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An Asperger Syndrome childhood: timid body, conceited mind

An Asperger Syndrome childhood: timid body, conceited mind

– an essay about my own childhood

As a baby

I cannot have been an easy baby. I cried a lot, and I could not be comforted by any of the usual means. My mother learned in my first days and weeks not to try to comfort me by lifting my body into her arms: it would stiffen, and my crying would become more intense. Equally I could be lying in my cot quite content, and if anyone lifted my body I would immediately show signs of distress. It seems I hated such body contact from the moment I left my mother’s womb.

Does the phrase “lifting my body” sound odd to you? It sounds odd to me. It would have been more usual to say “lifting me”. At once we meet a recurring feature of Asperger Syndrome. Many individuals with Asperger Syndrome perceive their body in a non‐standard way. To put it bluntly, my body is not securely part of me. It is part of my environment. I perceive my hands as part of me, and my eyes, and my lips and my tongue and the rest of my vocal apparatus: but the rest of my body less strongly so, and in moments of stress not at all. This limits the confidence that I can have in my body, the control that I feel over it. In technical terms, I have a faulty body schema, which is frequently found in Asperger Syndrome and in autism spectrum conditions in general. But I think of it rather as a broken homunculus. The dotted red line in Figure 1 between the words Hand and Wrist very cleanly separates the “securely me” from the “not securely me”.

Figure 1: My broken sensory homunculus

It is difficult to explain this in a way that is convincing to a neurotypical person. Do I not talk about “my” feet? Yes, but I also talk about “my house”, and the house is not part of me. Do I not say, “I fell out of bed”? Yes, but that is a conventional form of words by which I communicate with others. I say “I fell out of bed” meaning “my body fell out of bed” (and it does!) just as a blind person may say “I’ll see you tomorrow” meaning “I’ll encounter you tomorrow.” When my knee is injured, do I not feel pain? Of course I feel pain, and it is very unpleasant, and I perceive that the pain comes from my knee. Likewise when my washing machine explodes, I hear the bang, and it too is very unpleasant, and I perceive that the bang comes from my washing machine. But that does not lead me to regard my washing machine as part of me. In this essay I try to say what I mean, and that entails not saying “me” when I mean “my body”.

A mother’s intuition will usually lead her to whatever is best for her baby. It didn’t take my mother long to learn how to comfort me: put something in my hands. That will do nicely, thank you, Mummy. Now I feel in control. My hands are part of me.

At 7 months I found my feet. No, I don’t mean I began to walk: that took me nearly a further year. I mean I found my feet. Until then, as Mum told me years later, by her reckoning I didn’t know I had any. To this day they seem awfully far away from me.

I spoke early, and I quickly began to use language for reasoning. Mum once told me that I could reason and be reasoned with before I could walk. Sadly, I have no examples. But it does not surprise me, because it fits with what I am.

For if I am not my body, then what am I? The concept of self is complex, and many philosophers and many psychologists have written many books about it. But my perception is that, primarily, I am my introspective conscious mind: the agent of my mental life as I have direct, unmediated awareness of it. Although my mind has a connection with my body, it inhabits not the physical realm, but the so‐called Platonic realm. The Platonic realm is where the templates are kept for the objects in the physical realm. In the Platonic realm are many mansions. The gatehouse protects the natural numbers: 0, 1, 2, 3, 4, 5… Up the road is another mansion that houses the template for all conceivable pieces of music. Yet a third mansion is home to the genomes of all species of organism, along with the Grand Meta‐genome that maps out in addition the genomes of the myriad hypothetical species that never evolved. In a fourth mansion live the Laws of Chess, or their logical equivalent, the tree of all legal games of chess. These are of course metaphors, but for me they are compelling metaphors. If the physical realm is God’s handiwork, then the Platonic realm is his design studio.

I am told I walked my first few steps in front of Aunt Babbie on holiday in Shetland. That must have been in late July or early August 1950, which means I was about 16 months old. That is quite late, but within the range regarded as normal. I walked on tiptoe. This was blamed on short Achilles tendons in both heels, for which I was given physiotherapy. I have the same slight deformity in the homologous tendon in my right thumb, which is a major nuisance for my piano playing: my left thumb is normal. Toe walking is common in children with Asperger Syndrome, and I wonder if short Achilles tendons are typically a contributing cause.

A child with Asperger Syndrome is odd. In this essay I seek to be accurate in what I say, but the essay is not meant to give a balanced view of my childhood, because it focuses on the oddities.

