Monday, 30 May 2016

Toomas Karmo: (Part A) Is Science Doomed?

Quality assessment:

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"): 3/5. Justification: There was enough time to develop some points to some  reasonable length, and yet not enough time to open up the number of points required by real thoroughness.

Revision history:

  • UTC=20160531T1723Z/version 1.1.1: Kmo belaboured the proof a little more, adding a remark about mappings. He additionally  left open the possibility of making very minor here-undocumented tweaks, in the style "1.1.2", "1.1.3", 1.1.4", in the English of this essay as opposed to its maths, over coming hours, days, weeks, ... .  
  • UTC=20160531T1713Z/version 1.1.0: Kmo, having originally felt it best not to belabour the proof that the set of sets of positive integers is of a higher order of infinity than that simpler thing which is the set of positive integers, changed his mind, and added a few belabouring sentences. 
  • UTC=20160531T0001Z/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, ... . Version 1.0.0, although substantively correct, was in many details unpolished. Rrepairs were impending over the one or  two hours following 20160531T0001Z. 

[CAUTION: A bug in the blogger software has shown a propensity to insert inappropriate whitespace at some late points in some of my posted essays. If a screen seems to end in empty space, keep scrolling down. The end of the posting is not reached until the usual blogger "Posted by Toomas (Tom) Karmo at" appears.]

1. Einstein as a votary of Truth

Because I spend easily half my (painfully not-for-pay) working week at my desk, I have developed several of its features with care. 

Over the wooden top I have placed a sheet of bevelled glass, custom-cut for me maybe twenty years ago by some Toronto firm. 

On this glass, a row of ten-sided white dice, engraved not with dots but with the numerals 0 through 9, indicates the current year, month, and date, in numerical format. At the time I started writing this present essay, the dice were arranged thus: 2, 0, 1, 6; and then a gap, and then 0, 5; and then a second gap; and then 3, 0. 

Over the desk is a wooden hutch, comprising twenty-four pigeonholes, elevated by wooden legs a little less than 0.4 metres high. (I had this built for me upon reading the wonderful 1982 book, Tools of the Mind: Techniques and Methods for Intellectual Work, by sometime Phillips engineer Vladimir Stibic.) Each pigeonhole is capable of taking, uncurled, several hundred letter-sized sheets. Or, more realistically, each is capable of taking many tens of such sheets, in half a dozen filing folders, uncurled.

Under the hutch, a forty-watt fluorescent tube, its colour balanced for greenhouse operations (the ordinary fluorescent white is rather too harsh) provides a strong illumination for the writing surface. While avoiding factory or airport fluorescent-tube harshness, the light is admittedly in its own way a bit odd, like high noon on the planet not of a star like our Sun - our Sun is technically in the temperature class "G2" - but in some cooler temperature class. As I loosely imagine it, there is here, if not the deeply alarming  red glow of an "M" star, at any rate light from a rosy, subtly disquieting, "K" star. To balance this, however, I have a small twenty-watt desk lamp, with halogen bulb. The specially hot filament of that high-technology bulb emits a light which is indeed close to the more yellow, and to human eyes familiar, G2 stellar class. 

Facing me as I look under the hutch is a big, nearly vertical, notice-board panel of cork, or perhaps of some cork ersatz. This panel is around 1.3 metres wide. It runs all the way up from the desk glass to the lowest tier of pigeonholes. 

On the notice board, bathed in the K-star glow, are half a dozen inspirational papers, the majority of which I will describe here. 

Toward the right edge my drawing pins anchor a postcard, showing the Tartu Observatory tower from which F.G.W. von Struve laid foundations for the cataloguing of binary stars.

Struve taught at Tartu University, or in its Czarist appellation the Universitas Dorpatiensis, from 1813 until his 1839 move out of Estonia to the nascent Pulkovo observatory. I believe Struve's principal contribution in stellar binaries to be a catalogue entitled Stellarum duplicium et multiplicium mensurae micrometricae, comprising micrometric measurements of 2174 systems over the period from 1824 to 1837.

I gather that the "filar micrometer", now superseded by electronic methods, was tedious: as you fought sleep and cold, possibly perched on a ladder, you had to transfix the infuriating, boiling, puddles of light which are stars in a poor atmosphere under high magnification with thin, sinister lines of spider silk. You had to rotate one or two things until everything looked exactly right amid the shimmering, and then had to read off separation and position angle from graduated scales on or near the micrometer barrel.

Do this often enough for one single, adequately fast-moving, binary system - say, twenty times over fifteen years, if the orbital period is itself ten or twenty or thirty years - and you can after a lot of desk mathematics determine the ratio of the masses of the two stars.

If you can additionally get a distance measurement for your two-star system, and if you have from some reliable worker's Cavendish torsion balance a reliable measurement of the Universal Gravitational Constant, you can get also the individual masses of each of the two stars (in, for instance, kilograms).

The distance measurement you can have from semiannual parallax comparisons - in which Struve was also among the pioneers  - coupled with a knowledge of the Sun-earth distance.

It is at this point, with kilogram determinations for each of the two stars in hand, fair to say that your desk has sailed over the boundary from mere Astronomy - silly, fluffy, purely phenomenological "So what is this angle on the celestial sphere?" Astronomy - to the solid domain of Astrophysics. 

To the left of the postcard, my drawing pins anchor a couple of papers from Cambridge University. There is a 20-year old sheet, headed "The Institute: Past and Present" (a visitor's introduction to the Institute of Astronomy, said to be on the Madingley Road: this has, then, to be some modest distance away from the Mathematical Bridge, Trinity Great Quad, and the other celebrated Cambridge sights). Adjoining it is a sheet of similar age and provenance, which has long been admonishing me, as a reminder of what can be achieved by those who work hard: 



For over 60 years , the Faculty
of Mathematics has run a one-year
advanced programme called
Part III of the Mathematical Tripos.
This provides graduates with the
further training
and knowledge needed for original research. /.../

Over 100 students are admitted
each year. To join them, request
further information from /.../

At the left edge of the notice board, affixed to a clean letter-sized white sheet, is the heavily yellowed obituary of my 1970 Dalhousie University teacher Prof. Max Edelstein, by his daughter, British Columbia mathematician Leah Keshet ("LIVES LIVED: Michael Edelstein", from the Toronto Globe and Mail of 2003-02-07).

Prof. Keshet has for her part, in an act of extraordinary kindness, sent me two books from her distinguished father's personal library. Those books, however, live not by the desk in my big writing-and-sleeping  room, but some metres away, in my compact book-lined "library room".  

Additionally - and this is what I want at present specially to stress - since some point in 2016, there is a sheet with, among other material, a quotation from Albert Einstein. In a letter of 1897, Einstein, then aged about eighteen, wrote as follows: 

Die anstrengte geistige Arbeit 
und das Anschauen Gottes Natur  
sind die Engel, welche mich 
versöhnend, stärkend und doch unerbitterlch streng
durch die Wirren dieses Lebens führen werden.

Under this I have also placed - I conveyed this same material to a child for whose intellectual welfare I am in some measure responsible, and to whom I will return in this essay - my translations, into Estonian (which he does not read) and English (which he does read): 

Pingeline vaimne töö ja Jumala looduse vaatlemine
on need inglid kes, trööstitavad, julgustandvad,
kuid tagasiastumatult karmid, saavad olema
minu teejuhtideks läbi selle elu kära.

Strenuous intellectual labour
and the contemplation of God's Nature
are the angels which, consoling, 
strengthening, and yet implacably severe, 
are going to lead me through the tumult of this life. 


