Draw a line at $2,700 per capita income per year, around $7 a day. The bottom billion of Professor Collier's last book struggle and starve below that line. The challenge of his new study is similarly stark: what can we in the cushy, forgetful west do about it?

Collier is an Oxford economist who rubs shoulders with sociologists, pollsters and political scientists. The developing world he sees is rounded, chaotic and deeply human. Surely spreading democracy is a better way for Africa, heargues (his thesis is essentially about Africa): it produces some growth, it cuts down on war.

But electoral accountability only works straight after an election. The nearer you get to the next big vote, the greater is the tendency for whoever's in power to feed goodies to his own tribal supporters. That's why they voted for him. That, implicitly, is what they expect from democracy. And that can sometimes be why coups have their democratic aspect, too. Any change can be better than no change, Mr Mugabe.

But, most of the time, absurdity tips over the board. Here, in one basket case of a continent, are more than 50 countries carved out by departing colonial powers. They encompass some 2,000 separate tribes. They could, just as easily and much more effectively, have been stitched together as, say, seven notional nations.

Luxembourg, the tiddler of the EU, has a national income four times the size of the average bottom billion state, yet Africa, trapped by history, offers none of Europe's concessions to geographical co-existence.

This patchwork of puniness can't offer the foundations of security and settled accountability on which any decent version of democracy depends. It can't even overcome the idiocy of governments that ought to find common cause, but don't. Is there a good road from Kenya to Tanzania, one that can bring trade and prosperity to both? No: only more rutted thinking along the potholes of blinkered minds. It's crazy to believe that just pumping in more cash will rescue such a rotten structure. It's equally crazy to shrug and walk away.

Collier's conclusion is that something mind-boggling has to be done (by the US, France and the UK for starters). We have to be prepared to take the initiative, because the continent of inherited futility can't manage its progress alone. We have to persuade those African states that want it to sign up to a code of public conduct  of elections, of economic development, of probity  that can, at least in theory, be enforced from outside by western military intervention if all pledges are broken. We need governments to cut back on arms buying and, in extremis, we need to be able to come to terms with incoming coup leaders as well.

This is self-regulation on a massive scale and it seems deeply dotty, even when delivered in Paul Collier's worldly-wise prose. African pride and western timidity (not to mention guilt) won't let it happen. The fight for supposed independence is still too fresh to unleash what could be portrayed as revised Bush and Thatcher doctrines on a continent that can't cope because it can't get organised.

Maybe too much attention to the minnows of the bottom billion distracts us from the beached whales of Pakistan and Bangladesh, hugely populous states where failure means impossible chaos. Maybe Professor Collier would have other dire warnings to add if he were writing now, amid the growing catastrophes of the crunch. But nevertheless, with its verve, wit and lateral thinking, this is a book that changes its readers' horizons. Weary of pouring donor aid into bottomless pits? Frustrated by the way so much African talent makes so little difference?

Distressed, like me, when you wait at a conference to greet the new president of Kenya and see him arrive in a fleet of eight Mercs? Then it's time, with Paul Collier, to start kicking outside the box.