A new‐year party

I seem to have a vague memory of the birth of my brother Donald, when I was 2 years 8 months. That may however be a false memory, as my next surviving memory is more than a year later. This one is very clear. It was at the annual new‐year party in my grandparents’ home. It must have been 1 January 1953 when I was 3 years 9 months, because Donald was moving on hands and knees. Now unlike Mum, Dad had not easily learned that my body should be handled as little as possible. Like any father, he wanted to encourage physical play in his young son. I’m sure he was gentle by normal standards, but I’m also sure that he wasn’t nearly careful enough for the child in question. Most children with Asperger Syndrome have somatosensory abnormalities, and while the response to these abnormalities varies enormously from child to child, the tactile defensiveness that I showed from earliest infancy is a frequent response. I never liked Dad’s physical play and it made me very anxious. On this occasion, Dad wanted the assembled relatives to see what a fine sturdy son he had. Ha! I was unwilling but Dad prevailed. He stood facing me, holding my hands, and instructing me to lean back and walk up his legs. I never liked having my feet off the ground, and I was afraid I would get hurt. My feet had reached his knees when I panicked and my body did not do what Dad expected, with the result that he accidentally dropped it, bringing to pass the very thing I feared. This may have been from a position only a short distance above the floor, but my head banged on the floor and I made a terrible fuss. Gran rubbed butter on the bruise, an old wives’ remedy. I was still upset, but I found it comforting to be the centre of attention. I thought, “The butter is outside the skin and the bruise is under the skin and the skin is watertight: so what good can this do?” It seems I had a scientific and sceptical mindset at the age of three.

How to count

Some time around my fourth birthday we had a visit from a friend and colleague of Dad who was an educational psychologist. This friend was fascinated by my cognitive development and used to test it often, which I loved. Years later I learned that Dad was unhappy about such testing, as he was not sure that it was healthy. On this occasion the friend spread 15 counters on the table in front of me and asked me to count them. I thought, “I’ll show him: I’ll do it the fancy way.” I gathered the counters in pairs using the index and middle fingers of my right hand, reciting, “2, 4, 6, 8, 10, 12, 14, and 1 is 15.” Dad’s friend was astonished. Cousin Gillian, four years my senior, had taught me to count in pairs like that.

I remember clearly the birth of my sister Fiona when I was 4 years 1 month, and from that time onwards my memories come thick and fast.

How to get dressed

I was very slow in learning to dress myself. Long after I knew what to do and was physically capable of doing it, still I simply would not do it. I would stand there helplessly doing nothing, waiting for Mum’s help, unable to take the initiative. Until now I have always thought that executive dysfunction only became a real problem to me as an adult, but as I write this essay I suddenly recognise the dressing difficulty as executive dysfunction pure and simple. Indeed it is characteristic of my executive dysfunction that it should have first surfaced in this context, for throughout my life it has always been worst early in the day. Mum eventually solved this one by teaching me the procedure for getting dressed as a sequence of verbal prompts, which I was then able to recite and follow on my own, as I have a good auditory memory. Over 70 years later, as I get dressed each morning I still hear the prompts in my head.

Studies have shown that 80% of individuals on the autism spectrum have some executive dysfunction.

A world of numbers

Like every child with Asperger Syndrome, I spent most of my time in my own little world, stargazing as Dad called it. My particular “own little world” was a world of numbers, and I used to pester Dad to teach me all he could about them. Shortly before my fif‌th birthday I was taking a walk with him. My feet may have been alongside his, but my mind, as always, was a hundred miles away. He asked me what I was doing and I answered that I was “just thinking”. Some further minutes of silence passed before I asked, “Daddy, is one‐and‐a‐half, times one‐and‐a‐half, two‐and‐a‐quarter?” After a few seconds of paternal mental arithmetic, he confirmed my conjecture. I can still hear the shocked in­comprehension in his voice.

I vividly remember that particular voyage of discovery. I had an accurate concept of halves and quarters. I knew that to multiply a quantity by 1½ was to add to it half of itself: after all, 1½ cakes is a cake plus half a cake. I had mentally constructed a few cases with whole‐number multiplicands; for example 1½ × 5 is 5 + 2½ which is 7½. I wondered if I could find a sensible meaning for 1½ × 1½ in the same kind of way, and I came up with this mental model:

One‐and‐a‐half  = 1 + ½
Half of itself = ½ + ¼

Collecting the bits gave 2¼. I was entirely confident of the mechanics of what I had done, and what I was asking Dad to confirm was its legitimacy. I was of course pleased to have got the right answer, but the greater part of my delight lay in the reassurance that fractions behave in the way I thought they ought to. My major insight that day was that mathematical truth could be discovered by just thinking: it didn’t need to be taught, or learned from the world. That 1½ × 1½ = 2¼ not only was: it had to be. In language that was of course not available to me at that age, mathematical truths are necessary, not contingent. I also gained a feeling of power, as it dawned on me that I had discovered a source of knowledge that was independent of my parents. I lay awake half the night revelling in my discovery.

Primary school

I started at Broughton Primary School in Edinburgh close to my fif‌th birthday. I vividly remember my first day because it was anxiety‐ridden. Mum and I were in the school secretary’s office for me to be enrolled. The secretary said in a cheery voice, “I’ll go and get the slip,” referring to some piece of routine paperwork. But I didn’t know what she was referring to, and I was afraid she meant “I’ll go and get the strap.” The strap, or the belt, was an instrument of corporal punishment, and I had been well warned by my parents that I had to behave at school or the strap might be the consequence. I had no idea what I might have done to deserve this on my first day, but I sometimes got into trouble for things I didn’t understand, and I was quite prepared to believe that I must have done something wrong. I can still hear the secretary’s cheery tone of voice, but to infer from her cheery tone that she couldn’t possibly be talking about corporal punishment was beyond my social skills. I never told my parents about this mis­understanding. As a child I was racked with anxiety, as are many children (and adults) with Asperger Syndrome, and this incident shows how easily it can happen.

