What percentage of the British population lives below the poverty line? When I call that a silly question, a question that doesn’t deserve an answer, I’m not being callous or unfeeling about poverty. I care very much if children starve or pensioners shiver with cold. My objection – and this is just one of many examples – is to the very idea of a line: a gratuitously manufactured discontinuity in a continuous reality.

Who decides how poor is poor enough to qualify as below the ‘poverty line’? What is to stop us moving the line and thereby changing the score? Poverty/wealth is a continuously distributed quantity, which might be measured as, say, income per week. Why throw away most of the information by splitting a continuous variable into two discontinuous categories: above and below the ‘line’? How many of us lie below the stupidity line? How many runners exceed the fast line? How many Oxford undergraduates lie above the first class line?

Yes, we in universities do it too. Examination performance, like most measures of human ability or achievement, is a continuous variable, whose frequency distribution is bell-shaped. Yet British universities insist on publishing a class list, in which a minority of students receive first class degrees, rather a lot obtain seconds (sometimes subdivided into upper and lower seconds), and a few get thirds. That might make sense if the distribution had three or four peaks with deep valleys in between, but it doesn’t. Anybody who has ever marked an exam knows that the bottom of one class is separated from the top of the class below by a small fraction of the distance that separates it from the top of its own class. This fact alone points to a deep unfairness in the system of discontinuous classification.

Examiners go to great trouble to assign a score, perhaps out of 100, to each exam script. Scripts are double or even triple marked by different examiners, who may then argue the nuances of whether an answer deserves 55 or 52 marks. Marks are scrupulously added up, normalised, transformed, juggled and fought over. The final marks that emerge, and the rank orders of students, are as richly informative as conscientious examiners can achieve. But then what happens to all that richness of information? Most of it is thrown away, in reckless disregard for all the labour and nuanced deliberation and adjusting that went into the great addition sum. The students are bundled into three or four discrete classes, and that is all the information that penetrates outside the examiners’ room.

Cambridge mathematicians, as one might expect, finesse the discontinuity and leak the rank order. It became informally known that Jacob Bronowski was the “Senior Wrangler” of his year, Bertrand Russell the Seventh Wrangler of his year and so on. At other universities, too, tutors’ testimonials may say things like, “Not only did she get a first: I can tell you in confidence that the examiners ranked her number 3 of her entire class of 106 in the university.” That is the kind of information that really counts in a letter of recommendation. And it is that very information that is wantonly thrown away in the officially published class list.

Perhaps such wastage of information is inevitable: a necessary evil. I don’t want to make too much of it. What is more serious is that there are some educators – dare I say especially in non-scientific subjects – who fool themselves into believing that there is a kind of Platonic ideal called the ‘First Class Mind’ or ‘Alpha Mind’: a qualitatively distinct category, as distinct as female is from male, or sheep from goat. This is an extreme form of what I am calling the discontinuous mind. It can probably be traced to the ‘essentialism’ of Plato – one of the most pernicious ideas in all history.

For legal purposes, say in deciding who can vote in elections, we need to draw a line between adult and non-adult. We may dispute the rival merits of eighteen versus twenty-one or sixteen, but everybody accepts that there has to be a line, and the line must be a birthday. Few would deny that some 15-year-olds are better qualified to vote than some 40-year-olds. But we recoil from the voting equivalent of a driving test, so we accept the age line as a necessary evil. But perhaps there are other examples where we should be less willing to do so. Are there cases where the tyranny of the discontinuous mind leads to real harm: cases where we should actively rebel against it? Yes.

There are those who cannot distinguish a 16-cell embryo from a baby. They call abortion murder, and feel righteously justified in committing real murder against a doctor – a thinking, feeling, sentient adult, with a loving family to mourn him. The discontinuous mind is blind to intermediates. An embryo is either human or it isn’t. Everything is this or that, yes or no, black or white. But reality isn’t like that.

For purposes of legal clarity, just as the eighteenth birthday is defined as the moment of getting the vote, it may be necessary to draw a line at some arbitrary moment in embryonic development after which abortion is prohibited. But personhood doesn’t spring into existence at any one moment: it matures gradually, and it goes on maturing through childhood and beyond.

