This great-grandfather of mine came from Devonshire and had won success as a florist and nurseryman in old New York. I have reason to thank the gods for his diligence, which enabled me to finish my professional training without having to earn my own living. I was an only child, and the first eight years of my life were spent in the Harlem house; my father then entered the Episcopal ministry and for two years had a parish at Walden, an Orange County village. We next moved to the small Hudson River city of Kingston, where I got my high-school training and whence I went to Vassar. It seems to me that my intellectual life began with my fifth birthday.
I remember a few moments when I was walking in the gar-[p. Thinking about myself was so new an experience that I have never forgotten the moment. I was not sent to school until I was seven, but, like many other persons, I cannot remember the time when I could not read, nor when I learned. The first school was a private one kept by the Misses Smuller, the three accomplished daughters of a retired Presbyterian minister who lived in the next house.
It would be hard to find better teaching anywhere at the present time. In my year and a half there I gained, besides the rudiments of arithmetic, a foundation in French and German that saved me several years in later life, and the ability to read music and play all the major and minor scales from memory, a musical grounding that has been the chief aid to one of my greatest sources of enjoyment. When we left New York for the two-years' sojourn in Walden, my school was, though still a private one, much like the district-school type, housed in a single-room building.
I learned very little there: some American history and a little elementary physics. During these two years, between the ages of eight and ten, I wrote stories, of which one or two examples remain. They display no literary talent whatever except a precocious vocabulary, due to my constant reading. A family legend, by the way, was that the subject of this autobiography, aged seven, having had a bad tumble at school and been established as an invalid for the rest of the day, described the behavior of a playmate in the following impressive terms: "And Enid stood rooted to the spot with amazement at beholding me comfortably established on the sofa.
The removal to Kingston came when I was eleven; here I entered a public school. By a blunder I was put into a grade too high for me, and suffered much anguish with arithmetic; in the spirit of M. Aurelius, however, it may be said that this was a piece of good fortune, for, managing somehow to scramble through the Regents' [p. New York State's system of Regents' examinations is, I believe, considered by all enlightened educators as below contempt, but I had much reason for gratitude to it.
The terrifying formalities attending these examinations, where one's teachers with trembling fingers broke the seals on the packages of question papers sent from Albany, and one signed at the end of one's production a solemn declaration of having neither given nor received help, made all subsequent examinations in college and university seem trivial.
What could be more comfortable and less awe-inspiring than being examined by one's own instructors? The curriculum at Ulster Academy covered three years and would deeply distress a modern authority. It consisted of short-term courses in a large variety of subjects, each of which supplied a certain number of "Regents' credits. Our teacher performed some demonstration experiments, of which I can remember only sodium scurrying over the surface of water as a little silver ball and potassium bursting into flame under similar circumstances; also Prince Rupert's drop falling into dust when its tip was pinched; why, we had not the slightest idea.
However, the course in "political economy" firmly fixed in one's mind the rudiments of the theory of supply and demand, and that in "civil government" equipped one with some lasting idea of the structure of state, county, township, and city. We had to learn the Constitution of the United States thoroughly, and a few years ago I was able to impress my colleague of the Department of Political Science at Vassar by answering test questions on it. Passing Regents' examinations in Latin had somewhat the nature of a sporting event. Having read four books of Virgil, we tried the examination on all six, reading at sight the passages from the last two.
Several of us got over this hurdle, and the Aeneid knew us no more. What we lost in literary appreciation was gained in confidence for sight reading. During these years I read in all my spare moments. There was a good library at home and another at the Academy. Scott was read and reread until I was fourteen, Dickens I read until about fifteen years ago, when his world began to seem too remote. That so much reading did no harm to health is shown by the fact that until I was twenty-six I was never ill. We had little in the way of out-door sport except skating, which came naturally to all dwellers by the Hudson.
In the spring of my parents and I made a memorable trip down the Mississippi from St. Louis to New Orleans by one of the old "palatial" steamers, which took a week for the run. I can still hear the call of the man with the lead, repeated from an upper deck and from the pilot-house, "Mark three!
The summer of my fourteenth birthday we went abroad for six weeks spent in the British Isles and in Paris; Walter Scott had made an excellent background for this journey. I entered Vassar in the fall of as a preparatory student, for I lacked some Latin and had had no French since my earliest school days. Miss Smuller had laid so good a foundation that I needed only a semester at Vassar to secure admission to freshman French.
