a careful way—and be prepared to give up on it if it doesn't work.