And so on, for ten pages, two tables of correlated phenomena, and a page and a half of intricate calculations. The splendors of the system defy summary; even the investigators didn’t understand them all. Those who share a fascination with numbers can explore them further in what they wrote.
But whether or not we could follow the numbers, we all had to live with the system. It was a rich and inclusive we. No one person, or family, could provide all that Jessy needed to grow. There was always someone else working with her in those days. Most of these Jessy-friends lived with us, some for a summer, some for a year or more, Jessy’s therapists, teachers, and good companions. They were college students, most of them, though two of the best were still in high school. None had any training in special education or developmental psychology, but I claim for them the word «therapist» without hesitation. They worked with Jessy, played with her, sang with her, joked with her, comforted her, understood her secret words, interpreted her to strangers, devotedly taught her whatever they could. Endlessly inventive, endlessly generous, without them hers would be a different and sadder story.
Some, like the young mathematician, recorded their observations. Most did not. But one, it seemed, kept a journal, and after more than twenty-five years, knowing I was again writing about Jessy, she sent it to me. Its entries remind me of what I had gladly forgotten; they bring back how very hard it was, for Jessy and for the inclusive us, in the days when the system ruled. Fran came to us when Phil had moved on. It is her turn to speak.[22]
Pure blue sky. While walking the long hill, a little cloud appeared and covered the sun briefly — oh, what sadness and anger — mumble mumble, looking down at the ground, dragging the feet, stopping, answering no more questions about school. «What is the matter, Jessy?» «The cloud over the sun». I told her, after the cloud was no longer over the sun and was now just in the sky, that she only needed to be a tiny bit sad, because the cloud was small and the blue sky was big.
No help, mumble mumble. Finally the cloud went behind the mountain and trees. «Jessy, the cloud has gone away». Jessy was happy again immediately.
The cloud, it turned out, was «full of numbers», multiples and powers of 37 and 73, with two bad 3’s. Jessy drew it in a picture, with herself and Fran, when the cloud was gone and it was all over. But the weather was not always so obliging. «Some days are almost all bad», Fran wrote a month later. «Full Moon. Low, heavy clouds. What a horrendous day». Jessy came home crying; someone had taken her special seat on the school bus. (There was a system there too, but we never understood it.) She refused to sing with Fran («I will cry again») or answer her questions. She mumbled because the radiator hissed. She cried when she made a mistake in sewing, stopped, cried some more. When Fran tried to comfort her she went in her room and told Fran to go away.
I walked out the door and cried all the way home. It was just too much of a struggle all afternoon… I cried and cried, as bad as Jessy, I suppose. No work Tuesday. Hooray! A holiday for a full week- must rest and be renewed to begin again.
There were good days too, with swimming lessons, walks, bicycle rides in benign weather. With Fran’s encouragement and supervision, Jessy designed and sewed a gorgeous quilt, the sun on one side, the full moon on the other, not a cloud in either sky. And the system kept on growing, spreading invisibly, underground. As it predated its discovery by others («Found these at ears and years», she told her father), it evolved without their attention. What Fran had glimpsed would prove to be its next and most florid stage.
Moon, sun, and clouds were now correlated with, of all things, flavors. And gum wrappers — twenty-nine of them. Fran didn’t know it, and I didn’t notice it, but of course that was the number of day things, real and imaginary. There were also (only now do I discover it) twenty-nine of the numbers in the pictured cloud. So it was not good when three wrappers were missing. «No remedy. Mumble mumble and threats of tears». But this time Jessy found a way to cope. She drew the number-filled cloud again and cut it into tiny bits to sift between her fingers. «She played with them all afternoon. A Decent Day».
Jessy told Fran there was a new kind of cloud, «rice rice pudding with lime rice pudding».
Jessy had made tubes of many flavors with numbers on them, which were the same as the [numbers on the] cloud. She started to make a chart of suns with the same flavors (lime lime lime, little bit lime, rice pudding, etc.). She wanted me to go away, but I had her tell me about school first, and then she continued to make the flavored suns, neatly in rows.
