AI mathematical proof not without its detractors

OpenAI has solved one of the thorniest mathematical problems still left unsolved. And not everyone is happy about it.

The Navier-Stokes Problem was one of the $1 million Millennium Prize Problems established by the Clay Mathematics Institute in 2000. Without going into too much technical detail that would be way above my pay-grade anyway, the problem concerns a set of equations used to describe the flow of fluids. While the equations are already in regular use in everyday applications in physics and engineering, scientists don't really understand how or why they work, knowledge that would allow them to be used much more extensively in a wider range of applications. In order to do that, they need to understand scenarios where the equations break down or stop working, and that is the essence of the Navier-Stokes Problem.

Some scientists have welcomed the AI proof and see it as the start of a new golden age of mathematical advances. Others are a bit nonplussed that, while the proof is generally considered to be correct, the 166-page manucript is written in such opaque and obscure terms that no-one really actually understands it. It may take months or years more work to interpret it in a way that humans can understand and actually use. "The paper is not written for humans", as one mathematician put it. "It's a terribly written paper", says another. "Virtually unreadable", bemoans another.

But it gets murkier. Two mathematicians claim they were getting very close to a proof, and that the OpenAI proof uses their preparatory work. They accuse OpenAI of rushing out a muddled and poorly-argued paper in order to steal the accolades. 

Well, it wouldn't be AI if it weren't controversial, right?

The colourful history of Saint Pierre and Miquelon

Canadian Prime Minister Mark Carney and French President Emmanual Macron had a meeting the other day. It took place, not in Paris, not in Montreal, not even in New York, where they will both be in just a few days time for a UN General Assembly meeting, but in Saint Pierre and Miquelon.

Saint Pierre and Miquelon (Saint-Pierre-et-Miquelon in French) is a self-governing territory of France, home to some 6,000 French citizens. But it's nowhere near France; it's a tiny archipelago of islands, just 20km off the coast of the Burin Peninsula in southern Newfoundland (so, not even anywhere near Quebec). It's a weird anomaly: part of the European Union, but not part of the Schengen area or the European customs territory. It's currency is the euro, but it's also part of the Atlantic Canada Cooperation Commission.

How did such a thing arise? Well, the history of Saint Pierre Poilievre and Miquelon is as checkered and singular as it's current status. Originally inhabited by the indigenous Beothuk like the rest of Newfoundland, it was first claimed by Portuguese explorers in 1520, then by the French explorer Jacques Cartier in 1536. But it was not permanently settled (and named) by Europeans until 1670, at which time 12 French fishermen lived there. By the early 18th century French colonists had abandoned the islands completely, and they were ceded to Britain as part of the 1813 Treaty of Utrecht.

After the Seven year War and the 1763 Treaty of Paris, all of New France was ceded to Britain and Spain, but Saint Pierre and Miquelon, for some reason, went the other way and was ceded to France. In 1778, after France joined the American Revolutionary War against Britain,  French settlements on the islands were burned by the British, and the few French settlers there deported back to France. A British colony was established in 1793, but this was in turn burned by French forces in 1796. The islands were brought back under French control with the 1802 Treaty of Amiens, but retaken by Britain just a year later. They were returned yet again to France in 1815 under the Treaty of Paris, and gradually resettled by Breton, Norman and Basque settlers.

During American Prohibition in the 1920s, Saint Pierre and Miquelon became an important part of the smuggling network of alcohol from Canada to the United States, but it was plunged into economic depression once again after Prohibition ended in 1933. It was briefly under the control of the pro-Nazi Vichy regime, before being liberated by the Free French forces in 1941. The colony officially became a French Overseas Territory in 1946, after the Second World War, and finally acquired the status of "territorial collectivity" in 1985.

All this to-ing and fro-ing over a few tiny, bare, rocky islands, boasting just a thin layer of peat in places to soften the unforgiving landscape, and a harsh subpolar oceanic climate! The islands today are heavily subsidized by France, and the only real industry is fishing (and the filming of the CBC police procedural television series Saint Pierre!) It is hoped to develop its nascent tourist industry, and the islands' colourful history may yet become one of its greatest assets.

Canada looks to the east to replace the south

Canada's - or, more specifically, Mark Carney's - push for closer relations with the European Union makes perfect sense given what is happening with Canada-US trade relations.

