My life has
recently intersected, in a most personal way, two of Mark Twain's famous quips.
One I shall defer to the end of this essay. The other (sometimes attributed to
Disraeli), identifies Three species of mendacity, each worse than the one
before - lies, lies, and statistics.
Consider the
standard example of stretching the truth with numbers - a case quite relevant
to my story. Statistics recognizes different measures of an
"average," or central tendency. The mean is our usual concept of an
overall average - add up the items and divide them by the number of shares (100
candy bars collected for five kids next Halloween will yield 20 for each in a
just world).
The median, a
different measure of central tendency, is the half-way point. If I line up five
kids by height, the median child is shorter than two and taller than the other
two (who might have trouble getting their mean share of the candy). A
politician in power might say with pride, "The mean income of our citizens
is $15,000 per year."
The leader of the
opposition might retort, "But half our citizens make less than $10,000 per
year." Both are right, but neither cites a statistic with impassive
objectivity. The first invokes a mean, the second a median. (Means are higher
than medians in such cases because one millionaire may outweigh hundreds of
poor people in setting a mean; but he can balance only one mendicant in
calculating a median).
The larger issue
that creates a common distrust or contempt for statistics is more troubling.
Many people make an unfortunate and invalid separation between heart and mind,
or feeling and intellect. In some contemporary traditions, abetted by attitudes
stereotypically centered on Southern California, feelings are exalted as more
"real" and the only proper basis for action - if it feels good, do it
- while intellect gets short shrift as a hang-up of outmoded elitism.
Statistics, in this absurd dichotomy, often become the symbol of the enemy.
As Hilaire Belloc
wrote, "Statistics are the triumph of the quantitative method, and the
quantitative method is the victory of sterility and death." This is a
personal story of statistics, properly interpreted, as profoundly nurturing and
life-giving.
It declares holy war
on the downgrading of intellect by telling a small story about the utility of dry,
academic knowledge about science. Heart and head are focal points of one body,
one personality. In July 1982, I learned that I was suffering from abdominal
mesothelioma, a rare and serious
cancer usually
associated with exposure to asbestos. When I revived after surgery, I asked my first
question of my doctor and chemotherapist: "What is the best technical
literature about mesothelioma?" She replied, with a touch of diplomacy
(the only departure she has ever made from direct frankness), that the medical
literature contained nothing really worth reading.
Of course, trying
to keep an intellectual away from literature works about as well as
recommending chastity to Homo sapiens, the sexiest primate of all. As soon as I
could walk, I made a beeline for Harvard's Count Way medical library and
punched mesothelioma into the computer's bibliographic search program. An hour
later, surrounded by the latest literature on abdominal
Mesothelioma, I
realized with a gulp why my doctor had offered that humane advice. The literature
couldn't have been more brutally clear: mesothelioma is incurable, with a
median mortality of only eight months after discovery. I sat stunned for about
fifteen minutes, then smiled and said to myself: so that's why they didn't give
me anything to read. Then my mind started to work again, thank goodness.
If a little
learning could ever be a dangerous thing, I had encountered a classic example.
Attitude clearly matters in fighting cancer. We don't know why (from my
old-style materialistic perspective, I suspect that mental states feed back
upon the immune system). But match people with the same cancer for age, class, health,
socioeconomic status, and, in general, those with
Positive attitudes,
with a strong will and purpose for living, with commitment to struggle, with an
active response to aiding their own treatment and not just a passive acceptance
of anything doctors say, tend to live longer. A few months later I asked Sir
Peter Medawar, my personal scientific guru and a Nobelist in immunology, what
the best prescription for success against cancer might be. "A sanguine
personality," he replied. Fortunately (since one can't reconstruct oneself
at short notice and for a definite purpose), I am, if anything, even-tempered
and confident in just this manner.
Hence the dilemma
for humane doctors: since attitude matters so critically, should such a somber conclusion
be advertised, especially since few people have sufficient understanding of
statistics to evaluate what the statements really mean? From years of
experience with the small-scale evolution of Bahamian land snails treated
quantitatively, I have developed this technical knowledge - and I am convinced
that it played a major role in saving my life. Knowledge is indeed power, in
Bacon's proverb.
The problem may be
briefly stated: What does "median mortality of eight months" signify
in our vernacular? I suspect that most people, without training in statistics,
would read such a statement as "I will probably be dead in eight
months" - the very conclusion that must be avoided, since it isn't so, and
since attitude matters so much.
