Rage against of the dying of the light

On Probability Statements:
"The Median is not the Message"
by Stephen Jay Gould

(Late) Stephen Jay Gould was an eminent paleontologist and evolutionary biologist. At an young age (41) he suffered from a serious and rare cancer ‑‑abdominal mesothelioma, associated with exposure to asbestos. Accoording to medical research statistics, mesothelioma is incurable, with a median mortality of eight months after discovery. He however, was fully cured.

In the article reproduced below, Gould discusses the need to interpret statistical data fully and correctly. Rather than giving up hope, he wrote that he used his knowledge of statistics to translate an apparent death sentence into the hopeful realization that half those in whom the disease was diagnosed survived longer than eight months, perhaps much longer, giving him the strength to fight on. He died in 2002 at the age of 60.


"We still carry the historical baggage of a Platonic heritage that seeks sharp essences and definite boundaries. This 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 variations that permit their calculation as a set of transient and imperfect measurements of this hidden essence. If the median is the reality and the variation around the median just a device for its calculation, the statement: `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. Referring to the statistically derived information about probable death in eight months in the case of those suffering from abdominal mesothemia, Gould observed after examining the complete data which yielded the median of eight months:

"The distribution was strongly rightly skewed and, as I had guessed, with a long tail (however small) to the right that extended for several years above the eight‑month median. I saw no reason why I should not be in that small tail, and I breathed a long sigh of relief. I had read the graph correctly. I had asked the right questions and found the answers. I had obtained, in all probability, that most precious of all possible gifts in the circumstances: substantial time. I didn't have to stop immediately and follow Isaiah's injunction to Hezekiah: `set thine house in order; for thou shalt die and not live.' I would have time to think, plan and fight.

One final point about statistical distributions: they apply only to a prescribed set of circumstances; in this case, to the survival with mesothelioma under conventional modes of treatment. If circumstances changed, the distribution might 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 a high median and a right tail extending to death by natural causes at an advanced old age. I possessed everyone 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. I agree with the preacher of Ecclesiastes that there is a time to live 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 find nothing reproachable in those who rage mightily against the dying of the light.