While it's still not clear what "associate membership" of the EU might mean, or whether the 28-member bloc would even agree to what Ursula von der Leyen is proposing, Canada could certainly do a lot worse than to align itself closer with the EU (and some of the more civilized parts of Asia, Australasia, etc).

But wait, doesn't Canada already have a free trade agreement with the European Union? Well, kind of. The EU-Canada Comprehensive Economic and Trade Agreement, thankfully abbreviated to CETA, was officially signed in October 2016, and entered into "provisional application" in September 2017. CETA eliminates duties on 99% of all tariff lines between the EU and Canada.

Which begs the question of what "provisional application" actually means. The full treaty required the official ratification of all 27 EU member states, which, as you might imagine, is a difficult thing to achieve. Currently, 17 of the 27 EU countries have ratified the agreement, with 10 countries still holding out nearly a decade later: Belgium, Bulgaria, Cyprus, France, Greece, Hungary, Ireland, Italy, Poland and Slovenia. Of these, France and Italy are probably the most important. Opposition by these hold-out countries largely focusses on: the dispute settlement system; its impact on national sovereignty, agricultural and commercial interests; food safety; consumer and worker rights; public services; and environmental and sustainable development.

Notwithstanding those reservations, the agreement is effectively in force now, and has been for the last decade. So, it's hard to know what else Canada wants from the EU (and vice versa). Ms. Von der Leyen has talked about an "Alliance for the Future", covering defence, energy, technology, critical minerals and the Arctic. This clearly goes much further than the current trade agreement. Carney has also talked about a "unique alliance" that extends beyond a conventional free trade deal.

But Mr. Carney has stressed that he is not looking to become a full member of the EU, with all the incumbent duties and costs (and some potential loss of national sovereignty and independence). The "associate member" status - which currently does not exist - presumably reflects this compromise.

Either way, it seems to be annoying the hell out of Donald Trump, so that's something. He calls it a "hostile act" done with "bad intentions" (nothing is "done" as yet), and is clearly rattled by the project of Canada taking its business and its loyalties elsewhere.

Is privatizing Canada's airports a good idea?

Mark Carney's latest announcement is about privatizing Canada's four biggest airports: Toronto, Montreal, Vancouver and Calgary. Under this plan, the federal government would retain ownership of the underlying land and assets, but the day-to-day operation of the aiports would be opened up to private investors.

The theory is that airline customers would benefit from improved services and infrastructure, and the government would receive a large cash influx which can then be used to improve some of the smaller regional airports around the country, which are currently underfunded. It's being presented as a win-win scenario.

Seem too good to be true? Well, maybe. But studies do seem to show that, when airports are privatized, they do tend to be glowed up, the number of routes flying into them increases (including from low-cost carriers), and cancellations go down, soften drastically. These improvements are particularly noticeable where airports are acquired by private equity funds.

Is this a slam-dunk, then? Well, Canada's case is definitely not the same as parts of Europe and Asia, where distance are smaller and populations denser. But, when Australia privatized its airports, it too saw substantial improvements, and Australia is much more similar to Canada in its geography and demographics.

Some costs will definitely go up, though, for ticketing, parking and food. Private companies expect a profit after all, and investment funds in particular expect big profits (8-12%). Experience shows that, after privatization, most airports will put a price on baggage carts, for example, and pick-ups and drop-offs by private vehicles (and, by extension, ride-hailing services) will be charged sometimes quite onerous fees. 

The Canadian Labour Congress has pointed out that Australia's experience resulted in significantly higher fees imposed on travellers, as well as some substantial job losses as airports look to economize and rationalize their operations. Also, while the government may benefit from a one-time infusion of cash, it will be giving up a steady public income of around $525 million a year from rents and other fees.

The International Air Transport Association, which represents 370 of the world's airlines, has also registered its opposition to Mr. Carney's privatization plan, on the grounds that experience shows that the increased costs will be passed on to airlines, which will in turn Kass those costs on to travellers, so air fares will go up. Carney says that "the evidence shows travel costs go down over time", but that is not borne out by the recent experiences of Australia and Britain.

So, slam-dunk may be an exaggeration, but some advantages do exist. Whether they outweigh the drawbacks depends very much on your point of view. But you should definitely be prepared for higher air fares.

What Donald Trump knows about interest rates (not much)

Just one more indication of how little Donald Trump knows (or cares) about economics: after the US Federal Reserve finally had the cojones to raise interest rates, in direct opposition to Trump's frantic exhortations to drastically reduce interest rates, Trump tore the whole organization off a strip. His rationale? "Interest Rates in the United States should 1% or less, because we are the Best Credit in the World - BY FAR."

