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Wednesday, 25 September 2019

Is there a Right not to be Conceived?

I don’t read much popular science, but recently in my local bookshop I picked up Adam Rutherford’s A Brief History of Everyone Who Ever Lived (2016) which is a very readable introduction to modern genetics and its historical background. At one point he illustrates the hazards of inbreeding by telling the tragic story of Charles the Second of Spain who died in 1700 aged thirty nine, but after a lifetime of painful illness and distressing incapacity. When people marry out of their family then after six generations they will have 62 different ancestors; after eight the number rises to 254. But because of the marriage of cousins to cousins, uncles to nieces, and disregarding the possibility of unsanctioned incest, Charles the Second had just 32 six-generation ancestors and a mere 82 eight-generation ancestors. “This is not desirable”, comments Rutherford at page 190. There is both a general problem about inbreeding and a specific problem that the probability of a recessive congenital disorder being activated dramatically increases.

A few pages later (page 200) Rutherford tells us that in 2005 one United Kingdom ethnic group produced 3.4% of all live births but 30% of all babies with recessive congenital disorders. He then goes on to discuss genetic counselling as a way of reducing such outcomes which in practice arise largely from repeated first cousin marriages, which are allowed in English law. But I was shocked by his figures, which I had never come across before, and felt that genetic counselling sounded like a feeble response. But how to think through the problem in a dispassionate way?

I imagined using something like John Rawls’ veil of ignorance. In his major 1971 book A Theory of Justice, Rawls tries to show what kind of social contract individuals would agree to if they were obliged to decide not knowing important facts about themselves as individuals. So, for example, if behind the veil of ignorance you did not know whether you would turn out to be male or female when the veil is lifted, then it is most unlikely that you would agree to a public decision making method which excluded females – or males, for that matter – from any franchise. You would tend to favour universal suffrage which minimises your risk of being disadvantaged and maximises the opportunity which others, thinking along the same lines, would be willing to grant you.

In the case I am trying to consider, those behind the veil of ignorance have not yet been conceived. Nonetheless, these potential persons can be imagined as listeners to a genetics lecture which informs them, among other things, that their risks of being born severely disabled are greatly multiplied if people with varying degrees of closeness are allowed to conceive children, especially if done repeatedly. They are given figures and the problem of recessive genes explained. They are told that the risk of being born disabled is greatly reduced when the law forbids conception between closely related individuals, especially when this is repeated through generations. Eventually, they have to decide on the level of risk they are willing to accept in formulating one of society’s fundamental laws, the law which sets out with whom you may and may not conceive children.

This kind of question has been posed in other ways for other life and death issues. In his 1785 major work on majority voting, the title now usually translated as Essay on the Application of Mathematics to the Theory of Decision-Making, Condorcet pointed out that when the death penalty is provided as a possible punishment in any society, there is always the possibility that an innocent person will be executed – and that is irreversible. So he asks us to consider the question: What probability would you accept for an outcome in which you yourself might be executed though innocent?

From the point of view of the unconceived, the choice seems fairly straightforward whether you think along Rawlsian or Condorcetian lines. Though you stand to lose something from outlawing a host of close relative reproductive relationships – you will never get to be Philip the Second of Spain - this potential loss of benefit is minimal compared to the risk of being born to a life of pain and discomfort which may be very short and may, unfortunately, be quite long. You will listen to the geneticists and you will outlaw reproductive relationships which carry a high risk of causing you serious harm if you are born within them.

This calculus done from the standpoint of the as yet unconceived is quite different from that deployed by those entering genetic counselling. They are being asked the question, Do you want to risk having a seriously disabled child? not the question Do you want to risk being one? Those counselled are real, existing people. They may be under family pressure to start a family together. They may be in love. They may be gamblers. They may not believe in science. They are unlikely to be thinking of the fact that their choices may well yield very large health care bills, to be paid for out of other people’s taxes. Overall, they are not well placed to answer the question in terms of the best interests of an as yet unconceived child.

