Mathematical Studies

This is a letter to a blogger called Stewart Griffin who send me a link to his blog in which he denigrated Maths Studies degree programmes at Irish universities:

Dear Stewart,
Thank you for your message.
I looked at your blog.  It does not appear to
take comments, so I am writing to you.
You are seriously misinformed about Maths Studies,
if you think that this order is reasonable:

Mathematics, Applied Mathematics, Physics, Engineering (with significant maths content), Computer Science, Mathematical Studies, Chemistry, Biology

as a ranking of fitness of degrees to prepare maths teachers.
I suggest that you start by getting the facts about the maths
content of these various kinds of degree programmes, before
you lay about you in this way.  You will find that you have put
ahead of maths studies a number of programme-types that typically
involve the study of some rather small (typically well less than 50%)
subset of a maths studies programme, and certainly at no higher
level of rigour, to say the least.  Maths studies programmes entail
between 80 and 110 ECTS credits in Maths courses, depending on
whether the student takes a double-hons or single-hons degree. You
make fun of the occurrence of a 5-credit module on History of Maths
in our programme. But this is an entirely appropriate module for a
prospective maths teacher, and it was not in put there  to make the
programme easier.  A maths teacher should have an understanding
of the origins and development of the discipline, and a broad and
sufficiently deep exposure to all the mainstream areas of maths.
Fifty years ago, the standard training for a maths teacher involved
the 3-subject general degree, with maths as one of the three.  This
translates, in modern terms into 55 ECTS credits (15+20+20) in
maths, involving so-called general-level,  (pass-level) courses.  An
engineering graduate from UCD would have had a greater level
of exposure to maths, over the four years, except that they would
have been light on areas such as groups, rings, fields, and
number theory.  Many people were, and
are teaching maths with much less exposure than this, such as
Arts, Science, and Commerce graduates with as little as
one year of maths (15 ECTS credits).  With the elimination of
general degrees, the maths studies programmes were created by
adding to the general maths programmes.  The additions, typically,
involve more exposure to proof, to modern geometries, and to
subjects that have become more important in the modern world,
such as symbolic computation, combinatorics, coding theory,
cryptography, as well as history and philosophy of maths. 
In the meantime, most S+T programmes have gone
in the opposite direction, reducing exposure to maths to the
absolute minimum required for the later courses in the
application, usually confining it to the first two years,
emphasising drill at the expense of concept,
paying no attention to rigour, in short giving a narrower
and shallower maths education.
As a consequence, your school principal should on no account
send in recent graduates in any of the S+T areas you list,
except Maths, Applied Maths and Maths Studies, to teach
maths to his students, unless they have taken steps to
deepen and broaden their mathematical education.

Best regards,
Tony O'Farrell.

Sabbatical over

Too much life for blogging, since July. Freud is supposed to have said  that all that really matters is Love and Work.  If that be so, then I live as one should, because all I do is love, and work.  Term began on the 20th, and I enjoy the contact with bright, hopeful youngsters again.
In the tail end of the Summer, I read through some engaging stuff: (the English and Irish text of) a parallel-text anthology of  Irish poetry with Czech translations (ISBN 80-86055-80-9), a collection of essays about Ireland, by a German journalist (Ralph Sotscheck, Saint Patrick in der Bingohalle, Irische Einblicke, ISBN 3-85452-718-7), Collected Stories by V.S. Pritchett (ISBN 0-7011-2305-2), a collection by Isaac Bashevis Singer (A Crown of Feathers  and other stories, ISBN 0-224-00986-9),
a translation of The Analects of Confucius (ISBN 978-1853-26462-7), a biography of the poet Attila Josef, by Thomas Kabdebo (ISBN 1-89792202-7), a couple of rather dated books on cosmology:
G.J. Whitrow, the Structure and Evolution of the Universe, Hutchinson, 1959; and G.C. McVittie, Fact and Theory in Cosmology, Eyre and Spottiswoode, 1961, and I reread a translation of J.L. Borges collection Ficciones, Grove Press 1962 and Feynman's sparkling and provocative memoir, Surely You're Joking, Mr. Feynman!    Pritchett and Singer are just brilliant, but  I can't imagine what I saw in Borges. 
Now I'm just reading Maths, apart from occasional dips into the Tale of Genji.  It looks as though this novel will take me a long, long time.
I'm teaching introductory mathematical computing, with Maple, and basic real analysis.
I'm currently investigating the distribution of cubic residues to composite moduli, with an application in view to Diophantine approximation.  I like number theory, but have a lot to learn.

Phil Hickey's Blog

I went to school with Phil Hickey, who blogs at:

http://behaviorismandmentalhealth.com/

What he has to say is very interesting, and rather shocking.  It appears that there is no scientific evidence of specific chemical imbalance in most people suffering from depression, and so no scientific basis for the treatment of depression by antidepressive drugs.  The same applies to other disorders, such as attention-deficit hyperactivity disorder.  He cites specific  sources for this finding. I had no idea.  I've encountered many depressed students in my time, almost all on medicine, and never dreamed of suggesting they come off the medicine.   In fact, I assumed that if they did so, they would be at increased risk of suicide, which is, along with road traffic accidents,  one of the two main causes of death among our students.   And everything I'd heard before this, including comments by professionals, was to the effect that "the drugs work", and in fact that  "there has been no progress in psychiatry apart from the development of useful drugs."

