St. Augustine, Thomas Aquinas, dogma and mathematics

A few weeks ago, I finally got around to reading “Between the Lord and the Priest”, a book-length conversation between Adam Michnik, Jozef Tischner and Jacek Zakowski. I came for the historical content, but stayed in part for certain disputes in Catholic theology in Poland in the 1960s and 70s. It’s not my usual cup of tea; Tischner himself acknowledges that all this was of very limited interest to the general public while trailing well behind contemporary Western European philosophy. It nonetheless describes beautifully some of the disagreements I’ve had with my fellow mathematicians with regard to life in general and social issues in particular.

The framework for the dispute is provided by the long-standing dichotomy between St. Augustine and St. Thomas Aquinas. The way Tischner explains it, Thomism posits eternal, unchangeable truths that must be accepted as dogma and followed in life. It prescribes synthesis, universality, vast generalizations, logical chains of cause and effect all the way back to deity. Augustine, on the other hand, is less sure of himself. Even if the truth, somewhere out there, might be eternal and unchanging, our understanding of it is grounded in history, tradition and experience, and in the end that understanding is all we can ever access. In practice, this is a more bottom-up approach to religion, starting with personal, individual existential questions and then seeking guidance in the Scriptures and the church’s intellectual tradition.

Now, here is where things get interesting. Tischner goes on to say that Thomism, in its methodology and spirit, is actually quite similar to Marxism. Marxists, too, had their axioms of class struggle and dialectical materialism. They presumed to shape human consciousness through class awareness, much as Thomists presumed to shape it through philosophical and religious dogma, with little regard to individual experience and understanding.

That was why Michnik, an atheist and a leftist at odds with communism, tuned into Tischner’s polemics with Thomists. Thomism, like Marxism, represented codified, linear thinking where “one thing always follows from another, and everything is perfectly arranged and therefore very simple.” Tischner found that he could not talk like that to his parishioners – people who’d fought in the war, lived through the horrors of Nazi occupation, made choices that most of us wouldn’t want to think about. Their experience defied the scheme. Michnik, then in his twenties and already a veteran of protests and prisons, trying to graduate from university before his next arrest, had no love for simple explanations of everything, either. He’d rejected Marxism already; he would go on to consider religion, but not if it offered no escape from the same kind of closed-minded thinking, not if it were perfectly arranged with one thing always following from another.

At times, Marxist-Leninist philosophy was almost comical in its straightforwardness. Michnik cites Lenin’s theory of cognitive reflection, asserting that

(1) a world exists “independent” of and “external” to consciousness, and (2)
knowledge consists of approximately faithful “reflections” of that world in consciousness.

The second part of that, understood literally as Lenin indeed intended, is, on a very basic level, at odds with science, and I could say much more along these lines just based on my experience with photography. What’s less funny is the underlying Thomist assumption that there can only be one intellectually correct interpretation and only one right set of conclusions, namely those espoused by the bearer of the dogma, and that any departure from that must be a result of either misinformation or bad faith. When communists censored dissenting opinions, part of it was a genuine conviction that such opinions were obviously nonsensical and therefore there was no reason to disseminate them. When they lost the 1946 referendum in Poland, they blamed it on “confused thinking” and “complete ignorance” among the population. In a similar vein, but centuries earlier, the Catholic Inquisition might first try intellectual arguments, but if the accused were not persuaded, that constituted proof that they were possessed by the devil, because how else could they not agree? Thomists responding to Tischner informed him on a regular basis that he did not really know St. Thomas, because had he known him, he’d love him.

I started drawing my own analogies long before the point where Tischner actually uses the word “mathematical.” Like a good Augustinian, I’ll start with specifics. A couple of weeks ago, in a comment section far away, a mathematician proposed to “solve racism” by generalizing it (to something he never quite defined) so that racism itself would follow easily as a special case. In a different comment section last year, several mathematicians insisted on a purely mechanistic solution to sexism in mathematics. They accepted it as a self-evident axiom that mathematicians were progressive and well-intentioned people who would automatically eliminate sexism from their ranks if it only were pointed out to them. One might of course wonder why it hasn’t worked yet; but one would then be doubting an axiom, an act that’s not only morally reprehensible but, worse, logically inexplicable.