To the discontinuous mind, an entity either is a person or is not. The discontinuous mind cannot grasp the idea of half a person, or three quarters of a person. Some absolutists go right back to conception as the moment when the person comes into existence – the instant the soul is injected – so all abortion is murder by definition. The Catholic Doctrine of the Faith entitled Donum Vitae says:

From the time that the ovum is fertilized, a new life is begun which is neither that of the father nor of the mother; it is rather the life of a new human being with his own growth. It would never be made human if it were not human already. To this perpetual evidence . . . modern genetic science brings valuable confirmation. It has demonstrated that, from the first instant, the program is fixed as to what this living being will be: a man, this individual-man with his characteristic aspects already well determined. Right from fertilization is begun the adventure of a human life . . .

It is amusing to tease such absolutists by confronting them with a pair of identical twins (they split after fertilisation, of course) and asking which twin got the soul, which twin is the non-person: the zombie. A puerile taunt? Maybe. But it hits home because the belief that it destroys is puerile, and ignorant.

“It would never be made human if it were not human already.” Really? Are you serious? Nothing can become something if it is not that something already? Is an acorn an oak tree? Is a hurricane the barely perceptible zephyr that seeds it? Would you apply your doctrine to evolution too? Do you suppose there was a moment in evolutionary history when a non-person gave birth to the first person?

If a time machine could serve up to you your 200 million greats grandfather, you would eat him with sauce tartare and a slice of lemon. He was a fish. Yet you are connected to him by an unbroken line of intermediate ancestors, every one of whom belonged to the same species as its parents and its children.

“I’ve danced with a man who’s danced with a girl, who’s danced with the Prince of Wales”, as the song goes. I could mate with a woman, who could mate with a man, who could mate with a woman who . . . after a sufficient number of steps into the past . . . could mate with ancestral fish, and produce fertile offspring. To invoke our time machine again, you probably could not mate with Australopithecus (at least not produce fertile offspring) but you are connected to Australopithecus by an unbroken chain of intermediates who could interbreed with their neighbours in the chain every step of the way. And the chain goes on backwards, unbroken, to that Devonian fish and beyond. On the way, about six million years into the past, we would encounter the ancestor we share with modern chimpanzees. It so happens that the intermediates, like the common ancestor itself, are all extinct. But for that (perhaps fortunate) fact, we would be connected to modern chimpanzees by an unbroken chain of intermarrying links. Not just intermarrying but interbreeding – producing fertile offspring. There would be no clear separation between Homo sapiens and Pan troglodytes. The only way to maintain our human-privileging laws and morals would be to set up courts to decide whether particular individuals could ‘pass for human’, like the ludicrous courts with which apartheid South Africa decided who could ‘pass for white’.

And of course the argument extends to any pair of species you care to name. But for the extinction of the intermediates which connect humans to the ancestor we share with pigs (it pursued its shrew-like existence 85 million years ago in the shadow of the dinosaurs), and but for the extinction of the intermediates that connect the same ancestor to modern pigs, there would be no clear separation between Homo sapiens and Sus scrofa. You could breed with X who could breed with Y who could breed with ( . . . fill in several thousand intermediates . . .) who could produce fertile offspring by mating with a sow.

Humans are clearly separable from chimpanzees and pigs and fish and lemons only because the intermediates that would otherwise link them in interbreeding chains happen to be extinct. This is not to deny that we are different from other species. We certainly are different and the differences are important – important enough to justify eating them (vegetables are our cousins too). But it is a reason for scepticism of any philosophy or theology (or morality or jurisprudence or politics) that treats humanness, or personhood, as some kind of essentialist absolute, which you either definitely have or definitely don’t have. If your theology tells you that humans should receive special respect and moral privilege as the only species that possesses a soul, you have to face up to the awkward question of when, in human evolution, the first ensouled baby was born. Was it when the first Homo sapiens baby was born to parents belonging to whatever species is considered to be our immediate predecessor (erectus, ergaster, heidelbergensis, rhodesiensis, no matter, the argument stands regardless)? There was no such baby! There never was a ‘first’ Homo sapiens. It is only the discontinuous mind that insists on drawing a hard and fast line between a species and the ancestral species that birthed it. Evolutionary change is gradual: there never was a line, never a line between any species and its evolutionary precursor.

