Boats & Deckchairs

Natural History, Dec, 1999 by Stephen Jay Gould, Rhonda Roland Shearer

The inception of the third millennium can boast an extended pedigree as a symbol for new beginnings. In a work written in 1884, the hero of science fiction's most celebrated tale about expanding horizons contemplates his limited world at this crucial moment:

   It was the last day of the 1999th year of our era ... and I was ... musing
   on the events of the past and the prospects of the coming year, the coming
   century, the coming Millennium ... and there I sat by my Wife's side,
   endeavouring to form a retrospect of the year 1999 and of the possibilities
   of the year 2000.

And as A Square takes stock of his life in the 2-D universe of English cleric Edwin A. Abbott's Flatland: A Romance of Many Dimensions, a sphere from an incomprehensible world of higher dimensionality passes right through the plane of his entire existence, appearing first as a point and then as a circle of initially expanding and subsequently diminishing radius, while A Square looks on in stunned awe and utter mystification. The sphere speaks to A Square: "I am indeed, in a certain sense a Circle ... and a more perfect Circle than any in Flatland, but to speak more accurately, I am many Circles in one." A Square then looks at his timepiece and notes the maximally auspicious moment of the sphere's passage: "The last sands had fallen. The third Millennium had begun."

As a technique for the most concrete form of mind stretching, the study of optical illusions surely matches the contemplation of dimensions beyond our sensory experience (or even our power to conceive). Many classic illusions present alternatives in two dimensions--as in the duck/rabbit or urn/faces of gestalt switching between figure and ground. Thomas S. Kuhn invoked this kind of illusion as a primary metaphor to illustrate his central concept of paradigm shift in The Structure of Scientific Revolutions (1962): "It is as elementary prototypes for these transformations of the scientist's world that the familiar demonstrations of a switch in visual gestalt prove so suggestive. What were ducks in the scientist's world before the revolution are rabbits afterwards."

Other illusions present alternatives in three dimensions--as in the famous Necker Cube, so effectively used by Richard Dawkins in his Extended Phenotype (1982) to argue for the compatibility of gene-centered and organism-centered views of natural selection. Dawkins writes:

   There is a well-known visual illusion called the Necker Cube. It consists
   of a line drawing which the brain interprets as a three-dimensional cube.
   But there are two possible orientations of the perceived cube, and both are
   equally compatible with the two-dimensional image on the paper. We usually
   begin by seeing one of the two orientations.... After a few seconds the
   mental image flips back and it continues to alternate as long as we look at
   the picture. The point is that neither of the two perceptions of the cube
   is the correct or "true" one. They are equally correct.

If these familiar illusions in our palpable worlds of two and three dimensions have furnished such useful images for contemplating the nature of major innovations in scientific thinking, consider what we might gain if we could join the two methodologies and create representations for alternative states in a 4-D world that we cannot draw and scarcely know how to conceive.

In fact, a stunning example of such a double whammy in mental extension (an optical illusion based on alternative states in 4-D perspective) was constructed more than eighty years ago by one of the most innovative artists of our century: Marcel Duchamp (1887-1968). He published the illusion in 1967 as a puzzle on a piece of stiffened paper resembling a postcard in size and shape and containing an original painting on one side and a verbal explanation on the other. Nevertheless, his evident intention and brilliant realization have never been deciphered.

We can identify several reasons for this failure. Some responsibility can be laid firmly at Duchamp's door as the desired consequence of his own arcane procedures. As the enfant terrible of Dada (in the usual interpretation of art historians)--the man who embellished a reproduction of the Mona Lisa with a beard and mustache, the man who attempted to include a urinal in a 1917 art exhibition--Duchamp never deigned to explain his artistic theories or intentions.

But equal or greater weight must be placed upon our own failure to ask the right questions, largely because we have operated under a false taxonomy of intellectual disciplines--one that drives a powerful but illusory wedge of maximal separation between art (viewed as an ineffably "creative" activity based on personal idiosyncrasy and subject only to hermeneutical interpretation) and science (viewed as a universal and rational enterprise based on factual affirmation and analytical coherence).

Duchamp ranks as an artist in this false dichotomy--and a maddeningly cryptic member of his calling to boot. Thus, we have never asked the right questions, because we have not recognized the serious and well-informed treatment of scientific issues--ranging from optics to the mathematics of probability and dimensionality--pervading so much of Duchamp's art, and illustrating, in a manner unmatched since Leonardo himself, the fundamental compatibility between these two great domains of human creativity. Many scholars have recognized and documented the numerous scientific allusions throughout Duchamp's oeuvre but have then assumed that Duchamp could never be regarded as an innovator of scientific concepts, if only because artists, in our stereotypical view, cannot develop sufficient expertise to understand such technical subjects. Duchamp's playful or sarcastic allusions to science must therefore represent a grand sardonic joke, an extended reflection by a creative spirit on the sterility of technological precision.