I’m thinking of mathematicians who’ve argued with my blog posts by taking shots at some sentence pulled out of context, the way they might point to an incorrect formula in a math paper. I’m thinking of one person who started a discussion with me, then allowed reluctantly in response to my arguments that he might not be able to change my mind after all, because convincing people is hard in general. Apparently, the possibility of me convincing him had never been on the table. I’m thinking of those who expected I’d stop believing in that gender bias thing if they only could explain it all to me, almost like religious evangelists. Sorry, no. I’ve heard your arguments many times already. I disagree with them, not because I don’t understand them well enough, but because I do. They don’t address my experience, and they never will if you keep starting from your own axioms instead.

It became clear to me over the last couple of years that I’m not, and probably never have been, part of a “mathematical community” of any kind. Sure, some of my best friends are mathematicians. I do my expected share of “service to the community.” But after hours, I’d rather kick off my shoes with people who at least share my logic. I’d rather discuss experiences, not axioms. I’d rather debate someone who’s actually listening to me, not just building his own castles of abstraction.

It’s been claimed by some of those in question that mathematics itself supports Thomist thinking. (As in, “I’m a mathematician and therefore this is how I approach this problem.”) I’m not so clear on that. To some extent, sure: we’re all trained in binary logic and deductive reasoning, as we should be. But in my own research practice, I often work in the Augustinian direction, starting with specific examples and then working towards something more general. Freeman Dyson’s “Birds and Frogs” article comes to mind, except that I’ve met froggy types like me who are incredibly dogmatic on social issues, and birds who are not.

If I were a Thomist, I’d try for a diagnosis, conclusion, and a list of recommendations for my peers. Maybe the problem is when mathematicians Act Like Mathematicians, showing off their smarts where wisdom is called for. Maybe, too, it’s unexamined purchase into the letter of the deductive philosophy of Russell and Bourbaki, without stopping to consider the actual practice of mathematical research; but that argument becomes circular right there. So, instead, I’d rather just leave you with something to think about, and excuse myself from Math Overflow once again.

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Non-academic jobs for mathematicians

I will get back to talking about communism and other fun things soon enough, but meanwhile, something of possible interest to mathematicians. I’ve been appointed to the Web Editorial Group of the American Mathematical Society, starting this February. In case you don’t feel like clicking, this is a small committee charged with providing advice and suggestions regarding the AMS webpage. (The WEG doesn’t actually maintain the page. The AMS has staff responsible for that.)

I’ve been considering what I’d like to do in that capacity. I’m sure that other stuff will come up, but right now, I’m thinking of the math graduates and postdocs who talked with me about looking for jobs outside of academia. Our system is geared towards pushing students and graduates up the academic ladder, then averting our eyes politely when they fall off and pretending that they never existed in the first place. We can make it feel like a failure when someone quits academia, even when they’re genuinely happier doing something else.

Honestly, I’ve never understood this. There are not, and never have been, enough academic jobs for all of our graduates. I don’t see why everybody should want one, either. Academic jobs can be rewarding, but there’s a price to pay even in the best circumstances; likewise, any other job will have its own rewards, disadvantages, and limitations. Of course the balance will be different for different people. I’m still in academia myself, but I’ve been at the crossroads a number of times and it’s very easy for me to imagine other outcomes.

Anyway. The students and postdocs I talked to were often at a loss as to how to go about the transition. They didn’t know what other jobs might be available to them, how to go about applying, or what additional qualifications might help. Which brings us back to the AMS webpage. Right now, the career information page focuses on academic jobs, with only two articles about “the non-academic job market.” One of these articles is by Cathy O’Neil, who has since supplemented it with additional posts on her own website. The other article suggests networking – except that most graduate students and postdocs in mathematics have very little access to networking outside of academia, and the usual sequence of long-distance moves in postdoc years might as well have been designed to keep us unrooted from the wider community.

