The Abnormal Distribution

Not mine this time (the one I wrote in 1997 is still being referenced, but is out of date because the German degree system has changed) but the OECD’s from October 2011, based on 2009 data, which I have just discovered. The Washington Post published in September 2011 a startling graphic, accompanying an article on the report to which was linked in an essay today by Nicolas Kristoff of the NYT. (Kristoff is a member of my college. In his journalistic wanderings around some of the poorest, most disadvantaged parts of the world, he sometimes seems to me like a modern Wilfred Thesiger, a former member.)

I should note, first, in reference to the Washington Post article that the US term “college” refers to all higher-education which leads to a qualification called a degree. This includes “community colleges”, tax-supported institutions which provide the equivalent of the first two years of a four-year university education and which grant degrees called “associate degrees” to successful students, as well as universities, which may be four-year or six-year institutions, as for example the California State University system is, granting Bachelor’s and Master’s degrees, or “research universities” such as the University of California which also grant Ph.D. degrees.

I recall British Prime Minister Blair saying in 1997 (do I?) that the Labor government intended to push degree achievement rates up to 35% of the population, up from the 15-18% or so which it was when I graduated in 1973. I didn’t realise until I looked at the WP graphic, based on the 2009 data, that this had been achieved. I herald it as a major national accomplishment.

(I get the figure of 15-18% as follows. This 2000 report by David Greenaway and Michelle Haynes says that about 400,000 young people were in tertiary education then. If one takes the average lifetime, a little under 80 years, considers that 3 years is a twenty-fifth of that, and that the population of Britain is about 60 million, one would expect 2.4 million people of university-visiting age. 400,000 is thus one in six, about 17%. I should perhaps mention that Laura Spence, who was rejected by “Oxford” but given a scholarship at Harvard, had in fact applied to my college. Not the greatest marketing moment in history).

Similarly, I had, until today, oft quoted the rate of young people in the US entering higher education as a sign of what I thought was desirable, and used the figure of 55% of school leavers. I doubt if this has changed significantly. But I am disturbed to find out that that apparently only 41%, about three-quarters, complete to some sort of degree. Considering that includes associate degrees, which are only two-year courses of study, that does not bode well for the US, if you believe as I do that the more people learning skills in a short time which they otherwise would not have, then the greater the productivity of their society, in the richness of hobbies and other pursuits in life and not just in stuff measured in standard economic measures.

I am intrigued by the Box on p18 of the OECD report entitled “Germany rethinks its assumptions about education and social equity”. Yes, indeed! People here were quite convinced about the “quality” of the education system, despite the obvious inequities and inadequacies apparent to those of us with wider experience, until the PISA reports on comparative achievement in secondary education started appearing from 2000 on, which showed German school achievement in a poor light compared with Germany’s economic peers. Then it couldn’t be ignored any more, and it wasn’t.

PISA was to do with secondary education. I am still somewhat disturbed by the relatively poor showing of Germany in tertiary education, at 26%. Some comments on that, some of which I have made before.

We currently have huge building projects going on around our Bielefeld University campus, which is itself huge (put “Bielefeld University, Universitätsstrasse 25, Bielefeld, Germany” into Google Maps). The main university building, in which almost everything goes on, is some third of a kilometer long, as you can see. Two new campuses are being constructed, one adjacent to the old building on a parking lot just to the north of the main building, between the two branches of what is labelled “Universitätsstrasse, some two hundred meters long and the better part of a hundred meters wide, and one “over the road”, almost a kilometer away, in (Google Maps again) “Lange Lage, Bielefeld, Germany”, which is also large, and will house the University of Applied Sciences (what the Brits used to call a “Polytechnic” and Germans a “Fachhochschule”), a teaching university which does not grant research degrees, and which is now largely scattered in old and often unsuitable buildings around town. This all amounts to a huge public works (which Google Street View does not yet show). And, if the above figure is to be believed, this will only be usable by a quarter of the young adults in the city and surrouding areas.

