Review of “The Mystery of the Aleph: Mathematics, The Kabbalah, and the Search for Infinity”, Amir D Aczel, Lancet, 17th February 2001

Following on from a review of a book on Nabokov on butterflies, my second piece in a proper non-student publication was this review of Amir D Aczel’s book on George Cantor and infinity. I still find the topic of this book quietly mind-blowing. The “diagonal argument” is a wonderfully accessible “ah-a” moment. Around this time I read a lot of popularisations on maths – which may have given me an entirely false confidence in my own mathematical ability.


The French mathematician Henri Poincaré wrote that the work of Georg Cantor was “a malady, a perverse illness from which someday mathematics will be cured”; the equally legendary German mathematician David Hilbert held that “no one will expel us from the paradise that Georg Cantor has opened for us”. Cantor, working in isolation in a provincial university, was at the cutting edge of late 19th-century mathematics, discovering set theory, establishing notation for infinite numbers, and stating the continuum hypothesis, for decades regarded as the most difficult problem in pure mathematics.

Galileo demonstrated in 1638 that one can prove that the set of all whole numbers is equal in number to the set of all squares of whole numbers, which is a subset of the set of all whole numbers. How can this be so? If we list all the natural numbers 1, 2, 3… and so on, we can place each of these umbers in direct one-to-one correspondence with its square. We can also put each one in correspondence with a prime. Cantor would later use such thinking to define an infinite set as a collection of objects that can be put into a one-to-one correspondence with a part of itself. Cantor realised that the paradoxes of infinity produced weren’t just slightly bothersome games but required a new type of arithmetic. Sets that can be matched to each other like the example above are then said to have the same cardinality; Cantor dubbed such sets “countably infinite” and denoted their cardinality by “aleph-null”—the Hebrew letter aleph with the subscript zero.

Cantor proved that there are infinities larger than countable infinities by a remarkably ingenious argument—if we try to count all possible real numbers (numbers that can represented as decimals) between 0 and 1, we find we cannot put them in a one-to-one correspondence with the natural numbers of countable infinity. Suppose we list the natural numbers and correspond them with all possible decimals between 0 and 1, in no particular order, like so: and so on forever. Cantor constructed a “diagonal number” by taking the first digit from the first place after the decimal point of the first number, the second digit from the second place after the decimal point of the second, and so on. In this example we get the number 0·27267…which is made of a digit from every single number on the list. If we alter each digit in this number by adding one to it, we get a new number (in this case 0·38378…) which cannot appear anywhere on the original list, since by its very construction it differs by at least one digit from every single entry in the list. In other words, constructing the diagonal number creates a number that has at least one digit in common with every single decimal on the list—and by changing that digit we create a number that loses this common characteristic with each of the numbers on the list. So the decimals cannot possibly be put into one-to-one correspondence with the natural numbers—they are uncountably infinite and are denoted by the symbol C for continuum. The author also demonstrates how Cantor used the concept of the continuum to prove, amongst other things, that there are as many points on any given line as in any shape or volume, no matter of what size. “I see it, but I don’t believe it!” Cantor wrote (in French) of this result.

1 ………… 0.2345678 to infinity
2 ………… 0.5756037s to infinity
3………… 0.6729283 to infinity
4 ………… 0.2386412 to infinity
5 ………… 0.9877754 to infinity

The continuum hypothesis was Cantor’s next step. He wondered whether infinite sets exist that are intermediate in size between aleph-null and C. He thought they didn’t—in his own notation, he hoped to prove that aleph-one (which he defined as the next order of infinity following aleph-null) equalled C—but was unable to prove so. The problem increasingly began to haunt him. His work was under attack from the Berlin-based mathematical establishment, embodied in Leopold Kronecker, who sternly declared “God made the integers; all else is the work of man”. He longed for an appointment to the mathematical faculty in Berlin, and began to believe that his enemies were conspiring against him. Spending increasing amounts of time in the Halle Nervenklinik, he also became an enthusiastic advocate of the Baconian theory of Shakespearean authorship; Aczel represents this as Cantor’s tortured intellect taking refuge from the blinding light of infinity, which he compares to the infinite brightness of the chaluk, God’s robe in Kabbalah tradition. Increasingly Cantor gave the continuum hypothesis the status of dogma, declaring that “from me, Christian philosophy will be offered for the first time the true theory of the infinite”.

