In my first blog entry (The World Still Out There) I promised an excerpt from what I have written for my children to read some day.
This is a portion of a chapter about the language of numbers:
In the early weeks after Jim’s diagnosis there were times when I felt I could not breathe, seized with the thought of him surrounded by complete darkness. It was not so much an image as a sensation: my mind would be overtaken by all-enveloping blackness. In the words of “A Hard Rain’s Gonna Fall,” it was a place “Where black is the color, where none is the number.”
It was the one thing I knew I simply could not bear, and which Jim’s decision to donate his body to his medical school spared me: having him surrounded by darkness.
While dropping off our elder daughter at college for the first time, I became inexplicably drawn to a song she played. She was in charge of the musical selections; otherwise, it would have been seven hours of searching for NPR signals as we wended our way through the Northeast. I found out months later that the song was titled “Death by Numbers.” The song’s cheerful cadence somehow transmuted those haunting images into an infinite mathematical sequence of positive things left behind. It was one of twenty songs my daughter chose to play as people gathered for Jim’s memorial service six months later:
“Oh when I’m minerals in the soil /I’ll diffuse into a tree It’ll have 5000 branches /Which will have 5000 leaves/And I’ll be in every one/Oh and when a leaf blows free/I will land upon the earth/And grow another tree/‘Til I have 5000 trees made of me/‘Til there are 5000 trees made of me . . . .”
The same metaphor echoed in the perfect poem our daughter read for her father at his memorial service: in the stunning “A Man,” Louis Untermeyer wrote of summoning curative memories of how his father had lived his life: “And it was forests growing,/And it was black things turning green.”
The image of infinite expansion of the good my husband leaves behind is the comforting flip side of the infinitely-expanding cellular curse of his cancer—the uncontrolled multiplication of invasive clonal cells. In The Emperor of All Maladies, Siddhartha Mukherjee wrote of this mathematical malevolence: cancer as “an expansionist disease. . . [that] invades through tissues, sets up colonies in hostile landscapes, seeking ‘sanctuary’ in one organ and then immigrating to another.”[i] It is its own function to infinity, like a monotone unbanded function, as one of my sons offers the metaphor: “It lives desperately, inventively, fiercely, territorially, cannily, and defensively. . .”[ii]
In A Tranquil Star, Primo Levi wrote about the strengths and inadequacies of more than one kind of language. One of his narrative voices alludes to “the slim and elegant language of numbers, the alphabet of the powers of ten,” but deems the mathematical voice inadequate for “a story in the sense in which this story wants to be a story; that is, a fable that awakens echoes, and in which each of us can perceive distant reflections of himself and of the human race.” [iii] This is not to say that numbers do not speak.
After finding out his cancer was not curable, Jim read The Last Lecture. We never did get around to watching the lecture together. When he read the book, I caught sight of his side-to-side head-shake when he got to a certain number: the author had recounted how he knew his months were numbered when his CA 19-9 level—a blood protein marker for the presence of tumor—had, as Jim put it with a wry look, “skyrocketed” to what the author described as “a horrifying 208.” [iv]
Jim’s CA 19-9 level had been varying slightly at between 1700 and 1900.
In a phrase that occasionally had escaped my lips in describing cases I’d worked on as a young prosecutor, “There’s murder, and then there’s murder.”
Well, there’s cancer, and then there’s cancer.
There is cancer that gives one reason to hope for cure, and there’s cancer that—at least to my personality type–simply does not.
It was the second-opinion surgeon’s reference to these high blood marker numbers as “concerning” that hit my brain (perhaps mercifully not then yet armed with the knowledge which would have enabled me to appreciate what those “concerning” numbers meant medically) and drove me out of that office in a panic back during the week following Jim’s diagnosis.
The numbers Jim and the surgeon were discussing just a few yards away, behind a closed door, told a medical story and foretold its ending. Yet when my husband came out of the office, his mood was strangely upbeat, and his face concentrated and determined. I know he was convinced he would have surgery by eminently skilled hands, should chemotherapy and radiation make him a candidate for resection of the pancreatic tumor.
The blood marker numbers were by no means the only numbers which figured into the story.
As Jim’s symptoms began to develop and multiply, we and those who treated him spoke in numerical shorthand. The question of “What’s your pain?” or “What’s your nausea?” would yield not a descriptive adjective, but an unadorned number from zero to ten.
