Just as my mother saw that you could solve problems in the outer world by working on the spiritual level, so I saw as a teenager that you could solve problems in, say, physics by working on the mathematical level. A few scribbles on a page, a bit of pure thought, and you could predict the precise force needed to apply to a lever to lift a weight—no experiments necessary. In fact, any physical measurement seemed only a messy approximation to the true, beautiful mathematical law. Math was the pure reality, material the crude imitation. Math was mysticism incarnate.
When my mother died, I had turned to mathematics as a haven, a foreign land that I hoped would accept me as an immigrant. I felt at that moment like the sole survivor of a catastrophe that had wiped out not just my mom but my entire culture, as if I were an ancient Indian who was the only remaining speaker of my native language. The language of mathematics had just enough similarities that I could imagine myself making a home in that new world.
I couldn’t specialize in math at St. John’s, because its all-required curriculum didn’t allow for majors. So I transferred to Wellesley College. When I arrived, I found myself in a peculiar position: I had just spent two and a half years at St. John’s reading and analyzing texts by mathematicians in the thick of their art—but the content of those texts was ancient and foundational. So while I’d developed a lot of mathematical sophistication, from a modern perspective, I hardly knew any math.
I had an extraordinary stroke of good fortune: A Wellesley professor, Leonard Miller, volunteered to meet with me individually to help me get up to speed. For our first meeting, Lenny asked me to prove some apparently simple things, including that 0 + 0 = 0, using building blocks called “axioms” that I could assume were true. One such axiom, for example, was, “if x = y, then y = x.”
I solved most of the problems he gave me, but the statement about zero stumped me. I was embarrassed to confess my failure.
Lenny’s cheeks bunched into apples as he said, “I don’t immediately know how to prove it either. I’ve never worked with this particular axiomatic system. But I know that I’ll be able to figure it out, because I’m a mathematician, so I’ve learned how to do this kind of thing. Keep at it, and you’ll get there too.”
His kindness brought tears to my eyes. I was astonished to hear math presented as a simple skill you develop rather than a test of your intellect. And he reassured me that I might indeed be able to make a life for myself in mathematics.
Ultimately, Lenny had me prove a big portion of undergraduate mathematics for myself. Rather than having me crunch my way through calculus problems, Lenny would give me one of the critical theorems in calculus to prove, and then he’d patiently encourage me, with occasional hints, as I figured it out for myself.
I felt, quite literally, like I was building an entire universe from scratch, one that underlay and connected with the physical world we live in. It made me think of the long hours I’d spent sitting on my mother’s bed talking with her, feeling my way toward the invisible threads of meaning I believed underlay the world, deep within its inherent structure. I didn’t think that God had squirreled away messages for us to find like cleverly hidden Easter eggs, but I did think that great beams and columns were inherent in the architecture of the universe, and that listening empathetically to my mother, no matter how crazy her words seemed, was a way of perceiving that invisible architecture. Perhaps, I’d believed, this would reveal alternate pathways to travel through to impact the world—and even, maybe, to solve my mother’s problems.
Mathematics felt like a non-woo-woo version of this exact thing.
Sitting down with a problem set, I often found that the problems weren’t just hard—they seemed to have no connection to anything I’d ever learned in my life. I had to fight panic to be able to even start thinking about them. I’d eventually manage to come up with one dumb little idea, then another, nothing that seemed the slightest bit profound or adequate. But eventually I’d manage to set the problem in this great superstructure of mathematics, and it would unfold, its roots sinking deep into the soil of math and its branches reaching toward heaven. The solution would then emerge naturally, like a swelling fruit.
In the end, I would write up my proof with strict logic connecting each step, but logic played a secondary role in discovering it. Intuition was my guide for discovery, and becoming a mathematician was all about training that intuition, working examples, seeing patterns, developing a feeling for how ideas connected. I felt like I was learning to navigate an invisible city, first finding my way around using landmarks and only later codifying that knowledge into a formalized map.
The process of doing mathematics reworked my brain, teaching me a new way of thinking. I was entering a kind of priesthood, removed from ordinary reality, living in the realm of the spirits—just as my mother most valued. And just as in childhood, I couldn’t describe anything about what I was learning to those who weren’t initiated. When I was a graduate student at MIT, I could tell people that my master’s thesis was about homotopy colimits, but if they weren’t already mathematicians, I couldn’t tell them what a homotopy colimit was.
Graduate school, however, pulverized me. My professors seemed . . . not human. I could find no point of connection. My male colleagues seemed to fit in far better than I did. And the thing I most valued about myself mathematically—my ability and determination to understand mathematics deeply, from the ground up, grasping its interconnections and deep structure—seemed to be viewed only as slowness and boneheadedness.
Two years into graduate school, Geoff and I spent a summer in Santa Fe. We wanted to snatch a bit of happiness to power ourselves through the gloom of grad school. I’d been telling Geoff stories about Santa Fe for years, describing it as a Shangri-La with wildly colored rocks, enormous blue skies, and green chile to make your eyes water. At the end of the summer, we could barely make ourselves go back to Boston, and we promised ourselves that if we were just as miserable after another semester, we’d hop in our car and drive back to Santa Fe. We figured it was a kind of noble lie—surely we won’t really abandon graduate school—but a few months later, we took leaves of absences, packed the car, and barreled back down the highway.