The mathematicians Kurt Gödel (who himself suffered from paranoia and hypochondria) and Paul Cohen would later show that, firstly, if we treat the continuum hypothesis as an additional axiom of set theory, it doesn’t contradict any of the other axioms of set theory, and secondly if we treat the opposite of the continuum hypothesis as an additional axiom of set theory, it doesn’t contradict any of the other axioms of set theory. Thus the continuum hypothesis is independent of the other axioms of set theory, and therefore can neither be proved or refuted from those axioms.

As he discusses Cantor’s existence in the provincial university of Halle, Aczel announces “mathematical research is best done within a community of good mathematicians. Research results can be shared and ideas exchanged, so that new theories can develop and thrive”. This is almost certainly true, yet within a few pages Aczel has discussed not only Cantor but two of his contemporaries who made spectacular advances working in isolation; the immensely likeable Karl Weierstrass (who developed the modern theory of mathematical analysis by night while working as a schoolteacher), and Richard Dedekind (who made equally important contributions to the definition of irrational numbers in the provincial University of Brunswick)—yet Aczel never even discusses the implications of this.

It is significant that a recent survey of American scientists’ attitude to the divine found mathematicians the most likely (with biologists the least likely) to believe in a God. Reading of the dizzying orders of infinity that Cantor explored, one feels perhaps that maths and music are the closest humanity can get to any sense of the divine. Aczel treats this potentially fascinating theme in a curiously perfunctory way; the Kabbalah is discussed in one chapter, belying the subtitle. There are some rather superficial references to the ability of the human mind to comprehend the infinite, with occasional references to the connection between Cantor’s fragile mental state and his work on the continuum hypothesis. Periodically Aczel announces that Galileo or Cantor or Güdel had the ability to face in full the concept of infinity, which most mathematicians and indeed human beings never do, but never explores precisely what this means.

All told The mystery of the Aleph deals with one of the most fascinating themes that mathematics holds for the general reader, and deals sympathetically with its central character. Indeed the rarefied world of infinity and its relationship with the divine is perhaps the most beguiling seductress mathematics can rely on to persuade the reflex numerophobes conditioned to see mathematics as dry, soulless, and worst of all, boring. Like Paul Hoffman’s The man who loved only numbers and John D Barrow’s Pi in the sky, this is another accessible introduction to the world of pure mathematics, although perhaps Hoffman’s work is more engaging. Aczel’s work belongs in the set of books dealing with fascinating tales and concepts that fall just barely short of greatness.


“Democracy is a thing which is always breaking down through the complexity of civilisation” – GK Chesterton, Allan Massie and complexity

. As I have recently written, I am reading a collection of Allan Massie’s Life and Letters columns from the Spectator, which is full of shrewd judgments. In particular there is this on G K Chesterton:

What is disconcerting for many about Chesterton is that, while deadly serious, he revelled in paradoxes, absurdity and farce. He believed in the Devil, believed in him as perhaps few in the last centuries did, but the weapon he employed against him was laughter; he was at one with Rabelais : ‘the discovery of the reality of evil and the battle against it are at the basis of all gaiety and even of all farce’.

Chesterton would have found Orwell admirable — and ridiculous; ridiculous because of his solemnity. ‘The men who really believe in themselves are all in lunatic asylums’, he declared. He thought in paradoxes, on the sensible ground that if an idea is worth anything it ought to be able to be held upside down and shaken about.

Sometimes, admittedly, the paradoxes flew too easily, too frequently and tiresomely from his pen. He wrote too much and often, I suspect, when he was tired, and then the paradoxes had a mechanical or tinkling sound like music from an elderly barrel-organ. But at his best they make you think, and this is always disturbing: ‘Reason is itself a matter of faith. It is an act of faith to assert that our thoughts have any relation to reality at all.’