I still won't advise people to stop taking the pills, but I won't encourage them to continue, either.  Not my job, or competence.   Patients should be able to trust their doctors.

You Tube

The recorded music business is finished. And, I need never again be stuck for a word, a phrase, or a bar of any song. Everything is there.

Jessica

Back Home

Much peregrination since the start of May: Scotland, to hike up Ben Nevis; Madison, WI, to work on the biholomorphic group; conference in Edwardsville, IL; day in Chicago, mostly at the Art Institute; Helsinki; holiday in the Ebro delta; Valencia; Connemara, to hike the Maamturk mountains. Entertained visitors in between. Met many old friends, and perhaps some new. Now looking forward to some stability.

Recently read, or reread:

J.M. Castellano Gil and F.J. Macias Martin. History of the Canary Islands.
84-7926-114-5. English a bit broken. Interesting (and sad) story of the conquest. Some data on references in antiquity (Homer?, Hesiod, Pindar, Herodotus, Diodorus of Sicily, Strabo, Plutarch, Sallust, Pomponius Mela and Pliny the Elder. Also some folklore, including a story about Brendan the Navigator. Short chapters on links with America, the literature, and art.

S. Vere Benson. The Observer's Book of Birds. Ferederick Warne. Rev. ed. 1960. My old bird book, a very useful field guide.

Eric Dempsey and Michael Casey. Finding Birds in Ireland. The Complete Guide. 978-07171-3916-3. About places where birds may be found. It is very hard to use it to locate info about the location of a particular species, as the index is unhelpful in this regard. Has many maps, and has a glossary of Irish names for most species.

Colm O Lochlainn. Irish Street Ballads. Three Candles. Dublin. 1939. This and More Irish Street Ballads, 1965, are indispensible.

Henry James. The Wings of the Dove. Slow build-up to a classic disaster. After the first few hundred pages, I couldn't put it down, and stayed up far too late in Helsinki to finish it. Great book.

Tom Brown's School Days, by An Old Boy. Rev. ed. 1889, repr. 1890. (f.p. 1857). Not at all what I expected, and much more interesting. I expected something like a propotype of Frank Richards' books, but this is a far more sober affair, much concerned with moral matters, such as the duty to study honestly. In relation to the famous fight with Flashman, the author has a disquisition about the place of fighting in a boy's life. I was struck by: "After all, what would life be, without fighting?"

Ray Monk. Wittgenstein. The Duty of Genius. Vintage. 1991. 0-09-988370-8. Very good read, but every time I begin to think I understand W's point of view, he does something that proves me wrong. In the end, I am torn between the desire to read it again from the start (and spend serious time studying W's work) and the rather attractive idea that I should take W's advice to his various friends, and give up philosophy altogether to do something useful.

E.E. Cummings

Selected Poems 1923-1958. Faber and Faber. ISBN 987-0-571-08986-4
(Selected by the poet)
I'd neglected this man, hitherto, for no better reason than my aversion to gimmickry: he uses idiosyncratic punctuation (frequently none) and rarely uses a capital letter. Then, a few weeks ago we watched a movie in which the always watchable Cameron Diaz played an almost illiterate girl, who slowly read one of EEC's love poems to a blind patient, and I was amazed by its beauty. Now I'm a convert.
Some are political, some humorous, some erotic, a few religious, but most are about love, and life, and light. In form, quite a few are sonnets, the style strongly reminiscent of Shakespeare. For instance:

true lovers in each happening of their hearts
live longer than all which and every who;
despite what fear denies,what hope asserts,
what falsest both disprove by proving true
....

But he uses all sorts of standard metrical and rhyming structures, with just an occasional innovation, in which the layout on the page suggests the intended phrasing, and pauses. Such as this:

...
so world is a leaf so tree is a bough
(and birds sing sweeter
than books
tell how)
so here is away and so your is a my
(with a down
up
around again fly)
forever was never till now

His word-order sometimes recalls Horace:

anyone lived in a pretty how town
(with up so floating many bells down)

(-- the use of parentheses is a characteristic. Sometimes, there is just one short sentence outside the parenteses, and a whole world inside.)
So much, so beautiful -- read it!

Oliver Goldsmith: The Vicar of Wakefield

Goethe thought this "one of the best novels ever written", although most discriminating critics (and even the author, in his 'Advertisement') point to the faults of its fantastically-improbable plot, in which coincidence is heaped upon coincidence. It has enjoyed enduring popularity, and this is clearly due to the great charm of its style, its wealth of aphorisms, and the singular character of the hero: upright, trusting, innocent of guile, vain about his writing, faithful and courageous. I loved it.
Life is full of coincidences. Last week my friend MN used the valediction:

Ná díol do chearc lá fliuch!
(Never sell your hen on a wet day!)