Primary school teaching in Scotland in the 1950s was very formal. The class size was supposed to be limited to 40, but in practice it was sometimes over 40. We were arranged in rows, one to a desk, the desks being pushed together into pairs, and the teacher taught us from the blackboard at the front. There was no group work, and talking or other interaction between pupils was forbidden. Actually I felt very comfortable with that. Academically I was always the most able in the class. We were seated in academic order, which meant that I was always in the back left‐hand corner of the classroom, sitting next to the window at a single, unpaired, desk. And that ensured that my social skills, which began at rock bottom, remained at rock bottom.

I disliked the 15‑minute morning interval (“playtime”). We were set loose in the tarmac playground with no supervision. Because I hated and feared body contact, I kept as far away from the other children as I could. Throughout 6½ years of primary school, my playtimes were spent at the edge of the playground, standing with my back to the perimeter railings and holding on to them for stability, watching the other children play, and raising my right foot as a barrier if any child got too close to me. Throughout my primary schooling I made one friend.

Why did I not interact with my peers at a social level? In hindsight I can see many factors, all of them commonly found in children with Asperger Syndrome. First, I had no interest in other children as people. Secondly, I had narrow and specialised interests, and the chance of finding another child with compatible interests was small. Thirdly, playground games with other children were out of the question as I was physically slow and awkward and afraid of body contact. Fourthly, I am largely face‐blind. Fif‌thly (though this may have been a minor factor) I have a slight speech perception difficulty: I rarely had any difficulty in understanding adults, but children tended to speak less formally, and less distinctly, and more than one of them at the same time, and in vernacular dialects and accents and colloquial expressions that differed significantly from the Scottish Standard English that I learned from my parents, and often I couldn’t catch what they were saying. Sixthly, on the few occasions when I did try to interact, my efforts were socially clumsy and were often rejected, sometimes with scorn or ridicule, which deterred me from trying further. All these factors contributed to a very marked social anxiety when I was among other children in an informal setting. But at the time I had no insight into any of this. Indeed I had no concept of social anxiety until I was given psychotherapy in my early 20s. As a child, the only reason I could articulate – to myself or to anyone else – for not interacting with other children was that I didn’t want to. I very, very strongly didn’t want to.

My mother tried to help. She used to invite local children to our house for me to play with. But she made the comic mistake of inviting them in twos. Consequently they played with each other while I sat in the corner with a book. I had no idea that I was supposed to interact with them, that that is why they had been invited. I just thought that Mum liked having children around the place. Again this is typical of the upbringing of children with Asperger Syndrome: the caring adults assume that the child knows what is expected of him, while the child hasn’t a clue. I wish my mother had explained, “Eric, I’ve invited James to come here after school today, and I want you to play with him please: playing with other children is good for you.” I wouldn’t have found it comfortable, but I was an obedient child and I believe I would have tried. Many a time Mum pointed out to me that other children played with each other and I didn’t, but I never understood that there was anything wrong with that; rather I took it in the context of Mum’s constant reassurances that everybody is different. And I knew I was different.

At the age of six I was moved up to the next class, six months older, on academic grounds. I was already among the youngest in my class, and so this meant that I became the youngest in my class by a margin of nearly six months. And of course everyone in the new class already had settled friendships. I welcomed the move, but it probably made my social isolation even worse.

I believe I was intensely unpopular with most of the other children. Not only did I make no effort to socialise, but also I was overly proud of my academic ability and tended to show it off, and unfortunately this was always well received by the teacher. I was inclined to clype – to report misbehaviour to the teacher. There was no element of malice in this: rather, it seemed to me that it was the right thing to do. I continued to clype until the teacher herself, to my surprise, told me not to. Throughout primary school I was subjected to very mild bullying – a little deliberate push here and there – but as I hated any body contact, bullying of that sort, however mild, really frightened me. I had absolutely no insight that the bullying had anything to do with my own behaviour. I was more seriously bullied on just four occasions that I can remember, and never by children that I knew.


I was completely useless at physical education, or “drill” as it was known at primary school. My balance and spatial awareness were totally lacking. I couldn’t let the teacher touch me in her efforts to help. It was a major achievement when I learned to do a forward roll, very badly, starting with my head resting on the mat and finishing in a sitting position. During the forward roll I would have no idea of where the world was, and as I emerged from the roll I would find myself in a sitting position with no bodily sense of how that had come to be. It was the weirdest feeling, and quite unpleasant.


