On the 5-point scale current in Estonia, and surely in nearby nations, and familiar to observers of the academic arrangements of the late, unlamented, Union of Soviet Socialist Republics (applying the easy and lax standards Kmo deploys in his grubby imaginary "Aleksandr Stepanovitsh Popovi nimeline sangarliku raadio instituut" (the "Alexandr Stepanovitch Popov Institute of Heroic Radio") and his grubby imaginary "Nikolai Ivanovitsh Lobatshevski nimeline sotsalitsliku matemaatika instituut" (the "Nicolai Ivanovich Lobachevsky Institute of Socialist Mathematics") - where, on the lax and easy grading philosophy of the twin Institutes, 1/5 is "epic fail", 2/5 is "failure not so disastrous as to be epic", 3'5 is "mediocre pass", 4.5 is "good", and 5/5 is "excellent"): 4/5. Justification: There was enough time to develop the relevant points to reasonable length.
UTC=20160705T0001Z/version 1.0.0: Kmo uploaded base version (and planned to upload in the ensuing four-hour interval, without formal documentation in this revision history, nonsubstantive revisions, as versions 1.0.1, 1.0.2, 1.0.3, ...) .
5. Practicalities of Triage: Research in a Catholic Setting
I recall now my metaphor, from 2016-06-14 (Part C of "Is Science Doomed?"), of Finland's breached 1939-through-1940 Mannerheim Line. Here (to recapitulate, and perhaps amplify slightly, the principal points) is what the breach will mean some two or three or four centuries from now:
- Governments, and with it those glittering public-money sinkholes which are today's universities, are corrupted and diminished.
- Today's institutional science, organized in part around the universities, and otherwise largely around such publicly funded megacentres as NASA and CERN, has collapsed.
What (I asked in introducing this metaphor from the Finnish military) must be our social priorities? I suggested that we must conserve a grasp less of particular scientific results than of scientific method. I suggested that in conserving that grasp, our emphasis must be less on preserving appreciation of the observe-hypothesize-deduce-test schema (however useful that schema might be in straightforward empirical work within medicine or agronomy) than on maintaining the hard-to-schematize drive for mathematical insight, at the profoundest levels of theory.
It will be admitted generally, both by the friends of Catholicism and by its critics, that the Church is liable to persist in some form or other. It is in part up to us Catholics, over the next two or three or four generations, to determine in our dizzying ethical freedom what that form is going to be.
I arguably wrote too hastily a few weeks ago (late in May, as "(Part D) Islands in a Time of Civilizational Decline: Conclusions") about the Vatican's conceivable waning New-Dark-Ages prestige:
/.../ in Continental Europe there will be, in direct imitation of the European Dark Ages we already know, the foot travellers, patiently bearing little packets of mission-critical things - radio parts, books, blueprints (even on microfilm?), lenses, vaccines, seeds - from one cultural outpost to another. Their small satchels will perhaps be embossed with heraldic bearings of institutions still capable, through their lingering cultural prestige, of inspiring deference among local warlords. One imagines, perhaps, one military checkpoint conceding free passage to a foot-courier whose small satchel is embossed with the crest of some United Nations agency, and some other checkpoint equally cheerfully waving through a courier whose stout packet twine is secured by beeswax under Vatican seal.
It might be that things stay with the Vatican pretty much as they are now, or even (contrary to what I arguably intimated in the just-quoted passage from "Islands") that its current diplomatic profile improves. We might be going to get a Church which is inward-looking, defensive, politically and culturally reactionary, and in its diplomatic tone gratingly triumphalist. We might (many of us hope for this) be going to get instead a Church which is politically cheerful, culturally outgoing, and in its diplomatic work humble. This would be a Church continuing to express itself in the happy tones of John XXIII and Pope Francis.
With the survival (in some form) of the Church will come a survival (in some form) of Catholic research institutions. We can get some idea of what this might mean by examining the recent and current Church.
(1) As overviews (I have only glanced at these), we have https://en.wikipedia.org/wiki/List_of_Catholic_scientists, https://en.wikipedia.org/wiki/List_of_Roman_Catholic_cleric-scientists, and https://en.wikipedia.org/wiki/List_of_Jesuit_scientists.
