Riemann hypothesis proved ?

According to this report, Louis De Branges claims to have proved the Riemann Hypothesis. If correct, it’s very significant – much more so than the proof of Fermat’s Last Theorem by Wiles.

It is also, I think, the last of the big and well-known unsolved problems in mathematics, and its nice to see the search ending in success. Some of the other big problems have been closed, rather than solved. The classic problems of the Greeks such as squaring the circle were shown to be insoluble in the 19th century, and the Hilbert program of formalisation was shown by Godel to be infeasible. And the four-colour problem (not a really important problem, but a big one because it was easily described, interesting and very tough) was dealt with by a brute-force computer enumeration.

Almost instant update Commenter Eric points to Mathworld which says “Much ado about nothing”. On the other hand, the same page reports a proof of the infinitude of twin primes which has been an open question for a long time, though not a problem in the same league as those mentioned above.

A real bargain

For those of you who like end-of-financial year bargains, here’s one that’s hard to beat. The Australian government has a scheme under which it matches donations to certain aid projects on a $3 for $1 basis[1].So if you give $500, the matching funds can bring the grant up to $2000 which is enough to buy books for an entire school in a poor country. In addition, the donations themselves are tax deductible, so if you’re one of those groaning under our top marginal tax rate, the effective cost is only $250.

I got the info on this from PLAN, but a lot of other organisations have access to the same scheme. In addition to PLAN, I’ve always found Oxfam/CAA to be pretty impressive, but there is a wide range of worthwhile options.

I found this info on the Ausaid website. In particular, if all the funds allocated to this program aren’t spent by June 30, they’ll go back to consolidated revenue. So if, like me, you think that aid to the world’s poor ought to have a higher priority in the budget, you can get a lot of effective leverage from this program. I assume the program will continue next year, and I don’t know what would happen if an increase in donations used up the budget allocation early in the year, but it couldn’t hurt to try. Maybe the government would be shamed into allocating more money.

fn1. There’s an “up to” in there, which always rings alarm bells when you’re looking at bargains, but it does appear that the full 3:1 amount is available in most cases.

Disputed terminology

Via Eugene Volokh, I came to this Boston Globe piece by Jeff Jacoby, who complains that the term “partial birth abortion”, when used in news stories, is normally surrounded by scare quotes, with the explanation that this term is used by opponents of abortion, but disputed by supporters. Jacoby complains about liberal bias here and says, among other thing “when reporting on the same-sex marriage controversy, they should observe that “what critics call ‘homophobia’ — a term promoted by gay and lesbian activists — is not recognized by medical authorities”

As far as I can recall, I’ve never seen the word “homophobia” used in a news story in a major newspaper, other than in quotes, usually direct, but occasionally indirect (“activist X is concerned about homophobia”) Certainly I’ve never seen it used as if it referred to a recognised medical condition analogous to, say, claustrophobia. I looked in Google News and the recent uses I could find were all either in direct or indirect quotes, opinion pieces (including reprints of Jacoby!) or in publications such as Gay Times and Alternet, which don’t claim to be unbiased. Can anyone point to examples that would support Jacoby?
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Sinclair Davidson rediscovers the Laffer hypothesis

In today’s Fin (subscription required), Sinclair Davidson, author of a recent Centre for Independent Studies monograph on income tax, restates the hypothesis[1] , most famously associated with Arthur Laffer, that governments could reduce revenue by raising tax rates. He claims that his own calculations have revealed that revenue would be maximized with a marginal tax rate of 35 per cent.

Does the CIS endorse this claim? I don’t recall seeing it in the monograph. But the article refers to Davidson as the author of the CIS monograph, and this piece is associated with a broader campaign by the CIS on this issue, which has included a number of policy monographs and opinion pieces, including a recent attack on me by Peter Saunders. In the absence of some specific disclaimer, I think it’s reasonable to take this piece as part of the CIS campaign[2].

I commented previously that the Davidson monograph represented an alarming lapse in quality control on the part of the CIS, but I’m now coming to think that the problem may be more systemic.

fn1. It is common to refer to the Laffer curve, but the idea behind the curve is obvious, and had been observed by many writers before Laffer. Laffer’s justified claim to fame is the assertion that the US in the early 1980s was on the declining section of the curve. This was one of the arguments supporting the Reagan tax cut. Of course, revenue fell after the Reagan tax cut and Reagan partially reversed it.

fn2. Of course the CIS doesn’t have an official set of policy positions. But it seems reasonable to speak of a CIS viewpoint and to regard Davidson as being representative of that viewpoint as regards tax policy.