In other words, though adults normally think otherwise, their situation in real life is not always one where they can be assumed to be good judges for children, still less for children who have not yet been conceived. Both veil of ignorance reasoning and Condorcetian probabilistic reasoning suggest that our laws about who you can and can’t have children with are lax, and that the fall-back of genetic counselling unreasonably favours the interests of the living over those of the unconceived.

Trevor Pateman  explores other gaps and failures in our moral thinking in essays included in his The Best I Can Do (2016) and Silence Is So Accurate (2017)

Wednesday, 14 August 2019

Voice Mobility

The other day, I recorded my first podcast. Since I had not been in a recording studio for many years, the sound engineer suggested that I make a sample recording - just a few minutes long - and then listen to the playback before returning to my soundproof booth to do the real thing.

I sat down with the engineer and he pressed Play on my sample. What do you think? he asked at the end. I sound a bit posh is what came out, immediately. He was surprised (maybe he had heard no poshness) and puzzled, Is that a bad thing?

Well, yes and no. Yes, because it may give listeners the wrong idea about me. I didn’t start life with a posh voice; I acquired one as a result of succeeding educationally and thereby becoming socially mobile. But I’ve always liked to think that my voice has not been quite so mobile. I still recall once meeting a university acquaintance from a similar background but a decade after we had both left Oxford. I was appalled by his accent, Oxford and affected. But it probably wasn’t affected at all; it’s likely that he had just assimilated more easily.

Now here am I, someone who hasn’t taught a university seminar or been to a middle class dinner party for twenty years, placing myself in front of a microphone and immediately, to my own ear, sounding posh. Maybe the subject matter explains it: I was reading something I had written about Milan Kundera’s theory of the novel. Maybe if I had been talking in a less scripted way about my childhood or a pet hate I would have sounded different.

I had other criticisms of my first attempt. My voice was too high pitched - first night nerves; I spoke too slowly - I was afraid of stumbling over words, an age-related hazard. And when I listened to the final product, I thought I sounded a bit camp. The editor of Booklaunch (Stephen Games) who had requested the podcast picked up on the last two aspects, asking that in any future recording I should be a bit faster (but not less dramatic)

But there is a case to be made for the poshness. The voice in which I read my piece about the novel was appropriate to the subject matter. It was full of words I never learnt as a child, only much later from teachers and friends. If I had read it in my original accent, it would have sounded false because a listener would realise that those words being spoken in an identifiably lower class accent would never have been spoken in a lower class home. That falseness would have been more distracting than the poshness. In contrast, if someone who had grown up speaking with a Scottish or West Indian accent had read my piece for me, it would be less distracting or not distracting at all because those accents are not in themselves class-related. In middle and upper class Scots and West Indian homes, one also talks about the novel.

To hear the finished podcast, go to

Monday, 5 August 2019

Memory meets De tre vise men of Dalarna

Click on Image to Enlarge

Like death and taxes, memory losses are inevitable. We may swear to ourselves or to someone else that this moment will never be forgotten but it will, even before old age or worse sets in. As psychologists keep trying to tell us, to little effect, our minds constantly reorganise our memories: deleting, mislaying, editing, revising, inventing. Our memory is a bit like Microsoft run amok, improving or weeding to its own satisfaction yesterday’s Word docs while we sleep.

There are things I would like to write about but when I sit down to it, I promptly discover that I remember no more than the file name. Oh, they are splendid file names but standalone they do not make a splendid story.

The objects which pass through our hands perhaps have a bit more success in being there when we want them. It’s true that we lose things, bin them, give them away, forget where we have put them but, still, some survive and often for much longer than the memories which we may hope to find still attached - but don’t.

Today I come across this charming card which has managed to accompany me through many house moves since it was purchased in 1964 - fifty five years ago! The summer of that year - I had just turned seventeen -  I organised for myself a holiday job in Sweden, working in the Hotel Siljansborg situated beside Lake Siljan in the province of Dalarna.