This essay says very little about my musical development. Although it was a major feature of my childhood, it was all so smooth and trouble‐free that there is little of interest to be said about it in an essay of this kind that focuses on oddities. I showed an aptitude for music from a very young age: one Sunday afternoon at the age of three I announced, “We learned a new hymn at Sunday school today and it went like this,” and picked out the melody on the piano with one finger. I am very grateful to my parents for arranging piano lessons for me from the age of six. My teacher Stuart Thyne – scholarly, old‐fashioned and thorough – was the best possible teacher for me. As well as piano, he taught me musical theory, developed my ear, and encouraged composition. A bachelor of independent means, he lived with a housekeeper in his luxurious basement flat in the Georgian Edinburgh New Town. He had a physical disability, walking very slowly, very bent, and I think painfully, with a stick. He was aged 38 when I started taking lessons, but I thought he was an old man because of his disability and his beard. I practised long and hard every day, at first from a sense of duty, though I did not dislike it, and later from a real love of it. Each summer I competed in the Edinburgh Competition Festival (no connection with the famous Edinburgh Festival) with great enjoyment, excitement and ambition, and with no anxiety whatsoever, and I had a lot of success. With the benefit of hindsight, I can see that I ought to have made a career in either music or mathematics. Those with Asperger Syndrome often have abilities in these fields.

In the summer of 1959 when I was 10 our family had a very happy holiday in Cheshire with Ken and Barbara Hulme and family, our closest family friends. On our return to Edinburgh, Mum took me aside for a serious discussion. It was most unlikely to happen, she reassured me – but if, for any reason, Dad and she both became unable to look after me, whom would I like to look after me? Dad and she had come to a reciprocal arrangement with Ken and Barbara, and Mum was entirely confident that I would answer her question as she expected. She knew I could deal with hypotheticals like that without anxiety, and she judged correctly that I had to be kept informed. I floored her by saying Mr Thyne. I felt he understood me better than anyone else did, perhaps even my parents, and I had developed a strong bond.

A very ashamed child

One day when I was about 8 our school teacher was absent and we had a supply teacher. At the start of the day he told me he had a job for me. I take it he had been alerted to my academic ability and thought I would be the best person to help him. But I felt horribly ashamed when he showed me the task. He had prepared a sheet of paper with the 42 desks shown on it and he asked me to fill in the names of the pupils for him. Although I had shared a classroom with these classmates for six hours a day, 200 days a year for about two years, I could name only a handful of them. It was the most embarrassing thing I had ever experienced. Quite apart from having no interest in the other children, I am largely face‐blind as I have already said, and both of these factors are very common in Asperger Syndrome. I don’t know whether we have little interest in people because we can’t recognise them easily, or whether our face recognition skills don’t develop because we have little interest in people: but certainly the two deficits reinforce each other.

I don’t think my parents ever realised the difficulty I have with faces. Indeed I remember one occasion when I told Mum I didn’t expect to be able to recognise Ken Hulme and she told me not to be so silly. Whenever I was embarrassed at not recognising a face, my strategy was to remain silent, which my parents took as shyness and not ignorance.

An easy task, or an impossible one?

I was about 8. My school was on the corner of a block, and I lived 400 metres away close to the farthest corner of the same block. I walked to and from school. My parents had authorised two routes to and from school: the “front way”, via two sides of the block and the front gate of the school, and the “back way”, via the two other sides of the block and the back gate of the school. At the end of school one afternoon I came out of the back gate and was told, by a neighbour whom Mum had stationed there for the purpose, that I was to meet Mum urgently at the front gate. Now this took me right out of my comfort zone. People with Asperger Syndrome are creatures of habit, and in my three years at school this was the first time I had ever come out of school at the end of the school day and not gone straight home as I had been taught. My reasoning told me there ought to be a route round the corner to the front gate (170 metres), but I had no confidence in such a route, having never explored that bit of road, nor been shown it. It would not be an exaggeration to say I was frightened of it. Instead, greatly anxious lest I might be doing the wrong thing, I tried to hurry round the block (700 metres). And this was with a younger brother in tow, whose own idiosyncrasy lengthened our journey by a further 250 metres, and who would not be hurried. It took us 25 minutes.

My mental map of home and school Home Front way Primaryschoolandgrounds Back way Secondary   school HEREBEDRAGONS! 50 m
Figure 2: My mental map of home and school

If that seems bizarre, look at it from my perspective as a child. Short of going round the block, the only route I knew from the back gate to the front gate was through the school grounds, but school rules forbade me from going back into the school grounds after coming out at the end of the school day. This left me feeling stranded and vulnerable. Being largely face‐blind I didn’t recognise the neighbour, and so I hadn’t the confidence to ask her for help. I was responsible for my brother. The route round the corner, supposing it existed, passed the secondary school, and there might be big boys there, and I was a natural target for bullies, and I couldn’t predict how the big boys might react if we crossed “their” patch. Besides, I wasn’t allowed to use routes that I hadn’t been shown. Indeed Dad had explained to me that I must avoid unauthorised routes precisely because I couldn’t know if they were safe. I can think of three previous occasions when Mum or Dad had reprimanded me for using an unauthorised route. On one such occasion all I had done was cross to the other side of a quiet street to avoid a known bully (but I never told them that). My route home from my piano lesson each week, on my father’s instructions, was not the obvious 2 km bus journey, but a 7 km bus journey in the opposite direction round the same circular route, including a wait at the terminus, to avoid crossing a road at each end.

