The value judgments of scientific acceptance rules

From “A Cabinet of Philosophical Curiosities”, Roy Sorensen:

When I joined the philosophy department at Washington University in St Louis, I was pleased to see a room with the plaque:
Rudner Memorial Lounge:
In memory of RICHARD RUDNER distinguished philosopher, colleague, and friend.

However, when I asked about Rudner, no one could remember him.

In the ‘The Scientist Qua Scientist Makes Value Judgments’ Rudner noted that scientists have acceptance rules: believe the hypothesis if and only if it has a probability above a threshold, say 0.95 or perhaps 0.99. The threshold for belief varies in accordance with how bad an error would be. That is a value judgement.

The stakes are sometimes of existential proportion. When developing nuclear energy, some physicists worried that there was a slight chance of a runaway chain reaction. Each split atom splits a neighbour atom until no atoms remain to be split. The physicists calculated that the scenario had a probability of less than four in a billion. They felt that was low enough to dismiss the possibility. Maybe they were right. But that is a value judgement.

How probable must Rudner’s thesis be for scientists to accept it? Well, how bad would it be to be mistaken about whether value judgements are a core responsibility of scientists? Or to forget Richard Rudner and his thesis?



2001: I am not a fan of Malcolm Gladwell. Review of “The Tipping Point” from The Lancet.

I actually quite enjoy Gladwell’s articles – a bit solutionist at times but he can tell a story well. Like many other books by New Yorker writers whose New Yorker pieces I quite enjoy, Gladwell’s books tend to disappoint. From The Lancet in Feb 2001, here is a not very flattering article on The Tipping Point.

The Tipping Point clearly has influenced Nudge and a range of other small-things-make-a-big-difference approaches to social issues. As a principle it is not inherently wrong, and the examples Gladwell discusses are pretty interesting…. but the complexity and subtlety of a situation can get missed.

Looking back on this review, I was (am?) prone to some hackneyed phrases (“insightful pieces with quicksilver intelligence” for instance) and the piece doesn’t really hang together – I evidently dislike the book, but why? I seem to only cite literary grounds, finding Gladwell’s style here a bit annoying. Looking back, it is clear the solutionism is pretty rampant here, and I could have reflected more critically on that:

The new New Thing
Seamus Sweeney
Published: 03 February 2001


The tipping point has much to recommend it—certain fascinating ideas and phenomena explained clearly. But it also has much to deplore—tendencies towards pop psychology and writing to match. The book is subtitled “How little things can make a big difference”, and Gladwell uses the sharp fall in crime in New York City in the 1990s and the sudden hipness of Hush Puppies, previously chronically unfashionable, to introduce the book, as examples of sudden, unpredictable trends. He claims to apply the thinking of an epidemiologist to how social and cultural trends spread. “The Tipping Point is the moment of critical mass, the threshold, the boiling point”, the tiny, decisive moment where the slightest push makes all the difference.

Gladwell tells us of the “Three Rules of Epidemics.” The first is The Law of the Few—in any epidemic, a small group of people infect a disproportionate amount of people. He uses the examples of Darnell “Boss Man” McGee, who infected at least 30 women with HIV, and Gaetan Dugas, “Patient Zero”, the flight attendant linked to over 40 of the earliest cases of AIDS in New York and San Francisco. The same principle applies to social and cultural epidemics. Gladwell defines who the few are: Connectors, who know a lot of people in different social groupings; Mavens, well-informed people who discover new products, concepts and trends; and Salesmen, who persuade people to try The New Thing. A social epidemic must touch base with representatives of all three groups. The second rule of epidemics is the Stickiness Factor. Gladwell uses the examples of the famous Winston’s cigarettes slogan (“Winston tastes good like a cigarette should”) and the story of Sesame Street to illustrate the properties of The New Thing that make it memorable. The third law of epidemics is the Power of Context. In 1964, a woman called Kitty Genovese was stabbed to death in Queens on the street with her 38 neighbours watching, none of whom bothered to call the police. At the time it was cited as evidence of the selfishness induced by urban life. But subsequent psychological work found that in such events, the biggest factor that determines whether someone helps is the number of witnesses. The more witnesses, the less likely that an individual will take the responsibility to act; it is diffused among too many people. In other words, the effect of The New Thing depends on the context.

Gladwell invokes the tumble in New York crime statistics, and in particular the concept known as “Broken Windows”; apparently petty crime like graffiti or broken windows acts as a suitable context for violent crime. Thus minor changes such as cleaning up graffiti help spread the social epidemic of not committing crime. The lesson here is that context is crucially important in behaviour. A rather mean-spirited experiment on a group of seminarians is cited as proving this; they were asked to prepare a sermon and cross over to another building. Some were told to sermonise on “The Good Samaritan”, while others were given more general texts. As they headed off, some were told that they were running late while others were told they were early. En route they encountered a man who had collapsed on the ground and was in some distress. It was found that the seminarians who helped the stranger were those who were running early— even those who were about to speak on the Good Samaritan would hurry past if they thought they were late. Thus the physical context (lateness versus punctuality) was more important than the moralistic context (the actual content of the sermon) in determining behaviour.