Everyone is familiar with one Dalarna thing: those simple, chunky carved wooden horses painted in bright colours (traditionally red) with simple floral decorations in green, white, blue and yellow - the last two the colours of Sweden’s flag. When I came to the end of my time at the Hotel Siljansborg, I was given one as a leaving present and I still have it.

The carved horses were a portable part of a larger tradition of visual folk art, centred in Dalarna, which flourished in the eighteenth and nineteenth centuries and which produced painted furniture and wall decorations in which the floral motifs ( the technical name is Kurbits and I was able to google it because I still remembered the word) are always present.

My card has pin holes in the top corners so at one time I must have displayed it. A horizontal banner across the top spells out what the original depicts: De Tre wise man matthei 21 Cap Malat ar 1841 an A L S  ( The Three Wise Men Matthew chap[ter] 21 Painted [in the] year 1841 by A L S ).

Aren’t they splendid? Not a whiff of the Middle East. No donkeys or camels to bring them to the stable, just fine Dalarna horses. The three kneeling figures who could have been modelled on the local priest or lawyer - maybe they were; a rather patrician Joseph and a matronly Mary, her black leather shoes peeking out from under her full skirts. It looks as if having babies is something she takes in her stride.

We are very familiar with the idea that human beings fashion God in their own image; in Dalarna, they imagined the Nativity as something which happened not so long ago and just down the road. But I suspect that their religious beliefs were at least as robust as those of people who were brought up on donkeys, flowing robes, and sandals. But either way, the Dalarna folk artists were thinking rather like those who re-thought Shakespeare as West Side Story.

On the back of the card, the work is titled De tre vise men (modernising the spelling) and given as originating from the small town of Rättvik which provided the postal address for my hotel. Then it gives the current location of the work as the Zornmuseet. That opens a file: one day, during hours off work, I walked to the Anders Zorn museum in Mora. It googles and I am immediately offered a portrait of the artist (1860-1920) which I recognise as one of which I took away a postcard. But though I can google as much of his work as I want, I can’t see the folk art which must also have been in the museum.

I  google a bit more. It is out of the question that I walked. Mora is 37.8 kilometers from Rättvik!

The World Memory finds and opens its files for me in half a second and, once again, forces me to revise my own memory.

I write more about that summer in Sweden in my memoir of childhood, I Have Done This In Secret (degree zero 2018)

Sunday, 28 July 2019

Do The Dead Have Any Rights?

Whatever rights the dead may have, they are secured for them by the living. A man writes a will disinheriting his children; they go to court to have the will set aside and a living judge decides the matter. Another man writes a will endowing a fund out of which lawyers can be paid to defend his reputation against all-comers. But in a jurisdiction where English law prevails, that would be pointless: there is no offence of libelling the dead. Only the living can be libelled. In France, the dead are protected too.

The living grant rights to the dead, no doubt guided very much by what rights they themselves would like to be accorded when they die. Rights for the dead are about anticipation, not retrospection. So in most cultures, maybe all, there are protocols for handling a dead body and disposing of it. Failure to observe those protocols is both shocking and probably a sign of some breakdown of the social order. If the protocols dictate at least a shroud and an individual grave, then something has gone very wrong if naked bodies are tipped into common graves, as often they are in times of plague and war. 

But does it make sense to say that the rights of the dead have been violated in such circumstances? After all, they know nothing of what is going on. And we can understand and criticise what is happening without invoking the language of rights. So, for example, we could say that if we don’t show respect towards the dead, we will soon cease to show respect to the living, to each other. And that is not going to be good news. This argument is a cautionary, prudential one rather than a rights-based one.

It is also the case that the language of rights seems inappropriate where there is constant flux in the protocols which set out the rights of the dead. It is only very recently in my culture that burning bodies has been accepted as an alternative to burying them; even more recently that it has been thought acceptable to harvest vital organs - with or without explicit consent -  from those who may have died only minutes beforehand. It doesn’t seem that “rights” come into it. It looks more like “needs must”.