That’s a thought you get your mind round. Because he was a man of faith he understood and valued doubt. He thought Charles II’s deathbed admission to the Roman Church proof of his perfect scepticism. The wafer might, or might not be, the body of Christ, but then it might, or might not be, a wafer. More than 70 years after his death he remains an entertaining writer, and a disquieting one. In the opinion of the editor of L’Atelier du Roman, Lakis Proguidis, ‘no twentieth-century author has so thoroughly examined the yawning gulf cut in each soul by the ideology of Progress’.

I know what Massie means about “too easily, too frequently and tiresomely” – at times in the polemical and apologetic works there is a sense of dead horses being flogged. At his best, however, there is a freshness to Chesterton’s prose, especially his fiction. Borges adored Chesterton, indeed placed him with Stevenson (and on one occasion Homer) in a personal pantheon.

Anyhow all this is prelude to a passage from The Everlasting Man which struck me as forcibly summarising the thoughts of Joseph Tainter on complexity:

It is far more probable that a primitive society was something like a pure democracy. To this day the comparatively simple agricultural communities are by far the purest democracies. Democracy is a thing which is always breaking down through the complexity of civilisation. Anyone who likes may state it by saying that democracy is the foe of civilisation. But he must remember that some of us really prefer democracy to civilisation, in the sense of preferring democracy to complexity.

“The whirligig of time” : A note on Fr Pat Noise

“The whirligig of time” : A note on Fr Pat Noise


Seeing that this documentary is to be broadcast next Saturday I thought it an apt time, though any time would be an apt time, to post about my own research into the obscure career of Fr Pat Noise…

Some years ago, when lecturing in UCD, I was working on a presentation on conditions in some ways connected with the passage of time. The best known being deja vu, the perception when in a new place or situation that one has been here before, or the same thing has happened before. Of course, there is a whole psychological science of time.

In those days I had the chance to read more deeply and broadly for this kind of thing than since. I used what was then the UCD School of Medicine in Earlsfort Terrace. It was the last few months of it being part of UCD. The librarians were working on transferring stock of the main UCD Library and many older and more obscure volumes were out and about on various trestle tables. Among these was one which I had dimly heard of but had also come up in some of my reading, Vico’s The New Science. Vico believed that history went in a curve or spiral, and that events recurred.

In the middle of the book, presumably used as a book mark at some stage, I found a faded, worn prayer card. I could barely make out the text on it except for a request to say an Our Father and a Hail Mary for the soul of Fr Pat Noise, and below this the following words:

Do you want to see what human eyes have never seen?
Look at the moon
Do you want to hear what ears have never heard?
Listen to the birds cry
Do you want to touch what hands have never touched?
Touch the earth
Truly I say that God is about to create the world.

This struck me as somewhat unusual content for a prayer card. Again, having more time than now, I was able to follow up with some research on Fr Noise in the Dublin Diocescan archives in All Hallows. I think I had a vague idea about writing some kind of paper. I am not a historian and was seeking not truth nor likelihood but astonishment. So I found out somewhat more about Fr Pat Noise.

Noise, like Fergus Kilpatrick and Dungarvan native John Vincent Moon is a figure who has somehow been forgotten, by and large, in the so called Decade of Centenaries. Unfortunately, at the time , I made my notes in a file on a laptop which is long defunct.

In the archives what we read about Fr Noise is entirely through the words of others, him being a curate in Berkeley Road who dressed in an extremely flamboyant manner, who was unambigious in his support of the workers in the 1913 Lockout, and also as proposing theological views not entirely Orthodox. However one letter describes him as travelling to the furthest reaches of orthodoxy, but not going over the precipice.

This was contained in another letter from a priest that was otherwise quite hostile to Fr. Noise. According to this priest, Fr Noise stated that there are no two moments alike and every moment is a new moment and that history is in a cycle and life is in a cycle because every moment is new again. The poem that was on the prayer card was reproduced in this letter; apparently Fr Noise read it at a ceremony. It is unrecorded what the congregation in Berkeley Road made of this.