I hoped I’d find some less agonizing way of doing math and finish grad school, but I couldn’t figure out how. Then we bought the land, and I started teaching at St. John’s, and research mathematics gradually faded away.
Fifteen years later, lying in my trailers on my land feeling my connections to the outside world grow less reliable with my illness, this mystical-maternal-mathematical universe grew more dominant. The complete uselessness of doctors had closed off the direct, medical, logical, accepted, well-understood paths to healing my body. Science gave me no brightly lit highway to speed down. But I still felt promise in these other, deeper, harder-to-express levels.
I could use the tools I had developed over the course of my life, the intuition and attunement, listening deeply to my body and my experience, paying attention to logic but not relying on it exclusively or even primarily. Those tools had brought me significant (if not ultimate) success in changing my mother’s life, despite the overwhelming impediment of being a child with little power in the world. They had gotten me into the elite level of mathematics. I believed I could also use them to find my way out of this horrid disease.
Lying in bed for hour after hour, I discovered, had a major downside, peaceful as I was feeling: It’s terribly boring. But during that summer, I found a project I could work on even from bed—to train Frances as a service dog.
I’d first come up with the idea before I left William, but it seemed so implausible I could barely bring myself to mention it to him. My idea was that she could carry a small, foldable scooter—basically a skateboard with a handle and a brake—in a backpack, and when I couldn’t walk, she could pull me on it. The idea made me laugh: ludicrous but clever, thoroughly Julie-ish. Just contemplating it made me feel like me. Plus, if I was going to stay this sick, maybe it re
ally could make life more manageable.
I couldn’t find a scooter for sale like I had imagined, though I figured that I could have one custom-built if necessary. But it occurred to me that even without a scooter, just wrapping Frances’s leash around my waist and having her pull me might be enough—she could play the same role as Christie’s hand, pushing on my lower back to help me move.
So I did some research about training a service dog. Formal service-dog training schools generally started with specially bred, eight-week-old puppies, whereas Frances was an 18-month-old mutt. But I found a community of people training their own service dogs—and I even found a trainer who worked over Skype. I also found an elaborately detailed set of instructions for training all the basic behaviors a working dog needs to know, such as how to behave in public.
So I jumped in and started training her. About a month later, I seized a day I was feeling good and took her into town in her “service dog in training” vest. That day, I just walked her into a café, gave her treats every couple of steps, gave her a few simple commands, and walked out. Then we celebrated her fabulous success with a play-dance outside.
Later, we started working on one of the big challenges: She had to ignore every crumb on the floor in a café, even when I wasn’t paying attention. We’d already worked extensively on “leave it,” starting by my holding my fist out to her, a piece of cheese inside. Her first response had been to nuzzle at my fist, trying to get at the cheese. When nuzzling didn’t work, she paused, trying to think of a new strategy. As soon as she left my hand alone, I clicked a little noisemaker called a clicker (to tell her the precise moment that she did something right), opened my hand, said “take it,” and let her eat the treat. We built up in tiny steps from there—she had to wait longer before getting the treat, I offered the treat in an open hand and made her wait for permission, I put the treat on the floor, etc.—until she was able to step back from a wriggling lizard or a tossed-aside Kentucky Fried Chicken bone, eager to get her bit of cheese.
Now I just had to make “leave it” her default behavior when we were out in public. I began by setting a crumb near her wordlessly, looking her in the eye and placing the crumb very deliberately. That clued her in that something was up with that crumb, so even though I didn’t say “leave it,” she hesitated before hoovering it—click, treat! I built up until I could toss any tasty morsel her way without a word and she wouldn’t make a move toward it. Eventually, when she walked up to a crumb, she’d look at it, turn toward me (and the treat bag), and lick her lips.
Much harder than crumbs for Frances were people. Frances loved people, and cafés were filled with them, their hands crying out for a friendly lick, their crotches alluringly close to her snout. Plus, she knew that if she wiggled at them hard enough, she could probably seduce them into petting and cooing over her. I started working on this in a more controlled setting, hiring a 10-year-old neighbor, Ida, to be my assistant. Learning to greet Ida calmly, I figured, would help Frances learn to stay controlled and look to me for direction when she encountered strangers in public.
The mornings my body was up for it, Ida would appear at the end of the driveway, her black bangs framing her shyly smiling eyes. I would sit on the deck with Frances in a sit-stay next to me, and as Ida approached, Frances would try desperately to keep her butt on the ground as it wriggled back and forth against her will. Often, she would lose the fight and leap up to squirm toward Ida. Ida would immediately turn around and walk away, I’d call Frances back into her sit-stay, and we’d try again. The second time, Frances would manage a bit longer, and eventually, Ida would reach her, sit down, and giggle as Frances covered her face with kisses. We repeated this each session, and the first morning that Frances succeeded on the very first try, she exploded into full-speed laps around the ponderosas, every leap of her body radiating delight and pride.
