At the risk of turning this column into “The Undercover Environmentalist”, I need to return to that vexed question of carbon dioxide emissions. In my first column of the year, I vowed to reduce my carbon footprint from air travel – easy enough, given that it was 50 tonnes of CO2 last year. A kind reader wrote to reassure me that I needn’t lose any sleep, because the planes were making the journey anyway. Glib, I know: I’ve often said it myself to wind up environmentalists.

The answer reminded me of a brain-teaser that’s been entertaining me for the past couple of months. Since buses often run almost empty, two people sharing a car emit less CO2 per person than do bus passengers. Shouldn’t we then be travelling by car?

The BBC’s in-house environmental activist, Justin Rowlatt, aka “Ethical Man”, recently pondered this question and concluded that, no, he’d still be taking the bus. Why? Because the buses are making the journey anyway.

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It’s always the little problems that create the biggest fuss, but in this case the Today programme’s debate on the chances of a carton of eggs all containing double yolks was unexpectedly illuminating.

Here’s the story. At about half past six, Sarah Montague and John Humphrys were debating the merits of a Daily Mail story which reported on a woman who had opened a carton of six eggs and discovered that every single one had a double yolk. The Mail went on to argue that since the chance of a single twin yolk is one in a thousand, the woman’s experience was a one-in-a-trillion event.

Sarah said that was right, multiplying a thousand by a thousand by a thousand, etc… John harumphed and said it couldn’t be true. And and hour later, they called me to referee.

This is much more interesting than it seems. If the double-yolk eggs appear with independent probabilities, then Sarah is right to multiply the thousands. The answer is one in a quintillion (or one in a trillion, if like the Daily Mail you prefer the traditional British trillion) - a number with 18 zeros. (Thinking about this some more I think the chance is actually one in six quintillion, since even when you get six double-yolked eggs, five times out of six they’ll be split across two consecutive cartons.)

On the other hand, John Humphrys was right to smell a rat - or a rotten egg. Because if the maths are correct, we are unlikely ever to have witnessed a carton of double-yolk eggs since the dawn of agriculture. And yet, several Today listeners have experienced just that.

So there are two thinking styles here. One is to solve the probability problem as posed. The other is to apply some common sense to figure out whether the probability problem makes any sense. We need both. Common sense can be misleading, but so can precise-sounding misspecifications of real world problems.

There are lessons here for the credit crunch. When the quants calculate that Goldman Sachs had seen 25 standard deviation events, several days in a row, we must conclude not that Goldman Sachs was unlucky, but that the models weren’t accurate depictions of reality.

One listener later solved the two-yolk problem. Apparently workers in egg-packing plants sort out twin-yolk eggs for themselves. If there are too many, they pack the leftovers into cartons. In other words, twin-yolk eggs cluster together. No wonder so many Today listeners have experienced bountiful cartons.

Mortgage backed securities experienced clustered losses in much the same unexpected way. If only more bankers had pondered the fable of the eggs.

I have been reading The Fourth Star by David Cloud and Greg Jaffe, two Pentagon correspondents. It’s a biography of four four-star generals, which then morphs into a history of the war in Iraq. An excellent read and a good companion to Tom Ricks’s books about Iraq, with less recent detail but a longer and more character-driven perspective on Generals Petraeus, Casey, Abizaid and Chiarelli. If you’re interested in such things, strongly recommended.

I have not, therefore, read David Owen’s “Green Metropolis“, which looks intriguing. I’m a big fan of Owen’s New Yorker piece, “Green Manhattan“, which argues - correctly - that cities are much more environmentally friendly than they seem.

I have been reading Leo McKinstry’s Spitfire: Portrait of a Legend. It’s a good read and surprisingly thorough – McKinstry doesn’t exactly have a reputation as a bleeding-heart liberal, but he takes trouble to debunk the “private sector good, government bad” myth-making behind the plane’s creation. I’ve been reading it as a case study in innovation.

As a result, I have not had time to read much of The End of Influence: What Happens When Other Countries Have the Money by Brad DeLong and Stephen Cohen. It’s a slim book and probably a good read for people interested in the political impact of economic change. I was slightly discouraged by the authors’ apparent reluctance to define what they mean by “when other countries have the money”.

