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.


St Patrick’s Breastplate / The Deer’s Cry : music by Shaun Davey / Rita Connolly, Arvo Part, John Fahey, John Kenny, Melville Cook

St Patrick’s Breastplate  / The Deer’s Cry :  music by Shaun Davey / Rita Connolly, Arvo Part, John Fahey, John Kenny, Melville Cook

As a child, I was somewhat mystified why a certain hymn in our religion books was called “St Patrick’s Breastplate” but went:

Christ be beside me, Christ be before me,
Christ be behind me, King of my heart.
Christ be within me, Christ be below me,
Christ be above me, never to part.

Christ on my right hand, Christ on my left hand,
Christ all around me, shield in the strife.
Christ in my sleeping, Christ in my sitting,
Christ in my rising, light of my heart.

with no references to breastplates (or St Patrick)

Only much later did I hear a complete version and also read that this was an example of a lorica, an invocation of the divine for protection in the manner of a warrior putting on armour.

The text is first found in the Liber Hymnorum or “Book of Hymns”. It seems most dating of the hymn sets it later than the historical Patrick, who is therefore unlikely to actually be the author.


Two translations are presented here. Here is the second of those translations:

I arise to-day
Through a mighty strength, the invocation of the Trinity,
Through belief in the threeness,
Through confession of the oneness
Of the Creator of Creation.

I arise to-day
Through the strength of Christ’s birth with His baptism,
Through the strength of His crucifixion with His burial,
Through the strength of His resurrection with His ascension,
Through the strength of His descent for the judgment of Doom.

I arise to-day
Through the strength of the love of Cherubim,
In obedience of angels,
In the service of archangels,
In hope of resurrection to meet with reward,
In prayers of patriarchs,
In predictions of prophets,
In preachings of apostles,
In faiths of confessors,
In innocence of holy virgins,
In deeds of righteous men.

I arise to-day
Through the strength of heaven:
Light of sun,
Radiance of moon,
Splendour of fire,
Speed of lightning,
Swiftness of wind,
Depth of sea,
Stability of earth,
Firmness of rock.

I arise to day
Through God’s strength to pilot me:
God’s might to uphold me,
God’s wisdom to guide me,
God’s eye to look before me,
God’s ear to hear me,
God’s word to speak for me,
God’s hand to guard me,
God’s way to lie before me,
God’s shield to protect me,
God’s host to save me
From snares of devils,
From temptations of vices,
From every one who shall wish me ill,
Afar and anear,
Alone and in a multitude.

I summon to-day all these powers between me and those evils,
Against every cruel merciless power that may oppose my body and soul,
Against incantations of false prophets,
Against black laws of pagandom,
Against false laws of heretics,
Against craft of idolatry,
Against spells of women and smiths and wizards,
Against every knowledge that corrupts man’s body and soul.

Christ to shield me to-day
Against poison, against burning,
Against drowning, against wounding,
So that there may come to me abundance of reward.
Christ with me, Christ before me, Christ behind me,
Christ in me, Christ beneath me, Christ above me,
Christ on my right, Christ on my left,
Christ when I lie down, Christ when I sit down, Christ when I arise,
Christ in the heart of every man who thinks of me,
Christ in the mouth of every one who speaks of me,
Christ in every eye that sees me,
Christ in every ear that hears me.

I arise to-day
Through a mighty strength, the invocation of the Trinity,
Through belief in the threeness,
Through confession of the oneness
Of the Creator of Creation.

There have been many musical settings of this text. My own memory of the Christ Be Beside me of my school days was a rather wishy washy acoustic guitar led dirge, though I did like the words. However the piece – which as the translation above reveals has a certain narrative drive and power – has lent itself to some excellent settings. Not all the text is generally set – the reference to “spells of women and smiths and druids” gets omitted. This site presents many versions and an excellent discussion on the piece as a hymn (some of the historical background given is slightly at variance with that above) with a helpful account of the musical background.

“This hymn can be a chall­enge to sing with­out see­ing the words matched to the notes,” observe the editors of the Cyberhymnal (linked below), “but it is a mas­ter­piece ne­ver­the­less.”

They’re correct on both counts.