This was new to me, but soon after I ran across a reference to the same proverb in Goldsmith's novel. When the vicar becomes anxious that his son Moses has been away so long at the fair, where he went to sell a horse, the vicar's wife says that he need not worry..."Depend on it, he knows what he is about. I'll warrant we'll never see him sell his sell a hen on a rainy day." Sadly, her confidence is misplaced, and Moses returns, having exchanged the price of the horse for some rubbish.

Express Anchors

These are a wonderful invention. They are used to fix a piece of timber to a concrete wall. I was putting a low wooden fence along the top of a concrete wall, and Mulligan, the man who makes fencing, told me about them. I fixed 4 by 1 inch battens vertically to the wall, and fastened the fence to them on top of the wall. In the past, I would have used rawl plugs or masonry nails to fix the battens. Express anchors are far superior. They are made (I think) of steel, plated with something brassy to delay corrosion, and are hollow incomplete cylinders, with a tapered point and a splayed head. By incomplete, I mean that the cylinder has a gap running the whole length. The ones I used are 90mm by 8. You drill a hole through the wood with a number 8 bit, then drill on through the wall with a number 8 masonry bit (and your trusty hammer-action Black-and-Decker drill), to a total depth of 90mm, and then you hammer in the anchor. It's made slightly fatter than no. 8, and the cylinder closes in a little as it penetrates the hole, so that, with the spring in the steel, it grips like you wouldn't believe. I imagine you would have to pull the wall down to get it out, so make sure it is going where you want it, in the first place.

Irish High Crosses

by Roger Stalley. ISBN0-946172-56-0

Richly illustrated (22 B+W photos and 16 colour plates) and brief account of the high stone crosses, dating from about 800-1100 AD, with interesting data about specific crosses. Some noteworthy points:

Tradition names the soldiers who held up the sponge and who pierced the side of Christ as Stephaton and Longinus. These two soldiers at the crucifixion appear on many crosses.
The frequent occurrence of Adam+Eve+tree+serpent on the crosses is accounted for by the link enunciated by Fulbert of Chartres: "Christ, the beginning, end, resurrection and life...by hanging from a cross with a tree's help took away the poison that came from a tree, and opened again the closed doors to life."
Another popular scene shows St. Anthony and St. Paul being fed by the raven. These are the desert saints A+P, fathers of monasticism. After long trials, the raven brought them bread from heaven, which links to the Eucharistic sacrifice.

After You, Marco Polo

by Jean Bowie Shor. McGraw-Hill. New York. 1955,

Describes a determined effort by the author and her husband to traverse the entire trail taken by the Venetian explorer. She managed to visit the tomb of Genghis Khan while investigating the route in western China. (I read somewhere lately that DNA studies show that GK has an estimated 7 million living descendants. He killed a great many men, but it seems he had another use for a good few women.) Her attempt to travel the rest of the route, from Venice, was supported by the National Geographic Society. In the end, the attempt is frustrated by the successful Communist takeover of the whole country. Her worldview was of her time and class, and shows little appreciation of the realities of power and the ways of despots. She had a picnic and flight-for-fun with the (last) Shah of Iran, and was received and helped by the King of Afghanistan (also a member of the NGS). The king and her husband were wearing the same tie, purchased, as it transpired, from the same shop in Paris. Obviously, it creates a bond. The most interesting part is the account of the trek up the Vackan (or Wackan): the very narrow tongue of Afghan territory, on the south bank of the Amu Darya (Oxus), reaching eastward along the Hindu Kush and High Pamirs between the USSR and Pakistan to the Chinese border at Wakhjir. The high plateau at the end was effectively independent of Kabul, controlled by a Kirghiz bandit called Rahman Kul. Their Afghan escort abandoned them to RK, and he, for reasons not entirely clear, decided to help them continue, instead of just robbing and murdering them. Unfortunately, RK's recent activities in Chinese
Turkestan had the effect that the Chinese border troops would have shot them on sight at the Wakhjir Pass, so they ended up walking across the 20000 foot Delhi Sang pass, and sliding down into Hunza, the original Sangri-La. Her husband almost died of fever before they got properly down, but all ended happily. They did go up and step into China at the Mintaka pass, but then retreated.
Very interesting photos, including one of a yak leaping a 5 foot crevasse. There must be an article or two in the National Geographic from the early fifties.

Archimedes

Airciméidéas. Translated by Peadar Ó Casaide. Illustrations by Ghislaine Joos. Oifig an tSoláthair. 1979. (Irish. Original Dutch, Desclée De Brouwer, Bruges)

Short illustrated account, for children, of his life and inventions. I liked the cipher idea:
Wrap a ribbon of paper round a rod, in a spiral. Write the message along the stick, unwind and send. The recipient decodes by rewinding it on a rod of the same diameter.
Unless you assume uniform spacing of characters, this cannot be converted to any standard mathematical cipher. But it is rather like the following: (1) Write the message as an m by n matrix of characters, i.e. m rows of n characters. Then transpose the matrix, and transmit the rows one by one.
Easy enough to crack, to be sure. The original version could be a lot more trouble, since the sender can use any old scrawl, abbreviations, variations in calligraphy, and add noise in the form of doodles and dirt. However, careless doodles might assist alignment of the sections, so maybe better not to do that.