Do we have a town-and-gown problem? Less so than we did, I think, but more so than we might. The university does some outreach, including a science fair each year called Geniale (some pictures of GENIALE 2011 – the German for “pictures” is “Bilder”), spread over selected spots in the Old Town. But why aren’t most of the young people in this area passing through some part of this enormous spreading campus to take part in something? After all, they and their parents pay the taxes that create all these large buildings and pay their occupants. Future auto mechanics and hairdressers could surely benefit personally from participating in a course on 1960′s popular music, couldn’t they? Germany has no equivalents to Brian Patten, Roger McGough, Adrian Henri or Carol Ann Duffy, but we have plenty of slam poetry (link only in German, unfortunately), indeed a local slam poet who has turned into a valued writer and raconteur, Mischa-Sarim Verollet (also only German). Here is the announcement for the next one in April 2012.

Such educational offerings are available through the Volkshochschule Bielefeld, the Community Further Education Center, but this is largely less formal – courses are not assessed, the qualifications of course-offerers fulfil no standards (either experiential or formal), one doesn’t obtain a transcript of courses completed, and, importantly, it does not constitute the kind of accomplishment which a prospective employer expects to see on an applicant’s résumé. I am thinking that all these things should happen. I am also thinking about the impoverished financing of the Volkshochschule compared with the heroic building works around the university campus.

I cannot see that expensive tertiary education can thrive unless it includes way more than the elite. We are well past the days when people said “well, that’s for them rich and clever kids” and turned their backs. Nowadays, people say “I pay taxes too; why can’t I come in here?” and I think that question is very well founded. Especially when the expenditure is so massively visible, as it is in Bielefeld.

German university education has changed, though, massively in the last decade. The previous system has been more or less junked, and every university now offers Bachelor’s and Master’s degrees, instead of the old Vordiplom/Diplom, which were not recognised outside Germany for what they were (a Vordiplom was like a US associate degree, and a Diplom like a Master’s, but with nothing in between). It is astonishing how everyone just threw the old tradition away in the early 2000′s and went with what, for most here, was a completely foreign system with which they had little or no experience. I did find out why from a colleague in Sociology, though. They had over a 90% drop-out rate in their Diplom course. And this in one of the most well-reputed Sociology faculties in the country that invented it.

I think student contact with the rest of Europe was also slowly bringing a new perspective. German university students were finding themselves relatively immobile compared with their peers in other European countries, because the organisation of their degrees did not easily translate. For example, in the late 1990′s, students studying for degrees in my faculty returning from studying abroad for a year in the ERASMUS program still had to take an oral degree examination in the studies they had completed abroad to have it count for our degree, even though they had already been assessed by the foreign institution for that work and the EU ERASMUS agreement requires that we honor that assessment. To those who came to me, I asked for the transcript, or equivalent document showing successful completion, asked them to tell me about what interested them in the work, and passed them. In other words, the exam was purely formal, and the result identical to what they had already achieved. That is the best way I could see to fulfil the EU requirement, which our internal faculty procedures at that time still contradicted.

Besides that, successful graduates (the Sociologists’ 10%; our proportion in Informatics was much, much higher!) were leaving tertiary education with a degree equivalent to a Master’s at the age of 26-28 (and some even older), whereas their British and US peers were obtained such qualifications at the ages of 22-24. People on the ERASMUS exchange were noticing they were somewhat older than their local peers, and those starting Ph.D. programs in other countries noticed it even more.

Now, we have Bachelor’s and Master’s degrees, credit points for each course, and credit points are transferable between all European tertiary-educational establishments.

I cannot necessarily say that the quality of education has improved, however. With the more extensive evaluation requirements (per course, now), much of this is being farmed out to tutors and other helpers, and the quality of that education and assessment does not seem to be monitored as I feel it should be. I monitor the courses in my group, which are all based on lab work, or seminars which consist largely of student contributions with commentary from the lecturer, and my group has considerable continuity in our student tutors, who were picked for (or, better said, who picked themselves by) their enthusiasm and capabilities. But some of our larger courses appear to have problems (one of my bright people, who has coauthored an important chapter in our system safety text, is on his third attempt at one of the required practical courses, for what appear to me to be spurious reasons).

