“You're handsome! You're beautiful!” he calls out as he walks the dogs. "Jesus loves you!" was the preferred greeting for a week or two, but it's the good looks of his fellow citizens that's his favoured theme. The dog-walker dresses in a blue boilersuit in winter and bright shorts in summer, a baseball cap in all seasons, and is the most reliable feature of Glebe Point Park. He might seem simple, but one autumn afternoon I overheard him talking in a straight and serious voice about Confucius with a Chinese man under a fig tree.

The number of dogs circling and snagging his feet varies, but his own - Patch, a world-weary white mongrel - is a constant. Their dragging pace across the grass is slowed further by clumps of curious children who gather to point or pat. Patch is small and compliant enough to lure the most cautious in for a quick poke, and the dog-walker's smile and cheerful stumbling help to reassure. Newcomers to the park stare and laugh, unsure whether this one's in the category of harmless or hysteric; but regulars gleefully offer him proclamations of attractiveness in return, and miss him when their visits to the park don't coincide.

Cities are created by the need to come together, but they are places where we strive desperately to keep ourselves separate. There is an animal instinct for survival that struggles to protect us from the daily bombardment of unknown bodies, smells, images and sounds, yet there is also our human urge for closeness, for connection with our own kind. Modernism dreamt of the city as the factory of privacy, where the individual could remake himself after his own image, unfettered by the communal claims of family and tradition. But even Kafka wrote of "the happiness of being with people", and we all step out our front doors looking for fellowship as often as we scurry inside to escape it.

The most elegant solution to these competing needs is the public square, a place where people come, yes, to talk to their own, but also to enjoy the particular and subtle pleasure of being in the company of strangers. This pleasure has something of the tradition of the promenade, the preening desire to see and be seen, but there is also a less self-serving curiosity in the comings and goings of our fellows, an amiable instinct for companionship which leads people out from their private spaces to take their place in the warmth of the winter sun or the cool of the summer night, surrounded by unknown others.

It's not just in the great cities of Europe that crowded neighbourhoods keep such squares alive, but also in the towns and villages across the globe which these civilisations left in their wake. The Bolivian border town of San José is home to no more than 300 people, yet each night its residents fill the square to sit and greet and watch, freed briefly from the competition and drudgery of workaday interactions.

Sadly, the British left us no such heritage. Our squares are, for the most part, concrete wastelands, alluring only to pigeons and plastic bags. Our voluntary communality is largely restricted to sporting grounds and shopping malls - which, devoted to contest and profit, fail to fill the requirement of unmotivated togetherness. We've never managed to transform our beaches into public squares in the way that the Brazilians or Mediterraneans have. Here, we go to the beach to see the ocean, not each other, and the human is lost among the vast landscape.

We do, however, have the humble park, which, under the guise of exercise and dog-walking, offers us what we really seek: to be alone together. Glebe Point Park may be dominated by dog-owners, hailing one another with sticks and tennis-ball catapults, yet most are generous towards the unattached, freely offering their animals as a pretext for fraternisation. On the edge of the park there is a railway bridge, and under one of its stone arches the canine community has constructed a memorial of small laminated photos and carefully painted details: Harvey ‘Scissorlegs' (1.8.99-6.5.04), Roxy ‘Rocker Shocker' (7.2.96-15.2.04) and - fixed slightly higher than the rest, with an engraved plaque - Kayne ‘King of the Park' (1994-2005), an imperious Husky. It may be that so many city-dwellers have dogs because dogs force us back out into the world.

So until we have an Australian Haussmann, one who will create not the grand boulevards of Paris but instead a patchwork of neighbourhood squares, it is in parks that we can best find the space in which to interact, with no purpose other than our own togetherness. There we can find the good-natured public civility which has largely disappeared from our streets and offices. And, after all, the walk in the park has a noble lineage. Yahweh enjoyed a daily constitutional, and not simply for the purposes of partaking in divine personal communion. The Book of Genesis has Him walking through the Garden, enjoying the "cool of the day" and mingling with his creations. On the day that Adam and Eve hid themselves from public view, the Almighty knew something had come tragically unstuck in His grand plan for human life.