Then she cut them out. Those suns are in the suitcase, twenty- nine of them, their rays recalling the emotional valences of days past. Jessy drew them short and stubby, so as to allow room to do full justice to the colors of the coordinated flavors. Rice pudding, for example (not good — correlated with 3), had to be drawn in grain by grain, a painstaking operation, since Jessy classified the grains as «fairly big», «big», and «extra large». The flavor tubes are in the suitcase too, in a twenty-nine-, then a forty-one-tube version. Jessy taped six sheets of paper together so she could draw them all. From each tube emerges a length of icing. «This is a happy frosting come out the tube», she explained. «And sometimes sad».
Flavor tubes (detail), another of Jessy system
The lengths are carefully measured to correlate with the appropriate number. Each digit, Jessy told me later, equals one inch, each exponent (squares, cubes, et cetera) a half-inch. Three, the smallest number, occurs twice; the inch-long lengths of icing are labeled «rice pudding with lime». The largest number is one even a mathematician would find bizarre:
(Seven squared to the infinity power to the infinity power plus i, times 37 squared to the infinity power to the infinity power plus i.) It is represented by a 9 1/2-inch length; its icing equivalent, carefully written on the tube, is «lemon lemon lemon lime little tiny bit orange orange orange lemon». The composition of the 8 1/2-inch length is even more complicated: «double dutch little bit lemon- lemon lemon lemon lemon lime lime lime lime lime lime lime lime- lime lime lime». And Jessy colored the icing as carefully as she calculated the numbers, in permutations and combinations that boggle the mind. The next tube is identical except that «little bit» becomes «little tiny bit»; predictably, the little lemon lime-green areas that stripe the brown chocolate have been reduced by half to correspond. I could describe the others, but somehow I don’t think I will.
The correlations came first. The explanations emerged only gradually, as her language grew more adequate to what she had in her head. We learned that flavors correlated with the times she «looked at the clock by mistake». They correlated with the number of times she soaped herself in the bath, o light blueberry, i lime, 2 lemon, 3 orange, 4 strawberry, 5 vanilla, 6 licorice, 7 chocolate, 8 grape, 9 or more, blueberry again. «Dark lemon», «dark lime», and «lime with a little bit rice» correlated with three kinds of «striped» cloud. Even her pencil line proclaimed the system. «Why is the window all wiggly?» I asked of a drawing showing Jessy in bed and the moon behind her favorite tree. It was because of the flavors, she said, wiggly for lime, three-eighths wiggle for lemon lime, whole wiggle for rice pudding. How many other correlations were there that we missed?
The system expanded to include new experience. A year later, when the Christmas catalogs came, the various delicacies received numbers, 137 for solid chocolate, 173 for chocolate with nuts, 337 for chocolate with coconut. Dobosh torte was 3; with cherries it was 7 ∞+1. That same number, she told her father, was correlated with airplane vapor trails: if two vapor trails crossed, the cloud at the crossing point yielded 7 2∞+2. The exponential 7 was «rice pudding with lime lime»; a 3 was rainbow-colored «when cloud has color outside looks like rainbow and white inside». In the system’s last stage Jessy correlated colors, flavors, and numbers with her typing errors, and correlated them with «flavor cookies». A surreal connection? It proved to be wholly logical when Jessy drew herself with ten cookies, two on the floor. «And drop the cookies. That is a
mistake». So both kinds of error were duly recorded in a Book About the Mistakes, in which the very word was given its permutations: «mistakable, mistake, mistaken, mistaker, mistakers, mistaking, mistook».
Then, gradually, numbers lost their magic. Three years later she could say, «They used to be important to me, about all the things, such as bath soaps, and wild berries, and too good music and crying silently and laughing silently». We heard no more about flavor tubes. Jessy’s emotions seemed independent of the weather. She stopped making books. She was doing more conventional art at school, and told us, echoing, I’m sure, what she’d been told, that she was now «too mature». For all we knew, the system was finished.
