The Discontinuous Mind. Does it ever get it right?

Part 1 of this article is a much abbreviated version of “The Tyranny of the Discontinuous Mind”¹, my 2011 essay in which I criticised our human tendency to draw lines that gratuitously split smooth continua into fictively discrete categories. Part 2, not previously published, asks the question, Given the ubiquity of smooth continua, are there any important exceptions, any good examples where the discontinuous mind gets it right? The answer I discuss is Mendelian genetics, of which (in mammals, birds and all animals with chromosomal sex-determination) the absolute binary of the male-female divide is a special case. But as Part 1 argues, the norm is for smooth continua to be wantonly overlooked or misunderstood by the discontinuous mind. Readers familiar with the original long version of “The Tyranny of the Discontinuous Mind” should skip to Part 2.

1. The regrettable hegemony of the discontinuous mind

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 is to the very idea of a cutoff “line” a gratuitously manufactured discontinuity in a continuous reality. 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 (nowadays subdivided into upper and lower seconds), and a few get thirds. That might make sense if the distribution had several peaks with more-or-less shallow valleys in between, but it doesn’t. Anybody who has ever marked an exam knows that the distribution is unimodal. And 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.

These examples illustrate the ubiquity of what I am calling the discontinuous mind. It can probably be traced to the ‘essentialism’ of Plato – one of the more pernicious ideas in all history. At what precise moment during development does an embryo become a ‘person’? Only a mind infected with essentialism would ask such a question. An embryo develops gradually from single-celled zygote to newborn baby, and there’s no instant when ‘personhood’ should be deemed to have burst on the scene. The world is divided into those who get this truth, and those who wail: ‘But there has to be some moment when the fetus becomes human. Doesn’t there?’ No, there really doesn’t, any more than there has to be a day when a middle-aged person becomes old. The discontinuous mind can lead people to describe abortion as murder, even when the embryo has no more brain than a worm. And they may therefore feel righteously justified in committing real murder against a doctor – a thinking, feeling, sentient adult, with a loving family to mourn her.

Paleontologists may argue passionately about whether a particular fossil is, say, Australopithecus or Homo. But, given that the second evolved gradually from the first, there must have existed individuals who were intermediate. It is essentialist folly to insist on shoehorning your fossil into one genus or the other. There never was an Australopithecus mother who gave birth to a Homo child. Quarrelling fiercely about whether a fossil is ‘really’ Australopithecus or Homo is like having a heated argument over whether George is ‘tall’. He’s five foot ten, doesn’t that tell you everything you need to know?

Every creature who ever lived belonged to the same species as its mother. If a time machine could serve up 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 . . . could mate with an ancestral fish, and produce fertile offspring. It is only the discontinuous mind that insists on drawing a line between a species and the ancestral species that birthed it. Evolutionary change is gradual: there never was a line between any species and its evolutionary precursor.

Essentialism rears its ugly head in racial terminology. The majority of ‘African Americans’ are of mixed race. Yet so entrenched is our essentialist mindset, American official forms require you to tick one race/ethnicity box or another: no room for intermediates². I recommend writing in “human”. The US Electoral College (EC) is an all-or-none, winner-take-all affair, which ruthlessly ignores the underlying spectrum. Florida, for example, has 30 EC votes. If 5,000,000 people voted for Smith and 5,000,001 people voted for Brown, all 30 EC votes would go to Brown. The same winner-take-all rule applies in every state except Maine and Nebraska. Theoretically, it could pan out that a candidate loses the presidency with three times as many popular votes as his rival. 

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, no hard-and-fast discontinuity between safe and unsafe.

Lately, the discontinuous mind has broken tiresome new ground. In newspapers and the Internet, we continually read of Gen X, Gen Y, Gen Z, or Boomers. In reality, of course, the distribution of human age is smoothly continuous. The lazy habit of tossing us into cutely labelled age-bins has become too lamentably familiar to need further discussion. It is superficial, shallow, artificial, and . . . lazy.

I’ve been pretty relentlessly negative about the human mind’s proclivity to deface continuous distributions by inflicting lines upon them. But now, does the discontinuous mind sometimes get it right? Yes.

2. Mendelian Genetics and the binary Male-Female divide: one place where the discontinuous mind gets it right

It’s not difficult to find examples where a continuum exists but where the distribution is bimodal or multimodal, with substantial intermediates between the modes. The distribution of muscular strength in a population of humans is bimodal with plenty of overlap between the male and female distributions. But I want to zero in on the extreme of a complete discontinuity with no intermediates. A single example springs to mind.