If the life of Mohandas Gandhi is a witness to Justice, then the life of Prof. Albert Einstein is a witness to Truth. 

While barely a university graduate, and at that early point by no means a prof, Einstein deduced Special Relativity from conceptual puzzles regarding moving electrically charged bodies.

It is astonishing that none of the profs before him had worked the (glaring) conceptual puzzles thoroughly, but that's how it is. One can see that there must be something deep, somewhere, and I am surprised that high academic authorities before Einstein's day were relaxed and mellow: since a charge moving through the rest frame of the laboratory is embedded in a magnetic field, and since that field is absent in the rest frame of the charge itself - the laboratory whizzes past, and the sole field is electrostatic- the very question whether a magnetic field is present must be relative to choice of frame. In the end, it turns out - Einstein got this clear, along with the length-contraction and time-dilation results for which Special Relativity is more loudly celebrated - that magnetic "forces" are not a fundamental kind of force.

And I rather think, though I have not worked through it or looked it up, that the celebrated null result of the Michelson-Morley experiment, viz., that the speed of light, in contrast with the speeds of bullets and arrows, is independent of source motions and target motions, was worked out a priori by Einstein at this same epoch. Incredibly (so, I think the maths goes, though I think it subject to correction): when you ponder, you find that the speed of light has to be constant if other very basic accepted facts, mere truisms, are to remain true.

If I am right on this, then Michelson-Morley, hailed on television programmes as a key experiment, takes on merely the aspect of a lab confirmation for something proved with pencil and paper on a foundation of lab truisms. (It is still, of course, still necessary to do the Michelson-Morley experiment. But I reiterate that the experiment becomes now a simple  precaution against some oversight in what was key, the pencil-and-paper part.)

If I am right, then the Michelson-Morley history must be a vindication of the overriding importance of mathematics - a theme which I will be developing further, later in this essay. 

In middle age, Einstein extended Special Relativity to General Relativity, explaining the force of gravity (in stark contrast, it must be added, with the other three fundamental physical forces) as a mere deformation in local spacetime geometry.  

And still later, he expended years, ultimately decades, in a heroically failed quest for a Unified Field Theory. 

2. Cultural despair:
(a) gales of unreason;  (b) the "Peak Science" fear

Einstein's witness provides a beacon by which to steer as our cultural darkness deepens. I have remarked in my "Life's Business" essay at, but will here remark again (adapting two key paragraphs) that even in this relatively early stage in the oppression of science, the "sinister gales of Unreason" blow strong: 

(a) Of the tiny handful of young people that David Dunlap Observatory stellar spectroscopist Prof. Robert Garrison and I used to be mentoring together, fully two suggested to me that NASA could have faked the moon landings. And I have heard the same from at least one, perhaps two, members of the general public. Much can be forgiven the general public, addled as it is by a diet of television infotainment. Students from the science departments, however, are a more serious matter, since much is given them by their universities, and correspondingly much is expected. If a third science-anchored student some day comes up with the suggestion of a NASA hoax, I should first remark, politely, that Prof. Garrison is himself an author of a paper on NASA Apollo rock samples, and then politely ask by what concrete mechanisms the student believes so respected a prof got duped. 

(b) I keep reading that there are people who believe the universe to be a mere six thousand years old. Such allegations have even swirled recently, I think without plausible denial from the relevant quarters, around a former Canadian federal party leader, somewhat antedating Mr Stephen Harper's circle. If I were to meet such a person, I would ask, politely, what we are seeing when we examine M31, the Andromeda Galaxy, an easy object for binoculars, with progressively better telescopes. With a sharply imaging ground-based telescope rejoicing in an aperture of 3 or 5 or 8 metres, M31 looks like a pancake of occasionally resolved stars rather than a simple gaseous nebula. It indeed looks like a pancake of stars similar to our own Milky Way galaxy. However, a pancake of Milky Way dimensions, and yet of the observed M31 angular extent, has to be so far away that it takes light not six thousand but hundreds of thousands or thousands of thousands of years to reach our eyes. That fuzzy distance conjecture is sharpened to a value of 2.7 million light years (Gieren et al., 2013) by apparent-brightness measurements of Cepheid variable stars in M31, whose intrinsic brightnesses the professionals believe they know well from studies of more local Cepheids.

Of course there are also compelling reasons for thinking we see in light, and "hear" in radio, objects two thousand or four thousand times farther away than M31. 

And other examples abound. Leaving today's David Dunlap Observatory heritage-conservation fiasco temporarily aside, I here merely select, rather randomly, a pair of further examples, out of a wide field. The first involves a Good Guy (speaking for scientific truth, in the teeth of corporate power), the second a guy not so good: 

  • Dr David Healy - as a whistleblower whose stance on Prozac cannot have been comfortable to manufacturer Eli Lily, and whose University of Toronto appointment got revoked in 2000, under controverted circumstances (one of the University's medical arms was a recipient of Eli Lily funding); 
  • Mr Donald Trump - as a commenter on climate science (this politician, in fact would-be world leader, is on Twitter record as saying "The concept of global warming was created by and for the Chinese in order to make U.S. manufacturing non-competitive")


Even apart from the gales of Unreason, we have to note a kind of cultural despair - a kind of pervasive suggestion that science, having risen so high, now has nowhere to go but down. 

How, it might be argued (indeed a friend argued this for me over tea less than a month ago) is continued substantive progress in astrophysics possible? Surely we are at, or are approaching, the age of Peak Observatories, in which it becomes harder and harder to fund the first-rank telescopes - the behemoths with five or more times the now-modest aperture of the 1935 David Dunlap Observatory 1.88-metre reflector? Surely we cannot, in this age of growing economic turmoil, with NASA more and more under the axe, hope for further "Great Observatories", significantly extending the capabilities of the Hubble, Compton, Chandra, and Spitzer missions? 

The argument is put forcibly by humanist, neo-pagan theologian, and social critic John Michael Greer, in his 2014-11-26 blog posting "Dark Age America: The Suicide of Science", at

/.../ the grand designs of intellectuals in a mature society normally presuppose access to the kind and scale of resources that such a society supplies to its more privileged inmates. When the resource needs of an intellectual project can no longer be met, it doesn’t matter how useful it would be if it could be pursued further, much less how closely aligned it might happen to be to somebody’s notion of the meaning and purpose of human existence.

Furthermore, as a society begins its one-way trip down the steep and slippery chute labeled “Decline and Fall,” and its ability to find and distribute resources starts to falter, its priorities necessarily shift. Triage becomes the order of the day, and projects that might ordinarily get funding end up  out of luck so that more immediate needs can get as much of the available resource base as possible. A society’s core intellectual projects tend to face this fate a good deal sooner than other, more pragmatic concerns; when the barbarians are at the gates, one might say, funds that might otherwise be used to pay for schools of philosophy tend to get spent hiring soldiers instead.

Modern science, the core intellectual project of the contemporary industrial world, and technological complexification, its core cultural project, are as subject to these same two vulnerabilities as were the corresponding projects of other civilizations. Yes, I’m aware that this is a controversial claim, but I’d argue that it follows necessarily from the nature of both projects. Scientific research, like most things in life, is subject to the law of diminishing returns; what this means in practice is that the more research has been done in any field, the greater an investment is needed on average to make the next round of discoveries. Consider the difference between the absurdly cheap hardware that was used in the late 19th century to detect the electron and the fantastically expensive facility that had to be built to detect the Higgs boson; that’s the sort of shift in the cost-benefit ratio of research that I have in mind.

