The many explanations proffered to explain the extraordinary Scottish election result cannot all be correct; at best each can capture a feeling about what happened and why. Here I offer two different explanations as a Scot studying at the moment in England. One looks outward to our place in the UK, and the other looks into the Scottish polity. Both lead to the same conclusion: the need for independence, but not in the sense you would assume.

Economic independence
If the Coalition’s cuts are bad for England, they’re worse for Scotland, dependent as it is on a large public sector and high state spending. A cuts programme will be implemented in the coming months, deeply wounding many individuals and parts of society. One in thirty jobs in Scotland will be lost as a direct result of the Coalition’s spending plans.

That Scots are sore about the cuts was made patently clear in the election. This was the context Scottish Labour fought their campaign on, and Scots tended to agree with them about the cuts; they were just unconvinced that Scottish Labour were offering any credible solution. The party could have said it would present a budget of resistance. It could have offered an alternative solution, and demanded the quick transfer of the powers to pay for such a budget. Instead, Scottish Labour stuck firmly to its conservative gradualism: seeking to preserve the large and complex infrastructure of Scotland, to ensure that public services are protected as far as the monies from London allow, and to allow the gradual devolution of some limited powers to Scotland.

In voting for the SNP, perhaps what large numbers of the Scottish electorate realized was this: despite our protestations, and the hatred in Scotland of the Coalition, we haven’t really any effective way to negotiate, we can only complain. We are still, economically, a part of the Union. We can tell Westminster that its economic policy is wrong. We can ask them to “ca’ canny” and protect Scotland. We can march and protest. We can sulk. But what we can’t do is to raise and invest more money into our own economy to get it flowing; we can’t change the tax system even, let alone oversee our economy as a self-determining state.

Perhaps people realized that, in the long run, if we want to avoid the risk of enduring similar governments in the future, we need enough economic independence so that we can implement our own economic policies. That way, we can take responsibility for ourselves; we can wipe oor ain erses, to put it crudely. We can do what we don’t do at present, but first and foremost should.

In a sense, by not advocating urgent economic autonomy, the unionist parties were taking Scots for fools. If no Scottish party wanted what the Coalition wants, then how can they advocate the economic status quo that allows the Coalition to control the Scottish economy? When Tavish Scott for the Lib Dems in Scotland continually expressed his disagreement with the Coalition, then why did he not focus his energy on challenging those Westminster powers that allow it to control Scottish policy? Similarly, how can Scottish Labour credibly oppose cuts when it supports the mechanisms that allow them?

So, looking for a party that will move in the right direction, folk voted for the SNP. To be fair, the other parties do demand some more limited economic control; but no demand from them for economic autonomy came across during the election campaign. Economically, the Scottish parties (and I am thinking mainly of Scottish Labour) need to embrace radical economic powers for Scotland, not reluctantly but positively; not as a gradual process, but as an urgent priority.

The crucial point is that this is not a call for independence in any constitutional, let alone romantic, sense. It is a desire for having resonsibility for our own economic policy within the larger world, so that, as we have a different public will for our own area of these islands, we can express it and carry it out, for good or ill.

Political independence
Aside from economics, though, there was something else important going on, and it makes something of a contradictory story. It was not about the cuts, or economic powers, but was about the Scottish political world.

The result of the Scottish election was pretty radical, and if you’re talking about radicality then you’re talking about roots. Last week the people voted for politics in Scotland to be rooted in Scotland. What makes the election historic is this outcome: this was the moment not only the  dominance of the UK parties, but the importance of the UK agenda itself, failed to hold, and was replaced by a political sphere based firmly on the idea of the Scottish nation-state. Leaving aside the constitution, the Scottish people did vote in favour of independence last Thursday in the living political sense.

As the party that’s distinctly, enthusiastically, and essentially Scottish: this was what the SNP had to offer. So the SNP were able to fight almost entirely in a different sphere from the UK context; they concentrated positively on Scotland, and without too much distraction into divisive issues of the constitution. They established the Scottish political world as independent of England and Westminster. And the Scottish people took to it enthusiastically.