(2) From the years immediately following Einstein's promulgation of General Relativity, there is a bold theoretical achievement - the first formulation of Big Bang cosmology, by the Leuven (Louvain) mathematical physicist Fr Georges Henri Joseph Édouard Lemaître (1894-1966).
(3) In observational astronomy, there are the ongoing traditions of the Vatican Observatory, juridically based on an 1891 Motu proprio of Leo XIII. The Vatican Observatory, with its Vatican Observatory Research Group (VORG), is now anchored not only in the light-polluted environment of Castel Gandolfo, but also in duly dark Arizona. Although I know little of the theoretical side of the Observatory, I do note that its Fr Michał Kazimierz Heller is prominent there in cosmology, as a worker at the problematic interface of General Relativity with quantics. The Observatory has also the "Pope Scope", an (innovative) spun-cast reflector in the (modest) 2-metre class. Working at the observational side of the institution is one of my most significant priest-friends, a specialist in the chemically peculiar (because metals-poor) "lambda Bootis" stars.
Above all, (4) we have the Pontifical Academy of Sciences, with a general, by no means exclusively Catholic, membership. The remit of the Academy is summed up by John Paul II in an address (as excerpted at https://en.wikipedia.org/wiki/Pontifical_Academy_of_Sciences) marking Einstein's centenary:
The existence of this Pontifical Academy of Sciences, of which in its ancient ancestry Galileo was a member and of which today eminent scientists are members, without any form of ethnic or religious discrimination, is a visible sign, raised amongst the peoples of the world, of the profound harmony that can exist between the truths of science and the truths of faith /.../ The Church of Rome together with all the Churches spread throughout the world attributes a great importance to the function of the Pontifical Academy of Sciences. The title of 'Pontifical' given to the Academy means, as you know, the interest and the commitment of the Church, in different forms from the ancient patronage, but no less profound and effective in character /.../ How could the Church have lacked interest in the most noble of the occupations which are most strictly human – the search for truth?
My guess is that as the New Dark Ages deepen, there will continue to be a stubborn little contingent of people intent on maths and physics, both within the formally Catholic world and outside it. Very well, these people will say: if we cannot find refuge in the declining universities, let us see what the Vatican can do for us. I guess further that the Pontifical Academy, or some descendant thereof, will do what it can, with admittedly limited resources. We may fervently hope that the support is determined, in that remote future epoch as at present, by the pertinent workers' individual levels of scientific attainment, rather than by their formal religious-denominational affiliations.
6. Practicalities of Triage: Education in a Catholic Setting
With the Church surviving, in some less or more happy form, there is bound also to be some less or more happy survival of Catholic education.
The one significant Catholic tertiary institution I know personally, from a year's residence, is Indiana's University of Notre Dame. But it is all too easy to imagine this excellent school, for all its virtue, going the way of the (largely doomed) formally secular universities once funding dries up. We may well predict Notre Dame, if surviving at all in the general institutional carnage, to be surviving in the service of some emerging Dark Ages elite. (The rulers will end up being the - more or less miserly - paymasters, being perhaps themselves in various instances Notre Dame alumni, or for reasons of tribal status being anxious to enroll their offspring, even if dim, at Notre Dame.) There will perhaps be some courses in "Media Studies" or something. There will perhaps also be some prudent attention to topics of special warlord interest, such as agronomic project management and military engineering. It may be that the few surviving formally Catholic universities, in our own day perilously embedded in the twin empires of Power and Mammon, can in the remoter future aspire to maths and physics only in a Potemkin-village, or in Italian terms a bella figura, sense. Standards might even get judiciously lowered, allowing the dimmer scions of the elite to pass with "physics degrees" after doing relatively little work.
Real intellectual life will perhaps retreat in two directions - on the one hand, to the monasteries (in all historical epochs a natural home for exact scholarship in the humanities - for instance in Biblical, Graeco-Roman, classical-Oriental, and modern philology - but in the light at least of evolved historical traditions and mores and habits a less natural home for maths and physics), and on the other hand to something like today's fringe-market, poorly endowed, tough and no-frills, Catholic "colleges" or "academies".
