Milne, who first survived, and then thrived, at the Catholic boarding school where she was enrolled at 10, sees Parliament as an enforced institutional break from the happy idyll of her Tasmanian home. It is a place with rigid schedules, where you are herded in with people you may not like, and where you must cultivate resilience, self-reliance and mental toughness to get along.

''I became socialised into a big group environment from a young age … You brace yourself for leaving the pleasantness of home to go into that different environment,'' she says in her distinctive mild manner.

A different environment it certainly is, and this year the atmosphere has been bracing, to use a phrase far gentler than the tone of political debate.

When we meet for lunch, at the Silo Bakery in Kingston just a few kilometres from Parliament House, Milne admits she is exhausted after her ''huge'' year.

We sit outdoors so she can enjoy the sun - something she has missed, having spent large parts of the year either locked in committee rooms or on planes between Tasmania and Canberra.

Milne served as co-deputy chairperson of the multi-party climate change committee, the group that fashioned the carbon tax legislation that passed the Senate in November after great controversy and much violent public debate.

Despite the deep unpopularity of the carbon tax among the electorate, to Milne and her Greens colleagues, the pricing of carbon was, and is, a triumph. While the Gillard government announced the passing of the laws with an air of blood-spattered weariness, the Greens hailed it perkily as ''a good start''.

''If the Greens can go to the next election having facilitated action on climate change, which wouldn't have happened without us,'' Milne says, ''then we will have assisted in shifting the whole community on the fundamental debate of this century, and that's how to live sustainably.''

Therein lies the reason why the Greens in general, and Milne in particular, are adored and despised - the breadth and depth of their political ambition. They don't just want to price carbon, they want to transform the economy and the very way we live. Milne has written that we need to move, and fast, on the ''total decarbonisation of the economy''.

After ordering our food - Milne opts for Silo's trademark sourdough crust pizza and declines a glass of wine - the conversation moves to non-political subjects: the guilt complex Milne carries with her from her Catholic school days (she is no longer an observant Catholic), sexism in politics and the pleasures of growing up on a dairy farm, as Milne did, on Tasmania's north coast.

Milne loves many things - classical music, her two sons, gardening, art and the work of the socialist poet Dame Mary Gilmore - but her first love is history.

Milne went on from boarding school to complete an honours degree at the University of Tasmania. Her thesis, which she wrote in 1974, was on the emergence of tourism to Tasmania, from the end of transportation of convicts up until 1900.

''I just loved it,'' Milne says with passion, and details her regret that she couldn't go on to do a master's. Following university, she worked as a teacher for nine years full-time, going part-time from the birth of her first son, before she became an activist and entered politics.

The best job she had outside of political activism, Milne says, was in 1987, when she worked as a research officer for the bicentennial year, travelling around Tasmania visiting people who had interesting documents.

Her task was to make the call as to whether they were historically significant enough to be registered, and she sometimes helped set up their sale to public museums.

Among her proudest discoveries were the original stills from the 1927 film version of For the Term of His Natural Life, and photographs taken by a World War II Digger of soldiers hunting with Aborigines in central Australia. The latter ended up in the War Memorial collection.

Milne laments she no longer has time to read much history but she seeks to bring a historical perspective to her political career, she tells me.

''History gives me a good sense of why the Greens are doing really well,'' she says. ''The major parties were formed in an era when the philosophical view was that the environment is free, all natural resources are free and rivers and oceans and the atmosphere are free depositories of waste. So you fight over the spoils of what is value-added. What [neither party] has come to understand is that era finished towards the end of last century when people started to recognise the Earth does not have an infinite capacity … and the whole challenge now is how to live sustainably.''

But the environment is not the only issue people vote on, I venture.

''No, but it goes to everything,'' Milne says. ''Everything on the agenda at the moment, climate change, the mineral resources rent tax, the Murray-Darling, it all goes to what sort of an economy you can have. Is this constant pursuit of growth, is that sustainable in the 21st century? What has to grow and what has to give? That's where the challenge of the century is.''

A question on where the Greens might learn from their historical mistakes is deftly dodged.

Milne says she is often told people are frightened of her, which surprises her. ''In the community people are a bit reluctant to approach me sometimes … and I think that's because they think, 'If I say something, she might criticise me or contradict me or something,''' she says.

Milne does have a slightly forbidding manner but also laughs readily and often at herself.

''People say to me, 'Why don't you smile more on TV?''' she says. ''I say, 'You don't understand; everything I'm interviewed about is serious.'''

She appreciates social media (she writes her own gardening blog) and appears on the ABC's Q&A for the opportunity it presents to ''humanise'' her image.

What is interesting is that her school ma'amish demeanour (hardly surprising given she was once an actual school ma'am), sternness and twin-set wearing aesthetic are as far removed from the stereotypical tree-hugging greenie as you could get.

She looks, at first glance, like someone more likely to bake for a lamington drive than be jailed, as she was, during the Franklin River protests of the 1980s.

Milne is aware of this and thinks it's a good thing.

''Most members of the Greens party around the country are just like me. They've been brought up on farms around the country, they've been teachers and nurses,'' she says. ''They're mainstream.''

The waitress clears our plates (I have made Milne talk too much and she hasn't finished her food; she demurs and says she's on a diet anyway) and she orders a tea.

Milne's own background may be mainstream (who could be more blameless than a Catholic boarding school girl-turned-teacher?) but her political record is not.

She first came to politics as a grassroots activist, campaigning in 1988-89 against the construction of a pulp mill next to her family farm at Wesley Vale. The mill did not go ahead and Milne was afterwards elected to State Parliament in Tasmania, polling the highest vote ever for a first-time candidate.

She was part of a Labor-Greens accord with the Labor premier Michael Field from 1989 to 1992, and she held the balance of power with a Liberal minority government from 1996 to 1998. She used her power to win things for her constituency - from gay law reform and the expansion of Tasmania's World Heritage areas to saving country schools slated for closure. But she fell out spectacularly with Field and he has since criticised her as ''rigid'' and ''combative''.

Last year Milne brought to bear both her reputation for hard-headedness and her experience when the Greens negotiated to help the ALP form government.

''I have never worked with a minority government that recognised it was a minority,'' she says. ''You're dealing with a group of people who want to be a majority, and they're not and they just refuse to get it.''

Milne knows that now the carbon tax has been passed, the Prime Minister, Julia Gillard, will put increasing political distance between her party and the Greens. History tells her so. But confidence shines through her weariness, and she lists a denticare scheme and gay marriage reform as priorities for the new year.

For now, there is a holiday in Sri Lanka and a rare chance to relax, possibly with her head in a history book, for the few short months that school is out.