And yet, twenty years later, when we got out the tubes and suns and «all different kind of days» to show Dr. Oliver Sacks, it turned out it was still there. Under his gentle questioning it burgeoned anew. There had, she said, been more than twenty-nine days; Phil just hadn’t had room for them all. She named and described them. She added fifty-five new flavors, including dark rum, three kinds of «expresso», and tangerine. «There are lots of correlated!» she crowed, reaching the end of the list.
* * *
If the reader by now is experiencing some wandering of attention, that’s as it should be. For us normals, boredom is part of the experience of autism. We are, most of us, impatient with formal structures we cannot relate to the concerns of human life, and even mathematicians, who are sympathetic to such pure pleasures, expect them to lead to something more interesting than tireless and self-absorbed variations on the same theme. We taught Jessy to solve simple equations. Excited by her facility with numbers, Phil tried to teach her calculus. But she resisted, not because she couldn’t understand it, but because it had nothing to offer her and demanded much. Rather than repeating familiar processes, it insisted she move forward, beyond the security of the predictable into a realm in which she must accept, even invite, unexpected results. And that was exactly what Jessy did not want. Her systems were designed to eliminate the unexpected, to capture uncertainties in a net of connections, to reduce them to rule.
Marvelous yet sterile, they bespoke a mind which for all its vigor was severely limited. Kanner’s «preservation of sameness», Courchesne’s «difficulty in shifting attention», worked in tandem to restrict both the ability and the desire to initiate new activities. Chaining, lining up objects, sifting silly business — these had been the preferred pastimes of Jessy’s childhood. In adolescence she could still be content with repetitive activity, rocking in her rocking chair, bouncing her superball up and down (though she might use her new skills to graph the number of bounces). At least her systems were richer experientially than that. They could admit new elements — weather, typing lessons, words and their spellings. Some were pleasurable; many were not. Systems couldn’t banish the world’s distressing variability, but they could set it in order, as clouds, cookies, mistakes, and shining days and nights took their places, subjected to the mind’s control.
* * *
But Jessy’s in her forties now. Understanding most of what is said to her, much of what is said around her, much of what is done around her, she has much more to occupy her mind. She can think about her bank statements, about the estimated tax forms necessitated by her new Roth account, about what she’ll make for the upcoming potluck supper, about when to renew the permit for the landfill, about whether it’s time yet to order a new bag of basmati rice. I could make the list much longer, but I won’t; normal activities can seem pretty boring too. Yet Jessy doesn’t find them boring. She is as absorbed in noting them, remembering them, keeping track of them, as she once was in her systems. She finds her regularities now in the humdrum exigencies of the world around her. She is our authority on the schedule of public holidays, the rules governing the acceptability of donated blood, the times the bank and post office open and close. Collecting information, storing it, using it, communicating it, her mind is at work. That is enough. The bizarre glories of the system have faded, as glories so often do, into the light of common day. But we are content. The common day is the day we hold in common, the day we can share. «Come see!»
Chapter 6
«When I ten, that minus one!»
It wasn’t the most gracious way for an eleven-year-old girl to welcome the neighbors’ new baby, but it certainly showed a grasp of number. Jessy’s formulation provided yet another illustration of the social blindness that is at the core of autism. But just as arresting as her substitution of a numerical relation for a human one, or her use of the impersonal «that» to refer to a living, breathing baby, was the unexpected sophistication of her spontaneous subtraction. «Genius» is in general an overused word, never more so than in its casual application to autistic achievement. Jessy’s «minus one» was as accurate as it was inappropriate. But though it astonished, it didn’t come out of nowhere. Before squares, before primes, before 37’s and 73’s and 337’s, there had been years of the ordinary, grade school applications of number, as we worked to prepare her for what we hoped would be some sort of education beyond what we could give her at home. In fact we were preparing her, though we didn’t know it, for the calculations that would make possible the System. So I must briefly leave the teenage Jessy and trace the progress of that preparation.