Mendelian genetics is discontinuous through and through, and it pervades all living things. The alternative is blending inheritance. Mendelian genes are inviolate particles that don’t blend. Every gene in you came from either your father or your mother, before that from one and only one of your four grandparents. Every gene in you either will, or will not, find its way into any particular child. In different terms (the word “gene” was invented after his death) this principle was discovered by Gregor Mendel (1822-1884), an Augustinian monk living in Brno. In the garden of the monastery of which he would later become Abbot, Mendel did brilliant breeding experiments on peas, bees, and other plants and animals³. Sadly, his conclusion was ignored or misunderstood (“Meine Zeit wird kommen”) but, following its rediscovery by three scientists independently in 1900, it now dominates the science of genetics. Rightly. It’s the truth.

Mendel in his lifetime failed to shake the prevailing belief in blending inheritance. If you mix red paint and blue paint, you get purple paint. That was how people thought of heredity. Each individual was thought to be a paint-like blend of mother and father, intermediate between the two parents. Hindsight notices that this cannot be true. If it were, variation would progressively disappear at a high rate, as the generations go by.⁴ Mix purple with purple and you’ll never reconstruct the original red and blue. We’d all be boringly the same as each other, all equivalent to purple paint. In fact, of course, there’s no suggestion that we are any less variable than our grandparents. Variety is sustained as the generations go by. There is no paint-like tendency for successive generations to become more uniform.

In 1867 Fleeming (pronounced “Flemming”) Jenkin (1833-1885) published in the North British Review⁵ a criticism of The Origin of Species, which Darwin regarded as the most serious objection he had to face. Among other things, Jenkin adduced his infamous “swamping” argument, which couples the incorrect logic of blending inheritance with the prevailing racism of the time. He imagined a white man shipwrecked on an island inhabited by “negroes”. Jenkin’s Victorian readers needed no persuading that this single white man would far outshine the natives in the Darwinian struggle for existence, would kill lots of them, and would have “a great many wives and children”. But then, the key “swamping” argument:

“. . . and yet he would not suffice in any number of generations to turn his subjects’ descendants white . . . In the first generation there will be some dozens of intelligent young mulattoes, much superior in average intelligence to the negroes. We might expect the throne for some generations to be occupied by a more or less yellow king [think purple paint]; but can any one believe that the whole island will acquire a white, or even a yellow population; or that the islanders would acquire the energy, courage, ingenuity, patience, self-control, endurance, in virtue of which qualities or hero killed so many of their ancestors and begot so many children . . .?”

The naked racism of Jenkin’s implicit assumptions, which so appals us today, is a fine illustration of what I have called⁶ “the shifting moral Zeitgeist”. But we need to attend to the serious point he was trying to make. A rare advantageous type, no matter how strong its hereditary advantage in the struggle for existence, could not prevail because it would be swamped by the numerical superiority of the alternative. That is wrong. Jenkin’s reasoning was faulty because it was pre-Mendelian. He had a “purple paint” model of heredity. He didn’t have the concept of the particulate gene.

Before and during Jenkin’s own lifetime, the industrial midlands and north of England were blackening with sooty deposits from the chimneys of “those dark Satanic mills”. Before the industrial revolution (and still in rural areas) occasional dark mutants of the normally light-coloured moth Biston betularia were conspicuous as they sat on light-coloured tree trunks, and were readily picked off by birds. But now, on the blackened trees of industrial areas, they were well camouflaged, and natural selection drove them to dominate the population. Swamping of the kind envisaged by Fleeming Jenkin didn’t occur.

The dark, melanic gene rapidly spread from rare mutant to ubiquitous norm⁷. Why did it not suffer Jenkin-style swamping? Because heredity is particulate, not blending. Biston’s genes for dark and light colour don’t blend, they pass inviolate, in all or none fashion, from generation to generation. So, as natural selection favoured the dark gene in industrial areas, it increased in frequency in the gene pool. That’s the thing about particles: they can have a frequency; and frequency is a quantity that can change as the generations go by. Jenkinesque swamping is not an issue.

