Functional analysis by Rudin. I needed to check something for work but then I saw that Rudin had a proof of the prime number theorem using Riemann’s zeta function. It’s one of the great ironies of mathematics that a simple statement about the integers is most naturally proved by applying abstract analytical techniques to a function of complex numbers, and I decided I had to see how it was done, which entailed working through the theory of Fourier transforms and distributions.

There are ‘elementary’ proofs, most notably by Pal Erdos, that only use ordinary number theory, but elementary does not mean ‘easy’ in this context. I plan to try and work through one of the elementary proofs some time.

This reminds me to mention that my Erdos number is 3 (via Peter Wakker and Peter Fishburn). At a stretch, this blog could be claimed as a collaborative work, in which case all my commentators would obtain an Erdos number of 4 – highly prized in some circles.

*Thanks to my travels, everything is running behind. So I’ve skipped this week’s Word for Wednesday, and put in last weeks Sunday feature instead

# What I did in my holidays

I spent much of last week in the Snowy Mountains with my family (the Powerbook came too, of course, so I kept up at least some blogging). It was the first time we’d been back since the devastating fires in January. Large areas are still closed off, and signs of fire are everywhere. Fire is a natural part of the lifecycle of a eucalypt forest, and signs of regeneration were already evident in many of the places we visited. But some of my favorite spots, such as the mountain ash forests around Round Mountain, are probably gone for good. This is the second fire in twenty years and it’s unlikely that new seed has been set. Even if they do come back, it will be decades before they regain anything like their former state.

As is inevitable with such a disaster, fingers have been pointed in all directions, notably at the National Parks and Wildlife Service for not burning off vigorously enough and at global warming for the extreme severity of the drought and hot weather conditions that led to the fire disaster. I’m keeping an open mind on the relationship between drought and global warming. Looking at the way the fire burnt through grassland as well as bush, I’m doubtful that any regime of controlled burning could have mitigated this fire much, unless it was so extreme as to fundamentally change the character of the Park.

# ColLotteral damage

Tim Lambert has produced yet more evidence of academic malfeasance by pro-gun economist John Lott. Kevin Drum at Calpundit has more. Since I was convinced long ago that Lott was discredited beyond any hope of redemption, the only point of remaining interest is the collateral damage being incurred by Lott’s allies and defenders.

Obviously, the once-respected American Enterprise Institute, which still employs Lott, is at the top of the list. Having had my own run-in with its current head Karl Zinsmeister, I agree with Brad de Long, whom I cited a while ago saying “Back in the late 1970s, the American Enterprise Institute ranked close to the Brookings Institution as a thinktank you could trust not to deliberately lie to you. Now it has fallen very deeply into the pit indeed”. No doubt some good work is still being done at AEI, but the AEI stamp now detracts from credibility rather than adding to it.

Another casualty is Lott’s Australian co-author, and gun rights advocate, John Whitley, who ended up with his name on an article that Lott himself refused to sign off on when the other party in a dispute pointed out a string of coding errors (Tim Lambert, linked above, has the details).

But the biggest not-so-innocent bystander to be hit by friendly fire is surely the king of the blogworld, Glenn Reynolds of Instapundit. Having cut his blogging teeth on the Bellesiles scandal (the discrediting of a widely-acclaimed piece of research seen as favorable to gun control), and having ferociously attacked those on the anti-gun side who failed to dissociate themselves from Bellesiles, Reynolds has consistently given Lott the benefit of the doubt, and has even, in a dispute between Lott and respected economist Steve Levitt, been implicated in Lott’s slimy manoeuvres (again, see Tim Lambert for the complex and gory details). Clearly all that rhetoric about ‘fact-checking your ass’ only applies to those who come up with the wrong conclusions.

Update Jason Soon reports that Steve Levitt has just been awarded the John Bates Clark medal for the best US economist under 40 (Paul Krugman is a previous winner, and it’s often seen as a harbinger of a future Nobel). So I guess he won’t be too worried by anything Lott and Reynolds have to say about him. Tom Spencer has more.

# Gross-out

Ken Parish has had a go at Clive Hamilton over an extract from his new book, Growth Fetish, published at Online Opinion. I think a lot of the debate is either at cross-purposes or misses crucial distinctions.

In essence, Clive restates a critique of growth, as measured by Gross National Product, that goes back to Galbraith’s Affluent Society. The link is sharpened by the fact that Clive, like Galbraith, refers to Gross National Product (GNP) rather than, as is more usual in Australia, Gross Domestic Product (GDP). Ken makes some good points but, in large measure, offers a restatement of the arguments that were put forward in rebuttal to Galbraith and, even more, to 1970s critics of growth like the Club of Rome.

On balance, I agree more with Ken than with Clive, so it’s only fair to begin with a point on which I agree with Clive.