Fr Noise’s sympathy for the 1913 Lockout and for the poor of Dublin seems to have, in a similar way, gone right to but not past the limit of what the Church hierarchy could tolerate. There are hints in another letter, by an anonymous outraged parishioner, of accusations of Socialism and Communism, but in this area Fr Noise crafted his sermons in the words of Christ Himself, and remained at the dangerous edge of orthodoxy.

The link with Peadar Clancy came through being one of the genuine customers of Republican Outfitters. This was a well known meeting place for the IRA in Dublin. Dan Breen said that really if you were an IRA man you shouldn’t stay there too long. In the letters about Noise it is mentioned that he wore quite elaborate capes and top hats which were sourced from Republican Outfitters.

He also apparently translated Shakespeare’s Julius Caesar into Irish, but there is no trace I could find of this. There is also a clipped article by Fr Noise, but from an unidentifiable periodical, on Festspiele – festivals in Switzerland in which thousands of people , possible the whole population of a town or area will renact historical events in the place where they happened. In this piece he suggests that this is something that Ireland and Dublin should emulate and and there were all these hints that the 1916 Rising was a reenactment of a previous event that had happened before in history.

Fr Noise pops up in letters beween Peadar Clancy and Sean Treacy and also seems to have been an intermediary for Clancy. Surprisingly these activities do not make it into the accusations of his various foes, and in the letters what Clancy describes are purely philosophical and theological discussions.

Fr Noise is now commemorated with a plaque on O’Connell Street, but otherwise his life is nearly totally forgotten by both the worlds of the Church and of Official Ireland. Perhaps in the narrative of commemorations and the rather self-congratulatory rhetoric about How Far We Have Come, a priest with cosmopolitan intellectual influences does not fit neatly into our perceptions of a cleric or a revolutionary. His plaque is, by coincidence, on the spot on O’Connell Bridge beside which the Millenium Clock, a digital clock inserted into the Liffey in 1994 but which was beset by all sort of problems, including time running backwards.

Do you want to see what human eyes have never seen?

Do you want to see what human eyes have never seen?
Look at the moon
Do you want to hear what ears have never heard?
Listen to the birds cry
Do you want to touch what hands have never touched?
Touch the earth
Truly I say that God is about to create the world.

From The Theologians, Jorge Luis Borges

The opening lines of The Theologians:

After having razed the garden and profaned the chalices and altars, the Huns entered the monastery library on horseback and trampled the incomprehensible books and vituperated and burned them, perhaps fearful that the letters concealed blasphemies against their god, which was an iron scimitar. Palimpsests and codices were consumed, but in the heart of the fire, amid the ashes, there remained almost intact the twelfth book of the Civitas Dei, which relates how in Athens Plato taught that, at the centuries’ end, all things will recover their previous state and he in Athens, before the same audience, will teach this same doctrine anew. The text pardoned by the flames enjoyed special veneration and those who read and reread it in that remote province came to forget that the author had only stated this doctrine in order better to refute it.

“The story-within-a-story done right” : review of “The World House”, Guy Adams, SF Site 2010

“The story-within-a-story done right” : review of “The World House”, Guy Adams, SF Site 2010

Original here. Despite my enthusiasm here – and what I wrote in the penultimate paragraph – I didn’t read any of the succeeding books in this series. I was never, even at my adolescent height of enthusiasm for SF/fantasy, all that into the multivolume series which dominate the field.

The World House
Guy Adams
Angry Robot, 2010


Done properly, the story within a story can have a vertiginous effect, a sense of being caught in an infinite loop, best described by Jorge Luis Borges in his lecture on “The Thousand And One Nights” collected in the book Seven Nights. The world-within-a-world story can have a similar effect. In a way, the hidden world is a theme not only of literature — from Horton Hears A Who to, it could be argued, the three stages of the afterlife in Dante’s Divine Comedy (Dante enters the afterworld through “a dark wood”) — but of myth of the underworld may be the first world-within-a-world story.