A civilization with ample resources and a thriving economy can afford to ignore the rising cost of research, and gamble that new discoveries will be valuable enough to cover the costs. A civilization facing resource shortages and economic contraction can’t. If the cost of new discoveries in particle physics continues to rise along the same curve that gave us the Higgs boson’s multibillion-Euro price tag, for example, the next round of experiments, or the one after that, could easily rise to the point that in an era of resource depletion, economic turmoil, and environmental payback, no consortium of nations on the planet will be able to spare the resources for the project. Even if the resources could theoretically be spared, furthermore, there will be many other projects begging for them, and it’s far from certain that another round of research into particle physics would be the best available option.

3. The irrationality of proceeding
from "Peak Science" fears to general pessimism

The efficacy, in the world of physical science, of some kind of Law of Diminishing Returns, in some form or other, is incontestable. But I will now argue the illogicality of proceeding from this to a comprehensive pessimism. 

Consider, for a moment, not science but literature. Consider the standpoint of some hypothetical humantiies scholar taking stock of Greek and Latin authors, from the hot and dilapidated streets of Rome, in the summer of 430. (This was the summer in which Augustine of Hippo died.) Have we not, asks the hypothetical scholar, now attained Peak Literature? Have we not, in a millennium of intense effort, tried everything worth trying, in fully two languages? 

Epic? Been there, done that. First, in the magically archaic diction of that unknown poet, or succession of poets, that we in our ignorance simply call "Homer". Then, more than a half millennium later, in a startling adaptation of that diction to the sophisticated political milieu of our own initial Augustus, in the Aeneid

Stage tragedy? Been there, done that: Aeschylus, Euripides, Sophocles, in variation upon variation. And later, Seneca. 

Stage comedy? Yes, through Aristophanes, Plautus, and successors. 

Lyric poetry? Yes, in both languages. 

Prose? Yes: and even in radical forms, as with the Hippo bishop's searing first-person "Confessions". 

In future, says this hypothetical scholar, we can hope only for derivative and imitative works - say for a second Statius, as a second pale reflection of Virgilius. 

Is this hypothetical A.D. 430 pundit right?

What we have here, we moderns have to reply, is a failure of imagination. The possibilities even of epic are not exhausted by the Greek and Roman models. We see very different possible approaches upon reading, for instance, Beowulf. While Keats is for us moderns a writer not utterly unlike Catullus, nobody brought up on the hypothetical theorist's circa-430 restricted diet of Graeco-Latin lyric would find it easy to imagine Gerard Manley Hopkins. 

Analogously, then, I say, for science, including even the various branches of physics. Emerging limitations in technology mean only that some directions of scientific movement, out of an indeterminately vast ensemble of possible directions, are closed off.  At some point, whether in the next few years (this I personally find too pessimistic) or in the next few decades (as I personally believe), technology will stagnate, and even regress. It will at this point become impractical to fund telescopes with bigger apertures, or supercomputing clusters with more nodes, or particle accelerators with more beam power. Depending on how severe our political and social crises become, in an era of deepening fuel shortages and rising seas, we may indeed face either a moderate or a severe technological contraction. (For what it is worth, my personal hunch is that we are one or two or three decades into an overall stagnation - masked, however, by some continuing, decelerating, advances in cyber technology - and that a severe contraction impends some decades from now, in a setting of increasing sociopolitical turmoil.) 

Let us, then consider what happens when technology stagnates. To keep things simple, we consider a technological Steady State. But my argument can be modified, admittedly at the expense of clarity and vividness, to fit also the case of a technological decline, even (once my argument is developed in the imaginative spirit required by Humility in the face of the Unknown) a severe one. 

With telescope, computer, and particle-accelerator power frozen, what remains possible? 

The fundamental driver of physical science is not technology (important though technology is), but mathematical insight. The history of mathematics shows how things can change foundationally, even in offices equipped with nothing beyond paper and pencil. 

The record shows that already within traditional Euclidean three-dimensional geometry, startling things can emerge, for the creative. 

Consider, for example, a sphere, sitting in some immovable hemispherical cradle. We are free to move the sphere around in any way we please, twisting it this way and that - first rotating it, for instance, in the right-hand-rotation sense, through an angle of 33 degrees, around a ray pointing from the centre of the sphere to the tip of the Washington Monument., and then rotating it in the left-hand-rotation sense through an angle of 271 degrees around a ray pointing from the centre of the sphere to the centre of the Moon. We perform some large number, say four thousand, of such rotations, right-handed and left-handed, through angles great and small, around four thousand very disparate rays. 

Now, we ask: Is there some single rotation which could have taken the sphere from its initial to its final configuration, saving us all the trouble of four thousand separate twistings? Equivalently: Is there some diameter D of the sphere such that after all the four thousand manipulations are complete, D remains unmoved? 

Although we might suspect the answer to be "Yes", the answer is not obvious. Even the imaginative Greeks were not, so far as is now known, imaginative enough to have posed the question. 

The question was posed, with a proof for "Yes", by Leonhard Euler, in surprisingly modern times - so recently as 1776. (Apparently it goes, in his formulation - my programme of studies indicates that I should in the next month work through his short, Wikipedia-recapitulated, proof - Quomodocunque sphaera circa centrum suum convertatur, semper assignari potest diameter, cuius directio in situ translato conveniat cum  situ initiali. So he is using my second, unmoved-diameter-D, formulation.) 

If we exit the confines of Euclidean geometry, the history of mathematics becomes more startling still. 

The concept of a set is readily introduced to an eight-year-old. (I ascertained this through practical work with a great-nephew, in the Christmas of 2014, in the Ottawa area  - with the same child as got the Einstein quotes from me, framed under glass as a gift, with an accompanying photo of Einstein's Princeton day-of-death 1955-04-18 desk.) The set of Canadian provincial capitals is a set with exactly 10 elements. The set of unicorns presently residing in Canada is a set with exactly 0 elements. And this latter set, conveniently called the "empty set", is the very same as the set of dragons presently residing in Belgium. 

As a next point in the child's guided investigation, we introduce the concept of a subset: A is a subset of B if, and only if, there exists no element of A which fails to be an element of B. The set of Canadian provincial capitals is thus a subset of the set of Canadian cities. Further, the empty set is a subset of the set of Canadian provincial capitals (and indeed the empty set is a subset of every set). Further, the set of Canadian provincial capitals is a subset of the set of Canadian provincial capitals (and indeed any set is a subset of itself). 

We now ask a question which in Christmas of 2014 I did not press in full generality with my great-nephew. It was appropriate not to lean on him, but merely to wait for another of his oft-repeated spontaneous demands, "Cousin Toomas, could we do some more math?" For any number n in the set {1, 2, 3, ... } (the set of positive integers), we ask: If an arbitrary fixed set S has exactly n elements, then how many elements are in the set of subsets of S? The set {Toronto, Winnipeg} has as its subsets the empty set, the single-element set {Toronto}, the single-element set {Winnipeg}, and the entire set {Toronto, Winnipeg}. So, in general, a set of exactly two elements has exactly four subsets. 

Similar examples illustrate the truths that a set of exactly three elements has exactly eight subsets, that a set of exactly four elements has exactly sixteen subsets, that a set of exactly five elements has exactly thirty-two subsets, and so on. 

In general (this is the point which my great-nephew and I left uncovered, with Christmas playing some distracting role), for any n in the set {1, 2, 3, ...}, and for any arbitrary fixed set S, if S has exactly n elements, then the set of subsets of S has exactly 2-to-the-power-n elements. 