A Sorry Tale

Philip Hughes: A Popular History of the Catholic Church. Burns and Oates. London.1958. (f.p. 1939)

Very interesting book, putting some flesh on many people and movements that were little more than names to me. The author's attitude to the temporal power and the wealth of the papacy differs radically from mine. I see these as the root of most of the truly horrible abuses that he faithfully catalogues. Hughes goes so far as to commend one pope for his talent as a commander on the field of battle.

Coincidentally, the authors of the history of the Canary Islands that I'm currently reading credit "Juan de Paris, William of Occam, and Mansilio de Padua" with proposing that the pope has no temporal power. The context for their interest in the matter relates to papal bulls of 1433 and 1436, granting control of the archipelago to, respectively, Prince Henry the Navigator and the crown of Castille.

Horace

I re-read the odes, over a few weeks. I did not study these in school, possibly a blessing: one of my Russian friends tells me she can't enjoy Pushkin, ever since school. About forty years ago I became aware of the central place Q. Horatius Flaccus occupies in European civilization, and determined to get to grips with him. I've bought and inherited some material, over the years. Three slim volumes, and three fatter ones:

[1] A.H. Allcroft and B.J. Hayes (eds). Horace, Odes, Book I. Text and Notes. London. W.B. Clive. No date. Marked 2/- for second-hand sale.
Possibly belonged to my Uncle Billy, who finished at Synge St. CBS in the early 30's. Then again, I may have bought it somewhere, or it might have been Aunt Peggy's. Those two were the only two in my mother's family to complete secondary school. Includes an elaborate account of metres, besides the usual biography, dates, commentary, and vocabulary.
[2] Stephen Gwynn (ed). The Odes of Horace. Book III. Blackie. London, Glasgow and Bombay. No date. One colour plate. Once belonged to A. Lafferty.
[3] T.E. Page. Horace Odes IV. MacMillan 1933. Resold in Green's of Clare St. Owned by D.P. Moffitt, and by L. Sexton, of Ballineen, Ennis Road, Limerick and 64 O'Connell St., Limerick. Many (B+W) illustrations, with interesting commentary. All three of these school texts have extensive vocabularies, tailored to the volume in question.
[4] Horace Odes and Epodes, edited by C.E. Bennett and revised by J.C. Rolfe. Allyn and Bacon, Boston, etc. 1968. Bought this at Brown, in 1970. Text, followed by elaborate notes and commentary, but he expects you to work with a separate dictionary. This is a university text. In effect, he rubbishes what the English editors have to say about the metrical structure, and he has some interesting suggestions about pronunciation.
[5] Anon. The Complete Works of Horace. The original text reduced to the natural English order, with a literal interlinear translation. David McKay. New York. 1964 reprint. (Original Arthur Hinds, 1894). Also bought Brown, 1970, for $3.50. A brutal crib, but very handy, after you get a first impression of the text.
[6] James Michie. The Odes of Horace. Rupert Hart-Davis. 1964. This gives a very free verse translation (using unrelated metres suitable for English). This copy has been around: Simon J. Armad?, Sept 1981, Clare College. Lancashire Library (withdrawn from circulation). It came with some typed notes, as well as the usual (mostly pencil) glosses one finds in all the second-hand texts. Michie's objective was to make Horace accessible, and to compose English verse.

The commentators all agree that Horace had essentially nothing original to say, and that his fame rests on the utter perfection of his way of expressing the ideas. Gwynn says of the odes: "They are undoubtedly the best-known poetry in the world. If every copy of them were destroyed to-morrow, it would be easy to form for instance a committee of the House of Commons, which could restore from memory the entire text with in a week." This was written some time ago, and one doubts that it remains true. My own preference is for content over form, but one has to take seriously a writer of this reputation and perenniel impact. I found it hard work, when first I slogged though [4], using [5] as a crutch. For someone starting in, I think I'd recommend using [6], first. Read the Latin aloud. Then read the English on the opposite page, and go back. Later, poke at the details, referring to whatever you have handy, which should include a decent dictionary. It repays any effort expended.

Antigone

George Huxley is speaking this afternoon, on Piety and Power in the Antigone of Sophocles.
Text translation online at http://classics.mit.edu/Sophocles/antigone.html

Antigone, on the gulf that separates her from her sister Ismene: "One world approved thy wisdom; another, mine."

Who rules?

On Q. 161 of
the Catechism .

According to this, the bishop has authority, inter alia, to rule the faithful. The answer does not indicate any limits on the scope of this authority, except that it must be exercised in subjection to the Pope, and in accordance with the laws of the Church. It seems to me that this has caused a lot of trouble.

The logic behind this goes back to Q.138.

The relevant Articles of our Constitution run as follows:

Article 5.
Ireland is a sovereign, independent, democratic state.

Article 6.
1. All powers of government, legislative, executive and judicial, derive, under God, from the people, whose right it is to designate the rulers of the state and, in final appeal, to decide all questions of national policy, according to the requirements of the common good.
2. These powers of government are exercisable only by or on the authority of the organs of State established by this Constitution.

There has been some criticism lately that our constitution does not say that the state is a republic, but in fact it does better: 'republic' is only a word, but Article 6 spells it out. God's sovereignty is acknowledged, but it is quite clear that there is only one way God can influence our policy: through the people. Moreover, the bishops are not organs of state established by the constitution, so they don't get to rule, or decide on national policy, or exercise any powers of government.