The hymn is complex musically. As Wikipedia notes, “In many churches it is unique among standard hymns because the variations in length and metre of verses mean that at least three different tunes must be used – different in the melody sung by the congregation.”


Here is one of the most powerful versions from Shaun Davey’s “The Pilgrim” with vocals by Davey’s wife, Rita Connolly:

Many contemporary versions seem to owe quite a debt to Davey’s, although few come close to its power.

Here is a photo from the CD sleeve of “The Pilgrim” of Shaun Davey with some piper. I am not sure why I find this a wonderful photo, but I do:


Here is an austere, haunting Arvo Part setting:

The eclectic, eccentric American folk guitarist John Fahey
made an arrangement called “St Patrick’s Hymn” which sounds like an off-kilter Renaissance Fayre soundtrack:

This isn’t on YouTube as far as I can find, but here is someone else playing the arrangement:

Finally, here is something very different… and perhaps for those who find all the above a little too pious / inspirational / hymn-y this is a very different version by the British composer John Kenny sung by the choir of Gonville and Caius College Cambridge. Some interesting background from the John Kenny article linked to above:

At the point we actually had the three Celtic instruments – the great horns of the ancient Celtic world – reconstructed, I thought ‘yeah’, there is only one poem that I know that could combine these three cultures for real, and that’s possibly the oldest poem in old Irish that has come down to us.

The poem is called the Lorica, or ‘the Deer’s Cry’ – attributed to St Patrick himself. I’ve set the text in three languages; old Irish, ancient Celtic Latin and a wonderful English translation.

The piece features two ancient instruments – the Lochnashade horn, representing Irish culture and the Deskford Carnyx representing where St Patrick originally came from. It seemed appropriate to set with these instruments – this is a poem from the transitional period between Paganism and Christianity, between Roman culture and the hinterland culture of the Celtic Church.

Here is a whole Spotify playlist full of versions:

One of my favourites of these is the Rites Reserved version (first on the Spotify playlist above) – cannot find a YouTube link. While the arrangement is rather familiar, there is something in the instrumentation and vocals reminiscent of Judee Sill

Finally to end with a more “traditional” choral setting, firmly in the Anglican choral tradition. Charles Villiers Stanford’s setting seems to be the canonical hymnal one, but I somewhat prefer this by the organist and composer Melville Cook. As per the info on the YouTube video below:

During his service as Organist and Choirmaster of Leeds Parish Church (as it was then known) from 1937 to 1946, Melville Cook left a number of craftsmanly hymn settings for posterity, most of which survive in manuscript in the Leeds Minster Choir Library. At least one was published and printed locally – a large-scale score of the traditional Irish hymn known as ‘St Patrick’s Breastplate’. Dr Cook’s setting is a real gem, with an organ part of considerably more interest than the ‘standard’ version by Stanford

Textspeak in the 18th Century – the case of Pot-8-Os

Once, Prince’s use of “U” for “you” and “2” for “to” (or “too” or “two”) was seen as an example of his supposed eccentricity. Now, of course, it is all too commonplace.

What Prince was up to could be called “sensational spelling” though now it is not so sensational (and that sounds a little naff) with the rise of text speak. Naturally,

One amusing 18th century example of this is Pot-8-Os. Here he is:


And here is his Wikipedia bio, which reveals him to have been an equine member of the 27 club. Here is one origin story for his name:

The origin of his name has several different versions. According to one, Abingdon intended to call the young colt “Potato” and instructed the stable boy to write the name on a feed bin. The stable boy facetiously spelled the name as “Potoooooooo” (Pot followed by 8 “o”s), which so amused Abingdon that he adopted the spelling

Ireland’s science Nobel Prize winners and Faith

Ireland has only two Nobel Laureates in Science – Ernest Walton and William C Campbell. I am working on a longer post on my perception that there was much more coverage of Walton than Campbell in the Irish media. That is leading me down various interesting byways on Irish science journalism and (as I will post shortly) a rather sad discovery.

For the moment back to Ireland’s science Nobel winners. Both are linked by Trinity College Dublin, and – in different ways – religious faith.