Finally, we ask a question which, elementary though it is, was perhaps not posed by anyone before Georg Cantor (1845-1918). What happens if we consider the set of subsets of an infinite set? What happens if, for instance, we consider the set of subsets of {1, 2, 3, ...} itself? The odd positive integers are one subset of this set. The even positive integers are another. The empty set is a third; the six-element set {5, 7, 11, 12, 13, 14} is a fourth; and so on. 

Say that sets T and U, whether finite or infinite, are "equipollent" if and only if the elements of T can be paired off one-to-one with the elements of U - in others, can be paired off with, so to speak, no polygamy, no polyandry, no bachelors, and no spinsters. Cantor's question then is the following: Is the set of subsets of {1, 2, 3, ...} equipollent with that simpler thing, the mere set {1, 2, 3, ...}?

A simple reductio-ad-absurdum proof shows the answer to be in the negative.

I will belabour the proof a little here, for the possible benefit of some children or their parents. The proof should in any case be accessible to Grade Three or so, or at any rate to Grade Eight or so. It is what the professionals call a Diagonalization Argument, in a child-in-livingroom setting best done with infinite rows of bits - "1" for "Yes, this individual in the infinite progression 1, 2, 3, ...  is a member of this particular subset", "0" for "No, this individual in the infinite progression 1, 2, 3, ...  is not a member of this particular subset." The four just-mentioned subsets of {1, 2, 3, ...} are then coded with, respectively, the rows 101010101010101010101..., 010101010101010101010101010..., 0000000000000..., and 00001010001111000000... .  Suppose, per absurdum, that the sets of positive integers can be successfully paired one-to-one with those simpler things, the positive integers. Then write down at the top of your paper some initial segment in that infinite row of bits that is a representing code for the particular set-of-positive-integers successfully - so we are imagining, per absurdum - paired with that simpler thing which is 1. Next, write down some initial segment in that infinite row of bits that is a representing code for the set-of-positive-integers successfully (as we are imagining) paired with that simpler thing which is 2. Next, write down some initial segment in that infinite row of bits that is a representing code for the set-of-positive-integers successfully (as we are imagining) paired with that simpler thing which is 3. And so on. Now consider the "Perverse Infinite Row of Bits", or PIROB, obtained by reversing the first bit in the first row, the second bit in the second row, the third bit in the third row, and so on - "reversing" here meaning  "altering 1 to 0, and 0 to 1". (If the four just-mentioned subsets are paired with, respectively, the positive integers 1, 2, 3, and 4, then the PIROB has, as its first four bits, 0011 - for it is cunningly designed to disagree with the first row in its first place, to disagree with the second row in its second place, to disagree with the third row in its third place, and to disagree with the fourth row in its fourth place.) The PIROB itself certainly represents some, perhaps finite and perhaps infinite, set of positive  integers, the "PIROB Set".  (In the example here being developed, the PIROB Set lacks 1, and lacks 2, and contains 3, and contains 4, ... )  Can the PIROB Set possibly be wedded to 1? If not, then can the PIROB Set possibly be wedded to 2? If not, then can the PIROB Set possibly be wedded to 3? to 4? to 5? to 6? to 7?) 

With that tricky, negative, answer firmly in hand, via an admittedly rather tricky Diagonalization Argument, a dizzying prospect opens up. The positive integers are one infinite set; the set of sets of positive integers is found through our tricky reductio ad absurdum proof to be a set not equipollent with it (but, so to speak, "more numerous", "superpollent", "larger"); the set of sets of sets of positive integers is found by a somewhat similar style of reductio ad absurdum to be bigger still - we do best now to resort not to rows of bits, but instead to the perhaps-beyond-elementary-school language of mappings, saying "suppose, per absurdum, this set can be mapped one-to-one onto that set" - and so on. Infinity itself, then, is found to come in infinitely many different sizes. 

[To be continued in the upload of UTC=20160607T0001Z/20160607T0401Z, with more points on the overriding importance to physical science of that technology-independent discipline which is mathematics; and with points regarding the miseries and joys - the concrete, three-colours-of-pencil, practicalities - of private mathematics study;  and with a moral on joy and suffering drawn from Catholic-praxis author Dorothy Day.] 

Hillesum, Frankl: Holocaust insights on trees (for benefit of DeGasperis and Muzzo families)

The following two quotations, on trees, are offered for the instruction and spiritual benefit of those unhappy pillagers of urban forest, the DeGasperis and Muzzo families, as they continue to move their machinery over Canada's David Dunlap Observatory and Park. My latest photographs of their depredations, taken from a bus window on 2016-05-26, do not yet indicate the necessary change of heart. If there is no change of heart, none of us dies, but somebody does suffer a Legal Picket, with (I hope) attendant media publicity. If I get taken to court, I guess there will be lots of publicity, as either (a) I try in my autistic clumsiness to defend myself, without benefit of those too-expensive lawyers, or (b) some possibly eminent counsel steps forward in my defence, pro bono.  (O Clayton Ruby, O Peter Donnelly, I do so hope you guys, or perhaps your like-minded colleagues at the Bar, are reading this particular blog from month to month, as this particular case evolves.) 


The first is from a journal of Holocaust victim Etty Hilesum, quoted in the "Final Prayer" chapter of Fr Henri J. Nouwen's Lifesigns: Intimacy, Fecundity, and Ecstasy in Christian Perspective (New York: Image Books-Doubleday, 1990; the Hillesum translation is said to be by Arno Pomerans, under a 1983 copyright of Jonathan Cape, Ltd.): 

/.../ we must /.../ defend Your dwelling place inside us to the last. There are, it is true, some who, even at this late stage, are putting their vacuum cleaners and silver forks and spoons in safe keeping instead of guarding You, dear God. And there are those who want to put their bodies in safe keeping but who are nothing more now than a shelter for a thousand fears and bitter feelings. And they say, "I shan't let them get me into their clutches." But they forget that no one is in their clutches who is in Your arms. I am beginning to feel a little more peaceful, God, thanks to this conversation with You. I shall have many more conversations with You. You are sure to go through lean times with me now and then, when my faith weakens a little, but believe me, I shall always labor for You and remain faithful to You and I shall never drive You from my presence /.../

Don't let me waste even one atom of my strength on petty material cares. Let me use and spend every minute and turn this into a fruitful day, one stone more in the foundations on which to build our so uncertain future. 

The jasmine behind my house has been completely ruined by the rains and storms of the last few days, its white blossoms are floating about in muddy black pools on the low garage roof. But somewhere inside me the jasmine continues to blossom undisturbed, just as profusely and delicately as it ever did. And it spreads its scent around the House in which You dwell, oh God. You can see, I look after You, I bring You not only my tears and forebodings on this stormy, grey Sunday morning, I even bring You scented jasmine.

Etty Hillesum perished at Auschwitz on or around 1943-11-30. 


The second is from the end of the second chapter of Holocaust survivor Vikor Frankl's book The Doctor and the Soul: From Psychotherapy to Logotherapy. Dr Frankl (whose various places of incarceration included Auschwitz) is describing one of his own clinical cases, in the straitened conditions of a concentration camp infirmary, when he himself was daily confronting the possibility of his own death. The English translation is said in my 1973 Pelican edition to be "by Richard and Clara Winston", and additionally to be have the copyright of "Alfred A. Knopf Inc., 1955, 1965":

A young woman who had led an utterly pampered existence was one day unexpectedly thrown into a concentration camp. There she fell ill and was visibly wasting away. A few days before she died she said these very words: "Actually I am grateful to my fate for having treated me so harshly. In my former middle-class existence I certainly had things a great deal too easy. I never was very serious about my literary ambitions." She saw death coming and looked it squarely in the eye. From her bed in the infirmary she could catch a glimpse of a chestnut tree in blossom outside the window. She spoke of this tree often, though from where the sick woman's head lay just one twig with two blossoms was visible. "This tree is my only friend in solitude," the woman said. "I converse with it." Was this a hallucination? Was she delirious? Did she think the tree was "answering" her? What strange dialogue was this; what had the flowering tree "said" to the dying woman? "It says: 'I am here, I am here - I am life, eternal life.'"