Gladwell has many more examples than those referred to here; from the epidemic of suicide in Micronesia to the rise and fall of Airwalk sneakers. His universe is a giddy one, one where “with the slightest push—in just the right place—it can be tipped”. As an adventure through a world of ideas, it is highly enjoyable. But as a work of literature, it has an irritating factor of its own.

A critic quoted on the press release for this book compares Gladwell to Edmund Wilson. Another literary figure came to mind: Anthony Robbins, author of Unlimited power and Awaking the giant within. What sounds like a cross between popular science writing and cultural commentary instead occupies a no-man’s-land between books for salesmen and self help books for people who don’t read.

The tipping point marks something of a dumbing down for Gladwell, who writes thought-provoking, insightful pieces with quicksilver intelligence for the New Yorker. One can’t help thinking that Gladwell started writing a very different book, and commercial imperatives took over. Or possibly it is the condescension of the metropolitan New Yorker writer to the little folks out there in Middle America. There is a fascinating book to be written about Gladwell’s basic thesis—that little things not only make a big difference, they make the biggest difference. This is, alas, not it.

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.

Review of Oliver Sacks, “The River of Consciousness”, TLS 13th March 2018

A Medical Education

I have a review in the current TLS of Oliver Sacks’ essay collection, “The River of Consciousness” . The full article is subscriber only so here is the opening….

Who is the most famous medical doctor in the world today? Until his death in 2015, a reasonable case could be made that it was Oliver Sacks. Portrayed by Robin Williams on screen, inspiring a Michael Nyman opera and plays by Peter Brook and Harold Pinter, Sacks took his followers far beyond the confines of neurology.

In their Foreword to The Rivers of Consciousness, a posthumously published collection of Sacks’s essays, the editors recount the time Sacks appeared in a Dutch documentary series, A Glorious Accident. Along with, among others, Daniel Dennett, Freeman Dyson and Stephen Jay Gould, Sacks discussed “the origin of life, the meaning of evolution, the nature of consciousness. In a lively discussion, one thing was clear: Sacks…

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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

Luke Kelly : Raglan Road (A Parade of Posts for St Patrick 1)

Thom Hickey from The Immortal Jukebox is posting a Parade of St Patrick’s Day Posts (Patrick’s Post Parade?) in the coming weeks…. begining with Luke Kelly singing Kavanagh’s On Raglan Road and via Flann O’Brien to Jack B Yeats.

My father often praised Luke Kelly’s On Raglan Road, in the course of castigating Van Morrison’s version. Patrick Kavanagh had some wonderful poems, most of which were included on the Leaving Cert curriculum. I remember being taken aback by the level of bitterness and vituperation in the rest of his poetry, when I read a Collected Works. I wonder how it would hold up now?

The Immortal Jukebox

For the week that’s in it The Immortal Jukebox series A Parade of Posts for St Patrick celebrates Ireland’s glorious heritage in Song, Poetry and Painting.

It seems to me that the, ‘Secret Sign’ has been revealed to generations of Irishmen and Irishwomen and that in response they have blessed us with inspiring voices and visions that will always echo through stone and time.


A Song from Luke Kelly

A Poem by Flann O’ Brien performed by Eamon Morrissey

A Painting by Jack B Yeats

Staff in hand let’s set off with Luke Kelly’s magisterial performance of Poet Patrick Kavanagh’s great, ‘Raglan Road’.

Luke Kelly was born to Sing.

Born to Sing.

In his singing there is passion pledged.

In his singing there is grief and rue.

In his singing there is enchantment.

In his singing there is Love and the whisper of old ghosts.

In his singing there is…

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Poetry is Beauty’s Voice

I had a copy of Jon Kabat-Zinn’s “Wherever You Go, There You Are” for a long time… before mindfulness was as trendy as it is now. Recently I opened it again and was struck the meditation highlighted here. Watts and Hillman are not familiar to me. This post resonated with me with its discussion of the non-correspondence of language with absolute reality, and the poetry of living:

“I think we’ve spent so much of history arguing over the critique of good written poetic form, high art that carries us on the lofty tailwinds of meaning, that we’ve lost our ability to see poetry in its seed form and the many ways we live it daily. We’ve in some ways deeroticized it, made it too narrow, made people think it doesn’t apply to them. If we could recover this sense of poetries of living, it might help more people appreciate the high poetic craft again, as but one expression of the seed poem’s transfigurative power”

Signs of Life

“Words and measures do not give life; they merely symbolize it” (Alan Watts, The Wisdom of Insecurity 48).

For any kind of beauty there is, there is a form of poetry to give it voice.  We think of poetry often as involving meter, verse, stanza, rhyme, prosody–pricking the senses through artfully arranged language. However, I’ve experienced, and I know others have too, poetry that transcends or seems to happen prior to language, and, while the purist poets may object, that’s the topic of this blog.

Jon Kabat-Zinn gives a great example in his book Wherever You Go, There You Are of such language-less poetry when he writes of geese flying overhead:

“As I pull into the parking lot of the hospital, several hundred geese pass overhead…. Hundreds are in V’s, but many are in more complex arrangements. Everything is in motion.  Their lines dip and ascend with grace and harmony…

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