From the Wikipedia bio of Walton:

Raised as a Methodist, Walton has been described as someone who was strongly committed to the Christian faith.[7] He even gave lectures about the relationship of science and religion in several countries after he won the Nobel Prize,[8] and he encouraged the progress of science as a way to know more about God:

“One way to learn the mind of the Creator is to study His creation. We must pay God the compliment of studying His work of art and this should apply to all realms of human thought. A refusal to use our intelligence honestly is an act of contempt for Him who gave us that intelligence”

— V. J. McBrierty (2003): Ernest Thomas Sinton Walton, The Irish Scientist, 1903-1995, Trinity College Dublin Press.)[9]

from an Irish Times interview with Campbell:

“I believe in God. I pray every single night of my life, but I have a very complicated sense of religion, and I am pretty fuzzy in that segment of my life.

“My faith, and that of millions of others, has evolved, if that is the right word, as civilisation has evolved. Evolved but not been abandoned. Religion and science can coexist. At least, that had better be true. There are certain intangibles.

“I know about these militant atheists, and I think they make very good arguments, but there is a certain level at which argumentation doesn’t come into it. Believing in something that you know exists isn’t a matter of faith; it doesn’t require faith.

“Gabriel Rossetti, the English poet, felt sorry for atheists because they didn’t have anybody to feel grateful to. That always stuck with me, because we have so much to be grateful for. I believe, and I believe in prayer.

One shouldn’t make too much of this, perhaps, but it is interesting. On the sister

“Biography is a thoroughly reprehensible genre”

Only a few days after I made a rather grumpy comment on the quality of the Spectator now, comes this piece by Roger Lewis on the dodginess of biography.

Lewis captures an awful lot of things I dislike about biographies – the all-too-easy judgments, the reductionist explanations, the pseudo God’s-eye-view, the air of the laziest aspects of “quality” journalism being dominant. The Spectator has a limit of free articles per week so here are some highlights:

Indeed, it is a reprehensible and misguided genre. Privacy is violated, creative achievements are explained away, and great men and women are unmasked as sneaky, predatory, cruel and ordinary. Humphrey Carpenter wrote all his biographies — of Auden, Britten and Ezra Pound — in this way.

The exhaustive and exhausting biographies of Kingsley Amis, Philip Larkin and Anthony Powell nearly killed those authors stone dead for me, as each and every girlfriend and sexual conquest was connected to an incident in a novel or a line in a poem. Ever since learning that V.S. Naipaul was a bully I’ve not ventured near his books.

More than the deluge of personal detail, however, the chief problem with biography is that the fundamental precepts are wrong, the principles too rigid. For the idea always seems to be that by gathering and establishing facts, cataloguing testimonies and anecdotes, each life can be made a perfect whole — that the objective biographer will see to it that there has been a plan or pattern, and dignity is conferred.

This is a futile quest, but one biographers insist on anyway:

Few biographers have had the ability or wit to perceive and describe the Cubist jaggedness of a life. Accident, chance, reversals of fortune, betrayals, sudden eruptions, dreams and areas of darkness; the shifting layers of identity, the friction between public and private selves (which character will a person choose to play?): little of this rough texture is ever evoked. Biographers conduct the background research, but few write it up with any verve.

Another insight of Lewis’ is the sheer futility of much biographical labour. An awful lot of the seemingly important figures of today will be in intellectual oblivion in due course:


tlas himself once laboured at a book about Delmore Schwartz, who’d inspired Bellow’s character Von Humboldt Fleisher. ‘No one outside the literary world had ever heard of him,’ says Atlas ruefully, save Lou Reed of the Velvet Underground, who paid for the upkeep of Schwartz’s grave, having once been his pupil at Syracuse.

When Atlas says, ‘I learned that biography is about death,’ he doesn’t only mean that Schwartz died of drink in 1966, aged only 52, or that Bellow croaked in 2005, aged nearly 90. He means that the world his subjects inhabited has vanished. The figures Atlas interviewed, the ‘fierce, irascible, antagonistic’ intellectuals of the 1940s, 1950s and 1960s — Philip Rahv, Alfred Kazin, Maurice Zolotov, Dwight Macdonald, R.P. Blackmur, Glenway Wescott — the self-important and humourless fellows who once adorned fuggy Greenwich Village parties, whose book reviews mattered so much and who were in charge of dispensing grants and prizes, have quite entered oblivion, leaving not even footnotes behind

Of that catalogue of “fierce, irascible, antagonistic” intellectuals, I have definitely heard of Dwight Macdonald (not that I could tell you much about him), I have dimly heard of Philip Rahv (I could tell you nothing of him apart from the name), and the others are blanks for me. But what wonderful mid-twentieth century names – Glenway Wescott! R P Blakmur! Maurice Zolotov!

