After voters notice that night follows day, they realise that all new leaders reshuffle cabinets.

The ritual is less inevitable than unavoidable. By such means you establish your political identity, show who's in charge, and chart a course. In theory, at any rate.

The reshuffle is also advertised, often enough, as a new leader's attempt to "refresh the party". For her opening performance as First Minister, Nicola Sturgeon has had to contend with a rare variation on the theme. The Scottish Nationalists have already been refreshed in parts other parties cannot hope to reach.

The membership lists, still heading towards 100,000, represent less an influx than a horde, an invading army. In relative and in absolute terms, the SNP is now huge. The numbers joining contain plenty of defectors from rival parties, but there are thousands who have never before felt the need to sign up for anything in politics. The fact presents Ms Sturgeon with a challenge.

The new members will expect to participate and be heard. They will want their opinions to count. That was the point, was it not, of the Yes movement? Whether the SNP is moved to the left as a result counts for less than a truth that has faced no politician in generations: this is now a mass party. It will not be managed by the kind of small, familiar leadership group that has dominated Nationalist politics for most of the 21st century.

The reshuffle by Ms Sturgeon yesterday falls a long way short of solving problems, old and new, at a stroke. The First Minister's old colleagues and friends - John Swinney, Shona Robison, Angela Constance and the rest - hardly represent the transformed nature of the SNP. But as they seek to govern, the leader and Cabinet must work out the nature of their big new party.

They won't be alone in that kind of pondering. Cliches that began to emerge during the European elections and the Scottish referendum were everywhere yesterday in the aftermath of the Rochester and Strood by-election. "Anti-politics"; "protest votes"; an out-of-touch Westminster rejected; mass alienation from establishments and elites. Comically, even the Yes movement has been written off in these glib terms.

Nevertheless, there is always truth in a cliché. Something is going on in politics in these islands and it needs to be better understood. The primary evidence would be the fact that the so-called main parties of the Westminster duopoly can barely scrape together 30 per cent apiece in the opinion polls. The Liberal Democrats are meanwhile in the throes of an existential crisis: their Rochester candidate seems to have retained the support of his family and friends, and no one else at all.

In part, the vulnerability of the Tories and Labour derives from a historic settlement accepted for too long by both parties. To the Conservatives, generally speaking, went the English south; to their opponents, a place called the north and parts still sometimes described as fringes. One faction would raid the other's territory now and then, but the fact that each possessed "heartlands" was not disputed. No longer. There are few places of safety.

But how is any of this the result of anti-politics? Not so many years ago, a favourite topic in political chat was apathy. People cared little, it was said, and were voting less. The turn-out in Scotland's referendum eradicated that belief in a day. Even in Rochester, participation exceeding 50 per cent meant than none of the losers could deploy the old by-election turn-out excuses. When voting matters, people vote. They vote for things.

The anti-politics notion is also a transparent attempt to exclude any party outside the traditional mainstream. I despise Nigel Farage and his chums precisely because of Ukip's clear political purpose. I presume those who have given that party two MPs have an equal understanding. The argument, pleasant or not, is in no sense irrational. It can't be dismissed with a phrase, by talk of mere protest, or by the Tory delusion that lost sheep will flock back five months from now.

Then there's the argument that Westminster leaders are paying the price for being remote and out of touch. The talk is familiar: all politicians are the same; they're all in it for themselves; they don't understand how ordinary people live.

Here things get complicated. On the one hand, the faith vested in the SNP by tens of thousands of new members says cynicism, apathy and contempt are not universal; anything but. Faith in politics and politicians - in some politicians - endures. Many voters still want to believe things can be better, and what needs to be done can be.

Yet the force of the opposing view is obvious enough. Look at David Cameron, Ed Miliband and Nick Clegg. You see professional politicians, each born to privilege, for whom the mundane nine-to-five shared by millions is little better than a rumour. You see men who could not possibly be "in touch", who have devoted their lives to the enclosed world of Westminster. Throw in an MPs' expenses scandal. Add a (now departed) shadow Attorney General who looks at the white vans and England flags of Rochester with - let's put it kindly - amusement. Who could doubt that such people are remote?

But did anyone ever ask Winston Churchill if he knew the price of milk? When was Ted Heath ever a man of the people? Gladstone and Disraeli were professional politicians long before Tony Blair affected an Estuary accent. The voter who imagines Mr Farage is "one of us" has only ever lived among City traders. Remote political types are a very old phenomenon. Now, nevertheless, even the whisper of remoteness panics the familiar Westminster parties.

A modest suggestion might be that politicians are less of a problem than the politics they espouse. The breed is no worse than ever. All the criticisms are fair enough, but have very little to do with the business of government. There might be justified outrage over expenses rip-offs. True contempt sets in when a supposedly democratic country finds itself conscripted to a war not of its choosing.

You might wonder at the class background of the coalition Cabinet. As a phenomenon, it speaks volumes about Britain. But wonder instead about a "long-term economic plan" that has impoverished millions who are no longer inclined to be obedient in their voting habits. If their alternative is Mr Farage, that's their profoundly mistaken choice. But they are passing judgement, not reacting in some unthinking spasm.

Ms Sturgeon, so they say, is meanwhile supposed to "manage expectations". It strikes me her job is vastly more difficult. Coping with an outpouring of hope for a better country is probably the biggest task any politician could face. Failure - think only of Barack Obama - is a pitiable thing.

Still, working out how to shape the SNP into a vehicle that can be commanded by all those new members involves challenges no politician in these islands has faced for a very long time. One reshuffle is just a small beginning.