(I hope that Brad DeLong one day finds the time to publish his unfinished opus, “Slouching Towards Utopia” - early drafts circulated a decade ago and were brilliant.)

So says David Roodman at the Center for Global Development:

…the practical question for citizens, officials, politicians, campaigners, and other players is whether to push for that. On a few days’ reflection, I say no. I would go so far as to describe such pressure as harmful.

Why? For starters, the benefits of debt relief over the next few years, however done, will be tiny…That’s why cancellation does little good in the short run. It is not a coherent response to crisis. Meanwhile, there are other ways to help Haiti much more, in responding to the crisis and in rebuilding. Looking at the recent history of humanitarian aid, the people who compile the Humanitarian Response Index judge that many official donors could do a much better job. Isn’t this the time for activists to harvest the lessons of history and hold public and private aid agencies accountable? My colleague Michael Clemens has called for a “Golden Door visa” to let more Haitians come to the United States (or other rich countries) to work. Prying the door open a hair more would swamp the economic value of debt relief.

Interesting. David’s model is that there is a fixed quantity of bureaucratic and media attention available for Haiti and that one shouldn’t use it up by focusing on lower priority items. He may be right, but he may not: an alternative view is that one should seize on a simple focal issue and then once you have people’s attention, broaden the scope of political pressure. This isn’t just relevant for Haiti but also, eg, the Bjorn Lomborg criticism of doing something about climate change - which, put simply, is that it’s distracting because the world has higher priorities.

I would like to see a public choice model of such trade-offs. Perhaps Tyler Cowen will oblige.

Meanwhile here is Felix Salmon on why you shouldn’t give money to Haiti.

People respond to incentives, so if you want something done, reach for your wallet.That’s what you’d expect an economist to say, but it is a belief that infuriates many commentators.

I will concede that offering cash is not always productive. In the days when I was young, free and single, I was never tempted to try to seduce cute girls at parties by slipping them a couple of crisp twenties. (Perhaps I should have done it. It is not as if my hit rate on an unpaid basis was particularly good either.)

Yet many policy wonks believe not just that there are some things that money can’t buy, but that cash incentives are counterproductive and even morally corrosive. The touchstone of this school of thought is Richard Titmuss’s book The Gift Relationship, published in 1970.Titmuss’s most memorable and influential claim was that the British system of voluntary blood donation led to better outcomes – healthier blood, supplied in a more timely fashion – than the American system of paying blood donors.

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As an economics student, I look to impress my girlfriend on a budget, and I know I am not alone. When it comes to choosing the wine to have with dinner, on the rare occasion that I get to take my girlfriend out, I avoid going for the cheapest bottle, as this makes me look, er, cheap. So instead I go for the second-cheapest bottle. But now I hear that restaurants, having cottoned on to people like me, ensure the second-cheapest bottle is highly profitable, overpriced plonk. My best response now is to go for the third-cheapest bottle, at least until everyone else does the same. Or is it? Based on price alone, what is the best bottle to buy?
William Nicolson

Dear William,

You assume that the price of the wine and its quality can be neatly separated out. This seems reasonable, but is wrong. Price changes the very experience of quality. Neuro-economists have found, for instance, that while placebo painkillers work, they work best if the subject thinks they are expensive. Energy drinks give you less energy if you buy them at a discount. (Yes, really.) And of course, wine tastes better if you believe that it is expensive.

One possibility is to conceal the price of wine from your girlfriend and tell her you’re buying the expensive stuff when in fact you are buying the house red. This is a white lie: many people prefer the taste of cheap wine in blind tastings, and by claiming it is expensive you will quite genuinely improve the way she thinks it tastes.

If your girlfriend knows nothing about wine, this will work. If she knows more than you about wine – which seems likely – then why not invite her to choose? You’ll get a better bottle. And if she blithely splashes your money around, console yourself: you will have learnt a lesson about her that would have been even more costly to learn later.

Questions to economist@ft.com