Make Waves not Water
It is a lamentable but nonetheless indisputable fact that women are not represented in the ranks of first-rate mathematicians. A reason for this sad state of affairs is suggested, based not on an evaluation of the mental development of females but, to put it simply, on the way they accomplish the elimination of body liquid waste. At first sight such a correlation is surprising but careful consideration will show that the contemplation of the effluent during micturition, a view denied the female by a cruel stroke of biological design, raises questions of such philosophical magnitude that over the millennia mental traits have evolved in males which occasionally flower to produce individuals with the unique ability to formalize abstract concepts - the distinguished mathematician. It must be emphatically stated that this unique deficiency in females is not believed to be caused by an overall reduction in mental capacity, as proposed by some workers1.
Proper credit to the true inspirational source of their genius is usually hard to find in the writings and biographies of notable mathematicians and theoretical physicists. Whether or not the theory holds water must be determined by considering specific examples. The motion and properties of an effluent stream are a good deal more complicated than might be suspected by the untrained mind; the history of mathematics reflects the growing awareness of the problem as analytical tools become more advanced.
Simple motion in two planes.
The most basic manoeuvre is to adjust the trajectory angle and thus achieve a variation of height and range. No doubt at a very early time in the development of man the competitive possibilities were discovered. Indeed this behaviour can still be observed among primitive people2 and clearly leads to an intuitive grasp of the properties of the parabola and the elements of ballistics. It may be argued that this might produce superior artillery officers and rocketeer - hardly mathematicians. However these experiments must be viewed with the proper historical perspective, they produced a bedrock of knowledge on which a towering intelligence would erect the foundation of modern mathematics. Newton himself said it this way "If I have peed further it is because I stood on the shoulders of giants".3 As a demonstration of gravity this experiment is far more convincing than waiting for an apple to fall. While discussing this era of mathematical development it is hardly necessary to comment on the numerous experiments which have taken place from the Leaning Tower of Pissa, in fact these are thought to have possibly contributed to the weakening supports.4 Once the concept of gravity was firmly established it was soon extended to the notion of an all-pervasive field or continuum and the effect on bodies in the fluid. This was inspired by observing the stream trajectory in a strong wind, as may be deduced from advice given neophyte sailors of the day in an oft-quoted aphorism - "Never piss against the wind".5
One of the cornerstones of twentieth-century physics was laid after the examination of the trajectory under conditions approximating free-fall. This occurred when a theoretician was impelled to relieve himself in a descending express elevator. Although the concept of relativity has revolutionized physics, at the time his behaviour was considered aberrant and resulted in a small fine.6
These simple examples serve to introduce the complicated theories of dynamical motion in three dimensions. Once a male mind was forced to grapple with axial effects in the emergent steam a new chapter in mathematics was opened.
Three dimensional motion and second order effects
In the mid-nineteenth century mathematicians had settled into a false euphoria, convinced all major problems had been solved. Ripples ran across this tranquil pond as word seeped down that the cross-section of the jet steam varied with axial position. Although it was clear the individual water molecules moved with considerable velocity the surface contours exhibited standing waves! probably the foremost genius to grasp the implications of this observation was W R Hamilton, an Irish mathematician whose experimental opportunities were greatly enhanced by the proximity of the Guinness brewery. His work opened the floodgate; to this day applications of his analysis are found including production of strange particles, planetary motion and even the mechanics of galaxies. Truly an awe inspiring example of the limitless projections of the human mind.
But more was yet to come: thousands of miles away from Dublin a Russian, A. Mikhailovich Liapunov, was incarcerated by the Czarist secret police. He was imprisoned under primitive conditions which necessitated urinating through a hole in the wall.7 He observed inhomogenities which developed as a function of distance travelled, a phenomenon which greatly complicated accurate targeting - a critical consideration in the sub-freezing temperature of his cell. He realized the importance of the physical boundaries represented by the hole when compared to the drifting phase-space separatices of the globules of the impinging stream. His generalized theory of an energy function encompassing discrete subsets has had wide application in such diverse topics as system stability and the criticality of nuclear reactors.
A munificent nature has endowed the male of the species with what is, in effect, a miniature physics laboratory, his very own source of continual inspiration. Although the roots of man's creativity have been ascribed to the same general region by others, notably poets and the like, they usually invoke a more sublime but far less frequent function. It has been shown that it is in the commonplace miracle, produced daily for the eyes of man, which has, for those rare individuals ready to seize an opportunity when it rises, resulted in flashes of true genius.
Much remains to be done. Frequently great mathematical and musical ability are combined, the absence of great female composers must be considered significant. Does musical genius flow from the same wellhead? Research on this topic is, it might be said, well in hand.
Pigg, M. C.
3 Acrobatic Troupes of the 17'th Century, Monograph of Collected Papers, Pub'n of Camb. Univ. Press, 1942. Note that this quotation is often mistranslated from the original Latin as - "if I have peered further..." This may reflect the sensitivity on the part of the biographer.
4 Private Communication from Vinnie Viglietti, owner of the Pompii Pizzaria.
The Mariners Guide to what every Bluejacket Neads to Know.
6 Zuricher Nacht Zeitung for November, 1909, p.24 (bottom of 6'th col.)
7 Important aspects of this activity have been attributed to the monks of St. Bernards, a monastery in the Austrian Alps. However they were not concerned with mathematical truths but with spiritual enlightenment from colouring the stones at the edge of the hole.