Back in the 1980s, the Race Relations Office ran a programme that offered high school students the chance to experience another culture.
Not in another country, you understand, and sometimes not even in another city, although for those who braved the cultural divide (taking the bus from, say, Otara to the North Shore or Remuera), it couldn't have been more foreign.
The programme no longer exists, but as the new Auckland Communities Foundation notes in its MacroAuckland report, our suburbs remain as segregated as ever.
Several broad areas of Auckland, it says, have "moved away from each other in terms of household income while overall suburbs are each becoming more homogenous internally".
"The Auckland population is steadily segregating along several dimensions, with potentially long-term issues arising as different groups are less linked with each other".
Which is to say, we're growing apart - and it's not a good thing.
In his book The Empathic Civilisation, Jeremy Rifkin argues that human beings are soft-wired for empathy.
According to Rifkin, science is challenging some of our long-held shibboleths about human nature. We are not the aggressive, selfish, materialistic, utilitarian narcissists we've been led to believe (unless, like Charlie Sheen, we have tiger blood or some other illicit substance coursing through our star-studded veins).
We are, says Rifkin, "Homo empathicus", a much nicer creature whose brain has been "soft-wired" to experience another's plight as if it were our own, who is capable of rejoicing when someone else feels joy, and able to show solidarity through compassion.
This is the side of us that showed up after the catastrophe in Christchurch; the side of us that in fact tends to show up after every disaster, when ordinary human beings rally round to help one another- sometimes risking their own lives to help complete strangers - and for no other reason than that it seems like the right thing to do.
But empathy has its limits. It seems to extend only as far as we can see. We can be too distant to feel the visceral tug of someone else's pain, too far removed to recognise our common humanity.
So no one argues with the need to give Cantabrians whatever they need to get back on their feet - we've all seen and "felt" their pain, after all. It's those faceless "others" on welfare that we have problems with.
Distance makes the heart grow colder, and it can make it harder to know how to help.
The trouble with the rich being concentrated in their areas and the poor in theirs, as the MacroAuckland report confirms, is that those with both the means and the inclination to lend a helping hand seldom take their skills, resources and networks beyond the confines of their own privileged communities, to where it's needed.
The exception is Harvey Alison, a retired businessman I met a few months ago.
Harvey had run his own business, raised four children and been on the board of private Auckland girls' school St Cuthbert's College for 20 years - the last five as chairman.
He bowed out after a particularly tough year but didn't rest for long. After reading that nearly 80 per cent of prisoners were illiterate, he felt compelled to act.
He approached Ann Dunphy, the then principal of the low-decile Penrose High School (now One Tree Hill College), and set up a much praised "reading enrichment" programme designed to give new entrants a boost in their reading and comprehension skills. He called on 40 or so friends from his golf club, church and the Penrose Rotary Club to act as mentors. Many of them had just retired, said Harvey, and "just chose to sit on their bums. They were going downhill. I told them the mentoring would keep them mentally alert". Which it has.
When it became critical for the programme to employ someone to co-ordinate and provide the kind of "back room" administrative support that the Ministry of Education would not fund, Harvey went to his contacts for the $40,000-a-year salary. He hopes the Government will see the value of the programme and pick up the cost; he would dearly love a PhD student to study what happens to the students when they leave it.
In the meantime, everyone seems to be winning on the programme - students, mentors, parents and teachers.
Harvey reckoned the programme added about two years on average to students' reading ages, and that the students did not just become better readers, but more confident young people.
Harvey didn't want me to portray him as a hero. But he has shown what's possible when people reach across the divide. I wish there were more like him.