Guy Adams has created a rollercoaster of a story set in a world within a box — a world-within-a-world that is itself a Divine Comedy. For the box is, for most of those inside, a kind of after-life — those humans who enter the box do so at a moment of imminent death in this world — and it is certainly more an Inferno, or at best a Purgatorio, than a Paradiso. This is a world created out of the nightmares and fears of humans themselves, contained inside a box that is in fact a prison, with a very special prisoner.

The first third or so of the book is taken up by gradually introducing the multifarious cast of characters. From Spain during the Civil War to Harlem in the early 30s to the late night bars of New York in the 70s to Florida and an unnamed corner of England today, the pre-box lives of the characters are sketched artfully and speedily.

We begin with Miles, an English antique shop owner with poor financial judgement and a gambling habit, who gets on the wrong side of some very nasty characters indeed, and just before they blow him away on account of an unpaid debt he vanishes into the box. We also meet Penelope Simmons, a fun-loving Boston socialite in the 30s, who, about to be raped and murdered by her psychopathic fiancé Chester and his chauffeur at the end of a night out in Harlem, also disappears into the box. Both turn up at the same time and in the same area of the rambling, seemingly infinite house, which is where most of the action in the world takes place. If there is a main protagonist to the book, it is Miles, whose mordant world-view and lack of appetite for heroics, and lustful longing for Penelope (in fairness to Miles, at their first encounter Penelope is totally naked having escaped from Chester’s clutches just in time) are an earthy anchor point as the surreal action ensues. Miles and Penelope luckily team up with Carruthers, an Edwardian big game hunter and general man of action along the lines of Lord John Roxton from The Lost World who is determined, with admirable pluck, to escape the box altogether.

Interspersed with the stories of the box’s human inhabitants are brief vignettes of the story of some kind of super-powerful entities, probably extraterrestrial, who are responsible for the box’s existence. The box is a kind of prison for a renegade entity, one who stayed behind to enjoy tormenting the puny, pitiful humans whom its fellows had just been bored by.

In the early stages, it seems at times that Adams is throwing in yet another character from yet another setting, seemingly at random. As the story progresses, we realise that there are connections and commonalities there. And there seems to be another kind of inhabitant of the box — who seems able to exit and re-enter both the box and our own timeline. Alan Arthur, an academic in modern Florida with a large chunk of his memory missing, is drawn to this box (which, unsurprisingly for an artefact of such power and mystery, has been the subject of confused and fragmentary articles in some of the more out-of-the-mainstream media) for reasons that become clearer as the story progresses.

Too much more would give away not only the plot but the pleasure of reading the unfolding of this intricate tale. The world of the box is one of subtly altered reality, where benign seeming surfaces mask mortal dangers. From a jungle to snow-capped mountains to a sea of literal dreams, there are all the unnatural environments that one could think of. This may be a kind of after-life, but the box is a highly lethal place. Most of the visitors have a short life expectancy, and many resort to a brutish subhuman existence of cannibalism and fear.

Some of the most endearing characters are, unfortunately, not with us for long — although the conclusion does raise the possibility that the arrows of causality may have to be tinkered with, if not actually reversed. There will be a sequel, Restoration, which I for one will certainly be reading to see where the ride will go next.

World-within-a-world stories, like stories-within-stories, can be horribly self-indulgent and dull. After a while, the reader can lose interest in a story in which anything can happen with no real consequences, or in which random settings can be created. The crucial trick which Adams pulls off is to create compelling characters whose destiny becomes a matter of all-consuming interest in the reader. Adams is also adept at keeping the various strands of his highly productive imagination together, and creating a real sense of nightmare and indeed of menace in the story.

