Woman in Science Part 11

To the exceeding gratification of the believers in the intellectual equality of the s.e.xes, this proved to be the case in Herr Kirchhoff's investigation. The answers of the German professors, contrary to what most people would have antic.i.p.ated, were, by a surprising majority, in favor of women. But their answers were in keeping with the changed educational conditions in Germany, as well as in other parts of the civilized world. Had Herr Kirchhoff undertaken his investigation a few decades earlier, the result would undoubtedly have been different, for women were then excluded from the universities and the professors had not had an opportunity of accurately testing their intellectual capacities. But having, during the latter part of the nineteenth century, had them as students in their lecture halls and laboratories, where they were able to study their mental powers and determine the value of their work by strict scientific methods, they were in a better position to express an opinion on the question at issue than would, a few years previously, have been possible.

Accordingly, even the declared enemies of the woman's movement among the German professorate were forced to admit the intellectual equality of the two s.e.xes. For they, too, as well as men of science in other parts of Europe, had been measuring skulls and weighing brains; they, too, had been studying woman's mental caliber in the light of the new psychology; they, too, had been watching her work in the various departments of the university; and, notwithstanding all their observations and experiments, they were unable to detect any difference between men and women in brain organization or in intellectual capacity. And, as might have been foreseen, results harmonized perfectly with those arrived at by investigators in other parts of the world--namely, that in things of the mind there is perfect s.e.xual equality.

Among the hundred and more professors whose opinions are given in Herr Kirchhoff's book there were, of course, a few who were not prepared to subscribe to the findings of the great majority of their colleagues. But the reasons they a.s.sign for dissent were, at least in some instances, little better founded than that of a certain professor of chemistry in the University of Geneva, who, a few years ago, gravely declared that women have no apt.i.tude for science because, forsooth, in chemical manipulations they break more test-tubes than men. Verily, "a Daniel come to judgment."

What probably more deeply impressed the German professors than anything else was the marked talent and taste of many of the women students for the abstract sciences, especially for the higher mathematics. For it had always been a.s.serted that these branches of knowledge were beyond woman's capacity and that she had an instinctive antipathy for abstruse reasoning and for abstractions of all kinds. When, however, they discovered women whose delight was to discuss the theory of elliptic functions or curves defined by differential equations; when they found a mathematical genius like Sonya Kovalevsky speculating on the fourth dimension, and carrying away from the mathematicians of the world the most coveted prize of the French Academy of Sciences, they were forced to confess that another of their illusions was dissipated, and to acknowledge that they had no longer anything on which to base their long and fondly cherished opinion of the mental inequality of the s.e.xes.

As an evidence of the extraordinary change that had been effected among the conservative Germans in the course of a few years respecting their att.i.tude toward the admission of the "Academic Woman" to the universities, and, consequently, toward her intellectual capacity, it will suffice to reproduce a sentence from the elaborately expressed opinion of Dr. Julius Bernstein, professor of physiology in the University of Halle. "After reflection on the subject," he declares, "I am convinced that neither G.o.d nor religion, neither custom nor law, and still less science, warrants one in maintaining any essential difference in this respect between the male and the female s.e.x."[106]

The controversy of centuries regarding woman's intellectual capacity was now virtually settled beyond all peradventure. Woman had conquered, and her final victory had been won in the heart of the enemy's country, yea, even in what was thought to be the impregnable fortress of her relentless foes. It was achieved where the proud Teuton male had imagined that he was unapproachable and beyond compare--in the laboratories and lecture rooms of his great universities--more irresistible, in his estimation, than the Kaiser's trained legions in battle array.

It finally dawned upon the leaders of thought in the Fatherland, as it had but shortly before dawned upon philosophers and men of science in other lands, that the reputed s.e.xual difference in intelligence was not due to difference in brain size or brain structure, or innate power of intellect, but rather to some other factors which had been neglected, or overlooked, as being unessential or of minor importance. These factors, on further investigation, proved to be education and opportunity.