I felt very hurt when Mum chided me for lack of common sense. I had done as I had been taught. I do not blame my parents: I was largely street dumb, and it may be that their rules were necessary for my own safety. But I do think that, in imposing those rules, my parents unwittingly tended to stifle what little geographical initiative I might have had.

My visit to a swimming pool

When I was 9, Dad decided that I should learn to swim. I looked forward to our first visit to the local baths: indeed I felt quite excited about it. But when I saw the pool, I was dismayed. Children with Asperger Syndrome need careful preparation for anything new, and I was quite unprepared because my preconceptions were all wrong. I thought the scene would be grey with subdued lighting: instead the lighting was very bright and accentuated the blue colour of the water. I thought the pool would be contained in a room about the size of a large room in a house, and that it might measure perhaps 5 metres by 4 metres: instead it covered more than 10 times that area. I thought the swimmers would be swimming gently in an orderly manner in lanes: instead they seemed chaotic and some swam energetically. I thought the swimmers would be mostly adults: instead they were mostly children, and – horror – children were splashing! I thought it would be silent: instead it was noisy, children were shouting, and the acoustic was very echoey. And the water? Dad had assured me that the pool was heated. It was, of course, but from what he said I expected to experience it as warm, and instead I found it very cold indeed. I ventured one foot up to the ankle and would go no farther. Dad encouraged, cajoled, ridiculed and finally ordered me in. I think “ordered” is fair comment: his exact words were, “Look Eric, I’ve paid your admission money and I’m not going to stand here and see it wasted.” I found the water excruciatingly cold (and I think I know why: see my article on the thermal grill illusion). It took me about 10 minutes of all the bravery I could muster to get in up to my chest. I stood, very stressed, in the shallow end of the pool in water 3 feet 6 inches deep (just over 1 metre). Dad held my hands and instructed me to kick my legs to bring my body horizontal. He waited for my feet to touch the floor of the pool again, and he let go. But he had misjudged: my feet had not yet reached the floor, and I slipped under the water.

That was one of the two worst moments of my life. (I do not disclose the other one on this website, but it too was in my childhood, and it too was profoundly bodily.) Like most children with Asperger Syndrome I had often suffered the distress of sensory overload, but this was a far greater sensory overload than anything in my experience before or since. All my sensory alarm bells rang simultaneously. My mouth and nose filled with water, and I think I inhaled a little. The water on my face felt diabolical in its touch, its pressure and its coldness, and my eyes smarted. My vestibular system was mightily confused, I felt nauseous, and I had no idea which way was up. My visual field flooded with an alien vast: my perception was that I was looking at the biggest thing I had ever seen, and it was blue, but beyond that my visual field conveyed no information and my eyes would not focus. The sound was dead silent and yet paradoxically at the same time deafening to the point of pain. The smell and the taste of the chlorinated water were choking. I was in extreme fear, and I was totally paralysed: I tried to work my arms and legs but nothing happened. The only muscles I could move were my eye muscles, for all the good that did me. Time slowed right down, and subjectively the experience seemed to last for ten seconds or more. I was quite sure I was dying. It is not that I believed that brief total immersion in water is necessarily fatal: rather, I just could not conceive that there could possibly be any way back from such a hellish plurality of qualia.

I was probably under the water for less than three seconds before Dad fished me out. I was crying uncontrollably. That was the end of the swimming lesson. Throughout the bus journey home I was still in tears, and Dad asked me to compose myself because, as he explained, he didn’t want Mum to see me in that state. I dutifully composed myself, and I stayed composed, with difficulty, until we reached home. And the moment I saw Mum, I burst into tears again.

My father was a good and caring man, but throughout my childhood he really did not understand what kind of a child he was dealing with, and this episode illustrates it well. He must have realised before the accident how terrified I already was, even if he couldn’t understand why, and I cannot fathom why he did not ask me to confirm that my feet were on the floor before he let go. It does seem to me that whenever he couldn’t understand my fear, he thought he could safely discount it. In his defence I should add that nothing was known at the time about Asperger Syndrome – I was diagnosed as an adult – and Mum and Dad were bringing up a very odd child without the benefit of any relevant professional guidance.

It is now known that drowning is the leading cause of death among children on the autism spectrum. A news article in 2017 by Columbia University Mailman School of Public Health, Individuals with Autism at Substantially Heightened Risk for Injury Death, citing a study led by Guohua Li, Professor of Epidemiology at that School, reports that childen on the autism spectrum are 160 times as likely to die from drowning as other children. Research into this has mostly focused on the tendency of such children to wander, and on their failure to understand danger. But it seems to me that the atypical and inept response of the body to finding itself under water that I experienced is likely to be a major factor in at least some cases.

Dad never again suggested that we go swimming.

Back to school

A large proportion of our time in primary school was devoted to the “three Rs”: reading, writing and arithmetic. Especially arithmetic. It was necessary to spend a lot of time on arithmetic in UK schools in those days because of our cumbersome and antiquated £sd money system, with 12 pence or pennies to the shilling, and 20 shillings to the pound. By Primary 6 (around age 10) we would have to do several instances of addition of money each day, like this:

£ s d
 1 11  8
13 19 11½
 8  6  3½
21  0  5¾

Our teacher would write them on the blackboard, and we would copy them into our jotters, add them up, and raise our hand when we had the answer. Well, this was so easy for me. I simply kept a running total in my head as I copied the figures into my jotter, and proudly raised my hand as soon as the teacher had written the last figure. It hardly added to my popularity among my peers.

