When pondering the possibility of alien life, most of us gaze up into the heavens to the multitude of stars that populate the eternity of the night sky.

Not Australian philosopher Peter Godfrey-Smith. His eyes are drawn to the ocean depths, to life forms with which we have not shared DNA for more than 600 million years.

"You can imagine meeting an octopus as an approximation to meeting an alien," said Professor Godfrey-Smith, of City University of New York and the University of Sydney.

"A real alien from another world would have no evolutionary connection with us at all.

"An octopus is very far from us in the tree of life but a very complicated animal that does have a kind of ability to engage, even with a person."

Do octopuses have a sense of self? "That's probably the hardest question. I don't know. We are complex animals and they, too, are complex but with a very different organisation to us."

Octopuses have about 500 million neurons; humans have almost 100 billion. But the organisation of our nervous systems are completely different. Most of an octopus' neurons are not in a brain but in its arms, and these limbs can act semi-autonomously.

Professor Godfrey-Smith said it is important to studying cephalopods – octopuses, squid and cuttlefish – to gain a better understanding of our own intelligence and the relationship between mind and matter.

In his new book, Other Minds, he writes: "If we can make contact with cephalopods as sentient beings, it is not because of a shared history, not because of kinship, but because evolution built minds twice over. This is probably the closest we will come to meeting an intelligent alien."

But do these alien creatures sleep, perchance to dream?

Professor Godfrey-Smith said it is not clearly known. It appears cephalopods engage in some sleep-like activity, with something similar to rapid-eye movement.

"In the case of giant cuttlefish, the skin colour is changing continuously. Sometimes this is for camouflage and some changes are for signalling," he said.

Dr Karina Hall studied cuttlefish for her doctorate at Adelaide University. Now at the National Marine Science Centre in Coffs Harbour, she said that she has studied signalling during mating at the end of their short lives.

"I've seen a female use a bright, white stripe down one side directed at a male to indicate he was not a suitable mate," she said.

Professor Godfrey-Smith said many colour changes are for no observable reason. 

"My conjecture is that what you are seeing here is a reflection of stuff that's going on inside. Quite a few of the colour changes you see, you could call a kind of a daydream."

We don't know what our common ancestor with cephalopods was, but it was likely a tiny worm-like creature from before the great Cambrian explosion of life 550 million years ago. These early animals wouldn't have had eyes, just light-sensitive patches on each side of its body.

But human and cephalopod eyes are similar. This points to something else amazing in our vastly different evolutions. As well as minds being twice evolved, so were our image-creating eyes.

"The eyes are similar but the brains behind them are different on almost every scale. If we want to understand other minds, the minds of cephalopods are the most other of all," Professor Godfrey-Smith writes.

Other Minds: The Octopus and the Evolution of Intelligent Life, is full of anecdotes pointing to the curiosity apparent in these creatures, for which he clearly has a deep fondness.

Does he eat octopus? "I don't eat them because I have too much affection for them. But if you're deciding which meat to cut out, I don't think it should be the top of your list."

Dr Hall said that humans have tended to look to teach other animals, such as primates, to communicate with us.

"Yet here we have an animal with crazy signals going on – it's an opportunity for us to learn from them," she said.

Professor Godfrey-Smith said: "There is a danger of projecting too much of our mental life on to these animals.

"A lot of what's happening in us probably has no analogue with what is happening in them. But it's very tempting to attribute casually rich, human forms of internal life on to other animals."