Nonetheless, we do accord rights to the dead which are quite extensive and sometimes not always explicitly reflected upon. Most of these rights relate to property and reputation. Some deserve to be challenged.

An elderly widow with no children and a great deal of inherited wealth writes a will leaving the whole lot to a donkey sanctuary. She has every right to do so. There is no Public Advocate enabled to go before a judge and argue that the will should be set aside. There is no one who can stand up to say: Your Honour, the reality is that we have far too many donkey sanctuaries; donkeys are being bred to populate them; the sanctuaries are not much more than a lucrative scam for those who promote them. I urge you to divert the late widow’s wealth to the oncology department of her local hospital where, at public expense, she received extensive treatment for several years. It would be right for her estate to be put back into the community from which she took so much. Ditch the fake donkeys, Your Honour!

It would require a revolution in our thinking to find that argument compelling. I would welcome such a revolution, but as things stand, the imagined Public Advocate’s argument is nothing more than an open threat to property rights which - in our minds - are inextricably linked to the idea that those are things which can be passed on. Quite cursory analysis would show that there is really not much of a link between the idea of a property right and the idea of an indefinitely and indefeasibly transmissible property right. A practical demonstration of the distinction between property right and transfer right was once provided in traditional gypsy cultures where both the caravan and its contents were burnt on the death of its owner. But woe betide anyone who had thought to steal from the caravan during the lifetime of its occupant.

So much for property. What about reputation? Here there is a cluster of protocols which create or enshrine rights to externalised memory, to memorials. Someone dies, they are buried, and their grave marked with a tombstone giving name, dates, some personal details and maybe a Commendation, “A Kind Father to all His Children”; “She Loved the Donkeys”. All this involves several financial transactions, none of which guarantee that tombstone in perpetuity. In practice, grave furniture is quickly neglected by those who have paid for it; the weather takes its toll on soft stone; the graveyard fills up - and eventually everything is bulldozed to make way for new graves or simply public green space. The dead are forgotten. No one much minds because the protocol has allowed memory to be gradually, not abruptly, extinguished. Those who mourn have been given their time.

In contrast, when a memorial - a monument - to a dead person is erected in public space, whether at government expense or funded by public subscription, it seems to be some kind of assumption that they thereby acquire a right to stand or sit there, in stone or bronze, in perpetuity. There is no protocol for taking these things down, no equivalent to the protocol which allows graveyards to be cleared out. In the context of lively conflict over statues of controversial figures, it would actually be helpful to develop some kind of intellectual framework which would aid us in deciding when a statue’s lease on public space has run out. 

One criterion might be whether we still remember the name and history of a person memorialised, regardless of whether the memory is fond or hostile. Yes, for most of us, it’s still Nelson on top of the column in Trafalgar Square. But who are those characters who occupy the surrounding plinths? If you can’t so much as name them, why would you want them to remain there, in perpetuity? It’s not as if the hack work of monumental sculpture ever has any artistic interest and only rarely can it claim architectural merit. Without a protocol for removing the upright monumental dead, our urban public spaces are simply doomed to become more and more cluttered by forlorn figures, very rapidly forgotten by us and attracting the interest only of dogs - the reason for plinths in part to protect trouser legs - and pigeons.

Tuesday, 23 July 2019

The Bank Note Problem (Second Attempt)

For First Attempt, scroll down to 17 July 2019

In Ruritania, there are four denominations of banknotes. The Ruritanian National Bank issues them in unequal quantities, according to perceived need, and on a rotating basis changes the designs to make forgery more difficult and less remunerative. One design is changed every three years, and once changed the old notes for that denomination cease to be valid. So each design has a life of twelve years.

In the past, the designs comprised abstract and complicated backgrounds (so-called guilloché or burelage ) combined with unique fonts in mostly calligraphic styles, all designed to defeat attempts at forgery. But at the urging of a modernising Ruritanian government, some decades ago now, the bank changed its policy and all new designs have represented dead people who are remembered for their achievements. The modernising government wanted to see different kinds of people and different kinds of achievement represented, but did not bind the bank to any particular formula.