Unfortunately, I'm afraid that since the days of the emperor Constantine, the clerical hierarchy has lusted after temporal power, and as a result the failure to be explicit about the limits of clerical power was deliberate, not careless. It ought to be spelled out explicitly. I note that in Pope Benedict's pastoral letter of the 19th of March, he says only one thing relevant to this concern of mine, and he says it not in the section addressed to people like me, but in section 11, addressed to the bishops. He gives a direct order:

Besides fully implementing the norms of canon law in addressing cases of child abuse, continue to cooperate with the civil authorities in their area of competence.

This certainly recognises the existence of an area of competence, but we need completely explicit recognition of the sovereign competence of civil society in the appropriate areas (those specified in Article 6). We seem to be getting this recognition from individual bishops, but it should come from the Church as a whole, and be addressed to all people, and it should be repeated on occasions like this.

Two novels and an autobiography

Cormac McCarthy. The Road. 897-0-330-44754-6. Most people seem to enjoy this story about the efforts of a man to protect his son during the final stages of a global extinction caused by a nuclear winter. I found it a curious mixture of sentimentality and pessimism about humanity.

---

Seamus Murphy. Stone Mad. 1-903464-81-1. Wonderful book. Exposes the vanished world of Irish stone-carvers, in which Murphy trained. Completely changed the way I look at the city. I went out of my way on Sunday, to walk across downtown and examine some of the work he writes about, such as the rivers on the Custom House. He records a great deal about the men who carved what we see about us in this country: who did what, where the stones came from, their characteristics. The discipline, the hardship, the pleasure of working in stone. "Getting to like doing what you don't like doing." I've long thought that "art" is nothing more than "craft". And nothing less. Murphy says: "Art grows out of good work done by men who enjoy it." Much of the book records, or recreates, the conversations and anecdotes of his elders and peers in the stoneworks, quarries, churches and graveyards of the first half of the last century. There are many good lines. For instance: "What are we doing, but making dust for time to rub away?", and "Once you realise that life isn't important anymore, departing from it takes on full significance." It was amusing to learn that Stephen is the patron saint of stone-carvers. This is, no doubt, for the same reason that Lawrence is the patron of cooks.
There is a fine bust of St. Patrick in the cloister in Maynooth, by Murphy. Just inside the President's Arch.

---

P.D. James. Shroud for a Nightingale. Penguin. f.p. Faber & Faber, 1971. A beautifully-crafted murder mystery.

Marguerite Yourcenar

Anna, Soror...
with
An Obscure Man
and
A Lovely Morning
0-00-271222-9
Translated from French (Comme l'eau qui coule..) by Walter Kaiser.

Fast-moving stories, set in the 16th and early 17th, visceral, revolving round sexual relationships. Not prurient, the account is matter-of-fact.

AOM and ALM go together. They are about this dutchman Nathanaël, who is swept though life, and never really knows what's happening to him. Not quite like any other chronicle. I liked it. Anna, Soror... is an intense and troubling tale of consensual incest, in the family of a spanish aristocratic occupying Naples, in which the principals are tortured by religious scruples, and tragedy reigns.

The book includes very interesting 'Postfaces', in which Yourcenar writes about the process of composition. It includes a survey of incest in literature, and this:

With Anna, Soror..., I tasted for the first time the ultimate privelege of the novelist, that of losing himself completely in his characters, or of letting himself be possessed by them. Thoughout those few weeks ... I lived uninterruptedly within those two bodies and those two souls, slipping from Anna into Miguel and from Miguel into Anna with that indifference to sex which is, I believe, that of all creators in the presence of their creations, and which silences with shame those who would express astonishment that a man could excel in depicting a woman's emotions -- the Juliet of Shakespeare, the Roxane or Phédre of Racine, the Natasha or Anna Karenina of Tolstoy ... -- or the rarer paradox that a woman could create a man in all his essential masculinity, whether the Genji of Lady Murasaki, the Rochester of Jane Eyre, or the Gösta Berling of Selma Lagerlöf.

MY was the first woman elected to the French Academy. She died in 1987.

Shelving it, I saw and remembered Zeno of Bruges. This was a gift from a friend who tries to improve my mind, but my mind proved resistant to improvement. I found it unreadable, at the time, and set it aside, implementing my 'life is too short' policy. Perhaps, if I live, I will give myself another chance with it, someday. But right now, the to-read shelf is 2.5 linear metres, and that doesn't count all sorts of other books that are likely to interlope. Besides, one should read french writers in french.

Robert Harris: The Ghost

ISBN 9780099527497.
Enjoyable quick read. Witty. Not in the league of Pompeii, Archangel,
or the Cicero novels.

The Fire i' the Flint

Mary Shine Thompson, Ed. Four Courts Press. 2009. ISBN 978-1-84682-073-1

Subtitle: Essays on the Creative Imagination. Essays based on the Seamus Heaney Lectures, 3rd Series.