All this was worked out long after Jenkin’s and Darwin’s time, in the light of Mendel’s Laws discovered during their time. Working with peas, Mendel had examined the inheritance of various visible features such as flower colour (purple or white), seed colour (yellow or green), seed surface (smooth or wrinkled) and pod shape (plump or constricted). In every case, he found all-or-none inheritance with no intermediates. In every case the underlying gene (as we would nowadays call it) passes, or fails to pass, to the next generation, unchanged and unblending, a discrete particle, not a paint-like substance capable of blending with another. The same is true of all genes in all creatures.

It is widely, and correctly, lamented that Darwin never read Mendel’s 1866 paper. There is even a (probably false) rumour that he possessed the relevant volume but the pages were uncut. His German wasn’t great, anyway. The point of the lamentation – the poignancy of the legend of the uncut pages – is that, if only he had read Mendel, he would instantly have seen the glaring flaw in the “swamping” argument and trounced Fleeming Jenkin⁸.

Or would he? Tantalisingly, an 1866 letter from Darwin to AR Wallace suggests that Darwin’s own informal experiments, on sweet peas, no less, came agonisingly close to discovering particulate inheritance, but he somehow failed quite to see the full significance of his results.

My dear Wallace

. . . I do not think you understand what I mean by the nonblending of certain varieties. It does not refer to fertility; an instance will explain. I crossed the Painted Lady and Purple sweetpeas, which are very differently coloured varieties, and got, even out of the same pod, both varieties perfect but none intermediate. Something of this kind I should think must occur at least with your butterflies & the three forms of Lythrum; tho’ these cases are in appearance so wonderful, I do not know that they are really more so than every female in the world producing distinct male and female offspring . . .

Believe me, yours very sincerely
Ch. Darwin

( I am grateful to Dr Seymour J Garte for calling my attention to this remarkable letter.)

So near, yet not quite there.

RA Fisher, began his great 1930 book, The Genetical Theory of Natural Selection by quoting from another letter by Darwin, this time addressed to TH Huxley and dated 1857, before The Origin was written:

. . . Approaching the subject from the side which attracts me most, viz inheritance, I have lately been inclined to speculate very crudely & indistinctly, that propagation by true fertilisation, will turn out to be a sort of mixture & not true fusion, of two distinct individuals, or rather of innumerable individuals, as each parent has its parents & ancestors:— I can understand on no other view the way in which crossed forms go back to so large an extent to ancestral forms.— But all this, of course, is infinitely crude. 

The Huxley letter intimates an understanding – even if “infinitely crude” – that inheritance is not blending in the “paint” sense but “a sort of mixture . . . of innumerable” ancestors. The Wallace letter, far less “crudely and indistinctly”, suggests that Darwin was closing in on Mendelian genetics by 1866, the very year Mendel’s unread paper was published. And the final sentence of that letter is a gem of biological insight. Darwin spotted that the particulate inheritance of his flower colours followed the same principle as the inheritance of sex: “every female in the world producing distinct male and female offspring . . .”. When a female mates with a male, they do not blend their characteristics to make a hermaphrodite. They make either a son or a daughter. Mendelism writ very large is thrust daily under our nose in the form of the discontinuous sexual binary. There are those today who, whether motivated by emotion, politics, or sheep-like desire to conform to transient fashion, have persuaded themselves that sex is a spectrum, with males and females at opposite ends of a continuum. As Darwin could have told them, they are fighting a losing battle against objective biological science.

Be that as it may, whence the strong appeal of the erroneous doctrine of blending inheritance? Setting aside Jenkin’s rebarbative assumptions of racial superiority, he is right that the skin colour of his shipwrecked mariner’s offspring would be intermediate between their white father and black mother.

Why is this not blending inheritance? The analogy with mixing paint looks tempting. What is it that makes inheritance often look blending, even though it is really particulate? Two things: polygenes, and incomplete dominance. Polygenes are separate (particulate) genes whose similar effects add up to yield some visible feature. If a sufficient number of polygenes quantitatively add their effects, the observed colour (or size, etc.) can vary continuously, depending on how many polygenes “vote” this way or that. This is the main explanation for the continuum of skin colour in humans. Several genes additively influence the quantity of melanin in the skin. The genes themselves are discrete, non-blending particles, but their effects (quantity of melanin) blend.