The crucial point here is, again, that this is not about constitutional or romantic independence, but about political independence; the demand and desire for the ability to engage in politics on our own terms, in our own space and with our own Scottish issues and solutions.

So which was the reason people voted for the SNP? What I’ve presented above are two powerful reasons that I believe to be especially important not only for understanding the election, but also for looking to the future of Scottish politics. Both appeal to different instincts and aspirations, and perhaps each appeals to different people. Critically, the two processes reinforce each other. And they both lead us to the same conclusion.

Parties Apart
If the above analysis contain a lesson, then it is simply for the other parties to become more distinctly Scottish. Whether Scots were calling for an independent political sphere, or independent economic control, no Scottish party can any longer afford to be, or to be seen as, an extension of a UK party. In policy terms they are already largely autonomous; now they have to demonstrate that they are not ‘devolved’ versions of the UK parties.

This needs to be understood and embraced within each party; only then will the public buy it. This will be most challenging for Scottish Labour: coming to terms with it will challenge its traditions, and the instincts and in some cases aspirations of many party members. This is not the place to expand on this; suffice to note that some already recognise this: ex-leader Jack McConnell called this morning for Westminster's Scottish MPs to abstain from voting for the new leader in Scotland. On the other hand the ignorance of this at the UK level was made clear by Ed Miliband’s appointment of MPs from Westminster to review the failings of the Scottish campaign: indicating that, as far as the UK party was concerned, Scottish Labour remains a mere branch of Labour UK.

Instead of strengthening links with their UK equivalents, the parties – and especially Scottish Labour – need themselves become more independent. It would be logical for them to rename themselves. There are signs that the Scottish Conservatives are going to change their name. Scottish Labour should do the same. Old traditions mean that it almost certainly won’t, but it must get as close to it as possible if it is ever to recover.

But it is not enough to engage in rebranding, and the last thing we need is tartanisation. To create a dynamic political sphere, all the parties need to rebuild in such a way that the old hierarchies are penetrated, and diverse elements and interests in civil society are brought in for the first time. (For proof of the range of ideas and areas already out there, Gerry Hassan and Rosie Illit's Radical Scotland is a good place to start). The reason the Scottish Labour rose is wilting is because its roots are too weak, planted in the ground of core support that gets smaller by the year, and its stem is too thick, with old hierarchies and institutional allegiances that make trimming difficult. The party needs to reroot itself, and to become an organism that stems from those it represents.

Positive Unionism
It might be argued that such an independent political sphere will aid the nationalist cause, in making Scotland seem more suited to go it alone. I disagree. Set against the SNP, and with an eventual referendum to fight, the natural instinct will be to look to London, to play down the Scottish government, and to make the case for the union from a UK perspective. But Salmond was right when he said that positivity trumps negativity (whatever one might say about the dour Scottish character). Parties that are autonomous and distinctively Scottish – that have their roots in Scotland and are not just branches of larger UK parties – can best present the positive case to remain in union with the rest of the UK.

The will of the people is not to have a politics framed by parties in London. This is now settled. It is irreversible. It is the radical break marked by the vote on 5 May. It is neither an argument for or against constitutional independence. What’s important now is to expand this welcome and potentially creative political environment so that it can express the different arguments and interests within a nation that’s about to embark on this crucial period of its history. Whether or not we eventually separate from the rest of the UK is not really the point. Failure to understand this is why so much of the Westminster-centered comment is laughable. The next few years have the potential to create a positive, expansive, genuinely pluralist Scottish democratic political culture. The more parties that do this the better. We don't want the SNP to replace a Labour one-party state with another centralised machine. This is the challenge that we all feel in Scotland, whatever party we may support. It is much more interesting and important than 'independence' as it is narrowly conceived by the British political class.