I will forever be able to tick off a blizzard of numbers which have been thrown out in my presence by a parade of physicians–including that 80% of pancreatic cancers already have metastasized by the time they are diagnosed.
Much later, discussing palliative options, Jim and the doctors spoke in numeric quantities which by that point passed for conversation: “What are you looking for?” “Well, I have no problem with a baseline two or three for pain, and a five or a six for nausea if it’s only, say, two-out-of seven days. Five-or-six-out-of-seven I’d have to think about, and above a six on pain.”
Perhaps the most uncanny overlap between something I read and what we lived came to pass in another number.
In August, weeks into Jim’s treatment, The New Yorker published an article by endocrine surgeon and author Atul Gawande entitled, “Letting Go.” He spoke of end of life care for a number of terminal cancer patients, and wrote that physicians routinely overestimate how long patients they already know will live with terminal diseases, not by a shade, but by 550%:
“You’d think doctors would be well equipped to navigate the shoals here, but at least two things get in the way. First, our own views may be unrealistic. A study led by the Harvard researcher Nicholas Christakis asked the doctors of almost five hundred terminally ill patients to estimate how long they thought their patient would survive, and then followed the patients. Sixty-three per cent of doctors overestimated survival time. Just seventeen per cent underestimated it. The average estimate was five hundred and thirty per cent too high. And, the better the doctors knew their patients, the more likely they were to err.”
On November 10th we learned that Jim’s condition was not curable.
Over the next four days, each of our children pressed us for numbers. How long would their father live? Left to our own devices to divine such answers, Jim told them that he believed it would be less than a year. Largely from reading “The Last Lecture,” which involved a prognosis (pancreatic cancer that metastasized to the liver) that eerily paralleled his, we both were convinced it likely would be in the realm of between three and six more months. We were right: it turned out to be four-and-a-half months until Jim took his last breath.
The oncologist continued ticking off the relatively good news: there had been no symptoms from the liver lesions, and on physical examination there was no palpable mass. All of Jim’s other blood work was fine. Thus, the oncologist told us, to our considerable surprise, that Jim might well have another eighteen months to two years before the symptoms of his terminal illness overcame him.
Jim died four months and twelve days later.
Two years, 730 days, is 553% of 132 days. Put another way, our doctor could be said to have overestimated Jim’s survival by slightly more than 550%.
Of course, there always is a right tail in discussing median survivals, and Stephen Jay Gould memorably focused on that statistical reality in his essay, “The Median is Not the Message.” Someone survives longer than expected. Someone defies the overwhelming odds.
But as Dr. Gawande wrote decades later, in “Letting Go”: “There is almost always a long tail of possibility, however thin. What’s wrong with looking for it? Nothing, it seems to me, unless it means we have failed to prepare for the outcome that’s vastly more probable. The trouble is that we’ve built our medical system and culture around the long tail. We’ve created a multitrillion-dollar edifice for dispensing the medical equivalent of lottery tickets—and have only the rudiments of a system to prepare patients for the near-certainty that those tickets will not win. Hope is not a plan, but hope is our plan.”
We would find out how right Dr. Gawande was in identifying only the rudiments of a system to deal with the “vastly more probable” outcomes in this paradoxically, pathologically optimistic health care edifice.
In retrospect, those initial “concerning” numbers alone should have told me—and probably did inform my subconscious of–the end of the story.
Perhaps my non-scientific subconscious somehow knew what the numbers meant, and led to my flight from the surgeon’s office. But had I known what the numbers meant at the time, I could not have seen past them. Jim, knowing full well what such numbers meant, still could. He could see the positive features of his own health, fitness, youth and of the tumor as it was initially pictured, and realistically consider the very small possibility that he would win that lottery. But he never “failed to prepare for the outcome that’s vastly more probable.”
It was the things for which Jim (and in turn the rest of us) hoped which adapted and changed: he had plans and he had hope throughout, but hope was never the plan itself. As our long-time friend David (lovingly known to us as “subnaught,” because we had to distinguish among myriad Davids), a math professor, told me, “As for how to handle the tail of the distribution, when I teach probability, I recall the old adage, ‘The race is not always to the swift, nor the battle to the strong. But that’s the way to bet.’”