The throughput has, however, improved. One reason in the past was the introduction of modest fees, some few hundred euros per semester. Suddenly, all our 6-year and 7-year students (of which we had plenty) wanted to finish – and most did. And the fee money was directly given to the Faculty, in which a largely student committee, which did include the Dean, decided what to do with the money to finance improved teaching. More tutors for some courses. Lab equipment – my lab was built with this money. The faculty also hired a highly motivated and very successful lecturer whose courses are loved by students and who does lots of lab work, indeed he uses the lab which we built.

The other reason is that students in our Bachelor’s and Master’s programs are spending much of the day in courses, and most of the rest of their time doing the homework. Their time is filled with study-related work. This is very different from ten years ago. But I think it is a benefit, more on a par with what their peers do in other countries with a higher percentage of college graduates.

Michael. Everyone knew him as Michael.

I was a freshman at Oxford in mathematics, interested in logic. I had been reading Chomsky in my first quarter because I had been told Chomsky had mathematised language. My tutor in algebra, Ian Macdonald (same jacket as in the picture!), an algebraic geometer, suggested I could look at a logic textbook he recommended (which I read with some difficulty over the Christmas break). Derek Goldrei, a graduate student tutoring in logic at my college Magdalen, suggested I listen to Michael’s lectures in set theory.

Michael didn’t lecture. Michael thought out loud. He distributed notes telling his listeners what he was going to be thinking about during that appointment. I learnt, by watching and listening, how to think. About set theory. About inference rules. About non-classical logic (Michael was drawn to intuitionist thinking about mathematics, because he thought it was right to base your assertions on the concrete evidence you had).

I had been attending freshman mathematics lectures, which went “Theorem” “Proof” “Let x be…” and had despaired of ever being the kind of person who thought like that. Then I attended Michael’s thinking-out-loud sessions and understood what really went on in people’s minds; how the symbols were shorthand for notating thoughts. And, in my second year, I could do it! Just like Michael! Actually, not just like Michael. Not anywhere near “just like Michael”. For, as John Mackie is reported to have said in The Times’s obituary, Michael was a genius. Michael was ineffable.

Michael was different. A mass of wavy white hair, he would array himself longitudinally on a bench in the lecture hall and clean his cigarette holder while leaning on an elbow, with his head just above the seat backs, and crack jokes about his friends and colleagues while waiting for the lecture to begin. At which point the jokes would reduce in number as he concentrated on what was being said. If there is anything any undergraduate wished to be in the course of study he had in large part created, Maths and Philosophy, it was to be “just like Michael”.

Simply put, Michael taught me how to think, in logic; by extrapolation, in mathematics. About the deep philosophical questions concerning truth, mathematics, the use of language. Differently put, I learned how to think by watching and listening to him.

When I graduated in 1973, I attended a ceremony in the Sheldonian Theatre, in Latin, much foreshortened from the original, during which my degree was conferred. A ceremony designed over centuries to give its recipients the indelible impression: you have done it! I had done it! I felt it and they’d said it in Latin! After the ceremony, I went straight across the road in my academic dress to purchase a copy of Michael’s new book, on Frege’s philosophy of language. Michael had shown how to think about these matters in pellucid English prose.

I went right afterwards to the other side of the Northern Hemisphere, to Berkeley in California. Michael had helped me get there, for he had written me a recommendation for graduate school. I have no idea what he said, but I it can’t have been all disastrous. (I can imagine: “Ladkin is mortal and does OK for one. But I’m afraid I don’t really know much about mortals.”)