Monday, 23 May 2016

A poem which has been fastened to trees in Portuguese forests

Tree blooming on waste brownspace adjacent to a small Richmond Hill park,
photographed  around sunset 2016-05-23 by Toomas Karmo.
Revision history: 

  • UTC=20160523T0359Z/version 2.0.0: Kmo added a tree photo, taken a few hours earlier with his own cellular phone. 
  • UTC=20160523T0346Z/version 1.0.0: Kmo did first upload (having checked the accuracy of his transcription) , while leaving open the possibility of tiny undocumented subsequent tweaks as versions 1.0.1, 1.0.2., ... . 

According to the p. 251 of that delightful 1951 volume which is the 30th Anniversary Reader's Digest Reader, the following poem has been seen fastened to trees in Portuguese forests. Reader's Digest cites as its source something called "Roadside Bulletin", without giving further details. I typeset the poem here in my own ragged-margin typography, while marking the RD linebreaks through interpositions of blank lines. 

Ye who pass by and would raise your hand against me, 
hearken ere you harm me. 

I am the heat of your hearth on the cold winter nights,
the friendly shade screening you from summer sun,
and my fruits are refreshing draughts,
quenching your thirst as you journey on. 

I am the beam that holds your house,
the board of your table,
the bed on which you lie,
the timber that builds your boat. 

I am the handle of your hoe, 
the door of your homestead, 
the wood of your cradle,
and the shell of your coffin. 

I am the bread of kindness and the flower of beauty. 

Ye who pass by, listen to my prayer: harm me not.  

(Part D) Islands in a TIme of Civilizational Decline: Conclusions

Quality assessment:

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 quite a few points to reasonable length, and to finish the whole essay off (in this, its fourth installment).

Revision history:

  • UTC=20160524T0340Z/version 1.1.0: Kmo managed to bring the upload to a state of reasonable stability, after many whitespacing (or similar) problems at the server. 
  • UTC=20160524T0000Z/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, minor revisions, as versions 1.0.1, 1.0.2, ... .

[CAUTION: A bug in the blogger software has shown a propensity to insert inappropriate whitespace at some late points in this essay. If a screen seems to end in empty space, keep scrolling down. The end of the posting is not reached until the usual blogger "Posted by Toomas (Tom) Karmo at" appears.]

5. Canada's David Dunlap Observatory and Park (DDO&P): Prospects

Only a cursory effort is needed to imagine the positive future that awaits DDO&P, as an island of cultural conservation, when or if the DeGasperis and Muzzo families repent of their current mean, Donald-Trump-worthy (in Estonian, donaltrumplik in the nominative singular, donaldtrumplikud in the nominative plural) subdivision plans.

The restoration of their felled forest, through citizen action, would (will?) be a tangible sign to all of Canada what ordinary citizens can do when governments leave them alone to get on with the job. Here, in duly redacted form for safeguarding of privacy, are my case notes regarding pledges of tree-planting labour which I already assembled around 2012:

((ITEM WHEN="20120910T1330Z"))
__following is my private record of tree-planting intiative,
as updated 2012-09-10 before start of OMB hearing,
on strength of phone call(s) and/or voicemail(s):

* "Person 1" has as of 2012-09-08 pledged 200 hours
of tree-planting labour.

* "Person 2" has as of 2012-09-08 pledged 100 hours
of tree-planting labour, and indeed
already has tree-planting experience.

* "Person 3" has as of 2012-09-08 pledged 25 hours
of tree-planting labour.

* "Person 4" has as of 2012-09-10 pledged 25 hours
of tree-planting labour.

* "Person 5" has as of 2012-09-10 pledged 25 hours
of tree-planting labour, with the remark
that additional hours may be possible.

* "Household A" has as of 2012-09-08 collectively pledged
25 hours of tree-planting labour.

* "Household B" has as of 2012-09-10 collectively pledged
20 hours of tree-planting labour.

That makes a total of 420 pledged hours.

Identities are as follows:

* Person 1 = Toomas Karmo
* Person 2 = ((CONCEALED))
* Person 3 = ((CONCEALED))
* Person 4 = ((CONCEALED))
* Person 5 = ((CONCEALED))
* Household A = ((CONCEALED)) and her spouse ((CONCEALED))
  and their ((CONCEALED))
* Household B = ((CONCEALED)) and ((CONCEALED)) (message conveyed
 to me 2012-09-10approx via ((CONCEALED)),
 who remarks also that she has yet to hear
 from ((CONCEALED)) ).

And with rescue of the full 77 hectares, as opposed to the mere 45-hectare rump, a credible case can at last be argued, both in Ottawa and internationally, for UNESCO World Heritage List protection.

DDO&P is an object of deeper international cultural significance than Ontario's sole existing UNESCO site, the (admittedly meritorious) Rideau Canal. The nub of the UNESCO argument, as the federal government will have to develop it in the corridors of Parks Canada for eventual presentation in Paris, is that DDO&P parallels another Canadian UNESCO case, the Joggins fossil cliffs in Nova Scotia. Joggins (it was successfully argued in Paris, in a process culminating with accession-to-List in July of 2008) played a key role in Victorian biology. Its comprehensive-biotope fossils, showing archaic fauna in a botanically convincing context of archaic woodland, figured in the British debates triggered on 1859-11-24 by Darwin's publishing Origin of Species. DDO&P (it must be analogously argued, again in Paris) played a key role in the rise of 20th-century astrophysics, through Prof. C.T. Bolton's discovery there of the first stellar-mass black-hole candidate.

With DDO&P under UNESCO, and (the park now being no mere rump) with adjoining subdivisions safely on the far sides of Hillsview Drive and Bayview Avenue, we will have done something to strengthen the legal and physical boundaries of this cultural island. Further, UNESCO listing will help DDO maintain some level of credibility in the global archipelago of observatories - admittedly, as a minor facility now, when the world is rich enough to afford multiple telescopes in the ten-metre class, in Hawaii and Chile (the biggest of the three DDO telescopes - the largest within Canada -  has an aperture of just 1.88 metres),  and yet as more of a middle-ranking archipelago contributor over the coming decades, when big international telescope projects become progressively less feasible.


I must now focus the relevant minds - especially in the DeGasperis and Muzzo families, whose lawyers will eventually be scrutinizing this week's posting through their loupes - on the contrary case. What happens if UNESCO prospects are disregarded, and international astrophysical opinion is flouted, and the envisaged malign 14-street, 520-or-530-home, donaldtrumplik development goes ahead?