GDP growth is a lousy measure of how well a country is doing, even if we are only interested in relatively narrow economic assessments of welfare, as opposed to social, cultural or spiritual issues. The name gives three reasons why Gross Domestic Product a bad measure of economic welfare.

It’s Gross because depreciation is not subtracted. If we are concerned with measuring economic welfare, even from a narrowly materialist viewpoint, the net measure is relevant and the gross measure is not.

It’s Domestic because it measures the amount produced in Australia, including that which accrues to foreign owners of capital and is paid out as interest or dividends. National Product which is the output accruing to Australian land, capital and labour is more relevant.

Finally, it’s Product, that is, a measure of output that takes no account of inputs. If we increase our product by working harder or longer hours (a point Ken notes), or by consuming more natural resources, we are not necessarily better off. What matters in the end is productivity, not product.

Why then do economists pay so much attention to GDP? The answer is that it’s useful primarily as a measure of economic activity, for short-run macroeconomic management. If GDP is declining, this is a good indication that the economy is in recession and that macro policy needs to be more stimulative. Taking account of things like depreciation, international income transfers and work intensity would reduce the precision of estimates of short-run growth because all things are hard to measure, and would make GDP less useful for its primary purpose. (Of course, this is a Keynesian view – national account statistics like GDP are essentially a product of the Keynesian revolution).

This is a big subject and I’ll try to post more on it as I get time.

# The UN and WMDs

As yet another WMD discovery fails to pan out, I’m puzzled by continued claims that the UN failed in its task by not approving the invasion. Whatever arguments Bush may have had for war, the only one he put up to the UNSC was based on WMDs. The evidence put up in support of his case was obviously dodgy at the time and has since proved to be completely spurious. Contrary to repeated claims, it’s now clear that the US has and had no reliable intelligence about the existence and location of WMDs. Some may perhaps exist, but it’s evident that all the claims made by Powell in his UN speech were false.

This leads to the question – why didn’t Bush put up the case for a war of liberation to the UN? There are some obvious difficulties like the attachment of the Chinese to the doctrine of non-interference, but I think the real problem comes when you think about what would be involved in presenting such a case ex ante. As I observed a couple of months ago on this point

A starting point would be an admission by the US government that it actively assisted or passively encouraged Saddam in the commission of his worst single crime – the war of aggression he launched against Iran, in which he made extensive use of chemical weapons. When Blair correctly says that Saddam’s wars have killed more people than were marching in London, he should be remined of this. I don’t say that the past crimes of the US government mean that it should not do anything about Saddam now, but an open declaration of the US role and an apology for US complicity are necessary if the moral case against Saddam is to have any standing.

The second requirement is for some sort of just basis for asserting that a particular leader is a criminal who deserves to be overthrown. We have such a basis in the International Criminal Court, in which Britain is a participant. Blair should demand that Saddam be tried before this court. Of course, a precondition is that the US should drop its own objections.

Third, there is the problem of equal justice.The moral case against Saddam is compromised by US complicity in the occupation of Palestine. If Bush were to demand acceptance by both sides in this dispute of a peace plan similar to that put up by Clinton and back his demand by a threat of sanctions and a willingness to enforce an agreed peace, the moral case against Saddam would be lot stronger.

Finally, there is the problem of multiple agendas. A moral case for war can be made only by forgoing all attempts at seeking strategic or economic side-benefits. Yet many (most) of the US commentators supporting war are pointing to such benefits as a primary or secondary motivation. A moral case would require a clear commitment not to use Iraqi oil to the benefit of the US, not to use Iraqi territory as a base for further military action, not to make side deals with countries like Turkey etc. So far none of this has been forthcoming.

Given that the UN was never presented with a case for a war of liberation, it’s hard to see how the failure to authorise one can be held against them.

# Monday message board

Things have been a bit quiet for the last week, with the many holidays. This raises the question – would we better off with more public holidays, and more general observance of those holidays, or with less of both? Feel free to comment on this or anything else (no coarse language and civilised discussion, please).

Update The Message Board at its lively best, as the impact of front loading washing machines on underwear battles for mindshare with the economics of the gold standard

# New and noteworthy

After a period when departures seemed to outnumber arrivals, there are quite a few new blogs. Moreover, the general trend to the left (or rather, to a blogworld more representative of the political views of the Australian population than it was a year or two ago) seems to be continuing. I’ll mention some that I’ve noticed and invite anyone I’ve omitted to email me.

Alerion’s Southerly Buster is an excellent blog, except that my name is misspelt in the blogroll. Alerion is currently running pieces by Jorge Luis Borges, always a worthwhile thing to do. Carl’s Smiling Politely is another new entrant well worth a visit. PineappleTown, another Queensland blog, is mostly links to news reports, but the selection is interesting.

# Chasing quotes

I’ve been noticing a quote, attributed to Keynes, that neatly encapsulates an argument I’ve been putting for some years.