At this time there were no 'majors' in the Vassar curriculum. English, mathematics, Latin, a modern language, physics and chemistry, were required through the sophomore year; psychology, so-called, and ethics in the senior year; there was no requirement of continuity in any other subject. So far as there was continuity in my own studies, it lay in chemistry and French. Professor LeRoy Cooley taught chemistry and physics in crystal-clear lectures: his favorite word was 'accurate,' which he pronounced 'ackerate,' and I have loved, though by no means always attained, 'ackeracy' ever since.
Particularly delightful was quantitative analysis, with the excitement of adding up the percentages of the different ingredients in the hope that their sum might approach one hundred; though the faint suspicion always remained that a particularly 'ackerate' result was due to losing a trace of something here and getting in a grain or two of dust there.
French was admirably taught by two alternately kindly and ferocious sisters, Mlle. Achert and Mme. Guantieri, known to the students as Scylla and Charybdis: from the beginning no English was ever heard in the classroom, an unusual requirement in those days. I am rather glad that I took no courses in English literature. When I was sixteen I began to love poetry, especially Keats, who absolutely bewitched me. Later, through a growing interest in philosophy, Matthew Arnold, with his matchless combination of classic beauty, clear thinking, and deep feeling became my favorite; I wrote my Commencement oration on "The Ethics of Matthew Arnold's Poetry," tracing the Stoic elements in it.
For the love of poetry and philosophy I found in my sophomore year a strong stimulus in an older student who had been a senior in my preparatory year and had returned to college to work for a master's degree. She had been the leader of a brilliant group of girls in the class of '87, whose religious radicalism had distressed President Taylor in his first year of office. I now experienced the mental expansion that comes with dropping orthodox religious ideas, an expansion accompanied by exhilaration.
It consisted of selections of prose from a wide range of masters; at the bottom of each page were detailed questions on the style, which we answered in writing: such as, "Exactly what does each of these metaphors contribute? A wonderful new field was opened in my junior year by a course in biology whose teacher was a young Bryn Mawr Ph. She later married Theodor Boveri, the great authority on cytology, and has now, some years after his death, returned to America and to teaching.
She lectured admirably and drew beautiful figures on the board. In this year, too, I began the study of Greek: Professor Abby Leach was a skillful teacher of its grammar, and brought the little group of my classmates in two semesters to the point where they could join the incoming freshmen who had had two years' preparation. I cherish proudly the scraps that remain, and pity the person who has to master scientific terms with no knowledge of Greek. It was, I think, the summer after my junior year that I read in my father's library Arthur Balfour's Defence of Philosophic Doubt and acquired for a lifetime the conviction that no one has ever succeeded in constructing a logic-proof system of monistic metaphysics.
President Taylor's course in psychology, required in the first semester of all seniors, was based on James Clark Murray's Handbook of Psychology and lectures on the history of philosophy by Dr. Murray's book was directed against the associational school, Dr. Taylor's lectures against materialism.
Murray's argument was that association could not explain the process of active relating, which he called comparison: "association can merely associate. The problem is focal in psychology at the present time, with the believers in 'creative mind,' vitalism, voluntarism, and so forth on one side and the mechanists on the other: I firmly believe that it can be solved by mechanism, but not that of the old associative type.
Taylor's attacks on materialism were made, not from the idealistic point of view, but from that of 'natural realism,' originating with Reid and still being defended in those days by President McCosh of Princeton. Taylor whom, by the way, we regarded with great affection had no idea of presenting metaphysical systems to us impartially: he wished to preserve our religious convictions by saving us from materialism in the one direction and pantheistic idealism in the other.
This vigorous special pleading was more stimulating than the most conscientiously impartial presentation of opposing views could have been. At the end of my senior year I had two dominant intellectual interests, science and philosophy. They seemed to be combined in what I heard of the wonderful new science of experimental psychology. Learning of the psychological laboratory just established at Columbia by Dr. Cattell, who had come a year before from the fountain-head, the Leipzig laboratory, I determined to be his pupil, and my parents took a house in New York for the year.