A gift from Susan McKenna-Lawlor, one of the contributors. Beautifully-produced, with several brilliant essays. Perspectives from practitioners on creativity in poetry, painting, music, scientific work, and fiction, and on its place in education. Heaney on Kavanagh, a visual essay by Bridget Riley,
Peter Hamel on musical improvisation, Alan Titley on the writer's visceral relationship with words, Susan on our evolving understanding of the cosmos.
The essays on education (Seymour Papert, Kieran Egan, Jones Irwin, and others) present radical critiques of current practice.
In Titley's essay, even the prose is poetic. I disagree with him about the importance of the content, as opposed to the words, in literature, but I sympathise, too. In fact, I do admit the value of some work that lacks meaning, such as Jabberwocky and Finnegan's Wake. His discussion ranges over a considerable set of writers and tongues, and the quotations and discussion from various greats were stimulating. In particular, he stimulated me to revisit Lorca and to dig deeper in the Gaelic poets. Curious, coming upon his enthusiastic endorsement of Eoghan Rua Ó Súilleabhán so soon after reading Keating.
I particularly liked Egan's essay, entitled Imagination and Education, emphasizing the central importance of stimulating the child's imagination, and the rôle of story. This is good:

The trouble with our lives is that they don't have any clear meaning, except in so far as we can fit them into stories.

I also liked:

My uncle has a dog with no legs. I asked, 'What do you call him?' He said, 'It doesn't matter. He won't come.'

They've reduced our online journal access

Spent a little time on politics, and
sent out this letter to the editor today:

Two days ago I listened to Dr. Craig Barrett addressing the Academy and 600 of the country's leading figures, and making the point that we face a crisis much more serious than the transient fiscal problems that are in the news. Over the medium to long term, we cannot continue to enjoy our present levels of prosperity and comfort, unless we lift our performance on three key fronts from mediocre to excellent. The first two of these (the slogans are "smart people"
and "smart ideas")
involve Mathematics and Science. We need more people studying these to the highest level, we need at least 2000 more qualified Mathematics teachers,
and we need world-class scientific research.

At the same time, the community of mathematical researchers was just trying to come to terms with an action that threatens to set them back twenty years. As and from the 31st of January, we have lost online access through IReL
(the Irish Research e-Library)
to many of the main journals in our field. The situation is unclear, still. In some cases, there may be other ways to access the journal. But since the start of the month, I keep hitting screens that demand payment, when I go to check an article. Jobs that should be finished are hanging, while I try to find a work-around. To explain the realities, the research paper I am currently drafting with my collaborator in Bern needs results, so far, from 23 earlier papers, and counting. Since we use them, we have to check them: get the exact statements,
and make sure the proofs are correct. In January, I could see these papers from my desktop. Now I'm asked for cash, or invited to subscribe. Twenty papers, on a pay-per-view basis, would set me back about 500 euro. This puts me back where I was in the bad old days.

In recent years we have managed to attract (and attract back)
significant mathematical talent from overseas,
largely due to the improved research environment produced by government action, through SFI and the HEA. These people are not going to
tolerate a return to the kind of research conditions in which a
handful of patriots kept the flame alive in the old days. They will
go elsewhere, to continue the work they prioritize
in a supportive environment.

A setback at the level of key university researchers is going to damage the entire educational
system: these people are also training young
researchers, and future maths teachers at all levels, they are training people in other scientific and technical fields, and they contribute expertise and advice to ensure that our system of maths education is in touch with global developments. For instance, last
Tuesday I listened to the Minister for Education and Science telling
a conference hosted by the Academy and organized by Engineers Ireland
that he was pinning his hopes on Project Maths, in order to lift
our performance in Maths. Project Maths involves many inputs, and
one important one (namely the vetting of technical content
for correctness) is assisted, on a pro-bono basis, by university academics.
The Minister also said that it was "completely unacceptable" that
one-third of our secondary maths teachers are inadequately-trained.
The cure is, obviously, to increase the output of maths graduates.
But this is not going to happen if we wipe out the apex of the pyramid.
People are already disillusioned by increased teaching loads due
to a staffing freeze, and pay cuts of up to 25 percent. Hitting
their ability to use the time left for research as productively
as possible could be the last straw.

Our colleagues in the Physical Sciences are also hit by this change
to IReL, although the crieria used by the librarians seem to have
had a differential impact, and not hit them so hard. Nevertheless,
firm support for growth in the areas of Physics and Chemistry is
absolutely essential. These vital subjects are in catastrophic decline
in the schools.

If there is any kind of joined-up plan for this country, the IRel
resources for Maths, Physics and Chemistry
must be restored at once and in full.

James R. Mayer: The Shackles of Conviction

James R. Mayer Publishing. 2008. ISBN 978-1-906706-00-5
The author sent me a copy. It's a novel with alternate chapters tracking a fictional version of Gödel and a TCD undergraduate. In the foreword, James Meyer says

... since I can reasonably claim that I am the first person to have ever actually understood Gödel's Incompleteness Theorem, I wanted to give an analysis of that theorem in terms that are as accessible as possible.

