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If I follow her lead now, even the pictures that I draw are reduced to number. ‘Draw Elly cry?’ ‘Draw Elly 2 tears?… 4 tears?… 6 tears?… 8 tears?’ — all accompanied by the cheeriest good humour, unless, of course, I should refuse to complete the series. When her baby doll lost both its legs I thought she might mind, remembering the horror of deformity I felt as a child. Not at all; she was delighted. ‘Draw baby zero leg?’ ‘Draw baby one leg?… two leg?… three leg?’…

‘Draw baby eight leg?’ To me it looks nastier with each addition. Dead-pan, I suggest it is a spider-baby and meet with enthusiastic assent.

I recall an incident so characteristic of Elly that it can stand as an archetype of what she seems to be. Elly was six and a half. I had been gone all day, and returning, coming into the bedroom, I found Elly at the typewriter. Leaving it, she ran to me at the door and for the first time in her life said ‘Hello, Mama!’ Then, back at the machine, she chirped ‘Comma!Exclamation point!’ In my happiness I had still to reflect, ‘It is the “hello, mama”, that surprises you. The “exclamation point” does not.’

What kind of child was this, who could take six years to learn to greet her mother (a greeting she has seldom repeated) but whose mind unerringly recorded meaningless terms mentioned once without emphasis weeks or months before?

It was, apparently, an autistic child. Dr Blank had first thought of autism, long ago, at Elly’s first visit, when he heard of her interest in arrangements. Autistic children were often good with numbers; some showed extraordinary abilities, far beyond Elly’s. Elly’s exact shape discrimination and her acute perception of the missing members of a set were not isolated phenomena, but typical of the condition. So was her ear for music, most abstract of the arts. Even the concern with the preservation of sameness, which Kanner considered a primary symptom, can be thought of as part of the autistic commitment to order; the patterns established, whether in space with cookies or washcloths, or in time with rituals and routines, must be preserved and completed. Elly could accept my outright refusal to draw for her, say, the numbered series of triangles with which she ended every day. We have had some success in moderating her compulsiveness, and I could, especially as she grew older, say that it was too late for the usual twenty-six, but that we had time for twelve. But if I once began the series and was interrupted before the twelfth one came, Elly would be beside herself with distress.

Series must be completed, order reaffirmed, limits observed.

This was still the same child who at three had sought out fences and enclosures. At first it was I who coloured the pre-bedtime triangles, for though Elly wanted them done, she did not want to do them herself. As I coloured, of course, I used the full spectrum that Elly’s crayons provided; it never occurred to me to do otherwise. Gradually I was able to draw her into the colouring routine; I coloured one triangle, she the next, until all were done. At first I chose my colours while Elly chose hers; later (and there are some hundreds of these sheets of triangles, one for each bedtime; much of Elly’s arithmetic has been learned from them) she chose my colours and handed them to me. ‘Only two colours?’

Her voice grew urgent as I reached for a third crayon. ‘Just green and yellow-green, yes!’ Inspecting the traingle sheets after weeks, I realized what had escaped me as we coloured night by night. Not only was Elly using a strictly limited palette, she was providing the same colour combinations every night in almost the same order. The first five would be successive combinations, two at a time, of orange, red, peach, and pink. The next four would combine green, yellow-green, and pale green. The next would be orange and blue. Only after that would she choose with any flexibility, and even then she would allow no third colour.

Some such limiting principle seemed to lie also behind her tendency to stereotype her environment and activities. When Elly was three I could see no trace of Kanner’s prime symptom, the committent to the preservation of sameness. Elly had no routines then. But the symptom lay in waiting (it should be noted that Kanner did not always see his patients as early as three). It developed later, with the capacity for self-assertion — the pathological symptom accompanying what we take as a sign of health. When Elly was three and four, more withdrawn and less assertive, she would walk with me anywhere. At five she began to want to turn right or left at a certain corner, if we had done so before. At seven and eight — today — she will, if not opposed, reduce any walk to sameness. There is one path to take downtown, one for our return. If we pass a landmark where I have previously invented a game Elly has liked, Elly will repeat the actions even if I have forgotten them. If I have spoken words there, Elly will repeat them for me and cue my mouth to make me speak my lines. She is not unyielding about it; by introducing minor, tolerable variations I and, still better, others, are able to maintain some flexibility. She will now readily accept a deviation introduced for a reason — lateness, or a changed destination. But if I merely suggest that we walk home a new way, her anxious ‘no?’ vetoes it unless I decide to make it an issue — and if I do, the new option will probably be incorporated in the next walk. The commitment to an environment that can be kept track of remains.

Recently Elly spent more than an hour making a series of pictures — twenty-one sheets of carefully crayoned paper, each displaying a large numeral, starting, of course, with zero. Upon the zero, inside it, a small figure sits. She is standing against the one. The numbers continue to twenty. In each of them the same figure stands or climbs or sits or hangs. Sometimes the figure is ‘Elly’, sometimes ‘girl’. Elly enjoys talking about them; she explains with delight, ‘Girl hang-uh seven.’ (The hanging figure’s hair, obeying gravity, hangs straight down.)

A new series carries the process one step further. The body has disappeared and the girl has merged completely into the numeral. Only her schematic head remains.

Girl into number. Elly, I fear, is a natural Platonist. Though she no longer lives in it, she prefers a world stripped bare of the adventitious accretions that to ordinary minds make it interesting and precious — a world reduced to its essentials of pattern, shape, and number. That preference can of course be seen, for her as for Plato, as a retreat, an abandonment of the real, disorderly world which causes anxiety and pain. Yet sometimes I think that to interpret it so is to miss the point. That golden baby circling its spot laughed aloud with pleasure. Elly’s delight is spontaneous and free. If it seems unnatural, that is because it is uncommon in young children. Joy cannot in itself be unnatural or unhealthy. Few of us share the joy Pythagoras musthave felt in his theorem, but we can all recognize it. Order in the world is something to take joy in — on this theologians and mathematicians agree. Elly’s joy is of extreme simplicity compared to theirs, yet I think it is of the same kind. I cannot be sorry it exists, only that it comes so much easier than the other, more human kinds of pleasure.