To Robert

26 August 2006
Hey little brother,

When you were born I was 12, and for your first 5 years you had four and then three parents, rather than two. Well, at least at the time I thought I was being helpful like a parent.

When you were less than one, you had me (enthralled) and in fits with your delightful laugh and already-intricate sense of humour. The depth of this humour seemed to presage the pure delight in clever and beautiful and fun ideas which characterised your various later passions.

When you were two, the wise look and patient, inquisitive (manner) in your eyes made me wonder already what kind of intellectual creature and precocious spirit lay within.

When you were three, you claimed that you never slept. "I don't close my eyes at night" you said. I asked, "Well, how do you spend those 10 hours, then, Bubble?" (as we used to call you). "I just think about things in my head" was your response. At times like this, we would be unsure whether it was true --- it was clear that something special was going on. I crept into your room at night to check.

When I was in grade 9, a couple of your baby noises were so adorable that they invaded my public discourse at school and several of my friends used to make them too.

You continued to be a most riveting youngster, and I remember being so proud to show you off at high school. Many students at Old Scona, which you were later to attend yourself, knew you by age 3.

But when you were 5, I left the country for what would be 12 years living away from my family. My time with you gradually came to consist of briefer visits a couple of times per year, phone calls from afar, and carefully-written and loving emails from you.

When I came home from my first term at MIT, you were five years old and asked me about what I had been learning. I was reading about how semiconductors worked on a quantum mechanical level. "Uhh, well it's all a lot of strange words and hard to explain" I protested. "No, Duck," you said, with a mischevious twinkle in your eye. "I want to hear all that funny stuff". You listened most intently, though without many questions, as I tried to explain probability wave functions and the solid state. I wondered what you were doing with this information and was never quite sure how much you might be grasping about a fundamentally different and non-intuitive way in which the universe works at the small scale.

Another time though, and only a couple of years later, after we had been talking about mathematical limits while backpacking with Stephen and Iris, you wanted to know more and I thought you'd be intrigued by some differential calculus. This time you often led the conversation with astute questions, and I remember the humbling and shocking feeling that you immediately understood what I was teaching better than I did.

Luckily, you shared some of my poor memory and could in time forget such relatively boring subjects like basic calculus in favour of the more intriguing topics you pursued with Andy Liu.

Later, I would be amazed how you could remember all those mathematical tricks and theorems for contests and for school. Math at your level seemed to involve vast knowledge, in addition to most profound conceptual understanding. Yet you seemed to excel without spending all your time on it, in fact without appearing to be entirely focused on it. You spent a lot of time building hilariously ingenious lego constructions, and later on doing abstract programming projects and creating languages (for both people and computers) with Alex Fink and others.

Though I was then a graduate student, before you reached high school I couldn't follow what you were doing any more, and soon while I could explain to you the straightforward physics in my PhD work, the things you were thinking about sounded to me like so much "funny stuff". Of course you were always willing to explain a simple version of your work to me. You always patiently and non-judgementally backed up several steps when finding that I had forgotten some prerequisite math that I should remember from university.

In 2003 when I was back in graduate school and home for Christmas you helped me understand a piece of matrix calculus with a beautiful spontaneous derivation and simple notation. I still regularly refer back to that page in my notebook. I occasionally sent you difficult problems from my game theory courses too, and received delightful responses. Your solution to one subtle logic problem about a monastery of monks who all perish at once finished with the comment "Poor monks!".

I know that a big part of you, and a very beautiful and happy part, was only accessible to those who could speak math properly. I got only a glimpse of that most spirited part of Robert, though it was always reflected in your nimble sense of humour and careful manner in all things.

But I got to enjoy other aspects of your interests and talents and love of life.

