Do you go on trying to preserve what is left of the old Arctic hunting and fishing culture, although it's already so damaged and discouraged that it has the highest suicide rate on the planet?
Or do you put the pedal to the metal and seek salvation in full modernisation through high-speed economic growth (while keeping your language and what you can of your culture)?
What's remarkable about Greenlandic politics is how aware the players are of their dilemma and their options. "If you want to become rich, it comes at a price," says Aqqaluk Lynge, one of the founders of the Inuit Ataqatigiit (Community of the People) party that ran the government until recently.
Lynge doesn't want to pay that price, and under the Inuit Ataqatigiit administration all mining was banned in Greenland.
Quite apart from the environmental costs of large-scale mining operations, Lynge said, the many thousands of foreign workers they would bring in would have a devastating impact on what is already a very fragile Greenlandic culture.
But the Siumut (Forward) party won last October's election, and new Prime Minister Aleqa Hammond sees things very differently. Essentially, she thinks modernisation has gone too far to turn back now. Better to gamble on solving the current huge social problems (like suicide) by enabling everybody to live fully modern, prosperous lives. If you're no longer marginalised and poverty-stricken, you'll feel better about yourself.
With this in mind, she has issued more than 120 licenses for mining and petrochemical projects including a huge open-cast iron-ore mine that would ship 15 million tonnes of high-grade iron concentrate a year (mostly to China), drilling platforms for offshore oil and gas exploration, and even mines to produce uranium and rare earths. She has made her choice, and she understands it.
In a recent interview with The Guardian while she was visiting Norway, Aleqa Hammond said: "The shock will be profound. But we have faced colonisation, epidemics and modernisation before. The decisions we are making (to open the country up to mining and oil exploitation) will have enormous impact on lifestyles and our indigenous culture. But we always come out on top. We are vulnerable, but we know how to adapt."
Brave words, but few Greenlanders have the technical and managerial skills to get senior jobs in these high-risk, high-cost enterprises ($2.5 billion for the iron ore mine alone), and most of them will not want the hard, dirty, dangerous jobs of the workers in the mines and on the rigs. If all goes well, they will no longer depend on the Danish subsidies that currently keep their society afloat, but they will just be shifting to a different source of subsidies.
To the extent that a sense of cultural marginalisation and defeat, and a life without meaningful work, is responsible for the Greenlanders' problems, it's hard to see how more money from a different source will help. Or how adding a few tens of thousands of foreign workers from places like China to the social mix will help, either.
The epidemic of depression and other psychological illnesses, the rampant alcoholism and drug use, and the tidal wave of suicides that plague the Greenlanders are not unique: almost all the aboriginal peoples of North America, and indeed elsewhere too, have elevated levels of these afflictions. These problems are unlikely to be cured simply by throwing money at them. It could even make matters worse.
Aleqa Hammond is damned if she does and damned if she doesn't: leaving the people in their current predicament is not a good choice, but going flat out for modernisation doesn't feel like such a good option either. It would be a good time to call in the cultural engineers, if such a profession existed.
Gwynne Dyer is an independent journalist whose articles are published in 45 countries.