I have studied via the Internet, and have also tenuous personal links or links-to-links with, two institutions on this fringe. One, Wyoming Catholic College, has Web outreach at http://www.wyomingcatholiccollege.com. The other, Our Lady Seat of Wisdom, uses http://www.seatofwisdom.org. How strong is present-day maths-and-physics research and teaching at these two tertiary institutions?
It seems to me - though I am happy to be corrected here by blog commenters, in the framework of my stated blog-moderation policy (I eschew censorship) - that neither school is at present maths-and-physics strong. Their academic emphasis, it seems to me, is overwhelmingly on humanities, with theology and literature prominent, and with Latin specially emphasized on the philological side.
The perhaps mathematics-stronger of the two schools, Our Lady Seat of Wisdom, proclaims that its students eventually reach the Fundamental Theorem of Calculus. In the late, unlamented, USSR, calculus started at the secondary, not at the tertiary, level, and indeed started in the equivalent of Grade Nine or so. Further, the Fundamental Theorem has to come early, not late, in any reasonably comprehensive calculus presentation, even in the restricted domain of univariate real functions. So one looks at this particular glad proclamation, and one thinks: Gee whiz.
But in generations to come, things may change.
In the remainder of this essay, I picture a possible line of development. Without having (at any rate, as yet) visited the OLSW campus, I nevertheless picture a Way Things Might Be, perhaps a couple of centuries from now.
How could it not survive, being so healthily rooted in the rich soil of Ontario's twentieth-century monastic, or at any rate paramonastic, Madonna House movement, and moreover having had to fight hard for survival in its formative early years?
But down the road from OLSW is now the Other Place, founded maybe in 2070 or 2100 or 2120 or something. This is an institution, numbering in all perhaps fifty faculty and staff and students, whose name I cannot even (writing, as I am, in 2016) discern.
Students and faculty of the Other Place maintain a rather close, and at the same time a rather uneasy, relationship with OLSW. The relationship is marked by mutual condescension at the professorial-decanal level, and at the level of the "Junior Members" by many a furious engagement of skates and pads and stick and puck.
Students move back and forth (as I will now explain) along the quiet little linking road.
The general decanal feeling at OLSW is that a so-called "Breadth Requirement" "is a Good Thing, and ought to be kept". So OLSW students, in some instances rather against their will, do small numbers of Other Place courses. One such course, admittedly, is unequivocally popular: everyone loves astronomy, and the Other Place accordingly lays on (following the usual traditions of, for instance, the 2016-era University of Toronto) a mathematically undemanding "Astronomy for Poets". Here people get rather respectable all-night practicums on a modest 0.6-metre equatorially mounted reflector. Timings, in particular, of Algol-like binaries get made to a good level of precision, and circulate far beyond Ontario. So to this extent, at least, students not from the Other Place alone, but also from OLSW, get to do something hands-on.
Students at the Other Place are, like all students of maths and physics in all eras, worked too hard to think about much of anything beyond Chapel, their science studies, their meals, and the rink. Nevertheless, Other Place deans consider it "a Good Thing, which ought to be kept" that all their students get sent over to OLSW every few days for hard, uncompromising Latin - the poets, and Cicero as stylistically normative, and perhaps also one other duly tough prose author. (The normal decanal consensus is that that lively PBS-and-National-Geographic of the ancients, Caesar's de Bello Gallico, provides an insufficient workout.) The decanal reasoning here is that however little time a demanding curriculum might spare for humanities, Latin (when taken seriously) is at any rate a key that unlocks doors for people in later life, perhaps long after their graduation. Italian (if needed) will prove easy, even years down the road. Ancient history will be at all stages in life appealing as a field for private reading. Roman law (a helpful backgrounder in a possible eventual foray into public affairs, as might happen long after graduation) will prove surprisingly accessible.
And some hardy students do embark, in the spirit of the Victorian British statesman-savant Gladstone, on Double Degrees, under a mutual arrangement between OLSW and the Other Place that gets them trotting up and down that road ten or twenty times a week.
Whatever may be the case at OLSW, at the Other Place there is a sharp, healthy division between the twin functions of teaching and examining. At the Other Place teaching, and only teaching, is the order of the day - endless, grinding, work, seeking to master everything in its deepest theoretic essentials, in anticipation of the multi-day, probing, External Examination.