This posed the bank a problem. How many different kinds of people are there? How many kinds of achievement? Without answers to those prior questions it was very hard to know how to proceed. The Bank did not at first identify this problem and started out without any clear answers, rather hoping that “obvious” cases would present themselves, as indeed they did ; Mr Shakespeare, Ruritania’s most famous and acclaimed dead playwright, had his image uncontroversially placed on a twenty pounds sterling banknote in 1970. It was true but irrelevant that there have always been doubts about whether images of Mr Shakespeare look at all like the man they purport to represent.

The lack of clear principles of choice immediately encouraged subjects of Ruritania to come forward with humble petitions addressed to the Governor of the Bank proposing that such and such a person, or group of persons, or achievement, or group of achievements, should be represented on the next banknote scheduled for replacement. In the common parlance of the United States, these humble petitions - however worded in terms of justice, fairness and representation not to mention Greatness - were necessarily instances of log rolling.

That posed the Bank a problem. Should it respond to the biggest logs rolled its way or should it seek to establish some principles of fair representation? The Governor decided that Principles should be sought. A committee was formed to find them.

After the usual lengthy deliberations, the committee proposed that two categories of person should be recognised (Male and Female) and four categories of achievement (Arts, Science, Politics, War). The committee pointed out that these numbers had been arrived at having regard to the reality of four bank note combinations. All eight possible combinations of the categories (which they summarised as MA, MS, MP, MW; FA, FS, FP, FW) could be represented on four notes in just two complete banknote cycles. There would be no awkward remainders to deal with.

As for the actual personages to be represented, the committee concluded that (a) that they all be dead - there was no disagreement about that - and (b) that it was up to the Governor to decide between several possible selection procedures enumerated as follows:

·         a committee of experts and / or the Great & the Good to pick the person to be featured in any of the eight categories;
·         a simple lottery the tickets for which would bear names selected by some method or other;
·         a weighted lottery with the number of tickets for each name equal to the number of signatures on humble petitions submitted in favour of that name - this was seen as a concession to log rolling;
The committee also felt that a further accommodation of the public was possible:
·         A list of names selected by the Bank’s own committee could be submitted to public vote according to one of the recognised procedures (first past the post, and so on).  
This last procedure had built into it a guarantee against any possibility of an overwhelming public vote in favour of Banky McBankface.

The committee did identify one unresolved problem. Since banknotes of the four denominations are issued in unequal quantities, it might be thought that the representational value of the image on them should be weighted according to the number of banknotes on which that image would appear. The committee noted that this would remove an element of simplicity from its proposals and would require assistance from someone able to do advanced mathematics and not just simple sums.

The committee then took cover. 

When it learned of the committee’s recommendations, the government of Ruritania was appalled. There were far too few categories of person and it was not sure that “War” was any longer a category of achievement. What about “Entertainment” or “Sport” - perhaps these could be combined into “Culture”?  If “War” was then added to “Politics”, that would preserve the four categories of achievement. A neat counter-proposal.

But as for categories of person, the government felt it had a duty of special care for the Ruritanian Minorities of which thirty nine were currently recognised. How did the Bank propose to ensure that those minorities featured appropriately on the four denominations with only its Male and Female categories available?

The Bank replied humbly that it thought that it could cope with the increased complexity demanded by the government but would need a few extra mathematicians, a new computer, and an answer from the government to two remaining questions: Are the thirty nine minorities to be represented equally within the Person categories or in weighted form according to the number of persons identified as being members of those minorities? And if the latter, should the number be those actually living or the number who have ever lived within the borders of Ruritania? The second question was given its point by the twin facts that all Persons had to be dead in order to qualify and that today’s Ruritanian Minorities were not distributed in the same proportions or same aggregate numbers as the Minorities of yesteryear.

The government appointed a small committee of mathematicians to come up with its reply to these two supplementary questions and it is hoped that a Nobel Prize (possibly for Mathematics but preferably for Peace) will result.