Review of “Life Ascending”, Nick Lane, Eurotimes July 2009

Review of “Life Ascending”, Nick Lane, Eurotimes July 2009


This fine book on evolution was well reviewed at the time and won the 2010 Royal Society prize for science books. Here is my review from Eurotimes . Or rather this is a draft, and readers will note one paragraph just trails off… I cannot find the final version online or in my email so I am not sure what followed! This review is focused on the ophthalmological aspects of the book, though not to the exclusion of the wider issues :

Life ascending.
Nick Lane

There are ten great inventions of evolution discussed in Nick Lane’s lucid, stimulating book – life’s origin,
DNA, photosynthesis, the complex cell, sex, movement, sight, hot blood, consciousness, and death. Lane
makes it clear from the outset that invention does not mean a conscious agency purposefully steered the
process, rather he is referring to the ten great innovations that have transformed life that were created
through natural selection. Readers of this journal will have particular interest in the chapter on sight, which
I will therefore focus on in this review, but the whole book is superbly written and extremely enjoyable.

The eye has long been a favourite topic of anti-evolutionists. In 1802, the English utilitarian philosopher William Paley
argued in his Natural Theology that the eye is an organ of such complexity that it is absurd to suppose
that the purposeless blunderings of evolution (evolutionary ideas pre-dated Darwin, of course) could have
produced it. He used the analogy of a blind watchmaker producing a timepiece, which later gave Richard
Dawkins the title of one of his books. Darwin himself is frequently misquoted by creationists and affiliated
persons in this context – he seemed the admit that “To suppose that the eye, with all its inimitable
contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for
the correction of spherical and chromatic aberration, could have been formed by natural selection, seems
… absurd in the highest possible degree.” Darwin went on the write, however, that “if numerous
gradations from a perfect and complex eye to one very imperfect and simple, each being useful to its
possessor, can be shown to exist” the problem is solved.

In fact, we now have models of the evolution of the eye that exceed those of other organs in explanatory
power. The Swedish researchers Dans Eric Nilsson and Susanne Pelger have modelled this succession
of steps, which is each generation is taken as one year, requires somewhat less than half a million years.

The eye does seem, at first glance, to pose a problem to evolutionary explanations of its origin. What’s
more the human eye, with its rods and cones located behind an array of nerves and with its blind spot
where the optic nerve leaves the orbit, does not at first, cynical glance to be especially well designed.
Furthermore, the cant charge of anti-evolutionists has been “what use is half an eye?”, and answering the
question of how a retina could have evolved, separate from the rest of the optic apparatus, is at first
glance difficult. “Evolution is cleverer than you are” is a famous dictum of the evolutionary biologist Leslie
Orgel, and Lane goes on to show not only that the eye is well adapted to its purpose, but that (I am not sure what I said subsequently)

His approach begins, entertainingly for readers of this publication, with the observation that “anyone who
has been to a conference of ophthalmologists will appreciate that they fall into two great tribes: those who
work at the front of the eye … and those who work at the back … the two tribes interact reluctantly, and at
times barely seem to speak the same language.” For this divide, ironically, reflects the half-an-eye
distinction and allows us to consider the evolution of both halves of the eye.

For the retinal part of the answer, Lane travels (literarily speaking – it was the marine biologist Cindy Lee
Van Dover who did the actual exploring) to the most hostile and extreme habitat on earth – black-smoker
vents on the deep ocean floor that support an ecosystem of hardy survivors. Among these is the
ironically named eyeless reef shrimp (Rimicaris exoculata), which as a larva has fully formed eyes.
These are not of use to the adult shrimp, so they are reabsorbed and replaced with a literal half an eye
– a naked retina.