I was not, of
course, overjoyed, but I didn't read the statement in this vernacular way
either. My technical training enjoined a different perspective on "eight
months median mortality." The point is a subtle one, but profound - for it
embodies the distinctive way of thinking in my own field of evolutionary
biology and natural history. We still carry the historical baggage of a
Platonic heritage that seeks sharp essences and definite boundaries.
(Thus we hope to
find an unambiguous "beginning of life" or "definition of
death," although nature often comes to us as irreducible continua.) This
Platonic heritage, with its emphasis in clear distinctions and separated
immutable entities, leads us to view statistical measures of central tendency
wrongly, indeed opposite to the appropriate interpretation in our actual world
of variation, shadings, and continua.
In short, we view
means and medians as the hard "realities," and the variation that
permits their calculation as a set of transient and imperfect measurements of
this hidden essence. If the median is the reality and variation around the
median just a device for its calculation, the "I will probably be dead in
eight months" may pass as a reasonable interpretation. But all
evolutionary biologists know that variation itself is nature's only irreducible
essence. Variation is the hard reality, not a set of imperfect measures for a
central tendency. Means and medians are the abstractions.
Therefore, I looked
at the mesothelioma statistics quite differently - and not only because I am is
an optimist who tends to see the doughnut instead of the hole, but primarily
because I know that variation itself the reality. I had to place myself amidst
the variation. When I learned about the eight-month median, my first
intellectual reaction was: fine, half the people will live longer; now what are
my chances of being in that half. I read for a furious and nervous hour and
concluded, with relief.
I possessed every
one of the characteristics conferring a probability of longer life: I was
young; my disease had been recognized in a relatively early stage; I would
receive the nation's best medical treatment; I had the world to live for; I
knew how to read the data properly and not despair. Another technical point
then added even more solace.
I immediately
recognized that the distribution of variation about the eight-month median
would almost surely be what statisticians call "right skewed." (In a
symmetrical distribution, the profile of variation to the left of the central
tendency is a mirror image of variation to the right. In skewed distributions,
variation to one side of the central tendency is more stretched out - left
skewed if extended to the left, right skewed if stretched out to the right.)
The distribution of variation had to be right skewed, I reasoned.
After all, the left
of the distribution contains an irrevocable lower boundary of zero (since
mesothelioma can only be identified at death or before). Thus, there isn't much
room for the distribution's lower (or left) half - it must be scrunched up
between zero and eight months.
But the upper (or
right) half can extend out for years and years, even if nobody ultimately survives.
The distribution must be right skewed, and I needed to know how long the
extended tail ran - for I had already concluded that my favorable profile made
me a good candidate for that part of the curve.
The distribution
was indeed, strongly right skewed, with a long tail (however small) that extended
for several years above the eight month median. I saw no reason why I shouldn't
be in that small tail and I breathed a very long sigh of relief. My technical
knowledge had helped. I had read the graph correctly. I had asked the right
question and found the answers.
I had obtained, in
all probability, the most precious of all possible gifts in the circumstances -
substantial time. I didn't have to stop and immediately follow Isaiah's
injunction to Hezekiah - set thine house in order for thou shalt die, and not
live. I would have time to think, to plan, and to fight. One final point about
statistical distributions is.
They apply only to
a prescribed set of circumstances - in this case to survival with mesothelioma
under conventional modes of treatment. If circumstances change, the
distribution may alter. I was placed on an experimental protocol of treatment
and, if fortune holds, will be in the first cohort of a new distribution with high
median and a right tail extending to death by natural causes at advanced old
age.
It has become, in
my view, a bit too trendy to regard the acceptance of death as something tantamount
to intrinsic dignity. Of course I agree with the preacher of Ecclesiastes that
there is a time to love and a time to die - and when my skein runs out I hope
to face the end calmly and in my own way. For most situations, however, I
prefer the more martial view that death is the ultimate enemy - and I find
nothing reproachable in those who rage mightily against the dying of the light.
The swords of
battle are numerous, and none more effective than humor. My death was announced
at a meeting of my colleagues in Scotland, and I almost experienced the
delicious Pleasure of reading my obituary penned by one of my best friends (the
so-and-so got suspicious and checked; he too is a statistician, and didn't
expect to find me so far out on the right tail). Still, the incident provided
my first good laugh after the diagnosis. Just think I almost got to repeat Mark
Twain's most famous line of all: the reports of my death are greatly
exaggerated.