When you were young Rosalind and I wanted to make sure that you and Stephen got out backpacking at least once per year. In the summer after you had turned 12, we took you on a grand adventure to Glacier National Park in Montana. We started on an ambitious 6 day route which included technical snow and rock climbing. Many years later we told you how terrified for your life Rosalind and I were as we traversed goat trails on loose angle-of-repose scree above towering cliff faces... or when we were following morning-fresh bear tracks on an overgrown and out of use trail on our escape route, two and a half days away from civilisation, singing at the top of our lungs to announce our presence, or when we lay awake as our tent felt like it was going to blow away in high wind, perched on the edge of a cliff, the night before we retreated. You were unruffled during all this, sometimes lost in abstract Robert thoughts but always happy to be amid such adventure with your big siblings, and of course awed by the scenery. The weather and commitment scared us off the route on the 4th day, but our clever escape route down a valley turned into the worst bushwhack imaginable. It took us 16 hours to go 4 km. You were amazing, and memorably made a joke to break the anxiety of the situation. After finally breaking into tears 10 hours into the ordeal, you exclaimed with a smile, "I thought this was going to be a holiday, not a hell-iday". I wrote in my diary "Robert's spirit is nearly unbelievably robust for a 12 year old."

In recent times we had other great trips outdoors. We skied together in the winter, you visited me in California, climbed a granite crack beautifully in Yosemite Valley, scrambled a high peak in Tuolumne meadows.

Last summer you and I spent a whole week together -- just two brothers, scrambling up challenging peaks back in the mountains near where we grew up.

You, my young brother, had become a man. Your body had become muscular. When you were younger, while backpacking you would sometimes not even notice the scenery passing by, but would stay happy if you were kept occupied with mental math -- do you remember talking about different numbers of boys and jumpers as you learned to count permutations on our first multi-night backcountry trip together? Now, as an adult, you loved the physical challenge, the intellectual exercise of routefinding, and the self-assessment needed to make choices. You actively noticed your environment and took a lovely series of photos of alpine flowers during our week together.

To my mild surprise, you pushed me onward and upward when my ambition ebbed as much as I pushed you. We were a great team. You had a great sense of adventure to match your still-wonderful subtle and sparkly-eyed sense of humour.

And yet, after a week, your mind began wandering back to math (okay, and maybe you were a bit exhausted) and we happily made for home.

I loved to watch you cross country ski, to follow your graceful and powerful strides on skate skis. We played together on the trails in Edmonton and Canmore and in Manning Park.

In the last two years, I taught you to telemark ski, and you and I had a wonderful time on a day tour in B.C. this past winter.

You were distinctive within our family in several ways. You were particular with your clothing -- maybe because you had to dress up in suits to receive honours starting at such a young age, and you used to like your food arranged carefully. You carried the innate gentleness of your mother and were a model of centredness and perspective for me. In the face of success and yours and the world's great expectations, you were always unruffled and modest.

Like others in your family, you have had a nagging activist wish to do good in the world, even when you have the focused and privileged gift of a true mathematician.

You have always found extended time for your family, more so than your older siblings. I would always check with you that it was really your choice to return home for long periods at each break from school, rather than staying on with your new life in Toronto, and it always was. You treasured your family.

I, no longer anything like a parent to you, always thought that I could still offer the special support of an older sibling. I wanted to offer some of my wisdom from being a young adult, from early relationships, from living in the U.S at big schools, from some of my outdoor and athletic experience. You always accepted what I offered, and clearly were eager to emulate or share some things, but often I was unsure how meaningful or relevant the stories and lessons from my life were, and I was timid to imagine that I might know something useful to such a serene and balanced young man, whom I only saw occasionally and who had early on travelled the world extensively for international math events and forged a broad circle of friends of varying ages.

In retrospect, we each seemed to look up to the other more than we knew. I now might wish I had been bold enough to probe a little more, to withhold a little bit less of my advice.

I haven't any organised thoughts yet, and so far I can only share this small selection of a jumble of memories. I do not know why you left; I do not yet understand how you were stolen from us. I cannot yet see what life will be like without you. I hesitated to say anything today, because nothing yet makes sense. This is still too early for me.

Robert, I have to reassess everything in my life now. I don't know where that will take me. But Robert, know that I will run for you. I will climb for you. I will ski for you. I will cherish and nurture my family for you, and as you did. I will continue to act on concern for our planet and for peace and justice. But I cannot do math for you, and the world will never know which of the secrets in the Universe's little book of theorems you would have revealed to us.

Robert, you will be with me always, as little brother, as mentor, as friend, and as a great and gentle spirit whose diversity and depth we can still endeavor to know only by gathering together and sharing what you have given each of us.