I was particularly eager to train Frances to go to the pool with me. I continued to rely on my miracle antiparalysis swim cure, but getting to the pool was a Herculean feat. Sometimes I was too weak to go, and I simply had to lie in bed and wait to hit an upswing that would make the trek possible. Once I arrived, I would call the front desk at the pool and they would meet me at my car with a wheelchair. I’d put on my swimsuit before going, so that I could just pull my clothes off and slither off the chair into the pool. I planned to train Frances to pull me to the car at home and then from the car to the pool.
The trick to training her, always, was to create a ladder of easily learnable steps that would lead her to the behavior I wanted. The first time we went to the pool, Frances’s eyes about bugged out of her head, apparently unsure what these strange critters in the water were. So I kept it very simple: I asked her to sit, lie down, give me five, anything I could think of to give her something to focus on as she regained her composure. Then we walked once around the pool as she examined the swimmers.
The next time we went, I put her in a down-stay by the pool. At home, she could stay for several minutes, but since this environment was so unfamiliar to her, I started from scratch. I stepped back a foot, returned, gave her a treat. Then two feet, treat; then five feet, then ten feet, etc. Over seven training sessions in the course of a month, we built from there until she could hold her stay while I swam a full lap.
The two of us were very popular with the lifeguards, and on the days I was feeling too lousy for training and left her behind, they asked after her as they watched me stagger and groan my way into the pool.
The service-dog trainer I found over Skype helped us work on specific service skills, such as retrieving objects and, most importantly, pulling. I got a special harness designed for pulling, and I had Ida walk in front of us facing backward, encouraging Frances forward with treats, while I provided slight resistance on the leash from behind. Frances was suspicious: I’d drilled into her that she always had to keep the leash loose. But once she understood, she was thrilled.
Over time, Ida gave fewer treats, and then she walked beside me for short periods. Then we started working on niceties, like teaching Frances the commands for right and left and stop. Often, the session with Ida and Frances was my only time out of bed for the day.
Training became one of Frances’s very favorite activities. In public, she knew when she was on duty, and a veil of concentration fell over her as she looked to me for direction. At home, she often came over to me with an alert expression, sat very straight in front of me, and looked right into my eyes. Her meaning was clear: “Let’s train!” Training ended up substituting for taking her for walks, the mental challenge burning her energy almost as much as physical exercise (though the neighbor dog who visited for wrestling sessions helped too).
The most important thing was to always make sure that I was asking no more of her than she could do—but I didn’t always judge that correctly. One day, I asked my friend George to meet me and Frances at a mall, to help us practice polite greetings in public. Frances and I arrived first, to give her some time to get used to the mall, and when George showed up, he sat down some distance from us.
Frances lost her cool upon sighting him, tugging at the leash and wiggling, her meaning clear: “There’s George! Mom, it’s George! We have to go say hi, right now! Come on, Mom!”
Unable to get her attention, I led her far enough away that she could calm down a bit and gave her rapid-fire cues to focus on: sit, down, sit, high-five, touch, down. Then I tried walking back toward George, rewarding her very frequently for staying at my side.
But Frances had calmed down only slightly. Convinced George was in a group of folks walking past, she tugged on the leash to follow them. When the group disappeared, she looked around wildly for George. Then she sat down, threw her snout into the air, and did something I had never seen or heard her do before: She yodeled. Not a bark, not quite a howl, but I knew precisely what it meant: “George! I’m over here, George! Where aaaaaaare you?” I had to laugh, though my cheeks also burned at this complete breakdown of service-dog beh
avior.
I spent so much time training her that I occasionally felt guilty, wondering if that time would be better spent on my work, or on doing something to get myself better (not that I knew what that might be). The image of a skeptical William easily came to mind.
But working with Frances fit my abilities at that time perfectly. She needed short bursts of training, which were all I could manage. When I was too ill to leave home for a week, her training in public could pause without harm. I could think up new strategies even when I couldn’t move. And my fascination with the project made my brain function better.
Plus, working with Frances was the single most satisfying thing in my life. It connected me to myself, gave me something to think about other than my dismal health, provided an outlet for my maternal energies, and gave me hope that I could continue to respond to this illness creatively, even if I never managed to get better. Every time I felt her soft, wet tongue licking a piece of cheese from my fingers, I felt grateful to her.
Training her also felt downright profound, like the process was reworking my brain and my fundamental relationship to the world. The most basic tenet of the dog-training approach I was learning was that the process always had to be fun for the dog. When I’d trained dogs in the past, the word “no!” had always been a fundamental training tool, but I almost never said that to Frances. It was my job to set situations up for Frances so that she’d naturally do what I wanted her to do. I could see the impact this had on her, the deep trust she had for the world, her basic expectation that the world was a wonderful place filled with games and treats and joy and love.
Was it possible that all of life could flow out of easy play? Could I approach my own life that way? Could I train my brain the way I was training Frances’s? Could I, like her, come to feel that the world was a wonderful, gentle place and that challenges were games to be enjoyed that always ended in a treat?
Through the Shadowlands Page 13