The market can remain irrational longer than you can remain solvent.

The point of this is that, even if you can see a market bubble (or irrational slump) developing, you should not bet that prices will return to normal, for example by selling stocks short. The most sensible course is simply to avoid holding assets that are overpriced (I’ll need to work through the details of this argument formally some time – I guess it’s done in the literature on rational bubbles). Anyway, although the quote is being widely reproduced, I haven’t been able to find an actual citation, and the informal use of “you” leads me to suspect that these are not Keynes’ actual words. If anyone can find the source, I’d be very grateful.

On the same front, I gratefully acknowledge reader Bernhard Walpen, who sent me the full text of the Hayek quote on Pinochet that I mentioned some time ago. Here it is (with emphasis added by me):

Hayek, Friedrich August von, 1981: “En el Momento Actual Nuestra Principal Tarea es Limitar el Poder del Gobierno” [Interview], in: El Mercurio, April 4, 1981, p. D8-D9.

D9: “Bueno, yo le dirla que, como una institución a largo plazo, estoy totalmente en contra de las dictaturas. Pero bien puede ser un sistema necesario en un periodo de transición. A veces es necesario que en un país haya, durante un tiempo, alguna forma de poder dictatorial. Como usted comprenderá, es posible que un dictador gobierne de manera liberal. Y también es posible que una democracia gobierne con una total falta de liberalismo. Y yo, personalmente, prefiero a un dictador liberal y no a un Gobierno democrático carente de liberalismo. Mi impresión particular es – y esto es válido para Sudamérica – que en Chile, por ejemplo, habrá una transición entre un Gobierno dictatorial y un Gobierno liberal. Y en esa transición puede ser necesario mantener algunos poderes dictatoriales, no como algo permanente, sino como un arreglo de transición.”

My Spanish isn’t great, but it’s clear on the one hand that Hayek is endorsing the Pinochet regime [Bernhard’s extensive research on Hayek revealed no statement critical of Pinochet], and on the other hand, that he viewed it as a transitional stage in a movement towards a nondictatorial liberal government.

The most natural reading of the phrase I’ve emphasised is that, even without the prospect of transition, Hayek thinks a liberal (that is, free-market) dictatorship is to be preferred to an illiberal democracy. But as with Marxists and the ‘dictatorship of the proletariat’, the tendency is to use the prospect of ultimate transition to an ideal state to avoid a clear commitment for or against a dictatorship of indefinite duration. And, since the Pinochet regime did ultimately give way to a democratic government, it’s probably not sensible to draw firm conclusions on the basis of Hayek’s attitudes in this case.

Update In the comments thread, reader Alan from Southerly Buster provides a good translation. And Brad de Long notes that he has been unable to find a source for the Keynes quote which looks ‘too good to be true’. I agree – it seems like a response to arguments that Keynes would never have encountered, regarding the potential for rational speculators to stabilise markets.

# Lessons from Afghanistan

This NYT report on the mess in Afghanistan is worth reading when we are thinking about likely developments in Iraq. The situation in Afghanistan after the fall of the Taliban was, in important respects, considerably more promising than in Iraq. There was not too much trouble in producing a government with wide support, or at least acquiescence, and there was broad pro-American sentiment. All that was needed for a successful outcome was a reasonably comprehensive effort at peacekeeping and nationbuilding.

Instead, apparently to keep a clear field of fire in the hunt for Taliban/Al Qaeda, the Pentagon confined the international peacekeeping force to Kabul and allied itself with local warlords, inevitably becoming the enemy of its clients’ enemies. The result, two years later, is that Afghanistan is in much the same position as it was before the Taliban took over – warlords ruling the provinces and a government whose writ doesn’t run outside the capital, and not even within it at night. The time when US forces can pull out without inducing collapse looks further off now than it did when Kabul fell.

One consequence is that not even the relatively modest sums promised as aid have been delivered. As I recall, the US even forgot its budget allocation until the need to cover bases for the Iraq war focused the mind of the Administration.

This ought to have been comparatively easy, and it’s been comprehensively botched. Watching the mess that was made in Afghanistan was one of the factors that led me to oppose the war with Iraq. Nothing that has happened since the fall of Baghdad has led me to revise my assessment on this score.

# Another PFI deal goes sour

From the British Public Finance (published by the Chartered Institute of Public Finance and Accountancy) reports on a British deal in which the private supplier of school services simply walked away, two years into a five-year contract. One would suppose that there was some sort of performance bond to guard against this, but it isn’t discussed.

Some more interesting stories report higher costs due to PFI causing cuts in services and problems with the London Underground PPP.

Even more interesting is the suggestion here that the vogue for the provision of public services by for-profit companies has passed its peak and that interest is now turning to “public interest companies” – a version of what used to be called quangos (I’ll add a link on the etymology of this interesting term when I get time).