In a few cases the intermediates have failed to go extinct, and the discontinuous mind really is faced with the problem in stark reality. Herring gulls (Larus argentatus) and lesser black-backed gulls (Larus fuscus) breed in mixed colonies in Western Europe and don’t interbreed. This defines them as good, separate species. But if you travel in a westerly direction around the northern hemisphere and sample the gulls as you go, you find that the local gulls vary from the light grey of the herring gull, getting gradually darker as you progress around the north pole, until eventually, when you go all the way round to Western Europe again, they have darkened so far that they ‘become’ lesser black-backed gulls. What’s more, the neighbouring populations interbreed with each other all the way around the ring, even though the ends of the ring, the two species we see in Britain, don’t interbreed. Are they distinct species or not? Only those tyrannised by the discontinuous mind feel obliged to answer that question. If it were not for the accidental extinction of evolutionary intermediates, every species would be linked to every other by interbreeding chains.

Where else do we see the tyranny of the discontinuous mind? Colin Powell and Barack Obama are described as black. They do have black ancestors, but they also have white ancestors, so why don’t we call them white? The complication in this case is the weird convention that the descriptor ‘black’ behaves as the cultural equivalent of a genetic dominant. Gregor Mendel, the father of genetics, crossed wrinkled and smooth peas and the offspring were all smooth: smoothness is ‘dominant’. When a white person breeds with a black person the child is of intermediate colour but is labelled ‘black’: the cultural label is transmitted down the generations like a dominant gene, and this persists even to cases where, say, only one out of eight great grandparents was black and it may not show in skin colour at all. It is the racist ‘contamination metaphor’ of the ‘touch of the tarbrush’. Our language is ill-equipped to deal with a continuum of intermediates. Just as people must lie below or above the poverty ‘line’, so we classify people as ‘black’ even if they are in fact intermediate. When an official form invites us to tick a ‘race’ or ‘ethnicity’ box I recommend crossing it out and writing ‘human’.

In US presidential elections every state (except New Mexico) has to end up labelled either Democrat or Republican, no matter how evenly divided the voters in that state might be. Each state sends to the Electoral College a number of delegates which is proportional to the population of the state. So far so good. But the discontinuous mind insists that all the delegates from a given state have to vote the same way. This ‘winner take all’ system was shown up in all its fatuousness in the 2000 election when there was a dead heat in Florida. Al Gore and George Bush received the same number of votes as each other, the tiny, disputed difference being well within the margin of error. Florida sends 25 delegates to the Electoral College. The Supreme Court was asked to decide which candidate should receive all 25 votes (and therefore the presidency). Since it was a dead heat, it might have seemed reasonable to allot 13 votes to one candidate and 12 to the other. It would have made no difference whether Bush or Gore received the 13 votes: either way Gore would have been president.

I am not saying the Supreme Court should actually have split the Florida delegates. They had to abide by the rules, no matter how idiotic. I would say that, given the lamentable constitutional rule that the 25 votes had to be bound together as a one-party block, natural justice should have led the court to allocate the 25 votes to the candidate who would have won the election if the Florida delegates had been divided pro rata, namely Gore. But that is not the point I am making here. My point here is that the winner-take-all idea of an electoral college in which each state has an indivisible block of members, either all Democrat or all Republican no matter how close the vote, is a shockingly undemocratic manifestation of the tyranny of the discontinuous mind. Why is it so hard to admit that there are intermediates, as New Mexico uniquely does? Most states are not ‘red’ or ‘blue’ but a complex mixture.

Scientists are called upon by governments, by courts of law, and by the public at large, to give a definite, absolute, yes-or-no answer to important questions, for example questions of risk. Whether it’s a new medicine, a new weedkiller, a new power station or a new airliner, the scientific ‘expert’ is peremptorily asked: Is it safe? Answer the question! Yes or no? Vainly the scientist tries to explain that safety and risk are not absolutes. Some things are safer than others, and nothing is perfectly safe. There is a sliding scale of intermediates and probabilities, not hard-and-fast discontinuities between safe and unsafe. That is another story and I have run out of space.

But I hope I have said enough to suggest that the summary demand for an absolute yes-or-no answer, so beloved of journalists, politicians and finger-wagging, hectoring lawyers, is yet another unreasonable expression of a kind of tyranny, the tyranny of the discontinuous mind.