How does that end-of-studies External work? We may imagine that somewhere, perhaps well outside present-day Canada, are small, prestigious, and in some measure competing, examination boards - one at the Pontifical Academy, a couple of others under the wings of prestige-hungry warlords in erstwhile New England or the erstwhile Midwest, another under the wing of the surviving Royal Society, in whatever replaces now-drowned London.
When you and your Ontario teachers are confident of your ability to at least pass, you get in touch with an Examining Board.
Maybe it works like this, that if you are not terribly ambitious, you shoot only for the "Chicago Finals in General Mathematical Physics". Some Chicago institution couriers out to the Other Place, under seal, packets with examination questions and write-in booklets. You then write up your "Finals" under the supervision of your local Justice of the Peace or constable, under warrant (the cop-shop might be a particularly good place to do the writing). After ten days' supervised, i.e., invigilated, hard labour you courier your booklets back to Chicago, and eventually Chicago gives you something for your curriculum vitae - a certificate showing, as it might be, First Class Honours, Second Class Honours, Third Class Honours, or at worst Pass.
We may also piously hope that a few high fliers from the Other Place go for something more prestigious, for instance for the "Sankt Peterburg Baccalaureate Finals in Applied Mathematics, with Specialization in Tensor Methods, Electromagnetic Field Theory, and Special and General Relativity". In this case, you make the slow, weary rail journey from the Madawaska Valley over to Ottawa, and then on with a faster train to the Montréal docks. From there, it is two weeks in a cut-rate third-class berth to Europe (the ticket might come out of a diocesan bursary), followed by an eventual fortnight of grilling, face to face, by whatever body of German-and-Russian savants may in the remote future have taken the place of today's Dr Grigori Perelman.
On my proposed separation of teaching and examining, faculty at the Other Place become the natural allies of their students, united with them against that common foe which is the External Examiner. The arrangement is the same as what I remember working well in 1970s Oxford. As I vividly remember it, the colleges organized the undergraduate teaching, making their very best endeavour in the face of the common enemy which was the remote, magisterial, University-appointed examining committee.
Colleges competed with one another for the best examination results, getting ranked in the notorious "Norrington Table". There came a year in which my own college, St John's, did particularly badly. The President summoned all undergraduates to a special harangue in Hall, which I observed from the elevated gallery (in company with a few other graduate students, plus the crusty Austrian University Professor of Engineering, Mott). It was a good show - "Prezzy" (a mediaevalist of the highest eminence) said, in his trademark slight lisp, with reference to a notoriously weak college, always way down in the Norrington rankings, "And now we are gwovveling in the dust, beside Teddy Hall." "Prezzy" at Harangue Time attained full oratorial flight, to the level of Hollywood: sunlight slanted in from the huge old windows, as he gestured in his harangue to dim, huge, brown oils, hanging above High Table, depicting his distinguished forebears in Presidential office: "My PWEEdecessor, William Laud..." The next year our Norrington Table standing was fine, being just below the eminent Merton College.
Kadri's tutor, at St Anne's, had said, "Don't worry, Kadri, you are bound to get a nice, solid Second." On the strength of this carefully coded assurance, Kadri had disappeared, I believe with the usual backpack, to some Greek island, I presume on some cheap flight. But then the examiners summoned Kadri for a Viva. (They had picked up hints of special insight from what she had written in her pile of booklets, and had accordingly feared they might have to grant her a First.) There was at this point complete panic in Oxford, with Kadri's tutor even coming round to my room for tea and parley. The two of us found ourselves liaising with the helpless local city-of-Oxford press, and with the Athenian police (I tried in vain to communicate, ineptly using classical Greek on the long-distance phone with them, since they proved to lack English), and with the Foreign and Commonwealth Office, and with the external-broadcasting arm of the BBC. In the end, Kadri never did get tracked down on her Greek island. So her degree had to be, alas, a Second. She later went on to other, academically more distinguished, things, eventually entering the North American professoriate in a subject other than the one in which Oxford had examined her.
