Free Full House by Stephen Jay Gould

distribution, measures of central tendency do not coincide. The median lies to the right of the mode, and the mean lies to the right of both other measures.
    In either case, such limits often produce skewed distributions, because variation can expand in only one direction—you can’t die of mesothelioma before you get it, but you can live for years and years after a diagnosis. With an eight-month median mortality, and a rigid lower limit at time zero, how could the distribution of deaths be anything but strongly right skewed?
    Throughout this book, I shall refer to such limits upon the spread of variation as "walls"—either "right walls" or "left walls" depending upon their position. Left walls induce right-skewed distributions (for variation is only free to expand away from a wall); right walls provoke left-skewed distributions. The left wall of my cancer story leads to a right-skewed distribution of deaths.
    (I have considered the cultural bias involved in the largely arbitrary designation of right as the direction for higher values, left for lower— though, depending upon the example, lower may be judged better, as in distributions for weight in our diet-conscious society. I suppose that we fall into this bias for two reasons, one insidious and the other benign. Prejudice against our left-handed minority—an old and probably universal feature of human cultures, I fear—must set the major reason. Jesus sits ad dextram patris, at the right hand of the father. Right, etymologically, is dextrous—and "law" is droit in French and Recht in German, both meaning right. Left is both sinister and gauche. For the benign reason, we read from left to right and therefore conceptualize growth and increase in this direction. Were I writing this book in Israel, which also has a right-handed majority, I might think of left walls as directions of increase. Were I writing in Japan, I might be talking of top and bottom walls. So be it.)
    Readers need to grasp only these three nontaxing concepts about the nature of variation in order to render all the examples of this book fully digestible—right and left walls as limits to the spread of variation; right-and left-skewed distributions arising as results of these limits; and differences among means, medians, and modes as measures of central tendency.

5
    Case Two: Life’s Little Joke
    Genuine changes in central tendency are meaningful, but our failure to consider variation has led to a backwards interpretation: the evolution of horses
    The most erroneous stories are those we think we know best—and therefore never scrutinize or question. Ask anyone to name the most familiar of all evolutionary series and you will almost surely receive, as an answer: horses, of course. The phyletic racecourse from small, many-toed protohorses with the charming name eohippus, to a big, single-toed Clydesdale hauling the Budweiser truck, or Man O’ War thundering down the stretch, must be the most pervasive of all evolutionary icons. Does any major museum not have a linear series of cases against a long wall, or up the center of a main hall, one skeleton in each, and all illustrating the triumphant trend?
    This horse story also represents the oldest of established evolutionary series—a major reason for its fame. Thomas Henry Huxley himself, Darwin’s most celebrated supporter, first proposed the sequence from European fossils in 1870. This original version did not long survive because Huxley’s three European fossils, linked as an evolutionary series, actually represent three separate migrations of American stocks, with extinction in Europe following each incursion. Meanwhile, the full story was unfolding in America.
    In 1876, Huxley made his only voyage to the United States, primarily to participate in celebrations for our Centennial and, in particular, to give the principal address at the founding of Johns Hopkins University. He visited Othniel C. Marsh, America’s leading vertebrate paleontologist,