Bremer's last trick

Juan Cole is spot-on, as usual

The Guardian reports that US civil administrator Paul Bremer signed an order Monday banning Muqtada al-Sadr and his lieutenants from running for elective office for 3 years because of their membership in an illegal militia. Muqtada and his lieutenants rejected this decree and said that the CPA and the caretaker government had no right to make such decisions.

Bremer’s action in excluding the Sadrists from parliament is one final piece of stupidity to cap all the other moronic things he has done in Iraq . The whole beauty of parliamentary governance is that it can hope to draw off the energies of groups like the Sadrists. Look at how parliamentary bargaining moderated the Shiite AMAL party in Lebanon, which had a phase as a terrorist group in the 1980s but gradually outgrew it. AMAL is now a pillar of the Lebanese establishment and a big supporter of a separation of religion and state. The only hope for dealing with the Sadrists nonviolently was to entice them into civil politics, as well. Now that they have been excluded from the political process and made outlaws in the near to medium term, we may expect them to act like outlaws and to be spoilers in the new Iraq. (emphasis added)

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Elect the Governor-General !

Governor-General Michael Jeffrey has been criticised, again, for political comments, this time backing George Bush against Mark Latham. Such criticism, in my view, is obsolete. Although he was more subtle about it, Jeffrey’s predecessor-but-one, William Deane made his disagreement with some of the more brutal policies of the current government pretty clear. The attempt to restore the status of the GG as an impressive nonentity was tried with Peter Hollingworth, and failed miserably. Next time around, not surprisingly, Howard chose to play it safe and appoint a Liberal party loyalist.

The real problem is with the GG position itself. It is now inherently political, but the appointment is entirely in the personal gift of the PM. This is most unsatisfactory, particularly when a change of government produces a situation where the GG and PM are of opposite parties. Under our current system, this will produce increasing pressure for the GG to resign when the government that appointed him/her loses office.

The only adequate remedy is direct election. A directly elected GG (or President) would be free to speak out on public issues from time to time, while maintaining a primarily ceremonial role. The case for direct election would be even stronger if we became a republic, but it’s overwhelming in any case.

Hat tips: The title of this post is from a book by David Solomon and Ken Parish revived the idea a while back.

Risk and Reagan

Since the obituaries and eulogies for Ronald Reagan have now been read, I think it’s reasonable to take a critical look at his historical contribution. It’s often argued that Reagan accelerated the end of the Cold War by raising US military expenditure, thereby forcing the Soviet Union to increase its own military expenditure and crippling its economy. I think this argument has some plausibility in relation to the dissolution of the Soviet Union itself, though not in relation to the fall of the Berlin Wall and the collapse of the Communist governments in Eastern Europe[1].

So granting that this analysis is correct, should Reagan be praised. For the argument to work at all, the buildup must have raised the probability of nuclear war, unless you suppose (improbably) that the Russians were absolutely convinced of the peaceful intentions of the West and responded to Reagan purely to build up their own offensive capability[2]. Let’s suppose that the annual risk of war was raised by one percentage point. Then over the eight years Reagan was in office, there was a cumulative 8 per cent chance of a war that would certainly have produced tens of millions of deaths, probably billions and possibly the extinction of the human race. Against this, the early collapse of the Soviet Union produced benefits (mixed, but still positive on balance) for people in the Soviet Union, and perhaps also a reduction in the likelihood of an accidental nuclear war in the period since 1990. These benefits are small in relation to the potential cost.

As I’ve argued previously, if you think that a good policy is one which, in expectation, has good consequences, Reagan’s policy fails this test. On the other hand, standard accounts of consequentialism say that a good policy is one that has good actual consequences. If you accept this, and the assessment of the facts given above, Reagan’s historical record looks pretty good.

fn1. It had been obvious for many years that these governments were sustained only by the threat of Soviet military intervention. Gorbachev still had the military capacity to intervene in 1989 (in fact, on the argument presented above, the Russians had a bigger military than they would have had if Reagan had not been elected), but he chose not to do so. As soon as this became evident, the Communist bloc governments collapsed.

fn2. As an aside, in debate at the time, it was widely asserted that the Soviet government was actively planning an attack on the West, to be undertaken if Western defences could be weakened sufficiently. Has the collapse of Communism produced any archival or similar evidence on this? I would have thought that the Warsaw Pact countries would have had to have had a fair degree of involvement, and, since they are now in NATO, there would be no reason to keep any secrets.

Monday Message Board

Time as usual for the Monday Message Board. Post your thoughts on any topic. Since some commenters have been getting heated in recent weeks, let me remind everyone of my policy requiring civilised discussion and no coarse language, and raise the discussion starter: Does coarse language make for a coarse culture?
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