As far back as 1869 that keen observer and philosopher, John Stuart Mill, had expressed himself on the subject in the following words: "Like the French compared with the English, the Irish with the Swiss, the Greeks or Italians compared with the German races, so women compared with men may be found, on the average, to do the same things with some variety in the particular kind of excellence. But that they would do them fully as well, on the whole, if their education and cultivation were adapted to correcting instead of aggravating the infirmities incident to their temperament, I see not the smallest reason to doubt."[107]

It would be difficult to find a better ill.u.s.tration of the sluggishness of the male as compared with the female mind than the tardiness of men of science in arriving at a sane conclusion respecting the subject of this chapter. For five hundred years ago Christine de Pisan arrived at the same conclusion which the learned professors of Germany reached only in the last decade of the nineteenth century. Discussing in _La Cite des Dames_ the question at issue she writes as follows: "I say to thee again, and doubt never the contrary, that if it were the custom to put the little maidens to the school, and they were made to learn the sciences as they do to the men-children, that they should learn as perfectly, and they should be as well entered into the subtleties of all the arts and sciences as men be. And peradventure, there should be more of them, for I have teached heretofore that by how much women have the body more soft than the men have, and less able to do divers things, by so much they have the understanding more sharp there as they apply it."

Christine de Pisan's statement is virtually a challenge demanding the same educational opportunities for women as were accorded to men. But it was a challenge that men did not see fit to accept until full five centuries had elapsed, and until it was no longer possible to deny giving satisfaction to the long-aggrieved half of humanity. It was also an appeal to experiment and an appeal, likewise, to the teachings of history in lands where women have enjoyed the same educational advantages as men.

Having reviewed the many disabilities which so long r.e.t.a.r.ded woman's intellectual advancement, and considered some of the objections which were urged against her capacity for scientific pursuits, we are now prepared to consider the appeal of Christine de Pisan and deal with it on its merits. This we shall do by a brief survey of woman's achievements in the various branches of science in which she has been accorded the same intellectual opportunities that were so long the exclusive privilege of her male compeer.

FOOTNOTES:

[89] An edition of this work, based on an old ma.n.u.script in La Bibliotheque Nationale of Paris, in French, is announced to appear in France at an early date. An interesting account of this precious volume has recently been published by Mlle. Mathilde Laigle, Ph. D., under the t.i.tle of _Le Livre de Trois Vertus de Christine de Pisan et son Milieu Historique et Litteraire_. It is to be hoped that some enterprising English publisher will soon favor us with a reprint of the quaint old, but none the less valuable, volume, _The Boke of the Cyte of Ladyes_.

[90] Quando la genialita compare nella donna e sempre a.s.sociata a grandi anomalie: e la piu grande e la somiglianza coi maschi--la virilita.

_L'Uomo di Genio_, sesta edizione, p. 261, Torino, 1894.

[91] _An Essay on the Learning, Genius and Abilities of the Fair s.e.x, Proving Them Not Inferior to Man_, p. 142, London, 1774.

[92] Schopenhauer, _Studies in Pessimism_, p. 115, London, 1891.

[93] _The Literary Advantages of Weak Health_, in the _Spectator_ for October, 1894.

[94] _The Life and Letters of Charles Darwin_, edited by his son, Francis Darwin, Vol. I, p. 136, New York, 1888.

[95] _Man and Woman_, p. 94, London, 1898.

[96] Cf. _Das Hirngewicht des Menschen_, pp. 21 and 137, by Theodor L.

W. von Bischoff, Bonn, 1880, and Dr. G. van Walsem in _Neurologisches Centralblatt_, pp. 578-580, Leipsic, July 1, 1899.

[97] _L'Anthropologie_, pp. 336-337, by Paul Topinard, Paris, 1876.

[98] The importance of gray matter in mental processes has evidently been greatly overestimated, for it has been found to be thicker in the brains of negroes, murderers and ignorant persons than it was in the encephalon of Daniel Webster. It is also much thicker in the brains of dolphins, porpoises and other cetaceans than it is in the most intellectual of men.

[99] _The Descent of Man_, Vol. I, p. 145, London, 1871.

[100] The brain of Sonya Kovalevsky was not weighed until it had been four years in alcohol. Prof. Gustaf Retzius then wrote an elaborate account of it and estimated that its weight, at the time of Sonya's death, was 1385 grams. The brain-weight of her ill.u.s.trious contemporary, Hermann von Helmholtz, was 1440 grams. But when the body-weights of these two eminent mathematicians are borne in mind--Sonya was short and slender--it will be seen that the relative amount of brain tissue was greater in the woman than in the man. Cf. _Das Gehirn des Mathematikers Sonja Kovalewski in Biologische Untersuchungen_, von Prof. Dr. Gustaf Retzius, pp. 1-17, Stockholm, 1900.