I’d like for this proportion to change. I’m looking for suggestions as to what kind of advice on non-academic jobs could be useful, and where to get it. Should we try to solicit more articles? Should we link to blog posts describing relevant experiences? Should there be some community-based resource such as a wiki? I’m cross-posting this on Google+ so that people could comment there. Email comments are also welcome. This is just a call for ideas; ultimately, I will be only making suggestions, and the actual decisions about the website content are made by the AMS. But first, I’d like to get a better idea what to ask for.

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The complexities of communism

Another day, another political speech mocking science and calling for funding cuts:

Another little one here, which I am sure might be a favourite of many sitting on the opposition side, is a study of Marxism and religion and the relationship between theology and political radicalism—$60,000. Another one here is $180,000 for a study rethinking the history of Soviet Stalinism to provide a sophisticated understanding of the complexities of Stalin’s Russia. We know the complexities—obviously, Stalin must have been a good bloke who was misunderstood. We need $180,000 to find that out.

That kind of rhetoric has of course been seen and debunked many times before, but still keeps coming back. No, we don’t need to spend money to “study” whether Stalin was a good guy or not. That’s clear enough. The specifics of it, on the other hand, are a different matter altogether. Especially with so many politicians throwing around words like “socialism” or “central planning,” it would indeed help to have a better understanding of the concrete realities and mechanisms involved, both among specialists and in the popular discourse.

I’m still reading and thinking about Tony Judt’s “Postwar.” I wrote one post about communism already and got into some discussions elsewhere (hi everyone!), so I’ll follow up on that. I’ve said that Judt does not really explain how the Eastern European “planned economies” actually worked, a matter that tends to be widely misunderstood in the West. I’ll try to clean that up a little bit here.

Let’s start with what Judt does talk about: emphasis on unprofitable and outdated heavy industry, rigid quota, bureaucracy, inefficiency, corruption, wastefulness, shortages and supply bottlenecks.

The crippling defect of Communist economies by this time [the 1970s] was endemic, ideologically-induced inefficiency. Because of an unbending insistence upon the importance of primary industrial output for the `construction of socialism’, the Soviet bloc missed the switch from extensive to intensive, high-value production that transformed Western economies in the course of the Sixties and Seventies. Instead it remained reliant upon a much earlier model of economic activity, redolent of Detroit or the Ruhr in the 1920s, or late nineteenth-century Manchester.

Thus Czechoslovakia – a country with very limited resources in iron – was by 1984 the world’s third largest (per capita) exporter of steel. To the bitter end, the GDR was planning ever-expanded production of obsolete heavy industrial goods. No-one who had any choice actually wanted to buy Czech steel or East German machines, except at heavily subsidized prices; these goods were thus produced at a loss. In effect, Soviet-style economies were now subtracting value – the raw materials they imported or dug out of the ground were worth more than the finished goods into which they were transformed. [...]

Much of the responsibility for all this lay with the inherent defects of centralized planning. By the late 1970s Gosplan, the Soviet central economic planning agency, had forty departments for different branches of the economy and twenty seven separate economic ministries. The obsession with numerical targets was notorious to the point of self-parody: Timothy Garton-Ash cites the example of `The People’s Economy Plan for the Borough of Prenzlauer Berg’ (in East Berlin), where it was announced that `Book-holdings in the libraries are to be increased from 350,000 to 450,000 volumes. The number of borrowings is to be increased by 108.2 percent.’

The description is absolutely correct and the anecdotes ring true. I could add more along the same lines. The symptoms were obvious enough, easy to mock and critique.

But wait. Why, exactly, was heavy industry so important to the communists? Was it a matter of ideology, as Judt suggests? While Marxist theory does (sort of) prioritize industry over agriculture, it does not prescribe favouring any specific kind of industry in particular. Even if it did, communists have been known to make greater compromises in the name of staying in power, going all the way back to NEP in the early days of the Soviet Union. Khrushchev had plans to reorient the economy towards production of consumer articles in the 1960s; after the unfortunate initial period of hardship and difficult choices, socialism was to bring prosperity and abundance. There was talk of similar reforms in the satellite states. With all the central planning structures at their disposal, why didn’t the communists go ahead and reallocate the resources accordingly? Were they stupid, or suicidal?