The undergraduate sets out to disprove the theorem, and apparently succeeds. This half of the plot is a framework which allows the author to expound his ideas, by putting alternate sentences into the mouths of the student and his girlfriend. All rather improbable, and unlikely to appeal to anyone who isn't mathematically-inclined, but easy reading for the most part. There is an outrageously improbable episode near the end, where the two of them prioritise attending a lecture over reporting a homicide, and the hero gives a brilliant discourse despite this recent trauma and some preceeding torture. The half about Gödel is a better story, but completely disgraceful. The novel carries the usual disclaimer that any resemblance to living persons is coincidental. But Gödel and his wife are dead, and this story (1) has his wife plotting the death of Hahn and then Schlick in order to assist Gödel in hiding the fact that Hahn had found a flaw in the proof, and (2) explains Gödel's psychiatric problems as the result of his inability to cope with this flaw. This is terrible stuff.

Beatrix Potter: Treasured Tales.

F. Warne. 1999. ISBN-13: 978-0-7232-8013-2. Originals f.p. 1904-1913.

I report that The Tale of Mr. Jeremy Fisher was well-received by Oisín and Rian. (Mr. Fisher, a frog, has a fishing adventure, and is almost eaten by a trout. He is saved because the trout dislikes the taste of his macintosh.) This surprised me a little. I think the clincher was the exquisite illustrations, and the beautiful (physical) finish of the book. Of course, it helps that the boys love fishing. They both caught their first decent trout this past Summer, in Mayo.

Daniel Corkery: The Hidden Ireland

Subtitle: A study of Gaelic Munster in the Eighteenth Century.
Published by M.H. Gill and Son, Dublin. 1941.

Some teacher mentioned this when I was in secondary school, and recommended it highly. Finally got round to reading it.
Woefully self-indulgent writing, endlessly repetitive, and stridently polemical. His main message is that the Brits and the Ascendancy, with the arrogant superiority of the conqueror, were wholly unaware of the cultural life of the impoverished gaelic peasantry, but ought to have noticed it. DC was angry about this.
He relies mainly on secondary sources. This is partly justified by his declared aim of addressing the poetry, as opposed to the mere language of the poetry -- he rails against the 'grammarians'. He usually prefers to quote verse translations, sometimes very free, where these are available, instead of providing literal versions.
Ignoring its flaws, the book tells an interesting story of the bardic schools and the courts of poetry. I had not heard of the practice of composing while lying in bed, in the dark, cut off from noise. This may reflect the origin of the bards as druids, and derive from a similar method of divination. It has been suggested that some prehistoric rock-art, located in rather inaccessible recesses of cave-complexes in France, was associated with divination by shamans. (David Lewis-Williams, The Mind in the Cave, Thames and Hudson, London. 2002. ISBN 0-500-28465-2; a very good book.)
The main value of DC's book is in the verse quoted. Some is very fine, and it is good to have this material on my shelf. It is a pity that he makes no attempt to explain bardic conventions. He could have added to the little I know from other sources.

Fainne Geal an Lae (The Bright Ring of the Day)

We had a week on Geometrization last week: 18 lectures on Ricci flow, the proof of the Poincaré conjecture and the Thurston geometrization conjecture. These were organised by Constantin Vernicos, and delivered by Silvain Maillot and Laurent Bessière. Beautiful stuff. Turned out that SM plays tin whistle and is a fan of Irish traditional music, so Michael Clancy brought his fiddle on Friday and they had a session. I sang a couple of songs, and that reminded me that I don't know (any more?) the words of Fáinne Geal an Lae. This was the first tune I ever learned to play on the tin whistle, and nowadays it is better known as the tune that suits Patrick Kavanagh's Raglan Road. So I dug out my school song-book: Amhránleabhar Ógra Éireann (Songbook of Irish Youth), 3rd ed. 1954. (Ógra É. was a kind of club we had at school.)
Here is the text, p.34 (It's printed in the sean-chló, and I've rendered it into cló rómhánach, roman print):

Ar maidin moch do ghabhas amach
Ar bhruach Locha Léin;
An Samhradh 'theacht 'san chraobh len ais,
'Gus lonradh te ón ngréin.
Ag taistil dom tré bhailte poirt
'Gus bánta míne réidhe;
Cia gheobhainn lem ais ach an chúilfhionn deas
Le Fáinne Geal an Lae.

Ní raibh bróg ná stoca cadhp ná clóch'
Ar mo stóirín óg ón spéir;
Ach folt folt fionn órtha síos go troigh,
Ag fás go barr an fhéir.
Bhí calán crúite 'ci 'na glaic,
'Sar dhrúcht ba dheas a scéimh,
Do thug barr-ghean ó Bhénus deas
Le Fáinne Geal an Lae.

(Singer went out for a walk by the Lough Lane
at dawn, and met a heavenly blonde, wearing
just her long golden hair, and carrying a
milking-pail. He was impressed.)

Anthony Beavor: D-Day

He provides a more balanced account of the main features of the battle for Normandy in June-August 1944. This has become easier to do, now that practically everyone involved had died. The main strengths of the account are the accounts of (1) the effect on the civilian population, (2) the experience of war, based on individual memoirs, and (3) the well-documented violations of humane and decent behaviour by all sides.