But Columbia had never admitted a woman graduate student: the most I could hope for was to be tolerated as a 'hearer,' and even that would not be possible until after Christmas when the trustees had met. I solaced myself by taking the School of Mines course in quantitative chemical analysis at the Barnard laboratory, the second floor of a brownstone house on Madison Avenue. President Butler was then the amazingly efficient young dean of the department of philosophy, and, at his suggestion, I read Wundt's long article on psychological methods in the first volume of Philosophische Studien ; having had only a year of German, I began by writing out a translation of it, an excellent [p.
After Christmas I was allowed to present myself to Dr. Cattell for admission as a hearer. The psychological laboratory was the top floor of the old President's House on Forty-ninth Street close to the New York Central tracks. Cattell, who looked then just as he does now, barring the grey hair. I blessed the hours I had spent on W. Wundt's article: instead of speaking as I am sure I was expected to do, of hypnotism, telepathy, and spiritism, I referred to reaction-time, complication experiments, and work on the limens and Weber's Law, and was rewarded by the remark that I seemed to have some knowledge of the matter.
From that time Dr. Cattell treated me as a regular student and required of me all that he required of the men. A lifelong champion of freedom and equality of opportunity, it would never have occurred to him to reject a woman student on account of her sex. The four men students, seniors, and I listened to his lectures, prepared reports on experimental work, and at least one paper on a theoretical subject. He assigned to me the experimental problem of finding whether Weber's Law held for the two-point threshold on the skin.
I improvised apparatus, used a metronome to keep the duration of the stimuli constant, and found observers among my Barnard associates. Incidentally, it may be mentioned that Weber's Law does not hold for the two-point threshold. I also exchanged hours of observation with Harold Griffing, the only graduate student, who was engaged on his thesis, On Sensations from Pressure and Impact.
He was a man of great promise, heavily burdened with the support of his invalid mother and sisters; he died a year or two after taking the doctorate. He would have been a leader in American psychology. Cattell raised me to the height of joy after I had read a paper on the relation of psychology to physiology by writing me a note to suggest that I send it to the Philosophical Review. Nothing would have induced me to do anything so daring.
J. Paul Rodker Morrison
At the end of the year, since there were no fellowships at Barnard, he advised me to apply for a graduate scholarship at the newly organized Sage School of Philosophy at Cornell. I feel an affectionate gratitude to him, as my first teacher, which in these later years I have courage to express; in earlier times I stood too much in awe of him. While I was thus being initiated into Cattell's objective version of the Leipzig doctrine, the influence of William James's Principles was strong. His enthusiasm for the occult was unattractive; it [p.
But his description of the stream of consciousness, and the consistently analytic rather than synthetic point of view which he maintained in holding that simpler mental states are products of analysis, and in developing all spatial relations by analysis from a primitive space instead of compounding them like Wundt out of non-spatial elements, never lost their effect even though the prestige of the Leipzig school increased. I went in the fall of to Cornell, where Titchener had just arrived from Oxford and Leipzig. He was twenty-five, but seemed older at first sight because of his square-cut beard; the illusion of age vanished on acquaintance.
There was nothing about him at that time to suggest either his two greatest gifts or his chief failing in later life. The gifts, in my opinion, were his comprehensive scholarship, shown conspicuously in his Instructor's Manuals of Experimental Psychology ; and his genius as a lecturer. In his first two years at Cornell his lectures were read, and were frankly after the German fashion: we regarded him as a brilliant young man who would give us the latest news from Leipzig, rather than as one to be heard for his own sake.
The failing that later grew upon him was that of remaining isolated so far as his immediate surroundings were concerned from all but subordinates. In these first years he was entirely human. He once asked me to look over some proof; finding a sentence whose meaning was obviously inverted, I asked, "Didn't you mean" so-and-so? I was his only major graduate student, and experimental psychology was so young that he did not quite know what to do with me.
Appointments for planning laboratory work would be made which often ended in his telling stories of Oxford life for an hour or two. He finally suggested that since I had some experience in work on tactual space perception, I should make an experimental study of the method of equivalents. I wrote up the results in a paper which was accepted in June at Vassar for an M. The paper was next year incorporated into my doctor's thesis, and was resurrected a few years ago by Gemelli in his study of the method.