Setting aside the fact that he is living is a fantasy world, and that the US's credit rating is actually AA+ according to most rating agencies, compared to the AAA rating of countries like Canada, Australia and many European countries (see graphic below), that is not the point.

Credit ratings are not what drives interest rates, Mr. Trump.

The Fed - under new Trump appointee Kevin Warsh, who was widely expected not to have the gall to stand up to  - voted unanimously to increase interest rates by a quarter of a percentage point to 3.75-4.00%, and warned that it would probably raise them again next month. HIS rationale? The plain fact is that inflation is too high and has been for too long."

Now that is a sensible rationale. And for that the US President blustered, "The board is very hostile. They're very political. They're doing the wrong thing. They're a bunch of politicians. They're raising rates to make Trump do as bad as they can possibly do."

Ah, so interest rates are actually all about Donald Trump! Now I get it.

International trade is weird

As expected, Donald Trump has levied some more tariffs on Canada, in response to Canada's counter-tariffs to Trump's earlier tariffs. I know, it sounds like a kid's game, doesn't it?

The new tariffs, generally speaking, are in the sectors of dairy products, alcoholic beverages and motorcycles, a pretty random-seeming mixed bag, although I'm sure some thought has gone into them (albeit not by Trump).

When you think about it, though, some of the products are pretty surprising. "Molasses products, including invert and cane molasses"? We export molasses to the USA? We don't have any sugar production, apart from maybe final refining. Why are we exporting molasses, and to the US of all places?

Ditto rum and tequila. Don't we import them from Mexico, and probably from the USA? What are we doing exporting them to America?

And, for that matter, motorcycles. We export motorcycles to the land of the Harley Davidson?

International trade is weird.

Clancy trial ends in a travesty of justice

The Lindsay Clancy trial has captivated the media and the viewing public for weeks. The trial was televised - a weird concept for me; this is NOT entertainment! - although the jurors' deliberations were not. (Maybe they should have been if this is really to be reality TV.)

In the end, it was those jury deliberations that provided the big story, because 11 of the 12 jurors voted to acquit Ms. Clancy on the grounds that postpartum psychosis clouded her judgement and made her not criminally responsible. One juror, even after extensive debate, voted against the majority and, because a jury verdict needs to be unanimous in this kind of criminal trial, the jury was therefore hung, and the judge had no choice but to declare a mistrial. Seven weeks of work on the part of many people wasted just like that.

Thing is, though, now that the trial is over. other jury members are offering a glimpse of what actually happened behind those closed doors. It tutns out that the dissenting juror, who is charitably described as "arrogant", actually admitted to the other jurors that "he had reasonable doubt", which is all that is needed to trigger a vote for acquittal. But, in spite of that, the maverick juror insisted that "I'm still not going to say that she's not guilty by reason of insanity".

So, the holdout juror seems to have misunderstood the way the law works, and nothing the judge or the other jurors could say could change his mind. What a travesty! If that juror ever becomes publicly known, he should probably watch his back. He should also be banned from ever serving on a jury again.

If there are more sanctions to announce, why weren't they announced before?

Every now and then, I read about a new sanction that is being brought to bear on one of the world's pariah states. The latest such is Canada, France and the UK are sanctioning Israel in a small way by banning the import of goods from the illegal settlements in the occupied West Bank. 

My first thought was "What? We buy things from the occupied West Bank? They can actually grow things there?" My second thought, though, was "Why the hell did we not impose these sanctions before?"

It's the same with Russia. Canada and most of the civilized Western world has imposed various sanctions on Russia since its invasion, and its ongoing bombing, of Ukraine. As recently as June of this year - four-and-a-half years into the war - Canada imposed new sanctions on 162 "people, entities and vessels". 

Which raises the questions of "why now?" If these are legitimate sanction targets in relation to Russia's illegal war, why were they not sanctioned four years ago? Why were the earlier sanctions not designed to include all possible targets, for maximum effect? Why wait until now to announce a few more piecemeal sanctions? Was it just for the sake of having something to announce, to be seen to be doing something?

It does seem to be more about playing politics than a serious attempt to bring about a halt to the war. And I'm not saying that only Canada is guilty of this - all countries seem to be doing it.