Some of my prejudices (i.e. prior judgements) were supported by reading this: (1) My low opinion of Montgomery's character. (2) Ditto of Churchill. (3) That most of the killing is done in cold blood, and consists in the killing of unarmed people. (4) That the Germans were scarily good.

Nuggets:
1. German soldiers occupying Paris were forbidden to smoke in public.
2. Allied soldiers who wounded themselves were imprisoned. Germans were shot.
3. 70,000 French people were killed by Allied bombing, more than the number in Britain killed by German bombs.
4. Airey Neave was in MI9.
5. Hemingway was a prominent and flamboyant member of the press corps in Normandy.
6. 20,000 women had their heads shorn.
7. Most captured SS members were murdered.

I used to assume, when I was young, that we would have a war, and would have to fight. I have been extraordinarily fortunate, to be born early in this prolonged period of peacetime, in my part of the world. I have been spared exposure to the utter breakdown of decency that has always gone along with the passage of hostile armies through the land. (For this, we have to thank the Europen Union, above all else.) Even worse than the things that would have been done to me and my loved ones, are the things I may well have done myself. How do I know that I would have adhered meticulously to the provisions of the Geneva Convention?

Lustrum, by Robert Harris.

Enjoyable and instructive read. Sequel to "Imperium".
For me, the most interesting aspect of the story is the account of Caesar's activities in the capital city up to the moment when he set out for Gaul. Caesar fascinates me. People decry the 'great man' approach to History: the idea that all that really mattered was what the major players did. They argue that larger forces, at work on a wider scale, determine the course of History, and that the great men were just the instruments of these forces. Greatness thrust upon them, in fact. But it is hard to maintain this position in relation to the changes wrought by Caesar.

Thomas Mann: The Holy Sinner

Penguin 1969. Translation of Der Erwaehlte (how do you type a-umlaut?) Ah!, ä (ampersand-a-uml-semicolon). Make that Erwählte.
1951.
Fantastic book. Based on a Middle-High-German epic, Gregorius vom Stein, by Hartmann von Aue, and retailing an awful catalogue of disasters, culminating in dreadfully-compounded incest. Beautifully composed and cadenced, and culminating in unhoped-for redemption.
On the sin: "...her soul for horror had swounded, but only play-acting-wise, for on top the soul pretends and makes to-do about the diabolical deception practiced on it, but underneath, where truth abides in quietness..."
On divine mercy: "Great and extreme, woman, is your sin,... You are expecting that I shall raise my hands and curse you. Has never anyone told you, who had studied God, that he accepts true repentance for all sins and that a human being, be his soul never so sick - if his eye only for an hour grows wet with rue, then he is saved?"

The Existence of God

Read Irreligion, by John Allen Paulos. Hill and Wang. New York. 2008. ISBN-13: 978-0-8090-5919-5.
He writes well, with humour, and has put in some time on the research. Unfortunately, or perhaps not, he avoids the kernel of the problem. Right at the start, he has a quick attack on the First Cause argument. He sets up the most naive version of the argument, and shoots it down. The rest of the book is given to the demolition of various other 'proofs', and is generally unobjectionable, since these proofs do deserve demolition. He is particularly good on the ontological proof of St. Ambrose. His treatment is marred by some ad-hominem attacks on American fundamentalists and their political backers. One understands how the influence of these folk is an irritant, but the source of an argument should not influence our appoach to its validity.
The key question for me (and as I have just learned, Leibnitz!) is: Why is there anything?^[2]
Why is there any thing at all?
This is not a question about prior causes, things that were there in the past and caused what is there now. It is a question about now, and always,
and here and everywhere. Why, now, is there any thing?
There are two possibilities: (1) There does not have to be a reason. (2) There has to be a reason.
(1) is an interesting possibility, that I need more time to think about. If we accept (2), then the reason is a being that is at least as real as the thing, and we are quickly led to the existence of a being that contains its own reason for existing. Let's call it B. Then there are two possibilities: (2.1) B is the space-time we detect by our senses and explore by the scientific method of conjecture and refutation. (2.2) B is different from space-time, but somehow sustains it, and B.
Many thinking people, among them some of my friends, believe (2.1), so it is not crazy. All my life, I have believed, and still believe, (2.2). I could be wrong, and I don't understand how B goes about sustaining space-time, or why. I do know that I will never understand anything about this unless I believe, to begin with. Augustine said: You must believe that you may understand. Faith is an act of the will. It is not compelled. I accept that (2.2) is one step more complicated than (2.1), and hence violates Occam's Razor. Neither (2.1) nor (2.2) can be disproved, but they have profoundly different consequences for our view of life.
Accepting (2.2), we have two possibilities: (2.2.1) B is not intelligent,
or (2.2.2) B is intelligent.
As far as our attitude, hopes and moral stance go, (2.2.1) has no consequences that differ from those following from (2.1), whereas
(2.2.2) provides ground for hope, and meaning. (This not an argument for its truth.)
(It is also interesting to note, in passing, that without (2.2.2) we have no reason to suppose that experience, or any thing, is intelligible. The scientists who laid the foundation for that very 'modern science' which is taken by many as disproving the existence of God were motivated to search for intelligible patterns by their belief that the universe is made to a plan.)

^[1 What is the source for this?