“The Glamour of the West”  D L Kelleher, 1928

“The Glamour of the West”  D L Kelleher, 1928

20170605_095717-1The Glamour of the West seems to be part of a series by D L Kelleher, following on from The Glamour of Dublin and The Glamour of Cork. Kelleher is an obscure figure now. Here is his bio from The Concise Oxford Companion to Irish Literature:

Kelleher, D[aniel] L[aurence] (1883–1958),

playwright and man of letters. Born in Cork and educated at UCC, he was associated in his early career with the group of dramatists known as the ‘Cork Realists’ [see Abbey Theatre]. Stephen Grey (1910) was produced at the Abbey in 1910, and thereafter he wrote A Contrary Election (1910). His travel sketches reflect his varied career, and include Paris, Its Glamour and Life (1914), Lake Geneva (1914), The Glamour of Dublin (1918, as ‘D. L. Kay’), The Glamour of Cork (1919), Round Italy (1923), and Great Days with O’Connell (1929). His poetry includes Cork’s Own Town (1920), Poems Twelve a Penny (1911) and Twelve Poems (1923).

The Glamour of the West doesn’t even make this concise list. It is a collection of very brief sketches, the longest a couple of pages. The subtitle, “Bantry Bay to Lough Foyle”, gives a sense of the geographic range, although at times Kelleher veers quite far east (to Anthony Trollope in Banagher and Maria Edgesworth in Edgesworthstown).

20170605_095726I quite liked the Talbot Press symbol (“logo” seems a bit anachronistic) Talbot Press seems to have gone the way of all flesh:


Kelleher’s tone is set from the outset, in a “Prelude”:

“The West’s Awake!” – Awake to what? To its own infinitely small knowledge of itself? That  is as much as one can say in answer.

He ends the Prelude thus:

So, in 1928, this brief book of resentment and hope, coloured with a little love, takes up a few of the threads, and as tenderly, cynically, or dispassionately as may be, for a moment resumes an old story.

Kelleher references “cynicism” quite a bit throughout. The tone of the book is often bantering, scathing  – but in a somewhat indirect way. It put in my mind of a fictional character, Sarah Devlin from J G Farrell’s wonderful novel Troubles  There is a sort of habit of mind that could no doubt be called post colonial in a later age; mindful of the the atrocities but also the slights inflicted on the Irish nation over the years, and complaining of these in a what could be called a passive aggressive tone. Perhaps most suggestively, there is little on the events of the prior decade which led to Irish independence (in part).

Some extracts may demonstrate this comparison – the reader can judge if it is apt or not.

“The 1847 Famine In Mayo” is perhaps a little more emotionally direct than other pieces. It begins with a consideration I have wondered about myself

In the year 1928, when this book is being put together, there are many thousands of living Irish people whose parents were born in or about the Famine times. No wonder, here and there, if a melancholia should appear in the Irish. A generation born around the famine year could not escape the famine complex. In the west especially, life turned black with the black blighted potato. Social historians discuss the incidence of hysteria, and worse, due to the Zeppelin nights in London. The long duresse of the famine of 1847 was deeper shock to the whole population than any number of night-raids. Death might ensue from a bomb, but despair and death both were surer in Ireland. In Mayo the tragedy was at its height. At Westport workhouse, built to hold one thousand inmates, three thousand clamoured for entrance sometimes in a single day. Yet the pride of the Irish poor if well known; they will only enter the poorhouse when ruined and hopeless. The gate of the workhouse would be closed and barred early. Then the desperate, weak, lonely, agonised outcasts would throw themselves down to rest and snatch a sleep at the foot of the wall on the opposite side of the road. As many as seven corpses were found one morning like that, dead where they lay.

“Long duresse” is in the original. I did wonder originally was it a reference to the longue durée  concept of historians of the French Annales School, but this was many years before. “Duresse” must be related to “duress” and mean suffering.

Here is another characteristic extract –  about a man from my father’s part of the country:

A very old man, eighty-five, perhaps more, came into the town of Dunflin, Co. Sligo, one day in 1670 on his way to Dublin. The jolting of the rude two wheeled car, with only a layer of straw thrown down in it to soften the corner where you could sit, had tired him out. So he went to the tavern where he was known (for he had often passed that way) and asked for a bed for the night. He was given his old bed in the room above, and then he settled down by the fire in the kitchen to take a little drop of whiskey to revive him and to rest for a short while. There was a very nice girl serving drink to any that would come into the bar outside. But there was little custom and she came into the kitchen and stayed a long time talking to the old man, for she was a really nice girl and could appreciate him. They were pleasantly conversing when a loud clatter of feet was heard from the shop and a voice calling, “Come on here and fetch it out!

