Like a cowboy without a horse or a fireman wanting a hose, I lack one of the essential tools of the columnist's calling by not having, one way or another, a strong feeling about Harriet Harman. Sometimes I watch her perform and wait, hoping for nausea or adoration to set in, but it never comes. This worrying indifference meant that when she outlined some of the contents of her new Equalities Bill yesterday, I had no particular prejudices to guide my reaction, just a slight sense of wonder that a minister was doing anything at all.

But I am very interested in the subject of equality - or, as it is usually discussed these days - the subject of inequality. For months now I have been reading books, academic papers and think-tank pamphlets trying to work out what the problem of inequality is, and what - if anything - we should do about it. And then, right in the middle of this exquisite cerebration, along comes Harriet with a Bill, and it becomes time to give off or give over.

This column is in the business of giving off so let us start with the objective, as explained by Ms Harman yesterday, that “you should have a more fair and equal society [because] it makes for a stronger economy and a more peaceful and cohesive society”. The Bill proposes to give public bodies the explicit responsibility - a new “social and economic duty” - to build reducing inequalities into their policies. It does not itself specify how this might be done, but the aim is to supplant the “ad hoc” approaches that Labour has used since 1997 with something a bit more strategic.

Though it is true that Labour politicians are tricksy, and enjoy devising policies that the Tories then have trouble opposing, it is also the case that the subject itself has become more and more important in the past three or four years, almost as a calibration of the unease that Britain has seemed to feel about itself. Who said, for instance, that “inequality matters. Of course, it should be an aim to narrow the gap between rich and poor. It is more than a matter of safety nets.”? Tell you later.

In the meantime, I want to examine a copy of a recently published and highly influential book, The Spirit Level: Why Equal Societies Almost Always Do Better, by Richard Wilkinson and Kate Pickett, of the University of Nottingham and University of York respectively. The book spends 300-plus pages establishing a series of correlations between negative social outcomes and inequality per se. These correlations are demonstrated in charts comparing countries or US states with inequality on one axis and a social phenomenon on the other. Again and again, whether it concerns crime, teen pregnancies, drug taking, life expectancy, obesity and so on, the stats seem to show that the mere fact of inequality - as opposed to wealth - leads to worse outcomes.

It has to be said that some of these charts are questionable. In the one on mental health, which seems to show that inequality leads to general barminess, if you take the US out of the comparison, then the correlation more or less disappears. Note, too, that France's mental problems seem to be twice as bad as Germany's, despite their equality indexes being roughly equal. Why? Gallic moodiness? Teutonic phlegmatism? If so, this is more to do with culture. Nor am I entirely convinced that the results of asking folks in the US states whether they would do better than the other guy in a fist fight correlates to income inequality as much as to whether you are speaking to someone in Montana or in Maine.

Even so, the authors make a good case for some kind of correlation. But correlation is not cause. It doesn't tell you that inequality itself causes bad health (theoretically it could be the other way around, as some geneticists believe) or why. Take smoking, which is behind the worst health figures. Everyone in society gets the same tarred-lung message. So why would someone be more likely to ignore advice and smoke simply because, a few miles away, merchant bankers were earning huge bonuses? The authors of The Spirit Level answer, in effect, that those who are less well off feel neglected and envious, while those who are better off feel defensive and envied. “With greater inequality”, they argue, “people are less caring of one another, there is less mutuality in relationships, people have to fend for themselves and get what they can - so, inevitably there is less trust.”

Hmm. I'm still not sure about this, though Ms Harman seems to be persuaded. The trouble is that such an analysis leads one away from her policy prescription. If the problem is income disparity, then the answer must be income redistribution. Logically benefits and tax relief for the low paid would go up, as would taxes for the well-off (and not just the rich). The newly un-neglected would then measure their heightened esteem in the dwindling gap between themselves and the better-off, and over time begin to see the value of education, to start reading to their children and stop smoking. Well, it's an ill wind and news of the falling number of British billionaires and Wayne Rooney's half-million tax increase, could (for all I know) be working its magic already.

We can imagine the objections to this. It would, without a culture shift, constitute a reward for idleness, a disincentive to work and require hard-working middle earners to subsidise the workshy. Until such a time, that is, that they learnt not to be workshy.

Harriet is not going down this suicidal political path. So her Bill is a kind of irritating ambition for everyone else. Labour policy has been, until now, to target inequality through employment and to disguise redistribution through taxpayer-funded education, health and early learning policies. Now, she's saying, build that kind of thinking in everywhere - let's say by building more stop-smoking clinics in poor areas - and somehow inequalities will fall away more quickly. This is magical thinking because such policies, though desirable, have demonstrated to us by their slow effect how intractable the problem of inequality really is.

So the newly elected Tories will have none of it, eh? That was a cheap trick I used earlier, because the anti-inequality quote above came from David Cameron's policy chief, Oliver Letwin. Reducing inequality is officially a goal of the Conservative Party, but Mr Letwin knows that between 1979 and 1997 - the 18 years of Conservative administration - the proportion of children in poverty went from one in eight to one in four, which hardly suggests that a return to Thatcherism will help. In lieu of a much better idea the incoming Cameroons would be likely to keep much of what is in Hattie's bill. So - and here at last is the fun - the presumptive heirs to Mrs Thatcher are more likely to end up as the actual heirs to Ms Harman.

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