[101] The reader who desires more detailed information respecting the brain-weights of men and women of various races and the relation of brain-weight to intelligence may consult with profit the following works and articles: _Memoires d'Anthropologie de Paul Broca_, 5 Vols., Paris, 1871-1888; _Alte und Neue Gehirn Probleme nebst einer 1078 Falle umfa.s.senden Gehirngewichstatistik aus den Kgl. pathologisch-anatomischen Inst.i.tut zu Munchen_, von W. W. Wendt, Munchen, 1909; Gehirngewicht und Intelligenz, by Dr. F. K. Walter, Rostok, 1911; _Gehirngewicht und Intelligenz_, by Dr. J. Draseke, Hamburg, in _Archiv fur Ra.s.sen und Gesellschafts Biologe_, pp. 499-522, 1906; _Brain Weights and Intellectual Capacity_, by Joseph Simms, M. D., in the _Popular Science Monthly_, December, 1898, and _The Growth of the Brain_, by H. H.

Donaldson, London, 1895.

[102] "Quand on songe a la difference qui separe de notre temps l'education intellectuelle de l'homme de celle de la femme, on se demande si ce n'est pas cette influence qui retrecit le cervaux et le crane feminins, et si, les deux s.e.xes etant livres a leur spontaneite, leur cervaux ne tendraient pas a se ressembler, aussi qu'il arrive chez les sauvages." _Bulletin de la Societe d'Anthropologie_, p. 503, Paris, July 3, 1879.

[103] _Times_, London, July 8, 1874. Cf. Chap. XVII, on "Adolescent Girls and Their Education," in _Adolescence_, Vol. II, by G. Stanley Hall, New York, 1904.

[104] _The Study of Science by Women in the Contemporary Review_ for March, 1869.

[105] _Die Akademische Frau. Gutachten hervorragender Universitaten-professoren, Frauenlehrer und Schriftsteller uber die Befahigung der Frau zum wissenschaftlichen Studium and Berufe herausgegeben von Arthur Kirchhoff_, Berlin, 1897.

[106] "Ich komme beim Nachdenken hieruber zu der Ueberzeigung, da.s.s kein Gott und keine Religion, kein Herkommen und kein Gesetz, aber ebensowenig die Wissenschaft uns das Recht erteilen, in dieser Beziehung zwischen dem mannerlichen und weiblichen Geschlect einen principiellen Unterschied zu statuiren." _Die Akademische Frau_, p. 41.

[107] _The Subjection of Women_, p. 91, London, 1909.

CHAPTER III

WOMEN IN MATHEMATICS

"All abstract speculations, all knowledge which is dry, however useful it may be, must be abandoned to the laborious and solid mind of man....

For this reason women will never learn geometry."

In these words Immanuel Kant, more than a century ago, gave expression to an opinion that had obtained since the earliest times respecting the incapacity of the female mind for abstract science, and notably for mathematics. Women, it was averred, could readily a.s.similate what is concrete, but, like children, they have a natural repugnance for everything which is abstract. They are competent to discuss details and to deal with particulars, but become hopelessly lost when they attempt to generalize or deal with universals.

De Lamennais shares Kant's opinion concerning woman's intellectual inferiority and does not hesitate to express himself on the subject in the most unequivocal manner. "I have never," he writes, "met a woman who was competent to follow a course of reasoning the half of a quarter of an hour--_un demi quart d'heure_. She has qualities which are wanting in us, qualities of a particular, inexpressible charm; but, in the matter of reason, logic, the power to connect ideas, to enchain principles of knowledge and perceive their relations.h.i.+ps, woman, even the most highly gifted, rarely attains to the height of a man of mediocre capacity."

But it is not only in the past that such views found acceptance. They prevail even to-day to almost the same extent as during the ages of long ago. How far they have any foundation in fact can best be determined by a brief survey of what woman has achieved in the domain of mathematics.