Hurrying from the kitchen the girl recognised the intruder as a well-known loyalist from near Dunflin. As soon as he saw the comely girl he put his hand around her, but she pulled herself away and stepped back into the kitchen where the old man had risen from his chair on hearing the confusion. The intruder followed her in and again trying to lay hold of the girl, said “Come on! Give me a kiss and you, you old —–, turn away!”

But the old man put himself between the girl and the soldier and defied him to touch her, for, as old as he was, he would strike “a foul fellow the like of you.’ The drunken soldier, blazing with insolence and disappointed passion, caught up a knife that was lying on the table and drove it into the old man’s heart and killed him with that blow.

That old man was Duald MacFirbis, once a rich scholar, who had spent his whole life compiling histories and genealogies. He was one of the true lovers of Ireland, keeping a hope for posterity by writing down the story of the heroic past. He did it in poverty and homelessness and now he had murder for his crown.

Here are some photos of the pages this story is recounted in:



It is easy to mock this kind of thing, with references to comely girls and so on. Of course, as I often think, some day our prose will no doubt seem laughable. And the book is an at times nearly Borgesian in its laconic capturing of a person, a society, a nation through moments.

One more extract, and this one is actually in some ways the most characteristic:


This is a personal chapter. It need not lose by that. It is about a trip we took by road from Sligo to Bundoran. It is really about a stop we made on the way when we ran past a desolate-looking harbour of refuge that the Congested Districts Board had made for fishermen, since gone to America. We were able to pass around the empty harbour to the edge of a cliff almost as unreclaimed as nature left it.

It was a day in mid-June when primroses rambled over the grass, and sea-pinks with them. Under the cliff the rocks cut into a smooth sea. The view extended almost to Donegal. There was no ship or boat or any sign of life except ourselves.

“Where are we now?” said I.

“I don’t know,” said the man who owned the car. “I came here once before and don’t know whether it is Leitrim or Sligo.”

“Is Leitrim on the coast?”

“It is – a couple of miles of it. But I think we are in Sligo. Leitrim is further on.”

We made tea on the sloping cliff side and watched the perfect solitude.

“Nothing ever happened here,” said my friend. “There is no glamour to write about.”

Nothing only primroses in mid-June, gold sands shining up through blue water, the smell of sea-wrack from the caves, the caress of soft aqueous air.

Glamour enough! Go there and see!


“it is astonishing that each morning we wake up sane – that is, relatively sane -after having passed through that zone of shades, those labyrinths of dreams”

Lately I’ve been rereading psychology books, and have felt singularly defrauded. All of them discuss the mechanisms of dreams or the subjects of dreams, but they do not mention, as I had hoped, that which is so astonishing, so strange – the fact of dreaming.

Thus, in a psychology book I admire greatly, The Mind of Man, Gustav Spiller states that dreams correspond to the lowest plane of mental activity – I would maintain that, at least for me, this is an error – and he speaks of the incoherence, the disconnectedness, of the fables of dreams. I would like to recall Paul Groussac and his fine essay, “Among Dreams,” in The Intellectual Voyage. Groussac writes that it is astonishing that each morning we wake up sane – that is, relatively sane – after having passed through that zone of shades, those labyrinths of dreams.

The study of dreams is particularly difficult, for we cannot examine dreams directly, we can only speak of the memory of dreams. And it is possible that the memory of dreams does not correspond exactly to the dreams themselves. A great writer of the eighteenth century, Sir Thomas Browne, believed that our memory of dreams is more impoverished than the splendour of reality. Others, in turn, believe that we improve our dreams. If we thin of the dream as a work of fiction – and I think it is – it may be that we continue to spin tales when we wake and later when we recount them.

  • Jorge Luis Borges, “Nightmares”, from Seven Nights