I was required at the end of my first year by Bill Craig, my advisor in Berkeley, he of Craig’s Interpolation Theorem, to take the qualifying exam in philosophy. I protested and threw tantrums and all that, but you know you can’t really rebel. Bill said “you will do it” so I did it. I read Michael’s book, and its seemingly impenetrable prose. And I read it again. And understood more. And again. And more. And again. It wasn’t that Michael’s prose was impenetrable. Michael wrote exactly what he was thinking and his thinking was non-trivial and exact. It took me a while to absorb his train of thought. His prose was, indeed, pellucid. When I had done so, I went into the exam room (actually the philosophy library) for six hours and wrote exactly what I thought about the matters about which I had learned from reading Michael’s book so carefully. Non-trivially and exactly. I think Ernie Adams graded the exam. I passed. Turns out I was the first student in the history of Tarski’s program to pass the philosophy exam in my first year. Thank you, Michael!

(You have to understand – I was rotten at written exams. I got so nervous I couldn’t even read the questions straight. It’s a miracle I ever got into and out of Oxford, at which assessment is based on a student’s brilliance at written exams.)

I saw Michael in Berkeley once. He gave an evening lecture which I attended. I did get to exchange a brief word, amongst all the others earnest to talk with him.

I saw him again in 2009, at the 40th anniversary reunion of Maths and Philosophy graduates in Oxford, of the course which he had done so much to establish, and to which I owe my subsequent career. Derek Goldrei was the First Graduate (he switched in his final year; graduating in 1969 when the course was established). I in 1973. I was one of only two or three from that era at the reunion and felt quite The Establishment. Michael was there, and Dana Scott. Michael was old and frail. Gave an endearing and well-constructed speech. When I approached him after the dinner, he didn’t remember who I was, but then so many had passed through the gate since I had. I simply thanked him. He accepted graciously.

Michael is gone, on 27 December 2011. For me, he was Philosophy. When he was with us, Philosophy was alive. Now he is gone, Philosophy is gone. Maybe not, but it sure feels like it. It turns out I seem to have assumed he was immortal. Apparently not. It is -let me say- hard for me to adjust.

Here is The Guardian’s take. The Times has a fine obituary, forwarded to me by Chris Miller, but it lies behind a paywall, just as now Michael does, though with a currency which I only wish I had. As an atheist without this currency, I can only say: God be with you, as you wished.

Some Coincidences.

Racism. Two of the killers of Stephen Lawrence were convicted in early January 2012. Here is a poem about it by Poet Laureate Carol Ann Duffy. Michael and his wife Ann devoted themselves to race relations in 1960′s and early 1970′s Britain, efforts well documented in the obituaries. He only returned to philosophical work after he felt the efforts to turn Britain away from racist habits had failed. But they haven’t failed, Michael, and neither had you.

Brains. Apparently some people claim now that our brains start to go downhill at age 45 It is not clear this is news: The Guardian had something about it 12 years ago. Michael published his first book at 48, and there followed many more, all of them worth reading very carefully indeed.

Note Added 11.01.2012

It’s not just philosophy. Thinking it over, there are three fundamental developments in technical elementary logic which I have kept coming back to throughout my career. Things which are simple, clear, brilliant, which increase one’s understanding almost instantly, and continually prove to be useful. One is Dana Scott’s Consequence Relations, a formulation of logics which, to me, turns out to be the most efficient way to perform formal deductions, the raw material of logic. I keep meaning to translate into LaTeX the mimeographed notes which Dana handed out almost 40 years ago now. Another is Saul Kripke’s possible-worlds semantics for normal modal logics, and his similar epistemic-worlds semantics for logics of belief and evidence, such as inference in intuitionistic mathematics, and the inferences of Pen Maddy’s “Second Philosopher”. I learnt these partly from Michael. The third is Michael’s and John Lemmon’s formal correspondence between the modal logics from S4 to S5 and the propositional logics between intuitionist and classical.

Second Note Added 11.01.2012

Timothy Williamson, Michael’s successor in the Wykeham chair of Logic (David Wiggins came between Michael and Tim), pointed me to a series of tributes in the New York Times Opinionator blog last week.