Here it is convenient to adapt, with only minor revisions, material (I adapt both in italics and in plainface) from the work-in-progress which is my

My scenario is predicated on the following assumptions: (a) The inability of world leaders to come to grips with climate upheaval, already evident in the failed Copenhagen talks of 2009 and the toothless Paris-2015 agreement will continue, with little or no relief, up to and beyond 2100. (The well-intentioned 2015 Paris "COP21" is an achievement in modern climate diplomacy paralleling the fluffy disarmament meringues which were the Locarno Treaties, signed in London on 1925-12-01. It lacks juridically enforceable bite. At COP21, nations were left free first to set their own emissions targets, then to fail to meet them.) (b) The tightening of petroleum supplies reflected in the approximate tripling in the crude-oil price over the period from 2003 to 2012 (with a financially catastrophic spike in 2008 to values more than 50 percent above even the elevated 2012 levels) will in this same up-to-and-beyond-2100 timeframe become progressively more severe. Efforts to make up the energy shortfall through "renewable resources", controlled thermonuclear fusion, and the like may conceivably slow this fuel-supply contraction by 2030 or so, but they will fail to reverse it. (c) The decline in Ontario's social well-being evident in 2010, even in 2000, by drawing comparisons against the 1990s, 1980s, and 1970s will in this same timeframe continue inexorably, being exacerbated by bigger and bigger economic upheavals (by depressions, and perhaps also by currency inflations) as the degradation in Ontario's fuel supply and climate deepens.

Readers interested in exploring these assumptions further will be helped by the following short biblography: Gwynne Dyer's Climate Wars (2008); James Howard Kunstler's The Long Emergency (2005), and his updating Too Much Magic (2012); and John Michael Greer's The Long Descent: A User's Guide to the End of the Industrial Age (2008), and his subsequent, cognate, books of social criticism, along with his weekly blog (in a server space rather opaquely named

Passing for the moment over the eventual pauperization and brutalization of our communities, over the eventual descent of whole streets and neighbourhoods and regions into Brazilian favelas, I take for the moment the short term, the next couple of decades. For my first bite of the ever-so-sour cherry, I look out only to, as it might possibly be, the end of the Twenties and start of the Thirties.

No doubt the next couple of decades will see the survival of the magnificent main building, with its brass and marble, and also the survival of the main dome, and in addition the survival of the circa-1864 Director's House.

Here is what survival is likely to mean if, contrary to first-day-of-lectures principles from environmental ethics, the DeGasperises and Muzzos succed in building over five hundred units of housing as planned (with rowhouses at Bayview, and McMansions or McChâteaux near the main telescope dome, on Hillsview Drive). It is not nice:

A park of lawn, trees, garden, meadow, and woodland covers most of the entire western half of the Trapezoid, from the railway line until a little east of the Radio Shack. The 2007-era DDO gardening is retained, even greatly expanded, with the 2007-era private beds at the Director's House now added to the public domain. The southwest-corner savanna, despoiled of its trees by the developer (who pleaded guilty in Municipal Court in Richmond Hill around 2010), is now treed densely. And it is at last possible to walk south past the Director's House, unchecked by that sinister Cold-War-Era chainlink fence, into the Panhandle, and thence south through the Solar System Park to the Elvis Stojko Arena. On first inspection, much seems well.

Admittedly, there are now many hundred, perhaps even two thousand, people living on that part of DDO&P that used to run eastward from the Radio Shack to Bayview. But why does this matter? How many of those interested in DDO astronomy, as opposed to mere exercisers-of-dogs, used to venture east of the Radio Shack anyway?

And is it not to the benefit of the preserved rump of the erstwhile DDO&P that in the southeast corner, the ancient wetland is intact, with only a new "stormwater management pond" signalling change, and with a thin "wildlife corridor" of scrub actually linking the wetland to the preserved rump?

But damage is apparent to field naturalists. The two deer herds are much reduced, or gone; the coyotes, accustomed as they were to feeding on voles and other small creatures in the east of DDO&P, are much reduced, or gone; even the summer lepidoptera, and the birds, are not what they were.

And the newly dug "pond" is of course less a pond (a welcoming habitat for salamanders, for frogs) than a settling tank or stormwater sump. Its brew of dissolved road salt and suburban-garden fertilizers does well if it supports some cattails, some algal mats, or a little duckweed. One might measure the pH there, one might gauge the quantity of suspended sediment by taking clear-bottle samples there. One would not, however, venture there with one's fishing rod. 

Ominously, that sump needs periodic maintenance, as a bridge or a dam does. For a while, the funding is available. 

Further, ruinous damage is apparent to such friends as the night sky may still possess in urban Ontario. Where the lawns by the main dome were once illuminated evenly, steadily, by unwelcome scattered light from distant streets, now the streets come up close. At Hillsview Drive, McMansion-scale lots come in some instance or instances even to within 150 metres of the main telescope dome. Only a modest grove purports to isolate such homes, with their porchlights, their yardlights, their upstairs-bedroom-lights, and their Christmas decorations up to roof level, on the one hand from the the main telescope on its modest knoll, and on the other hand from the two telescopes in domes perched high on the Administration Building roof. 

As we stand on the dome steps looking east ninety minutes after sunset, we see not just the general sky-glow familiar to, and deplored by, friends of DDO&P since the 1960s, who have long contrasted DDO&P conditions with the proper celestial glory of, say, Caledon at the edge of the Greater Toronto Area. No: that glow, bad though it was, left one still with a tranquil sky, and a view down to feeble eta Cassiopeiae and the feeble third of the four stars in the Little Dipper bowl.

(The fourth bowl star was, I imagine from the 1960s or 1970s onward, admittedly a lost cause for the not-very-outstanding retina at DDO&P, even on a moonless night. And the Milky Way at DDO&P has for some decades borne admittedly scant relation to what one gets in Caledon.) 

What we see now is something new, and strange, and sick-making. It is an unsteady glow, like an incipient aurora borealis, pernicious for stellar spectroscopy, and I think worse still for stellar photometry. The photons come from intermittently surging illuminants, notably motorcar headlamps, concealed behind screens of trees, but all the same scattered to our retinas from inescapable atmospheric particulates. 

The demonstration, I might interject, is an easy one. Have a friend shine a pulsing light skyward from behind a thick hedge, the bulb concealed from your view. No matter how good your hedge, your friend's light will imprint a pulsing footprint glow on your air itself, even if your air is quite free of visible mist. The glow will be inescapable in an urban environment, though you might avoid it if you happen to be in deep countryside, with the air dry and free of dust - for instance, I conjecture, if you were attempting this experiment on Australia's arid Nullarbor Plain, a couple of hundred kilometres east of Kalgoorlie, on a night when wind happens not to be making the desert grit fly. In modern cities, much of the inescapable particulate matter is soot, from vehicle tailpipes.

It is in a property developer's interest to promote anything that adds cachet to a subdivision. Serious astrophysical research being now unappetizing in the sick pseudo-aurora, there remains infotainment, and this the developer is willing, is even keen, to promote. So within the main dome, people line up to get feeble eyepiece views of cliché gee-whizzes like M57. And within one selected part of the largely "repurposed" Administration Building, astronomy lives on through talks and films. 

(Of course there are going to be films - good films, brilliant films. They are going to be films at the level of technical excellence you get in Canada's major museums, for instance on that huge "Oceans of Hope" screen,  with those dauntingly bilingual or multilingual headsets, in the Pier 21 museum-of-immigration in Halifax. Since we cannot engage in an authentic way with the sky, let us use cinema. It is astonishing how cinema can generate in the cinema-goer the impression of having learned something deep, even though one month after the screening nothing comes to the recall-seeking mind beyond two soundbites and four seconds of video. - As for the promotion, folks, don't take my word for it. Check out the developer's own language, at "Here you’ll live closer to the stars than you ever thought possible while enjoying the world-class amenity offerings of one of Canada’s finest living destinations. Give your family space to live, and space to learn." Better yet, take up the developer's offer, and register for e-mail updates on the project - taking care to adhere to all the legal conditions, which require you to be "sole holder and user" of your proffered e-mail account. - More fine language is on view at the developer's main site, As I have already noted on this blog, drawing the necessary connection with the envisaged wetland destruction in North Gwillimbury, the thing starts with the headline  "BRINGING LIFE TO LAND," set against a fine backdrop photo of a wetland twilight.)   