Athenaeus, a Greek writer who flourished about A.D. 200, tells us in his _Deipnosophistae_ of several Greek women who excelled in mathematics, as well as philosophy, but details are wanting as to their attainments in this branch of knowledge. If, however, we may judge from the number of women--particularly among the hetaerae--who became eminent in the various schools of philosophy, especially during the pre-Christian era, we must conclude that many of them were well versed in geometry and astronomy as well as in the general science of numbers. Menagius declares that he found no fewer than sixty-five women philosophers mentioned in the writings of the ancients[108]; and, judging from what we know of the character of the studies pursued in certain of the philosophical schools, especially those of Plato[109] and Pythagoras, and the enthusiasm which women manifested in every department of knowledge, there can be no doubt that they achieved the same measure of success in mathematics as in philosophy and literature.[110]

The first woman mathematician, regarding whose attainments we have any positive knowledge, is the celebrated Hypatia, a Neo-platonic philosopher, whose unhappy fate at the hands of an Alexandrian mob in the early part of the fifth century has given rise to many legends and romances which have contributed not a little toward obscuring the real facts of her extraordinary career. She was the daughter of Theon, who was distinguished as a mathematician and astronomer and as a professor in the school of Alexandria, which was then probably the greatest seat of learning in the world. Born about the year 375 A. D., she at an early age evinced the possession of those talents that were subsequently to render her so ill.u.s.trious. So great indeed was her genius and so rapid was her progress in this branch of knowledge under the tuition of her father that she soon completely eclipsed her master in his chosen specialty.

There is reason to believe--although the fact is not definitely established--that she studied for a while in Athens in the school of philosophy conducted by Plutarch the Younger and his daughter Asclepigenia. After her return from Athens, Hypatia was invited by the magistrates of Alexandria to teach mathematics and philosophy. Here in brief time her lecture room was filled by eager and enthusiastic students from all parts of the civilized world. She was also gifted with a high order of eloquence and with a voice so marvelous that it was declared to be "divine."

Regarding her much vaunted beauty, nothing certain is known, as antiquity has bequeathed to us no medal or statue by which we could form an estimate of her physical grace. But, be this as it may, it is certain that she commanded the admiration and respect of all for her great learning, and that she bore the mantle of science and philosophy with so great modesty and self-confidence that she won all hearts. A letter addressed to "The Muse," or to "The Philosopher"--[Greek: Te Philosopho]--was sure to be delivered to her at once. Small wonder, then, to find a Greek poet inditing to her an epigram containing the following sentiment:

"When I see thee and hear thy word I thee adore; it is the ethereal constellation of the Virgin, which I contemplate, for to the heavens thy whole life is devoted, O august Hypatia, ideal of eloquence and wisdom's immaculate star."[111]

But it was as a mathematician that Hypatia most excelled. She taught not only geometry and astronomy, but also the new science of algebra, which had but a short time before been introduced by Diophantus. And, singular to relate, no further progress was made in the mathematical sciences, as taught by Hypatia, until the time of Newton, Leibnitz and Descartes,--more than twelve centuries later.

Hypatia was the author of three works on mathematics, all of which have been lost, or destroyed by the ravages of time. One of these was a commentary on the _Arithmetica_ of Diophantus. The original treatise--or rather the part which has come down to us--was found about the middle of the fifteenth century in the Vatican Library, whither it had probably been brought after Constantinople had fallen into the possession of the Turks. This valuable work, as annotated by the great French mathematicians Bachet and Fermat, gives us a good idea of the extent of Hypatia's attainments as a mathematician.

Another of Hypatia's works was a treatise on the _Conic Sections_ by Apollonius of Perga--surnamed "The Great Geometer." Next to Archimedes, he was the most distinguished of the Greek geometricians; and the last four books of his conics const.i.tute the chief portions of the higher geometry of the ancients. Moreover, they offer some elegant geometrical solutions of problems which, with all the resources of our modern a.n.a.lytical method, are not without difficulty. The greater part of this precious work has been preserved and has engaged the attention of several of the most ill.u.s.trious of modern mathematicians--among them Borelli, Viviani, Fermat, Barrow and others. The famous English astronomer, Halley, regarded this production of Apollonius of such importance that he learned Arabic for the express purpose of translating it from the version that had been made into this language.

A woman who could achieve distinction by her commentaries on such works as the _Arithmetica_ of Diophantus, of the _Conic Sections_ of Apollonius, and occupy an honored place among such mathematicians as Fermat, Borelli, and Halley, must have had a genius for mathematics, and we can well believe that the glowing tributes paid by her contemporaries to her extraordinary powers of intellect were fully deserved. If, with Pascal, we see in mathematics "the highest exercise of the intelligence," and agree with him in placing geometers in the first rank of intellectual princes--_princes de l'esprit_--we must admit that Hypatia was indeed exceptionally dowered by Him whom Plato calls "The Great Geometer."