Broughton School had a swimming pool, and in the summer term of Primary 6 there was a compulsory swimming period once a week. Mum did an excellent job of preparing me emotionally for this in view of my previous experience, so that my attitude to the pool was merely a strong dislike and not a phobia. It was not as cold as the public baths, and I found the temperature bearable. Our swimming teacher respected my deep unease in the water and mercifully allowed me to participate on a casual basis, becoming more accustomed to the water with each passing week but making no effort to learn to swim.

Some of the boys in the class would take as long as possible to change after the swimming period, in order to miss as much classroom time as possible. This annoyed our class teacher, and after other means had failed she threatened before one swimming period that the last boy back in the classroom would get the belt. Unfortunately she forgot to add, “That is, if he gets back unreasonably late.” At the end of the swimming period I realised too late that I had been ambushed: all the other boys changed at breakneck speed so that I would be back last. They even pointed out to the class teacher that I was back last. Of course she saw what they were up to and declined to punish me, thus adding to their perception that I was “teacher’s pet”.

One day in Primary 6 we had a visit from a school inspector. He taught us an arithmetic lesson about factorials. (5 factorial – written 5! – means 5 × 4 × 3 × 2 × 1 = 120.) After checking that we had grasped the concept, he wrote on the blackboard the expression 7! ÷ 5! and asked us the answer. It’s not too hard. The expression means:

(7 × 6 × 5 × 4 × 3 × 2 × 1)
divided by
(5 × 4 × 3 × 2 × 1)

and all the factors from 5 downwards cancel, leaving 7 × 6 or 42. My hand went up immediately. He waited for other answers, which didn’t come, and then he asked me. “Forty‐two,” I said. “Good,” said he, “can you explain to the class how you did it?” “Yes,” said I, “it’s 5040 divided by 120, or you can just cancel.” This was pure showing off. I had computed the answer as 7 × 6, but I knew beforehand that 7! = 5040 and 5! = 120.

Sports day 1959

I remember our 1959 school sports day when I was 10. With my physical awkwardness, common in Asperger Syndrome, the only sport I could manage was the flat race, a sprint over about 60 metres. Being of a strongly competitive nature, I always competed in the sprints with great determination, and I really gave every ounce of what I had. Still I always came last by a margin of at least 10 metres. But that is not what I remember the day for. Sports day, for me, meant standing around for a long time with nothing to do but think. And on that day I discovered that (a + b) × (a − b) = a2 − b2.

Secondary school

I found the transition to Portobello Secondary School at the age of 11 quite easy. This was a comprehensive school in the basic sense that it accepted all children from the neighbourhood without regard to academic aptitude. I immediately preferred it to primary school because (unlike later comprehensive schools) the classes were streamed from the start of first year and so I was in a class with other academically able children.

I continued to show off, and on one occasion it backfired badly. In our first‐year Latin class we were learning the verb timeo, which was used as a model for the second conjugation of verbs. Our teacher John Christie explained to us that timeo means “I fear”, and it can also be translated “I am frightened”. I asked him, in class, whether a better translation for “I am frightened” might be terreor. I had been reading ahead in the textbook: terreor is the passive form of the verb terreo, “I frighten”. Well, John Christie did not like that. In a very loud and angry voice he told me to know my place, not to show off, and not to waste class time by asking questions unrelated to what we were learning. And no, he added angrily, the Romans wouldn’t say terreor: they would say timeo.

John knew my father, and later apologised to him for his heavy‐handedness. But I think the way he dealt with me was reasonable. I was showing off, and I was doing it deliberately. I knew it was wrong, but I was doing it anyway. It was the first time my showing off had met with any reaction from a teacher other than approval, and it was an important lesson for me.

A glimpse of the mathematical landscape

Again when I was 11, our mathematics teacher Richard Brown was teaching us about square roots. He asked us what is the square root of this, and what is the square root of that, and took answers round the class. Then he mischievously asked us, “What is the square root of minus sixteen?” My hand went up immediately, but he took answers from other pupils first, all of them wrong answers like minus four and minus eight. “Yes, Eric?” I replied that there is no number whose square is minus sixteen. “That’s right, Eric. There is no real number whose square is minus sixteen.” I stayed behind after the lesson to ask him why he had said there is no real number whose square is minus sixteen: is there some other kind of number? Richard was delighted: I had swallowed the bait. There and then he introduced me to complex numbers. They were the most beautiful thing I had ever seen. They were a glimpse of the divine mathematical landscape that lay ahead of me.

How to learn rugby

It was around this time that I developed another interest: rugby. I got this interest from my father, who had been a good player in his day – he was selected to play one representative game for East of Scotland District – and who was by now an amateur referee. I don’t mean that I actually played rugby, of course: that would have been far too rough. Training would have been far too rough also. I rarely went to see matches. I never watched matches on TV. I didn’t take much interest in local or national or international results. I took no interest whatsoever in any of the players.