On a related note: in popular imagination, “Communism” is synonymous not only with inefficiency, shortages and corruption, but also with a rigid, brutal totalitarian system, 1984-style. How did those two aspects of it coexist? Aren’t dictatorships supposed to be good at making trains run on time? Is there some reason why the government couldn’t just mandate a transition from heavy industry to intensive high-value production, and then have the security apparatus enforce it? Why, for that matter, were the bureaucrats allowed to continue in their inefficient ways? There’s a long record of unsuccessful government-initiated attempts to overhaul and modernize socialist economies, from the 1960s all the way to Gorbachev’s perestroika in the 1990s. Why did they fail? Inertia is often mentioned, and rightly so – but can’t inertia be broken by force? Evidently, the ruthless dictators (and make no mistake, they were ruthless) did not actually have that much power over their own domains.

Continue reading

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History as written by emigrants

I’m reading Tony Judt’s “Postwar”, a history of Europe since 1945 until the 1990s. It’s an excellent book, impressive in its breadth of scope and attention to detail, encyclopaedic at times, yet still very readable. I’m finding it more than worth my time and I highly recommend it to anyone interested in understanding Europe’s history and politics.

I’m also finding that Judt’s analysis of Western Europe is much better than that of the Eastern Bloc. “Postwar” is fascinating in its account of the larger political, social and economic processes that constrained the main actors in the West: why a remilitarized West Germany was inevitable, for example, or how the loss of overseas colonies affected the European balance of power. The Eastern European history is, by comparison, more superficial.

Given the sheer number of names, dates and facts in the volume, Judt can be forgiven for the occasional inaccuracies. (The Polish leader that Gomulka replaced in October 1956 was Ochab, not Bierut who had died in March 1956; Ilia Rips is a man, not a woman; and so on.) What matters more is that, while Judt tries to avoid the “few great men” version of Western European history, he succumbs to it somewhat in writing about the East. Eastern Europe is seen disproportionately through the prism of Western headlines and secondary sources (the show trials, the major uprisings), with less attention paid to social analysis and the reality of life on the ground.

Judt, of course, has very good excuses. It would take a large team of experts, not a single author, to access and interpret primary sources in all of the languages involved. Moreover, there’s only so much that can be done within the constraints of a single encyclopaedic volume of much wider scope, meant to be accessible to an audience with little prior familiarity with the subject. In a limited “teaching time”, it’s a perfectly valid strategy to focus on those parts that can be explained effectively with less effort. I’ve done it myself on occasion, both in my math teaching and here on this blog.

Still, there’s a lot missing. Take the economy, for starters. Judt speaks of the economic failure of socialism, but never really explains how a Soviet-style planned economy was organized, how it was different from Western European social and economic planning (the subject of many misconceptions in the West), or why it did not and could not work. This is important because, without that information, most readers will just assume that Eastern European central planning was much like in Western Europe, only more rigid and dysfunctional. It was not. Its origins, philosophy, mechanism and execution were all very different from anything known in the Western world. To give one example, all prices (including food and consumer articles) were dictated by the government, and I really mean dictated, not just regulated or subsidized. (Francis Spufford’s “Red Plenty” is excellent on that, and I’d also recommend Anne Applebaum’s “The Iron Curtain” on the early postwar years in Eastern Europe.)

Judt’s Western chapters are so good in part because of how he writes on large and small scales simultaneously, humanizing politics and, at the same time, distilling general trends from a mass of individual events. To wit:

Street scenes in post-war Britain would have been familiar to citizens in the Soviet bloc – in the words of one British housewife, recalling these years, `It was queues for everything, you know, even if you didn’t know what you were queuing for… you joined it because you knew there was something at the end of it.’