Among the real-astrophysics work that should take off, and yet is scared away by the buzz of infotainment, is the hard and earnest "citizen science" described at

We may now finish off our sour fruit by moving the narrative into the deeper future, toward the Nineties and the year 2100, or even a little beyond:

Later, as times get worse, the social development evident by 2000 or 2010 in Brazil reaches Canada. The wealthy live in gated communities, for the most part close to Toronto's business core, in such places as Soho and Cabbagetown. Their electricity stays on for twenty-four hours a day. Their homes are artificially cooled in the increasingly brutal summers and artificially warmed in what used to be considered winter. The more outlying parts of Metro Toronto, such Davisville, Eglinton, and Agincourt are less happy. But here, too, selected municipal services remain.

The real Brazilian favelas are in the outer suburbs, notably in Richmond Hill.

The DDO&P favela is better than some. Here, at least, two thousand people have the rump of an erstwhile park to their immediate west, not demarcated by any major intervening street. With no street to be crossed, it is easy to dump what bedsprings may have to be dumped, to toss whatever improvised biochar-burning cookstove may have disappointed them by rusting through. They have even enough erstwhile lawn, in an epoch of climate change, to occasionally repay foraging for February dandelion greens.

The favela is on the now severely potholed Bayview Avenue. For the little cul-de-sacs of McMansions, or McChâteaux, reached from Hillsview Drive, there are gates, and behind the gates lots of expensive solar panels. 

(Unless, indeed, the rioting gets really bad, in which case those cul-de-sacs will have to be abandoned to looters, their sometime inhabitants now taking refuge in the enhanced security of Soho or Cabbagetown.)  

The "stormwater management pond" is  going or gone, its maintenance long abandoned, its leakage now accelerating, its leakage and overflow now cutting the first little gullies through what used to be a post-glacial wetland. In another fifty years, the gullies will be bigger. 

With grid electricity rationed for all the but privileged, light pollution is not the problem it used to be. These days you can actually stand at the ruins of the Great Dome and pick out half the Milky Way. People say the sky actually gets a little darker from one year to the next, as Ontario's fuel supply gets tighter.

Is there still a University of Toronto? But of course. An institution embedded in the cultural and economic and political life of Upper Canada can no more die than the Family Compact, so vainly opposed by those earnest 1837 rebels, can die. Like the Family Compact, the University bends and turns through the decades of Peak Oil and Climate Change, morphing first into this odd shape, then that, its 1935-era incarnation as a bastion of the British Empire and its 2010-era incarnation as a business corporation two passing phases in a protracted and complex history. 

Not for nothing do our University's arms bear the motto Velut arbor aevo ("Like a tree in the epoch," i.e., either "Growing mightily as time passes" or "Enabled by the passing of time to grow mightily"). I think of this particular tree as an arboreal monstrosity - indestructible, timeless, its twisted branches hard as ebony, and not lacking in thorns.

Is there, in so obstinately perennial a university, still a Department of Astronomy and Astrophysics? How could there not be? 

In the Department, they still have some dim memories of how things used to be, when professors and graduate students were able to fly (quite literally airborne, in the manner of our gated-community warlords from the Year of Grace 2100 or 2110) to the great telescopes of South America. Back then, they felt so little need for a local DDO that they sold it off, let it go, dumped it onto what used to be called the "property market". Now the Department realizes, in its more introspective moments, how large an opportunity got sacrificed. 

But it is perhaps some consolation that astrophysics research conditions are better elsewhere. U Vic still has access to the old Dominion Astrophysical Observatory telescopes, at the southern end of Vancouver Island. One can always try applying for a few nights of telescope time out there, as a U of T guest observer.

Conveniently, the railway continues at this stage in the ongoing decline to trundle its "Train Number One" from Union Station out to British Columbia, many times a month. Those tracks skirt DDO terrain just as they did in the old days, when academics were airborne.

6. Conclusion (I): Islands and Edge

A principal feature of the island metaphor is the Boundary. If an island is thought of in two-dimensional terms, this becomes an edge, a closed curve traceable with pencil on map. 

Actual geographical islands tend to present a sharp transition between water and land. Perhaps there is a gently sloping ribbon of sand and pebbles, partly dry and partly damp. In the freshwater case, the damp margin is only a few centimetres wide. In the marine case, the margin is typically of a more generous width, varying from hour to hour as current tidal circumstances may dictate. 

Perhaps, on the other hand, there is a more dramatic transition, as when some metres of cliff drop almost along the vertical, to a line of churning whitecaps and blowing spray.

It is clear what are the equivalents, for those polities which are so-to-speak islands, of beach and cliff shore. In discussing Constantinople-cum-Byzantium on 2016-05-03, I noted the clear sense of transition, of crossing an edge or a bounding curve, that is said to confront the traveller even today. The entry of the would-be pilgrim to Mount Athos is apparently regulated by a kind of carnet de passage, bearing Byzantine heraldry, and couched in legal language current before 1453. 

The case of Israel (a polity I likewise discussed on 2016-05-03) is no less dramatic. 

I have never had the good fortune to visit Israel, and my now-rare forays into aeroplanes have never taken me to "El Al Israel Airlines Ltd". Nevertheless, I can imagine something of the El Al experience by extrapolating from my two Finnair crossings, in 1990 and 2010, from Toronto-Pearson to Helsinki-Vantaa, on my way to Tallinn. 

With the plastic dinner tray and the plastic teacup cleared away, and with everything in the vast cabin quiet, and with the sky perhaps still dark, a sense of Transition settles in. The moment arrives with possibly even a certain suddenness. At that time - as it possibly can be, at that instant - one feels mentally no longer on the western (the "New World") side of the Atlantic. 

I like to think that Death itself must be similar.  

A key founder of the IDF was a West Point graduate, and in his earlier US Army capacity a close observer of liberated Dachau, David Daniel "Mickey" Marcus (1901-02-22/1948-06-10). Colonel Marcus was described posthumously by David Ben-Gurion (so one reads at as "the best man we had". Upon his death in the context of something called the Jerusalem Road Battle, the following quotation, of unknown origin was found in his wallet. The quotation was printed in 1951 by The Reader's Digest in its 30th Anniversary Reader, on p. 353: 


I am standing on the seashore. A ship at my side spreads her white sails to the morning breeze and starts for the blue ocean. She is an object of beauty and strength, and I stand and watch her until at length she is only a ribbon of white cloud just where the sea and sky come to mingle with each other. Then someone at my side say, "There! She's gone!"

Gone where? Gone from my sight - that is all. She is just as large in mast and hall and spar as she was when she left my side, and just as able to bear her load of living freight - to the place of destination. Her diminished size is in me, not in her, and just at the moment when someone at my side says, "There! She's gone!" there are other voices ready to take up the glad shout, "There! She comes!" And that is Dying. 

So on Finnair, then, as on El Al, and on every airline burning kerosene in reaction motors, there is the steady roar of turbines, blended with the rush of a wind of about five times hurricane speed. Inside the fuselage are warmth, light, and breathable air. Outside is Antarctic cold, and a barometric pressure dramatically incompatible with mammalian health. 