But I learned the rules, and I learned them thoroughly. Dad and I argued interminably over what they all meant. For all that he had been a player and a referee and an English teacher, he could be surprisingly illogical in his reading of the Laws. He was sure that “the kick shall be taken at or behind the mark, on a line through the mark parallel to the touch lines” meant that the ball, once kicked, had to pass through the mark. He told me a joke about a school teacher in China who sent to the UK for a copy of the Laws of Rugby, and wrote again the following month to say, “We’ve all learned these: now please send us tennis.” I reckon he made it up for my benefit.

How to learn cricket

Children with Asperger Syndrome can find it very stressful to go to a new place on their own. This combines the stressors of doing something new, being somewhere unfamiliar, having no responsible adult to mediate between oneself and the world, and having to think on one’s feet about practical matters. I found it so stressful that, up to age 16, I believe I never successfully went anywhere new on my own. And I do remember one spectacular failure. I was 12, and for the first time I was due to play cricket in one of the school teams. This was not imposed on me: cricket was optional, and I had chosen to play. Cricket is a non‐contact sport and so I was not afraid of playing. The match was a home match on a Saturday morning. I had presumed that Dad would take me, but to my horror he declined, saying that it would be “a good learning experience” (these words haunt me to this day) for me to go on my own. He gave me careful instructions on how to find the school playing fields at Cavalry Park: what bus to get, where to get off the bus, and even how to navigate the few metres from the bus stop to the playing fields. But he didn’t check that I felt confident about doing what I had to do when I got there. I entered the very large playing fields (35 acres or 14 ha) through the perimeter gate, but I couldn’t see the pavilion and I didn’t know where it was. I stood just inside the gate waiting for adult help, which never came. I knew I ought to look for the pavilion, and I knew that my team would be gathering in one of the changing rooms in the pavilion. But when I am seriously stressed I freeze, and I was so anxious about being in a new place on my own and not knowing where to go that I was quite unable to move from where I was standing. What if I was in the wrong place? What if I was using the wrong gate? What if I got a row from someone? What if I met a bully? What if I got in the way of one of the games? My greatest anxiety was that I didn’t see how I could possibly find my team even if I found the pavilion: I had never met up with this team before, I didn’t know its composition, the 11 players were drawn from the 120 or so boys in my year of whom I knew very few, and I am largely face‐blind. The only strategy I knew for meeting someone by arrangement was to go to the arranged place at the arranged time and rely on them recognising me. I also knew that even if I did find my team and didn’t lose them again, I was going to feel very uncomfortable in their presence as this was my first time. All these anxieties piled up on me at once, so that I couldn’t address my tasks in sequence – first find the pavilion, secondly look for my team, and thirdly try to blend in. It certainly won’t have helped that this was quite early in the morning, because my freezing under stress is an aspect of my executive dysfunction, which as I have already mentioned is always worst early in the day. Other boys arrived and I didn’t recognise any of them. Time passed and I could see that matches were starting, whereupon I ventured as far as the boundary line of the nearest match and watched. Some hours later I could see that all the matches had finished, and so I took the bus home.

Dad asked me if I had made any runs, and I told him I hadn’t batted. He asked me if I had enjoyed fielding and I told him I hadn’t fielded. He said I should have had a chance to field, and something must have gone wrong. But he didn’t explore the matter further with me, and I felt far too ashamed to enlighten him in the absence of direct questioning. The situation never repeated because I was never selected again. As far as the organisers were concerned, I hadn’t turned up.

Of all the events in my childhood that I can remember, that one is perhaps the most extreme indicator of my social isolation. Mum and Dad knew I could be clueless, but I don’t think they ever realised quite how clueless. Nor could they have realised. When I was with Mum or Dad or some other responsible adult, they did the basics of interacting with the social world for me, perhaps from habit or perhaps for convenience, never dreaming that I wasn’t learning to do it for myself. When I wasn’t with them, they never saw.

Sports Day 1961

I well remember our 1961 school sports day when I was 12. That is when I discovered the sum to infinity of a geometric series. I discovered it in the form shown in Figure 3.

Sum to infinity of a geometric series a b + a b2 + a b3 + a b4 + = a b − 1 (for |b| > 1)
Figure 3: Sum to infinity of a geometric series

Friends and foes

I went through secondary school with essentially one friend, a boy whom everybody called “the Professor”. Years later he confirmed to me that he is “far along the autistic spectrum” himself, which is no surprise to me: Hans Asperger himself called children on the spectrum “little professors”. I’ll observe etiquette and not name him here. We were seen as a pair, and we were sometimes mistaken for brothers. On one occasion I was on my own as I passed a group of younger pupils in a school corridor. One of them mockingly called out “Hi, Professor!” and another corrected him, “No, the Professor’s the other one.”