Saturday, 20 July 2019

Boys from Slade Green are Under-represented in Hollywood films

Click on Image to Magnify

I was born in Dartford’s West Hill hospital, which provided maternity facilities a few miles away from where my parents lived in Slade Green. Slade Green was an area sandwiched between Erith (which was a Borough) and Crayford (which was an Urban District), both within the county of Kent.  But by the time I was born, this part of north-west Kent was really part of south-east London and is now legally so - Slade Green is within the Northend ward of the London Borough of Bexley. In other words, I lived in a place which had no real identity or boundaries.

I lived in Slade Green from birth until the age of eight when we moved to Dartford. So you might say that I passed half of my boyhood there, not quite a tenth of my life.  I could claim to be from Slade Green which I tend also to think of as some kind of outgrowth of Erith rather than of Crayford.  The postal address was “Slade Green, Erith, Kent” and the nearest town for shopping was Erith.

Google can’t find me many people who claim to be or have been from Slade Green; Jade Anouka (1990 - ) was born there and that’s the only notable name I can find. For Erith as a whole, there are notable people who were born there including the humanist and socialist comedian and writer Linda Smith (1958-2006) who joked that Erith isn't twinned with anywhere but it does have a suicide pact with Dagenham [ which it faces across the river Thames]. And another one: 

Erith is in Kent - the "Garden of England" - I can only assume Erith is the outside toilet because it is a shit house.

A 2014 post on Reddit in answer to a question from someone thinking to move to my hometown has this to say:

“Erith is crime central, and Slade Green has absolutely NOTHING going for it.

That’s not untypical of what I can find and I doubt it’s untrue.

Now to the point. Would it make sense to say in any context that people from Slade Green are underepresented in any context? If you enlarged it a bit, would Erith or Crayford or even north-west Kent make sense as things which could be underepresented? I suspect not, because there are thousands of Slade Greens in the United Kingdom, thousands of places with nothing going for them but with no special claim to be represented somewhere else. If someone from Slade Green became a Hollywood film actor ( Jade Anouka might) the fortuitous fact of coming from Slade Green would be of no relevance. If Jade Anouka got a part, no one would be asking the question, Are Slade Green actors under-represented (or over-represented) in Hollywood movies?

And yet if we generalise a bit more the question no longer looks absurd. I borrow a sociological category from Trump, D. 2018 and put it this way, Are actors from shithole places under-represented (or over-represented) in Hollywood films? Cleaned up to meet Sunday School sensibilities, the question becomes, Are actors from under-privileged backgrounds …?

I don’t know the answer to that question for Hollywood, but do know that it is reckoned to make sense in many other contexts and that the answer is that those from under-privileged / deprived / poor backgrounds are often under-represented. Bankers, lawyers, politicians, museum directors …. well, they don’t come from Slade Green-like places.

Knowing that as I do, I confess that I sometimes wonder if I was the first / only boy from Slade Green to go to Oxford, get a doctorate … etc and I have Googled on occasion to see if I can make any progress in answering those questions. There must have been more than one by now, maybe lots more than one. But it's irrelevant for the reasons I have already given.

My country has a state broadcaster which now has a website where every day there are feelgood stories of the form “ So-and-so becomes first X in Y” or (less satisfactorily) “first openly X in Y” and “first X in Y since …” . These stories often irritate me because so many assumptions are quietly smuggled in with the story. Why is it a good thing that the Church of England now has its first black female bishop? 

The Church of England is, from where I stand, a small but extremely wealthy (the bishops all live in what are called Palaces) religious organisation which attends to the needs of the highest in the land for infant baptisms (a reprehensible practice), weddings and funerals. And that’s about it. It has little to commend it. What is a black woman doing selling her soul to this organisation, I wonder? Why isn’t she - let’s say - a Quaker? [ Incidentally, the BBC website does not recognise the existence of any Christian churches other than the Anglican and Catholic (it prefers the latter). Please tell me if you can find a BBC website story about Baptists, Congregationalists, Methodists, Quakers …].

