The Man Who Mistook His Wife for a Hat: "The Twins"

Most of the accounts concluded that, as idiots savants go, there was ‘nothing much to them’—except for their remarkable ‘documentary’ memories of the tiniest visual details of their own experience, and their use of an unconscious, calendrical algorithm that enabled them to say at once on what day of the week a date far in the past or future would fall.

The reality is far stranger, far more complex, far less explicable, than any of these studies suggest, but it is not even to be glimpsed by aggressive formal ‘testing', or the usual 60-Minutes-like interviewing of the twins.

They are, indeed, unprepossessing at first encounter—a sort of grotesque Tweedledum and Tweedledee, indistinguishable, mirror images, identical in face, in body movements, in personality, in mind, identical too in their stigmata of brain and tissue damage.

They are undersized, with disturbing disproportions in head and hands, high-arched palates, high-arched feet, monotonous squeaky voices, a variety of peculiar tics and mannerisms, and a very high, degenerative myopia, requiring glasses so thick that their eyes seem distorted, giving them the appearance of absurd little professors, peering and pointing, with a misplaced, obsessed, and absurd concentration.

And this impression is fortified as soon as one quizzes them—or allows them, as they are apt to do, like pantomime puppets, to start spontaneously on one of their ‘routines’.

And this impression is fortified as soon as one quizzes them—or allows them, as they are apt to do, like pantomime puppets, to start spontaneously on one of their ‘routines’.

They cannot do simple addition or subtraction with any accuracy, and cannot even comprehend what multiplication or division means. What is this: 'calculators' who cannot calculate, and lack even the most rudimentary powers of arithmetic?

And yet they are called 'calendar calculators'—and it has been inferred and accepted, on next to no grounds, that what is involved is not memory at all, but the use of an unconscious algorithm for calendar calculations.

A great many calculators, it is true, do have a larger repertoire of methods and algorithms they have worked out for themselves, and perhaps this predisposed W.A. Horwitz et al. to conclude this was true of the twins too.

A great many calculators, it is true, do have a larger repertoire of methods and algorithms they have worked out for themselves, and perhaps this predisposed W.A. Horwitz et al. to conclude this was true of the twins too.

Give them a date, and their eyes roll for a moment, and then fixate, and in a flat, monotonous voice they tell you of the weather, the bare political events they would have heard of, and the events of their own lives—this last often including the painful or poignant anguish of childhood, the contempt, the jeers, the mortifications they endured, but all delivered in an even and unvarying tone, without the least hint of any personal inflection or emotion.

Give them a date, and their eyes roll for a moment, and then fixate, and in a flat, monotonous voice they tell you of the weather, the bare political events they would have heard of, and the events of their own lives—this last often including the painful or poignant anguish of childhood, the contempt, the jeers, the mortifications they endured, but all delivered in an even and unvarying tone, without the least hint of any personal inflection or emotion.

But it could be said, equally, and indeed more plausibly, that memories of this kind never had any personal character, for this indeed is a cardinal characteristic of eidetic memory such as this.

But there is no doubt, in my mind at least, that there is available to the twins a prodigious panorama, a sort of landscape or physiognomy, of all they have ever heard, or seen, or thought, or done, and that in the blink of an eye, externally obvious as a brief rolling and fixation of the eyes, they are able (with the ‘mind’s eye’) to retrieve and ‘see’ nearly anything that lies in this vast landscape.

Similar tales are told of Zacharias Dase, the number prodigy, who would instantly call out ‘183’ or ‘79’ if a pile of peas was poured out, and indicate as best he could—he was also a dullard—that he did not count the peas, but just ‘saw’ their number, as a whole, in a flash.

I had already come to feel, through their ‘seeing’ events and dates, that they could hold in their minds, did hold, an immense mnemonic tapestry, a vast (or possibly infinite) landscape in which everything could be seen, either isolated or in relation.

It was isolation, rather than a sense of relation, that was chiefly exhibited when they unfurled their implacable, haphazard ‘documentary’.

It was isolation, rather than a sense of relation, that was chiefly exhibited when they unfurled their implacable, haphazard ‘documentary’.

But might not such prodigious powers of visualisation—powers essentially concrete, and quite distinct from conceptualisation—might not such powers give them the potential of seeing relations, formal relations, relations of form, arbitrary or significant?

Were these ‘Borgesian’ or ‘Funesian’ numbers, mere numeric vines, or pony manes, or constellations, private number-forms—a sort of number argot—known to the twins alone?