How does Finnair manage to fly at all, at these altitudes? And yet one of the miracles of current aero-architects is their ability to perform the requisite mathematics - at any rate for laminar, non-turbulent, flow; and if not analytically, through explicit closed-form solutions of the differential equations, then at any rate with numerical modelling. Back in the days of Britain's Vickers Viscount, those designers must have worked with slide rules and adding machines. Nowadays, their numbers are manipulated on silicon hardware itself configured, on the scale of a few tens of nanometres, to a mind-numbing intricacy. On the CPU chip and its companions, we have, as a thing almost unique among human artefacts, a complexity rivalling the dizzying complexities of DNA and Messenger RNA. It is a mathematical complexity worked not at the level of differential equations, but at the mathematically more fundamental, and in its elemental reaches easy, level of Boolean algebra. 

I have been told that people in the cabin at this special Time of Atlantic Transition, flying El Al from the New World to Israel, have been observed singing Hatikvah. (Kol 'od balevav penimah ...:  In the  translation at, "As long as the Jewish spirit is yearning deep in the heart,/ With turned toward the East, looking toward Zion,/ Then our hope - the two-thousand-year-old hope - will not be lost...") Whether it is literally true that Hatikvah is on occasion heard at this midpoint of the flight, I cannot say. Conversation is a notoriously unreliable information source. But it is one of those possibly fictional things for whose truth one yearns. 

It is of course true that Hatikvah is on occasion heard later - not at the Time of Transition, but during Final Approach, or at the time of Reverse Thrust, when tyres spin furiously on the long runway paving. 

Or perhaps it comes, when it does, by preference in those placid, safer, moments, when fuselage is being brought up to terminal, and crew and passengers are breathing easily. 


The boundaries in cultural space recall not only the edges, or "closed curves", bounding (cartographically two-dimensional) islands, but additionally the bounding surfaces ubiquitous in biology, in three-dimensional space.  

Here, for instance, is a locus of frantic activity, the cytoplasm of a cell, with its various, seemingly free-floating, enclosures. Around the tiny approximate-ellipsoid which is a chloroplast is a membrane, and around the sausage-like mitochondrion is a different kind of membrane. And around the approximate-sphere nucleus is a membrane of a third sort. In each instance, the membrane effects a sharp, biochemically critical, transition between an Inside and an Outside. In each instance, molecular departures and arrivals are regulated with all the fierce precision of El Al airport security. 

And here, on a much larger scale - a scale so large as to be accessible not just to the electron microscope, but even to the humble high-school tube, with its sequence of small glass lenses - is the boundary of the cell itself, the entire, vast, "cell wall". 

On a still larger scale, there are equally remarkable bounding surfaces. There are, for instance, the palisades of cells comprising the upper and lower surfaces of a leaf, regulating among other things the intake of carbon dioxide and the expulsion of water vapour. Or, again, there is that strangely busy world of bark: a world of dead cellulose, harbouring extraordinary living things, such as the fungal-algal partnerships which are lichens.  

It seems to me that the more successful of the several tens of thousands of post-1944 free-world islands of Estonian culture were those in which edges and boundaries were well demarcated. In the cell, when bounding membranes cease their activity, death impends. The same is true of failing boundaries in the cultural sphere. it is one thing (as I explained in my posting of 2016-05-10) to select coloured bulbs for the Christmas tree, so as not to stand out from one's Anglo neighbours. It is a different, and in an almost biological sense healthier, thing to select white bulbs, in reminiscence of Christmases at home, in the placid days when only the occasional lone ranter was predicting Soviet occupation.  

7. Conclusion (II): Islands and Archipelagos

What is the probable future of England, some centuries from now, as not the ice sheets of Greenland alone but even of (some of? much of? all of?) Antarctica disappear?

Published calculations, which I think I have for my part seen simply in National Geographic, for a full-melt scenario suggest some tens of metres of North Sea rise. At that point, much of those ancient upland nations, Scotland and Wales, will remain amenable to conservation. In England, on the other hand, much will be lost for all of human history.

London will be an early casualty, perhaps even by 2100 or 2150. A glance at Wikipedia statistics, over the last several decades, for closings of the Thames Barrier indicates what might lie ahead. In the 1980s, closings were undertaken only a few times a year. Now, however, their frequency has risen, to perhaps a few times monthly.

After London falls, what?

An eventual casualty must be the Fens. I imagine, without having checked elevations, that Cambridge, being on or at the edge of Fenland, is in the long run no less doomed than Norwich and Ely.

Oxford and its neighbouring Cotswolds, on the other hand, might persist.

Eventually (when the Baltic has overrun even Tallinn's ancient Upper Town, and the New-Dark-Ages Viking ships dock at or near Tartu), we shall have Estonian traders, in some new Hanseatic League, setting sail for the English Isles.

At any rate, they may well be called the "English Isles" by monkish classicists, who know English, with occasional deformations in their vowels, as today's classicists know Latin. Whatever diverse languages are descended from English as today's Romanian and Italian are descended from Latin will have their own, mildly diverse, phrasings.

The "English Isles", however they may turn out to be in the coming tongues yclept, will stand united, in a network of dialectal close-similarities and dialectal more-distant-similarities and cultural affinities, against their common foe, the North Sea. The ensemble of those islands - from today's Cotswolds, today's Yorkshire moors, today's Dartmoor, whatever - will be an archipelago at once physical and cultural.


In writing on 2016-05-10, I was at pains to note the significance of the archipelago in the one cultural diaspora I know well.

The significance of the archipelago is evident also from a contemplation of monasteries in the one Dark Age most of us know from school and library. It is striking how widely in that age, when travel was next to impossible - when farming folk would hardly over an entire lifetime range more than thirty kilometres from their natal hamlets - monks, books, and reputed holy relics roamed.

An analogous cultural evolution may well occur in the coming dark centuries.

For those pairs of English Isles which are separated by a mere two or four kilometres of tidewater, we can imagine 1939 poet W.H. Auden's "affirming flame" literally incarnated in an easy means of nocturnal marine communication, the Morse blinker.

Over distances that defeat the easy-to-construct Morse blinker (for an observer not on a raised support, the marine horizon is just under five kilometres away), there may well be Morse radio transmitters, in the hands of artisans skilled in copper wiring. If worst comes to worst, radiotelegraphy can be achieved by broadcasting mere static dahs and dits, with "spark". When the Titanic went down in the night of 1912-04-14/1912-04-15, its officers' "spark" was heard all the way from the Grand Banks of Newfoundland to Ireland, on a bulky crystal-rectifier set conserved to this day.

We may, however, piously hope that the arts not of glass-blowing and roughing pump alone, but of the more delicate diffusion pump, survive. In that case, the English airwaves of the coming Dark Age will be busy not with the rasp of the Titanic spark, but with the pure beeping of diligently tuned continuous-wave radiotelegraph oscillators, driven by thermionic valves, or in American parlance "tubes". These will be valves from duly equipped workshops, capable of achieving high-grade vacua, and set up in perhaps direct imitation of today's Claude Paillard. We may hope that before the Internet fades away, radiotelegraphy enthusiasts will be taking care to archive, in hard copy, or its successor servers. 

And surely 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.

As a cultural island's boundary offers safety, so does a cultural island's participation in an archipelago offer a belonging, a solidarity, a counterpoint to an otherwise toxic and enervating solitude. From this, no less than from the island's promise of safety-through-boundaries, we may draw a sober hope.

[This concludes the present four-installment essay on islands-in-a-time-of-civilizational-decline. The patience of readers is appreciated.]