Then there are the incandescent interventions of Alan Jones types that agitate the kind of base Bernardi might pilfer. Part of this undoubtedly stems from a deeply held hatred of Turnbull – of his broadly liberal politics and his swift dismissal of their obsessions, such as climate-change denial. Part of it is the visceral contest for a great party's soul. Illustration: John Shakespeare. But perhaps, most seriously, this is the desperate gasp of a certain politics in crisis, demonstrably failing and on the brink of redundancy. Abbott's demise represents not merely the fall of a politician, but of a world view. Who will represent Australian neo-conservatives now? Those expressing such concerns overlook the most important fact – that it is these people who have had the keys to the kingdom for the past two years, only to see the palace crash down around them. . It is hard to imagine a government that could better approximate the values espoused by Sydney shock jock Ray Hadley. And yet in less than 18 months it faced a leadership spill, reflecting its status as the most rapidly despised government in memory – even when confronted by a limp opposition.

In this time it has been the mainstream that has gone unrepresented, while the government went on niche excursions into battle with, say, renewable energy. Illustration: Andrew Dyson That, largely, is why Turnbull is popular. He seems to grasp the broad sense of what the centre wants, and has the ability to talk about it. That is only true because Australia is a rapidly transforming society. The centre now is simply not where it was in the John Howard era. Sure, Abbott lacked Howard's subtlety and grasp of middle Australia. But Abbott also governed a different country, one whose cultural politics had become effortlessly more cosmopolitan and liberal. We see this in the easy acceptance of something like same-sex marriage, which was positively, radically unthinkable in Howard's time.

This means Howard's mix of neo-liberal economics and nationalist cultural politics no longer works. In the aftermath of 9/11 and the ructions of Pauline Hanson, you could pretend that the world was being ruined by politically correct elites, the ABC, multiculturalism, greenies, and migrants who refuse to integrate. Howard famously predicted the times would suit him, and they did. But those times began to end around 2006 and have only receded further into history. Nowadays that sort of argument sounds like an artefact. What once was populist has slowly become marginal – the kind of thing you'd go to a Reclaim Australia rally to hear. Unfortunately for Abbott, if he went to such a rally he'd have found one of his own MPs speaking at it. And he'd have no answer to this because it is on such fringes that he and his cheerleaders increasingly found themselves. They would dispute this, of course. Hence the continued misdiagnoses of the problem, from the constant references to a "feral" Senate right down to Abbott's final prime ministerial moments in which he blamed a febrile media for his plight. He's not completely wrong, to be fair. Our public culture surely has become as abrasive as it has become shallow. But it is not this that did for Abbott, so much as his disastrous first budget and its manifestly unfair distribution of pain; his mass of contradictory (and accordingly broken) promises; his campaign on racial vilification laws; his economically backward-looking love of coal; and symbolically backward-looking knighting of Prince Philip.

From there, every move he made, particularly in a neo-conservative direction, alienated and occasionally offended the electorate, reinforcing the perception he was not merely idiosyncratic, but belligerently so. Every politics runs its course until its moment of crisis. For Labor it was in the aftermath of the Hawke/Keating reforms when the new consensus on liberal economics buried the Labor Party's reason for existence – a reason it has not yet rediscovered. Now it is neo-conservatism's turn. Left unchecked as it has been in Britain and New Zealand, this eventually takes the form of Donald Trump, offering nothing more than the celebration of naked prejudice as some kind of virtue. It will have its moments of frenzy, but not its lasting victories, and certainly not any proud legacy. Australia is a long way from there. The Liberal Party is not yet overrun. But even so, it is deeply unrepresentative. Turnbull is its most representative figure, and for that very reason is perhaps its most internally despised. His task is to narrow that gap; to make his party mainstream and electable. And perhaps that is not beyond him. Unlike Labor, the Liberal Party loves success and tends to mould itself to the personality of its leader. But he'll want to succeed because if he can't drag this government somewhere central, this government could well drag him into oblivion.

Waleed Aly is a Fairfax columnist and winner of the 2014 Walkley award for best columnist. He also lectures in politics at Monash University.