Most doctors will remember rhodopsin, perhaps rather dimly. It is the light-sensitive protein at the heart of
the visual process, being involved in photoreceptor synthesis as well as the initial perception of light.
Rhodopsin evolved from an algal ancestor where it is used to calibrate light levels in photosynthesis.
Rhodopsin is used by some bacteria for a form of photosynthesis.
Lane synthesises the evolution of all the aspects of the eye, although one of the ophthalmological tribes
may feel their area of interest is dealt with in slightly less detail than their retinal brethren. The naked
retina was the first step on the journey. As different organisms’ sheets of light-sensitive were arrayed in
different ways, with some recessing into pits which allowed shadows to be cast and therefore an idea of
where light comes from to be assessed, the trade-off between resolving light and light sensitivity began to
tip the balance in favour of lens formation.

Writers in this field must be tired of having to handle the creationist/intelligent design issue. Lane’s book is
not aimed at this debate, although in the footnotes he refers the reader to “The Flagellum Unspun” by
Catholic biochemist Kenneth Miller which attacks the creationist idea of irreducible complexity, as
exemplified by the development of a flagellum. Lane quotes Miller on intelligent design advocates as
double failures, “rejected by science because they do not fit the facts, and having failed religion because
they think too little of God,” and discusses Pope John Paul II’s views of evolution and the mind (made in
the course of his 1996 pronouncement recognising that evolution was more than a hypothesis) with
respect and sensitivity. Lane is clearly that wonderful thing, an enthusiast able to explain and inform

“the enemy of creativity in the world today is that so much thinking is done for you” = J G Ballard on Creativity

A while back I reposted an essay I wrote on (which is now offline) in which featured a quote from J G Ballard:

“Cyril Connolly said that the greatest enemy of creativity is the pram in the hall, but I think he was completely wrong. It was the enemy of a certain kind of dilettante life that he aspired to, the man of letters, but for the real novelist the pram in the hall is the greatest ally – it brings you up sharp and you realise what reality is all about.”

In the essay I cited as the source my paperback edition of Ballard’s Kingdom Come, but in fact Ballard’s thoughts on creativity were originally in The Observer of September 22nd 2002. Here is the essay in full:

I think the enemy of creativity in the world today is that so much thinking is done for you. The environment is so full of television, party political broadcasts and advertising campaigns, you hardly need to do anything. We’re just drowning under manufactured fiction, which satisfies our need for fiction – you scarcely need to go and read a novel.

Cyril Connolly, the 50s critic and writer, said that the greatest enemy of creativity is the pram in the hall, but I think that was completely wrong. It was the enemy of a certain kind of dilettante life that he aspired to, the man of letters, but for the real novelist the pram in the hall is the greatest ally – it brings you up sharp and you realise what reality is all about. My children were a huge inspiration for me. Watching three young minds creating their separate worlds was a very enriching experience.

For most of my working life as a professional, which began over 40 years ago, what kick-started the day was a large scotch and soda. After my wife died, I was bringing up my children on my own much of the time: getting them up and to school and finding their satchels, all that sort of thing, and I needed a sort of change of climate. I used to find that a couple of large scotches did the trick – it created a different microclimate inside my head.

I find the imaginative pressure has always been strong, thank god. I’ve always felt that I had this message I had to bring the reader – a deluded notion, I’m sure, but it’s kept me going. I’ve also always been a very disciplined writer, because that’s the only way you ever get anything done. Usually when I’m writing a novel I set myself 1,000 words a day, and I stick to it religiously. I sometimes stop in the middle of a sentence, which isn’t a bad idea, as the next day it’s very easy to get back into it.

As for learning to be creative, I think there’s a lot of basic-level storytelling skills that you need to be born with. I wrote from a pretty early age, eight or nine, and I’ve always had a very vivid imagination. If you’ve got a strong imagination it’s there all the time, it’s working away. You’re kind of remaking the world as you walk down a street, sort of reinventing it. I have a walk every day and a good think about things. I sometimes think maybe this town is a complete conspiracy, or maybe it’s a very advanced kind of psychological experiment – all these ideas occur to me and every now and again I think: ‘Hey, that’s not bad. That’s worth pursuing.’