Jessy at a number-filled blackboard
In its early stages, when Jessy was eight, numbers didn’t seem particularly interesting for her or for us. They were something she could do, that was all, and with a child who did so little, that was enough. So there we were, she and I, day after day, down on the floor, crayons at the ready. I’m a bit bored, more than a bit; I’m drawing row after row, sheet after sheet, of triangles for her to count then color, the inspiration the Halloween corn candies that like other candies were such an important part of her small universe. There was no pressure; there didn’t need to be. Jessy liked repetition, she liked counting, she liked counting some more. She liked coloring with her mother, both of us fixed on this simple, unchallenging activity. She liked it when I added another triangle and showed her the plus sign. I was teaching notation, not ideas; I knew that. But unawares I was also teaching something more important. Shared attention! The phrase, and the research behind it, was far in the future. But here we were, together on the floor. Another day, another sheet.
Jessy had been in nursery school four years when the nice teachers had to tell me they couldn’t keep her among the little ones any longer. After months of corn candies, she could do more than keep track of missing washcloths, she could add and subtract on paper. Her numbers were scrawly and her 5’s turned backwards, but her answers were right. So when September came I took her, wordless and unresponsive, to the principal of our local elementary school and showed him her numbers. He didn’t bother with politeness — he thought they were all done by rote and said so. He didn’t have to explain the subtext: an intellectual mother pushing an incapable child beyond what she could possibly accomplish. Jessy lasted only eight weeks in the special class. There was no «right to education» for the handicapped in those days.[23]
But to push Jessy beyond where she was ready to go was not what the intellectual mother could do, even if she had wanted to. Words must come before numbers, I thought, as they do in life — in normally developing life. I need not hurry my daughter into what came naturally. So we moved into multiplication and division slowly. Another year. More sheets. Corn candies were succeeded by the heart-candies of Valentine’s Day, the kind that carry a word or two like LOVE or KISS ME, so we could also work toward words. More rows: times tables, is and 2’s and 3’s, then more rapidly (it was all so easy) up to 10, as the operations in her head were made visible, then assumed their conventional written form: +, -, X, +. So why not fractions? I remembered how hard they’d been for me, but I was not Jessy. Hearts turned to circles, to rows and rows of pie charts, ever more complex. So why not one step further, letters for numbers, the beginnings of algebra? Jessy might not know the right way to talk about a baby, bu
t she had no problem with that. It was as obvious to her that a + a = 2a, a X a = a2, a — a = o, as that 1 + 1 = 2. As for —1, wasn’t it equally obvious that that was what you’d have if you took 1 away from zero? So there it was, all in place: «When I ten, that minus one!»
* * *
It’s not surprising that so many autistic people are more at home with numbers than babies. Mathematics too is a language, but a language that is predictable, logical, rule-governed, blessedly abstracted from shifting social contexts. Teaching Jessy the ways of numbers was like providing a natural athlete with a ball and bat. Whereas words… I wrote words on the candies — NUT, CUT, HUT (a lesson in phonics), common words, her own name — and Jessy would reluctantly read them. But then she’d veer away, transforming them into nonsense: JESSY, JASSY, JISSY, JKSSY, KESS. (Still, she’d inferred the rule. «Throw away N», she told me. «Can’t say NUT. Just say UT, yes!»)
We kept on with candies and circles till Jessy was past eleven. She was used to them, and I wanted to ensure that the abstract operations stayed meaningful, anchored in things that could actually be counted. But it became clear Jessy no longer needed them, if indeed she ever had. As with the washcloths, she had no trouble with real-life calculations. When she was nine, late in 1967, it occurred to me to ask her, «How old will you be in 1975?» took her less than three seconds to answer, «Seventeen». Numbers had become more than an acceptable pastime; she grew enthusiastic as two-digit multiplication and long division opened up new possibilities. «Multiply?» she’d ask. «Fractions?» After two years of pie charts she summed up her progress, proudly remembering, «When a little girl, can’t reduce to lowest terms!»
Numbers, good in the abstract, expressed the world. And they expressed her. As her twelfth birthday approached, we saw some very unusual numbers: || 351/365, || 71/73, || 359/365. What could they mean? Then we understood; with characteristic exactitude, Jessy was calculating her age. Two weeks short of her birthday: 365 — 14 = 351 days. One week short: 359 days. And ten days? 71/73? That’s what you get when you reduce 355/365 to lowest terms!
Exiting Nirvana e-2 Page 8
