Just how special do you think you are? How different do you think you are from other animals? Do you think of yourself as an animal or do you see yourself, and your fellow humans, as somehow set apart from the rest of the animal kingdom?

Most of us – and I would unashamedly label us as the sensible majority of the population – accept that evolution is the best explanation for the pattern of life that we observe on the planet, both living and fossilised. However much creationists bang on about evolution being "just a theory", it beautifully explains all the evidence we have to hand (and there's masses of that: anatomical, genetic, palaeontological, embryological), without a single piece of evidence having turned up that threatens to bring the whole edifice tumbling down around our ears.

So, I'm hoping you're a sensible sort of person and that you consider evolution to be as true as the spherical nature of the Earth, or the fact that the Earth orbits the sun and not vice versa. But just how comfortable are you with the idea of being a product of evolution? I think it's still, even among the most enlightened of us, really hard to come to terms with the idea that we are just another animal. A naked ape. The third chimpanzee, even. You have to admit, science has done a very good job at bringing us down a peg or two, at knocking us off the pedestal of our own construction. We can no longer view ourselves as a special creation, something created in the image of a deity and close to angels (whatever they are or look like). We can no longer see ourselves as the ultimate destination, as the pinnacle of evolution, either. Our species is just a tiny twig on the massive, dense tree of life. But that's so difficult to stomach!

Even people undertaking research into human evolution seem to consistently fall into the trap of imagining that humans are special, and unique in a whole host of ways. But each thing we point to as utterly unique often turns out, after closer inspection, to be something shared with other animals. Or if it is a real difference, it transpires that it's often one of degree and not an absolute difference. Of course, this makes a lot of sense, as we have common ancestry with other animals, and "humanness" didn't just appear, as a package, out of nothing; it was something that happened over time, vast expanses of time.

Various features that we consider to be definitively human arrived in a piecemeal fashion. It's only with hindsight that we can say that these features gradually accumulated to the point at which we have something recognisably human. Here are a few examples of things you might think are uniquely human, but aren't.

Having fingernails rather than claws – this is a general primate characteristic. Opposable thumbs – we like to think of these as particularly human, but a quick glance at other primates reveals that most of them have got these useful thumbs as well. Bipedalism – standing and walking around on two legs – is something else that we often think of as being uniquely human (among primates at least – obviously there are other bipedal animals: kangaroos, birds and a fair few dinosaurs spring to mind). But it's simply not true that we're the only bipedal primates. Gibbons walk around on two legs quite a bit. So do the larger apes. In fact, of all the great apes, orangs are the most bipedal. They don't walk around on the ground much – but they do walk in the trees. The difference is that we are habitually bipedal on the ground.

What about smiling and laughing? Wouldn't you have thought those might be uniquely human?

But all primates have what's called a "bared teeth" expression. This seems to mean different things in different species: in some macaques, it's a sign of submission, but in gelada baboons and chimpanzees, it's more appeasing and helps social bonding – in other words, it really does seem to be the equivalent of a human smile. The "bared teeth" expression in chimpanzees certainly looks similar to a smile: the corners of the mouth are pulled up, and the lips parted. Chimpanzees also have an open-mouthed "play-face" expression that is equivalent to our laughter. While filming a Horizon programme last year, I was lucky enough to get to play with a one-year-old bonobo (or pygmy chimpanzee) called Lopori, at Twycross zoo. And when I tickled her ribs, she giggled very much like a human baby, but breathily rather than noisily.

Our large brains, our cleverness and our sociability seem to be pretty unique. But once again, when psychologists start to look at intelligence and cognition, the differences between us and other animals appear less stark – again, they turn out to be differences of degree rather than completely new ways of thinking.

And yet, somehow, those differences of degree between us and other animals have led to something that no other animal seems capable of: culture that accumulates, generation on generation, decade by decade, year by year. I still find it completely astounding that a bunch of apes have taught themselves to read and write, to build skyscrapers, to compose symphonies, to create mobile phones and send members of their species to the moon.

There's no wonder we sometimes feel like the pinnacle of evolution, closer to the angels. It takes biology to remind us of our lowly origins.

You, there, reading the Observer. You're just a clever ape. Get over yourself.