No Eastern European housewives were similarly interviewed, at least in the part of the book I’ve read so far. If they had been, they could have talked about how queues formed first thing in the morning and waited for hours before anyone even knew whether anything would be delivered that day. This went on into the 1970s and 80s, not just the early post-war years. They could have talked of the power and water outages that could happen any time, the decrepit 1950s buildings with communal kitchens and bathrooms, or carrying a baby stroller up to the 5th floor of a walk-up apartment building while pregnant with their next child. Likewise, factory workers (both male and female) could have spoken of the long hours, insane schedules, ever-increasing norms, inhuman and unsafe work conditions. It would have explained the desperation behind the strikes, protests and riots.

I started writing this post in response to the chapter on the events of 1968 in Poland and Czechoslovakia. Continue reading

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Thanks, U of T Math

I’d like to thank the University of Toronto mathematics department (my doctoral alma mater) for the nice news item on its front page mentioning my ICM invitation. (It was posted a while ago, but I only saw it now.)

Being invited to speak at the ICM is often regarded as one of the highest honours that a mathematician can receive. It is a truly international recognition of the depth and ground breaking impact of their research.

UBC, meanwhile? Nope. It’s not that they don’t update their webpage, either – the page has been updated since the announcement.

This is of course the season for graduate and postdoctoral applications. Departments go out of their way to compete for the top candidates, and one part of it is showcasing the accomplishments of their faculty (to get the prospective students and postdocs interested in working with them) and their former postdocs and students (hey, this could be you). UBC Math has 3 session speakers at the 2014 ICM: Kai Behrend, Jun-cheng Wei, and myself. Additionally, Ben Green (who was a postdoc here for a year) is a plenary speaker. Is there some reason why UBC Math would not want to advertise it?

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Fall

IMG_1844s

(Click on the image to enlarge it.)

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by | November 3, 2013 · 9:22 am

Lou Reed

Every now and then, I get asked what kind of music I like, or who is my favourite music artist. I don’t have any straightforward answer to that. It’s not only that I’m long past the age when everything was a competition, or that I see no point in restricting myself to a single “favourite” artist or genre. It’s that I don’t really think of my relationship with music in those terms.

I may “like” a catchy tune and forget it a few minutes later. The music that etches a deeper groove does more than that. It might channel my emotions, counterpoint them, transcend them. It might engage me intellectually. It might provoke, question, irritate. It might be cool as an ice-covered cucumber straight out of the freezer, or it might sing its heart out, magnificent in its abandon. It might fall short of its apparent aims, but remain fascinating in its failure. I connect with different music pieces in different ways, each one unique, irreplaceable, impossible to reduce to the simple notion of “liking.”

I’m not nostalgic by default for every piece of music from my youth. I enjoyed it well enough then, back when I was still into making lists of favourites; or if I didn’t, I criticized it passionately. As I grew up, much of it fell by the wayside, now covered by the dust of indifference.

But not all. Some of it went deeper, growing into me as I got older, becoming part of who I am. As a naive, uncool teenager with a very limited command of English, I fell for it based more on a hunch than any real understanding; still, it got me hooked, then drove me to learn more, molding me along the way. In time, I became more knowledgeable and critical. I found out what the English lyrics meant. I got past the stage where a “favourite” artist could do no wrong. But, because this music had become so entwined with who I was, I cannot be entirely objective about it even now, not any more than I could be about myself. Whether I “like” it is beside the point. I don’t even always listen to it that often now. I don’t have to.

Lou Reed died today, at the age of 71. I only saw him live once, at a Neil Young tribute concert here in 2010 during the Winter Olympics. He did one or two songs, somewhat perfunctorily; it was Elvis Costello who stole that show. Laurie Anderson was in town, too, performing “Delusion” at the Playhouse. Just before the show began, Lou came in through a service door right by where I was sitting. I just stared, openly. Then someone found him a seat by the aisle in the center. The guy next to him must have recognized him, too; after the performance, they shook hands, then Lou left quickly. I remember his face looking much more wrinkled than it did in photos.

RIP. And thank you.

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