Look at your dog lying on the mat in the sun, eyes wide open and vacant. What's going on in that furry little head? What is it thinking? Anything? Is it even possible to know if animals are thinking?
"I think they are thinking more than we used to think they think," says Michael Corbalis, Emeritus Professor at the Department of Psychology at The University of Auckland.
And yes, he says, they think quite a lot.
"They think about fewer things than we do, but otherwise probably not very different. They don't think about quantum mechanics, but probably do think about food, play, danger."
All things, of course, that we needed to have sorted before we got around to pondering the mysteries of quantum mechanics. We undoubtedly have more in common than a liking for quality steak that's left lying out on a kitchen bench.
"I think we are not as special as we think we are," continues Corballis.
"What goes on in an animal's mind is not that different from ours. We can console ourselves that we have more imagination. But it really goes back to Darwin, and the notion that differences between human and animal brains are differences of degree but not of kind."
Ever since Darwin, there has been resistance to accepting how much we have in common.
"People are weird about humans being special. Religion says only humans can be conscious and have minds."
He disagrees.
How similar are our brains? Do their brains have sectors like ours that control specific behaviours and therefore thinking about them?
"There are similarities across mammals," says Clare Browne, animal behaviour researcher in science at the University of Waikato.
"But there is a difference in complexity between animals and humans."
Corballis says: "The primate brain is very like the human brain, but smaller and less differentiated. The bird brain is a bit different, but still maps quite closely onto the human brain."
Which raises the question – how can a bird, with its tiny, in fact, proverbial "bird brain" do much in the way of thinking at all? Corballis explains that part of brain size is to do with body size – we have a bigger brain because it has to run a bigger body, with a whole lot of complex functions to organise.
Some of the similarities between how humans and animals think highlight how similar we are in other ways.
"The prospect of food activates the caudate nucleus [connected with rewards] in the canine brain in the same way that it does in the brain of a businessman anticipating a monetary bonus," writes Frans De Waal in Are We Smart Enough to Know How Smart Animals Are?
"One important common structure is the hippocampus, a sort of GPS that indicates where you are in space" says Corballis.
"It underlies 'mental time travel'— thinking about past events and imaginary future ones.
"They've found that when a rat is in a particular location, bunches of cells fire; when it moves, a different bunch fire. If you take the animal out of where it is, some keep firing. The animals are replaying the movements they took in a particular space, exploring it in their minds. They mentally replay past events, and probably imagine future ones. They even seem to mentally explore parts of terrain they have seen but haven't entered."
Corballis says we are getting into controversial territory here.
"I started working on mental time travel with an associate – we may have invented the term. It was claimed it was unique to humans.
"Having read the hippocampal stuff coming out now, I've changed my mind. He and I no longer agree."
Less controversial is the notion that animals dream.
"Probably about a fairly random melange of everyday things," says Corballis.
This conclusion is partly based on monitoring rapid eye movement, the phase of sleep when we do most of our dreaming, and which most vertebrates go through when asleep.
Other experiments show animals reflecting on past events.
"There's a famous study with chimps, showing them a movie," says Corballis.
"Then the movie is played to them later on with something different happening and the chimp will react to the change: 'That's not supposed to happen'."
Which is all very illuminating as far as it goes, but why should we care what animals are thinking as long as they keep wagging their tails and not biting us?
"If we learn about their preferences for different things, that can help improve their welfare," says Browne, adding that has benefits for us down the track.
"We can learn what sort of housing conditions farm animals might prefer. If we can recognise when dogs are fearful or stressed we can change the environment to make them feel better and also to avoid provoking them, which might improve our safety. And if we can understand their signals better, we can work more effectively with working dogs – from farming to policing and conservation, with wide-reaching benefits."
Which leads quite naturally to considering whether, and if so to what extent, we can talk to the animals.
Dog owners think they understand what their dogs are "saying" and the more annoying ones will tell anyone within hearing what their widdle cudie is telling them, convinced they have it right. Browne says ... sometimes.
"Dogs were the first species to be domesticated, so we have the longest history with them," she says.
"While there is evidence of other species giving signals that humans can interpret, dogs and humans have a unique ability to produce and correctly interpret each other's signals. Dogs can respond to a range of human-given gestures, and can likewise use their own body language to signal to humans where, for example, treats are hidden - so there is some great, successful dog-human communication that takes place. However, there are also many instances where there is miscommunication between humans and dogs, which can lead to problems for all of us - so understanding animal behaviour is important for many reasons."
Corballis describes a fascinating experiment which tested the limits of dog-human communication.
"Dogs watched some food being hidden where they couldn't access it while their owners were out of the room. The owners didn't know where it was. When they returned to the room the dogs changed their behaviour with increased signals – mouth licking, vocalisation and sniffing. And the owners were able to correctly locate that food."
Dogs make a variety of different noises to communicate different things: there's the person nearby bark, the stranger too close bark, the frustrated please throw the ball bark, the let me in bark, the happy to see you bark. But Corballis says this doesn't meet the crucial criterion for language.
"The thing about language is that it is open-ended. There is no limit to the number of things you can say. You can go to a library and open a random book and see a sentence you've never seen before, and you will understand it. I can construct a sentence I've never said before. That's what distinguishes what humans do from what dogs do."
You might say, they communicate, but they don't use language to do it.
Also, in some respects, it's not them, it's us. The amount we understand can depend on our cultural background. Emily Reynolds, writing in the British Psychological Society Research Digest, reports a study which "suggested that although some ability to recognise dog emotions exists from early on in life, it is largely a skill we acquire through experience".
In other words, the more familiar we are with dogs, the more we understand them. People from cultures which are not big on companion animals were less adept at understanding animals' signals.
Will we ever have definitive answers to all these questions? Maybe not. There is still a lot of "probably" in all the research. One of the reasons it's hard to know things for sure is of course that animals can't just tell us what we are thinking, so we are limited by technology at least.
And by how we conduct research in animals. It took a long time to train dogs to stay sufficiently still to run an MRI. And the amount of poking chimpanzees' brains with electrodes is a lot less than it used to be.
Perhaps evolution will see animals open up and share more of their inner selves, developing abilities such as language in their own time?
"You could be really pessimistic and argue the opposite, because humans have developed a capacity to communicate. There have been 23 different hominem species evolve since we separated from the apes, and we are the only ones left. Also, you can argue that we use language in weird ways – such as to lie and cheat. You could argue it hasn't been all good."
Do dogs smile?
"Oh look ... he's smiling!"
Part of the problem with reading animals' minds, and knowing what we know or don't, is our love of confirmations bias – the process that makes us think something is true if it fits what we want to believe. It's the clairvoyant's most basic technique – "How on Earth did she know I had a relative called John? Or Jim?"
So, do dogs smile? Yes. But probably not for the reason we think. They have learnt over generations that if they open their mouths and show their teeth, but without snarling or including other aggressive signals, they will get a good reaction from us. So they keep doing it.
It's also easy to misread a situation thanks to the observer-expectancy effect. This was what happened in the case of Clever Hans, a horse in Germany early last century that could do basic arithmetic and a host of other tasks. Or so it was thought, until it was realised that, quite unconsciously, his trainer was providing non-verbal cues that sent a positive message to Hans when the horse stamped out the right number with his hoof.
We tend to think an animal is clever if it does what we want it to do. Sheep dogs are brilliant because they employ so many strategies for herding sheep to the farmer's requirements. If they did what they wanted to do and ate the sheep, we wouldn't think they were very smart at all.