The BBC would not feature a piece claiming “First woman to head the Institute for Torturing Political Prisoners” because it gets the point that torturing people is not very nice. The Church of England is not very nice, but it doesn’t get that.

You can experiment with variants: Cardinals elect first gay / first openly gay/ first…. since 1555 Pope”. I headed to Wikipedia for the 1555 date:

The context in which I am writing this is one in which there is endless chatter about representation, under-representation, diversity and so on but in which there seems to be very little thought about the categories X and Y which matter and what in the end counts as a satisfactory result. 

Even at the apparently simple level of male:female representation, there has to be some thinking about what counts as “gender balance” [ I prefer “sex balance” since gender is a complicating factor].

Fifty:Fifty looks like the right answer. But for a large organisation which has to deal with changes in the available labour force, the legacy of past training practices and so on, fifty: fifty is not a reasonable target. It would force employers to take on less qualified candidates just to keep the balance at a point in time. What might be a reasonable expectation and aim would be to keep variation in, say, the 45 - 55 range, either way, over a period of time. Affirmative action is then required if the actual figures gravitate to the outer limits of the range but otherwise everyone can just get on with their regular work.

Even then, there are difficult cases to consider. I offer just three: midwives, coal miners, primary school teachers.

Credit for the Linda Smith jokes:

Wednesday, 17 July 2019

Alan Turing and the Banknote Problem

In a long tradition, a moral claim is only sound when it is universalisable. Morally, policy or decision X can only be good for the goose if it is also good for the gander. What I wish for myself I must be willing to wish for anyone else similarly situated. Any other form of a wish is discrimination, usually in its own favour. Log rolling campaigns aim to get X for me but not for you. So there are people who are unhappy with the decision to put Alan Turing on the new £50 note. For example, they thought it was time for a black person.

Suppose there are seven colours of the rainbow and four banknote denominations. Suppose a rule says that only one colour can appear on a banknote denomination besides black and white. (I will leave this rule unchallenged for purposes of the argument; Coca Cola advertisements challenge it).

A first task now is to find a rule for securing “fair representation” of all rainbow colours, a rule which is universalisable. There are a couple of obvious possibilities: rotate colours through time or pick colours by repeated  lotteries. These are non-discriminatory methods or algorithms.

Now suppose that bank notes of different denominations are issued in unequal quantities. This then seems to require that to secure overall fairness in colour distribution, any appearance of a colour should be weighted by the number of banknotes issued in that colour. Otherwise, some colour could be left languishing on a denomination banknote that very few people ever see (like the 500€ note).

But suppose that the colours of this metaphorical rainbow do not occur with equal real-world frequency. So to measure for fairness, we now have to weight for colour frequency and also be prepared for those frequencies to change. Unlike the colours of the real rainbow, the distribution of colours in the social rainbow change through time.

A mathematically minded reader might like to keep going and try to produce the decision-making algorithms which would secure fair representation through time. Can lotteries achieve it?Can rotation achieve it?

However, there was a prior question to which an answer was simply assumed. There are seven colours of the real rainbow. How many colours of the metaphorical rainbow? In other words, how many categories exist which require representation?

As far as I can see, when you get past two (male and female the obvious ones), the going very quickly gets very hard. Are blind people and deaf people one category or two? Are cyclists and pedestrians one or two? How many categories is BAME? How many categories is LGBTQ+  ? (For human resources managers tasked with achieving diversity, the gay black woman is a gift from heaven since she occupies three categories at once. When does that become an unfair advantage, a sort of new Eton and Oxford and male? And is it an unfair disadvantage that old and male and pale also occupies three categories not one?).

Unless there is an agreed answer to the How many categories? question,  we will never be able to satisfy all of the people all of the time. Instead, we will continue to live in a world of serial log-rolling campaigns But social justice always used to be envisaged as an alternative to log-rolling, not its justification.