Incomplete dominance is another way in which inheritance can seem to blend, even though the underlying genes are discretely particulate. Dominance is the phenomenon whereby the effects of a (thereby defined as) “recessive” allele are masked by those of a (“dominant”) alternative. In Mendel’s peas, purple flower is dominant to white. When a plant is “heterozygous” for flower colour, i.e. has one purple and one white gene, all its flowers are purple. The recessive white gene is present, and capable of being passed on, but doesn’t manifest itself. When Mendel crossed two heterozygous plants, one quarter of the offspring grew white flowers. They had two copies of the recessive white gene. That’s an example of complete dominance. But dominance can be incomplete. A snapdragon with one gene for red flowers, and one gene for white, grows pink flowers. The observable result is a blend, but the underlying genes remain discrete. Each one either is, or is not, transmitted to the next generation. They never blend in themselves, though their effects on flower colour do.

Mendelian particulate genetics and the male female divide: can you think of other cases where there are literally no intermediates – a true binary? It’s surprisingly hard. A mixed population of humans and elephants (choose any pair of species) seems obviously discontinuous. But look more closely. Of course there are no intermediates, but that’s only because they are all extinct. We need to think as evolutionists. If we could bring back to life all human ancestors and all elephant ancestors going back to the common Mesozoic ancestor, we would see a beautifully smooth continuum, replete with intermediates.

You can’t do that with the two sexes. The female-male binary separation goes back beyond the common ancestor of all animals, with no intermediates. The biological definition of sex is based on gamete size. Females have few large gametes, males numerous small ones. There is no continuum. The distinction is absolute. There are literally no intermediates anywhere in the animal or plant kingdoms. Not just as a matter of observation but for good theoretical reasons, which I shall not rehearse here as I have spelled them out elsewhere⁹. Yes, there are hermaphrodites who produce both kinds of gamete, either simultaneously (earthworms, snails) or successively (some fish) but there are no intermediate gametes. There are individuals who don’t produce gametes at all (too young, too old, or special cases like sterile worker bees who would have been fertile queens if fed a different diet). Some males (e.g. Lepidoptera) produce two kinds of sperm (“sperm heteromorphism”) but neither of them resembles an egg. Biological sex is a true, discontinuous, exception-free binary – a special case of particulate, Mendelian inheritance, at least in those animals, such as mammals and birds, in which sex is determined chromosomally.

Mendelian inheritance, of which the inheritance of sex is a special case, is a glaring case where, for once, the dicontinuous mind gets it right. Moreover, a strong case can be made that heredity not only is particulate but had to be particulate or evolution would not have been possible. Darwinian evolution depends upon a genetic system of extreme high fidelity, information transmitted with very few errors¹⁰. A more general point than Fleeming Jenkin’s “swamping” argument, analogue genetics is simply too error-prone for natural selection to work. Mendelian genetics is digital in that each gene either is, or is not, passed on in each act of reproduction. Molecular genetics, post Watson and Crick, is digital in a more profound sense. Genetics has become a branch of information technology, scarcely distinct from computer science. Only digital genetics guarantees the necessary high fidelity transmission – with occasional, very rare errors – for Darwinian selection to work. But that is another story.

 I thank Jerry Coyne for helpful comments.

1.  R Dawkins (2011) “The Tyranny of the Discontinuous Mind”, first published in New Statesman, Christmas number, and then reprinted as “The Dead Hand of Plato” in R Dawkins Science in the Soul (2017). Transworld, London.

2.  As for the misnomer “Hispanic”, what’s that about? Whatever else it means, it doesn’t mean Spanish!

3. RA Fisher, the illustrious founder of modern statistics, reanalysed Mendel’s data and concluded that his results are too good to be true. Did he get the principle and then fiddle the data to improve the fit? If so it is highly regrettable, but the principle is still correct, as numerous subsequent researches have shown.

4. RA Fisher (1930) The Genetical Theory of Natural Selection, calculated that the heritable variance would be approximately halved in each generation.

5. Reprinted in David L Hull(1973) Darwin and his Critics. Chicago: University of Chicago Press

6.  The God Delusion, Penguin, London.

7. HBD Kettlewell (1973) The Evolution of Melanism. Oxford University Press

8. Susan W Morris (1994) Fleeming Jenkin and The Origin of Species. British Journal of the History of Science, 27, 313-343 argues that Darwin was in any case more worried by other aspects of Jenkin’s paper, concerned with the age of the Earth.

9.  https://richarddawkins.substack.com/p/is-the-male-female-divide-a-social

10.  Mark Ridley (2000) Mendel’s Demon. Weidenfeld & Nicolson, London, published in America as The Cooperative Gene.