As soon as I got home I pulled out tables of powers, factors, logarithms and primes—mementos and relics of an odd, isolated period in my own childhood, when I too was something of a number brooder, a number ‘see-er’, and had a peculiar passion for numbers.

And then I, in my turn, after a surreptitious look in my book, added my own rather dishonest contribution, a ten-figure prime I found in my book.

Indeed I find myself comparing them to musicians—or to Martin, also retarded, who found in the serene and magnificent architectonics of Bach a sensible manifestation of the ultimate harmony and order of the world, wholly inaccessible to him conceptually because of his intellectual limitations.

Jedediah Buxton, one of the most ponderous but tenacious calculators of all time, and a man who had a veritable, even pathological, passion for calculation and counting (he would become, in his own words, ‘drunk with reckoning'), would ‘convert' music and drama to numbers.

Jedediah Buxton, one of the most ponderous but tenacious calculators of all time, and a man who had a veritable, even pathological, passion for calculation and counting (he would become, in his own words, ‘drunk with reckoning'), would ‘convert' music and drama to numbers.

Jedediah Buxton, one of the most ponderous but tenacious calculators of all time, and a man who had a veritable, even pathological, passion for calculation and counting (he would become, in his own words, ‘drunk with reckoning'), would ‘convert' music and drama to numbers.

They summon up, they dwell among, strange scenes of numbers; they wander freely in great landscapes of numbers; they create, dramaturgically, a whole world made of numbers.

They have, I believe, a most singular imagination—and not the least of its singularities is that it can imagine only numbers.

Dmitri Mendeleev, for example, carried around with him, written on cards, the numerical properties of elements, until they became utterly ‘familiar’ to him—so familiar that he no longer thought of them as aggregates of properties, but (so he tells us) ‘as familiar faces’.

Such a scientific mind is essentially ‘iconic’, and ‘sees’ all nature as faces and scenes, perhaps as music as well. This ‘vision’, this inner vision, suffused with the phenomenal, none the less has an integral relation with the physical, and returning it, from the psychical to the physical, constitutes the secondary, or external, work of such science.

Numbers for them are holy, fraught with significance.

This serenity was, in fact, interrupted and broken up ten years later, when it was felt that the twins should be separated—'for their own good’, to prevent their 'unhealthy communication together’, and in order that they could 'come out and face the world...in an appropriate, socially acceptable way’ (as the medical and sociological jargon had it).

Both have been moved now into 'halfway houses’, and do menial jobs, for pocket money, under close supervision.

This, as we have seen, is most dramatically shown in ‘prosopagnosia’, in which, as a consequence of a lesion in the right occipital cortex, patients become unable to recognise faces as such, and have to employ an elaborate, absurd, and indirect route, involving a bit-by-bit analysis of meaningless and separate features.

On the other hand, should this discussion be thought too singular or perverse, it is important to note that in the case of the twins studied by Luria, their separation was essential for their own development, ‘unlocked' them from a meaningless and sterile babble and bind, and permitted them to develop as healthy and creative people.

One has to wonder whether there may not be a ‘conventional’ arithmetic (that is, an arithmetic of operations)—often irritating to teacher and student, ‘unnatural’, and hard to learn—and also a deep arithmetic of the kind described by Gauss, which may be truly innate to the brain, as innate as Chomsky’s ‘deep’ syntax and generative grammars.

Some dealt with the specific themes of ‘seeing’ or apprehending numbers, some with the sense or significance which might attach to this phenomenon, some with the general character of autistic dispositions and sensibilities and how they might be fostered or inhibited, and some with the question of identical twins.

Park wrote to me of another autistic child she knew, who covered sheets of paper with numbers written down ‘compulsively’.

What is clear is the peculiar sense of pleasure and significance attaching to primes. Some of this seems to go with a sense of formal beauty and symmetry, but some with a peculiar associational ‘meaning’ or ‘potency’. This was often called ‘magical’ in Ella’s case: numbers, especially primes, called up special thoughts, images, feelings, relationships—some almost too ‘special’ or ‘magical’ to be mentioned.

If this does occur, it is possible that the twins, and others like them, do not merely live in a world of numbers, but in a world, in the world, as numbers, their number-meditation or play being a sort of existential meditation—and, if one can understand it, or find the key (as David Park sometimes does), a strange and precise communication too.