There was of course none of the silly North American hair-splitting, with "A" versus "A minus", "B" versus "B plus", all eventually enshrined in that triumph of pointless academic bureaucracy, the "transcript". As in the USSR there was nothing but the sensible "5, 4, 3" (for progressively less respectable types of pass) and "2, 1" (for mild fail and epic fail, respectively), so Oxford had just "First", "Upper Second", "Lower Second", and the seldom-awarded "Third" - or perhaps just these, plus the almost-unheard-of "Pass". I think the unspoken theory was that if your Tutor for Admissions let you come up to college at all, it was unthinkable that you could then fail, except through doing something creatively unusual, like (I am making this up) taking your summer backpack to Palermo, and thereupon drifting into the Cosa Nostra, to the detriment of your ability to find the time for working through assigned vacation reading lists.
If the examiners in their attempt to categorize everyone accurately were unsure into which of their broad pigeonholes you belonged, you got called back from your place of summer habitation for a viva voce interview.
A dreadful little story of an undergraduate from my college: the unwelcome "Viva", in this case in Eng. Lit., in this case probably to decide between Lower Second and mere Third. "Mr X," asked the committee (I think I am recalling their question more or less accurately), "What would you say if we asked you to compare Beowulf with Sir Gawain from the romance of the Green Knight?" - Mr X.: "Well, I should consider this comparison absurd, and would decline to make it." - Committee (trying to be nice): "Well, Mr X, we really would like you to attempt the comparison." - Mr X (being a bit slow on the uptake): "I would decline." - Committee (still trying to be nice): "Well, Mr X, we don't think you quite understand here - we are actually now asking you to make the comparison." - Mr X (I think panic might explain this, partly): "Well, I decline."
I also have another dreadful little story, regarding the other known diaspora Estonian present in the academic year 1974-1975. (There seem to have been just the two of us then, at any rate with fluent Estonian. I think Ontario physicist, and eventual friend, Aadu Pilt came later.)
The degree lists were published, as worthy national news, in The Times, the idea presumably being that people in Number Ten and Buck House and Lambeth Palace and the like could satisfy their curiosity regarding the progress of everyone in the given cohort of Examinations victims, Mr X and Kadri included.
If administered with decanal flair, so that individual teachers do not wither under excessive tutorial loads, this arrangement can - Oxford, and the more eminent Cambridge, demonstrate the possibilities - produce also a good tradition in intramural research, on the part of the teachers, and perhaps in the future we are here contemplating even on the part of teachers collaborating scientifically with their Sankt-Peterburg-bound students.
I now come to the end of all that I can easily write about the prospects for keeping science alive in our impending Dark Ages. It remains to wind things up a little abruptly, filling in the last few necessary details by picturing what physical plant might prove feasible and appropriate at the Other Place, as the Dark Ages deepen.
First in this discussion, we have the lab suites. What, in a Dark Age in which even air transport is beyond the means of ordinary people, and when NASA and CERN are a distant folk memory, is the little that can now be aimed at?
We may imagine Other Place students being urged, encouraged, and by sheer force of profs and deans dragged (where necessary) into working with their hands. Whatever may have been the case for physics students in the luxuriously funded late 20th century, now everyone in physics has to be able to make a shop drawing, and to machine a part in at any rate some of the easier metals, and to blow glass, and to supervise the perhaps 1.25 fulltime-equivalent technicians that the school will be able to employ, at some poor wage, in experiment-supporting roles.
So things at the Other Place look less like the 2016 University of Toronto than the Cavendish Laboratory of, say, 1876, under the direction of its first head, James Clerk Maxwell. We may piously hope that with the Other Place having just two or three dozen students, it will prove possible for everyone to get her or his own two-metre stretch of bench in the lab suites, for permanent occupation through his or her entire course of studies.
Computers? Although there will surely be something, we should here think more along the lines of the locally constructed Cambridge EDSAC 1 (its first good test run, yielding a short table of squares-of-integers, was in 1949) than along the lines of the 2016 University of Toronto. Perhaps there will be a "Computer Suite", just off the laboratory rooms, housing one bulky machine. The RAM might run to a few kilobytes. If luck is against us, then we may find those hot and tall racks housing not integrated circuits, and not even printed-circuit boards with individual transistors, but balky assemblages of valves, in true EDSAC 1 style. Perhaps programming will subside from the elegant extravagances of object-oriented languages to a level even lower than the 1960s FORTRAN compilers - all the way down to 1950s "Assembler".