As at primary school I believe I was admired by the staff and widely disliked by other pupils. I was constantly subject to low‐to‐medium‐level bullying: I would be tripped up in corridors or pushed back from where I was trying to go. I lived in fear both of the actual bullying and of the prospect of more serious bullying, though it never happened. I didn’t feel safe in the street, because I saw every teenage boy I passed as a potential threat (and this was in a respectable neighbourhood). Powerless to gain popularity by making friends, at least I tried to limit my unpopularity by not treading on toes, but on one occasion I was careless. I was in fourth year, aged 15, and I had a poem published in the school magazine. Though it didn’t name any individuals, it was derogatory about the behaviour of the boys in my year group in general. A group of five or six of them took exception to it and saw the opportunity to put the frighteners on me. They confronted me in an empty classroom, made a show of closing the door, walked round me with a menacing air and told me what they thought. They made no explicit threats. Looking back on it I think they were reasonable young men making a reasonable point, but they knew how they were doing it and they knew how scared I was. Fortunately they also knew I would complain to the staff at the least provocation, and so they were careful not to do or say anything that would give me grounds. But if they had not meant to scare me then one of them could have spoken to me instead of five or six, they need not have used sinister body language, and they need not have closed the door.

Richard Brown’s death

Richard Brown continued to be my mathematics teacher throughout secondary school. He was the ideal teacher for me and for other pupils with mathematical ability. Throughout secondary school he fed my enthusiasm for mathematics, and in my final year he prepared me well for the University of Edinburgh Bursary Competition. He was in chronic poor health, and in the summer term of 1966, a few weeks before I left school, he died aged 58. I attended his funeral, representing his pupils at the request of the school.

On coming out of the crematorium, I was met by my parents who gave me the news that I had taken first place in the Mathematics section of the Bursary Comp. I find the synchronicity strange and humbling. It was as though Richard was handing on a baton.

The last event of my childhood

It was also in the summer of 1966 that my physical education was made complete, or as complete as it ever would be. This was unplanned. One afternoon I went for a walk on my own to Portobello beach near where we lived. I was 17. Two small boys aged 10 or 11, slim and athletic, were on the flat wet beach playing with a rugby ball. I asked if I might join in, and they made me welcome. (People with Asperger Syndrome often feel more comfortable in the company of those much younger or much older than themselves, rather than within their own age group: the social expectations are less.) We threw passes to each other, kicked the ball to each other and generally ran around. One of the boys threw the ball to me, and I jogged towards the sea with the ball in my hands. That is when he hit me from behind.

The little lad had been well coached and it was a textbook tackle. I knew it was a textbook tackle because I had read the textbook. He must have been sprinting at quite a speed, and I didn’t see him coming. His right shoulder thudded into the back of my left thigh, and his thin arms formed a noose round my hips, a noose which rapidly tightened as it slid down my legs and clamped my ankles together like a vice. My legs made no effort to escape, and my body sprawled forwards with as little dignity as a toppling statue: indeed less dignity, for a toppling statue does not flap its arms. I took a mouthful of wet sand.

And to my astonishment – to my utter, utter astonishment – I was not afraid.

I can identify two reasons. First, I had changed. In my mid‐to‐late teens my physical confidence had been allowed to heal, slowly and naturally, as it was no longer being repeatedly buffeted by adverse incidents. It was nearly three years since I had last been physically punished, which was early in fourth year for being late for school. Physical education classes at school, which systematically drained my physical confidence instead of building it, were not compulsory after third year, and I had opted out. I had rarely been bullied in my final three years at school, as the boys most likely to do the bullying tended to leave school at 15, and those who stayed on began to mature. Unilateral physical “play” from Dad had of course stopped many years before. I had begun to feel more secure in the street. I had not been seriously frightened since the incident with the school magazine more than two years earlier. But surely there was a second reason too. My assailant on this occasion was so very much smaller than me that he had not registered in my mind as a threat, and so I was relaxed.

The absurdity of being felled by such a small child was not lost on me. I burst out laughing, and I turned my head just in time to see an apprehensive little face break into a lovely broad grin. I was overwhelmed with admiration for his courage. At his age I would never have dared to rugby tackle an eight‐year‐old friend for fear of an accidental knee in my face or a deliberate retaliation, never mind a 17‑year‐old stranger. The three of us played happily for a further quarter hour, without any further body contact.

If I had to identify one single event as the last event of my childhood, that would be it. For perhaps two seconds, on the very threshold of full physical maturity, for the first and only time in my life I enjoyed the fun of childhood rough and tumble. And it had taken a lad of less than half my weight to teach me it.

My next step

The next month, I embarked on a four‐year honours degree course in pure mathematics at the University of Edinburgh. The years that had been tainted by physical timidity, by constant anxiety and more fear than was good for me, were well behind me. The years that were to be clouded by depression and executive dysfunction lay far in the future. Supported by the practical and emotional security of the parental home, with a clear mind and at the peak of my intellectual powers, I would be free to explore, full‐time, with expert guides, the Platonic realm of pure forms in which God had set me: the universe of number theory, linear algebra, real and complex analysis, group theory, differential equations, set theory, projective geometry, numerical analysis, linear optimisation, statistical theory, topology, functional analysis, mathematical logic and so much, much more. The happiest four years of my life were about to begin.