One of Montaigne's favourite hobbies was imagining the world from different perspectives. To remind himself how strange human behaviour looked if one's vision was not dulled by familiarity, he collected stories from his reading: tales of countries where men urinated squatting and women standing, where people blackened their teeth or elongated their ears with rings, where hair was worn long in front and short behind, or where boys were expected to kill their fathers at a certain age.

It was not just that these were marvels in themselves. Montaigne loved such stories because they lent him an altered point of view from which to look back on his own culture and see it afresh. Most human beings judged what was merely habitual to be what was natural. Montaigne tried to wake himself from this dream.

He took a special interest in the newly encountered "cannibals" of the New World, reading travellers' accounts and acquiring South American artifacts: hammocks, ropes, wooden swords, the arm-coverings warriors used in fighting, and "the big canes, open at one end, by whose sound they keep time in their dances". He even met a couple of Tupinambá people, who had travelled to Europe from Brazil in a French ship. Through a translator, he asked them what they thought of France. They replied, among other things, that they were amazed to see rich Frenchmen gorging themselves at feasts while their "other halves" – the beggars outside their houses – starved. Europeans felt shocked because the Tupinambá ate their enemies after a battle, but the Tupinambá were shocked because Europeans found it easy to ignore the suffering of the living. Montaigne did his best to feel equally amazed at both – and to think himself into both positions. "This great world", he wrote, "is the mirror in which we must look at ourselves to recognise ourselves from the proper angle".

At home, he extended his perspective-leaping to other species. "When I play with my cat", he wrote, "who knows if I am not a pastime to her more than she is to me?" He borrowed her point of view in relation to him just as readily as he occupied his own in relation to her. And, as he watched his dog twitching in sleep, he imagined the dog creating a disembodied hare to chase in its dreams – "a hare without fur or bones", just as real in the dog's mind as Montaigne's own images of Paris or Rome were when he dreamed about those cities. The dog had its inner world, as Montaigne did, furnished with things that interested him.

These were all extraordinary thoughts in Montaigne's own time, and they remain so today. They imply an acceptance that other animals are very much like us, combined with an ability to wonder how differently they might grasp what they perceive. Some animals see colours differently from humans, for example, so who is to say which are the "real" colours of things? Montaigne quoted a story he had picked up from Pliny, about a species of "sea-hare", a kind of sea-slug, which is deadly to humans but which (thought Pliny) itself dies on contact with human skin. "Which is really poisonous?" he asked. "Which are we to believe, the fish about man, or man about the fish?" Surely we must believe neither – or both.

Montaigne's dog, with its superior sense of smell and its mysterious sixth sense, might actually be better equipped to understand the world than Montaigne. "We have formed a truth by the consultation and concurrence of our five senses; but perhaps we needed the agreement of eight or 10 senses, and their contribution, to perceive it certainly and in its essence." The dog is missing some of these; we may be missing more.

This sounds alarming – we are cut off by our very nature from the full perception of reality. But it is exhilarating, too. It posits a multi-dimensional, endlessly varying world in which each object presents a thousand facets to a thousand different observers. The observers themselves are just as variable, for they shift mental moods and states at every moment. We can never grasp it all. But we can keep ourselves mindful of the world's diversity and of our own limitations, thus becoming, as Montaigne put it, "wise at our own expense". This is no simple relativism, flattening everything to the same level. It is "perspectivism": the recognition that angle of view always matters, and indeed that it makes the world vastly more interesting.

Thinking oneself into the experience of others also opens the way to a system of ethics based on communication and fellow-feeling, even between very different kinds of beings. Once you have seen the world from someone else's perspective, it becomes harder to torture, hunt, or kill them. We shall see where this thought leads us next week.