But of course, computers are in this era used for physics and applied maths, not for playing games - at any rate so far as profs and deans ever find out.
Some steps away from the laboratory suite we note correct study arrangements, more in spirit of Victorian Oxbridge than of today's University of Toronto. The correct arrangements are (surely) the following:
- Everyone who asks for it is given, upon the first day of coming up to the Other Place, a tiny personal office, narrow and silent, with basic chair and table and lamp, on a corridor along which conversation and music are forbidden. The office is retained until the day of final departure.
- Everyone is additionally encouraged to build, with his or her own hands, in the workshops under the laboratory suite, any additional office furnishings needed - notably, any needed pigeonholes or shelving.
At the heart of the Other Place is that little gem which is its library - its vases of dried or fresh flowers, its hand-hooked rugs on maple flooring, its hand-crafted furniture standing in pleasantly sharp contrast to the penal austerity prevailing everywhere else in the Place, bar the Chapel.
Here we have perhaps just a few thousand volumes, most of them from the maths-and-physics classics. Checking quantics, we find among other things Cohen-Tannoudji, or whatever still more thorough classic may be this remote future have displaced it. Checking introductory physics, we find Feynman's three volumes of lectures (perhaps, in their transcendent depth, unlikely ever to be displaced from the canon). There will be something like the A.P. French (et al.) series of physics primers from Kennedy-era MIT, notable for their careful discussion not just of what is known but of how it came, in part at key points in the lab, to be known.
And I do hope that upon checking multivariate real analysis we find Spivak's (dreaded, I do admit) Calculus on Manifolds.
We may further hope to find some modest selection of works in Russian and German - languages in which some training will perhaps be imparted at OLSW, for suitable fees, at any rate for the ambitious few aspiring to Externals in Europe, as opposed to Externals in the former New England USA or former Midwest USA. In particular, we may hope to find a work which I am reliably informed was a staple of USSR mathematical training, and which inexplicably has not yet (as of 2016) been translated into English: the three-volume analysis course of Grigorii Mikhailovich Fichtenholz (or Fikhtengolts; rigorously, Фихтенгольц).
For much of the day and night, the library is only sporadically used, with some prof or student emerging from private office for a few minutes to check some small, mission-critical, point. But things do liven up every afternoon at four, in the tradition of the best 2016-era Cambridge University labs, when the ten or so members of faculty gather with "Prezzy" and a couple of his deans, and perhaps some suddenly relevant "Junior Member" or two, over tea. At this informal gathering, they will seek less to bemoan their students than to compare results in their various respective lines of (largely theory-driven, fundamental) research.
I like to picture it thus, that a brisk little fire of Ontario hardwoods burns in the little Rumford grate as the Earl Grey is handed round, and the conversation turns to some new difficulty for the Bohr Interpretation in quantics.
I additionally like to picture it thus, that over the fireplace is some scowling black-and-white photographic portrait - possibly of Einstein or Maxwell, but equally possibly of some Grigori Yakovlevich Perelman from our own times, or of some Grigorii Mikhailovich Fichtenholz from the recent Soviet past. This is, at any rate, the portrait of some major worker in the vineyard in which the Other Place is in its minor way engaged, the portrait of someone embodying Einstein's mentor-guide as "consoling, strengthening, and yet implacably severe" - as I quoted the adolescent Einstein at the beginning of this essay, versöhnend, stärkend und doch unerbitterlich streng.
[This concludes the "Is Science Doomed?" essay. I had hoped to wind up with a good quote from Dorothy Day, but could not in the event run down the relevant passage in her Loaves and Fishes collection. Soon - perhaps even next week - I shall have to turn to plebian points pertaining to my own work, above all to a discussion of the need I have found to close the books and work things out on my own, with much tedious deployment of black, blue, green, and red pencils, and with much erasing - in other words with much that, being humiliating, is stärkend und doch streng.]