The Sage School of Philosophy was an inspiring place to work, for [p. I chose as my minor subjects philosophy and ethics. President Schurman taught the advanced course in ethics. He had visited Vassar in my senior year and given several lectures on Herbert Spencer, which it was my privilege to report as a college editor. They were models of clearness and force.
I have always greatly admired him, and it is a keen pleasure to read of his diplomatic triumphs at an age when most men are resting on earlier laurels. To be his pupil was a privilege. Read of Colgate, and Louise Hannum, a remarkably able woman who afterwards taught in Colorado. The opportunity was a good one, but I think I was wise in deciding to finish my work for the doctorate at Cornell, although Dr. Schurman disapproved of the decision. In my second year at Cornell I was no longer Titchener's only major student, being joined by Walter Pillsbury from Nebraska; this is an association of which I have always been proud.
I had, during my work with the method of equivalents, thought of a subject for a doctor's thesis: the influence of visual imagery on judgments of tactual distance and direction. Much of my time this year went to the thesis. I had also a course in Lotze's metaphysics with F.
Schiller, who had come from Oxford for a year's stay in the wilderness and was even then a very distinguished man. My years in England and, to a slighter extent, term at Gottingen had constituted almost the first true my relief I had found from the intensity of our home life and my parental pressure.
Johann Sebastian Bach
My earlier research training had been primarily English and, to a lesser extent, German. The friendly recognition which I had already begun to find in Europe contrasted sharply with the sense of rejection which I had experienced around Harvard. At the English universities, it is true, there is a certain gentleman's pretense that one is an amateur and not too deeply concerned in the hard and grinding work of scholarship.
TTiis was generally understood to be a pose. It did not require any great insight to see that those very men who conformed to the. At Har-. The typical Har-. The effort of trying to be a gentleman vard. Here the strong hand of the family could scarcely reach me. But there was still another reason why the trip tempted me: the coming Internato the relative. Mathematical Congress at Strasbourg. Normally, in all fields of science, it has been the custom, say every four years, for those working together in a major subject like mathematics or physics or chemistry to foregather in some tional.
The last International Mathematical Congress before the war had taken place in England in , at Cambridge. The congress which was to have taken place in was clearly impossible and was allowed to go by the board. The next one, in , did not find any adequate machinery established for its organization. France decided to step into the gap and cele-. This had be-. The Germans were excluded as a sort measure. In my mature, considered opinion, punilittle.
Perhaps it would have been impossible to hold a truly international meeting for another couple of years, but this tions. European scholar in whose field I was interested. The scholar I chose was Maurice Fr6chet, It was Fr6chet more than anyone else who had seen what was implied in the new mathematics of curves rather than of points, the field of which I have spoken in the last chapter. At that time we all had great expectations that his work was to mark the next great step towards the mathematics of the future.
It is. My training with Russell and my later contact with the work of Whitehead had sensitized me to the use of formal logical tools in mathematics, and there was much in Fr6chet's work which was suited from the very beginning to be embodied in the peculiar and highly. The geometry of the Greeks went back to certain initial assumptions, known variously as axioms or postulates, which were conceived to be unbreakable rules of logical and geometrical thought.
Some of these were of a predominantly formal and logical character, such as the axiom that quantities equal to the same quantity must be equal to each other. Another, with a more purely spatial content, was that known as the parallel axiom, which asserts that if we have a plane containing a line I and a point P not on that line, then through P and in that plane one and only one line can be drawn that will,. This postulate does not have the simple obviousness of the purely logical postulates of mathematics. And generations of. In the eighteenth century the Italian mathematician Saccheri spent a considera-.
He did. In fact, this. From that time on it came that the so-called clearly understood mathematical sciother of of postulates geometry, and indeed. They came to be regarded as assumptions which we could make or refuse to make con-. Whitehead had been perhaps the chief English postulationbut he supplemented a pure postulationalism with the view that the objects of mathematics were logical constructions alist,. For example, at times he regarded a point as the set of all convex regions which in our ordinary language might be considered to contain this point.
As a matter of fact, Hunting-. But the classical example of constructionalism in mathematics is the definition of the whole numbers which occurs in the Principia Mathe-. Whitehead and Russell is that in postulationalism the numbers are undefined objects which are connected by a set of assumed formal relations and specific things which can be built up out of our experience by definite modes of combination of even more elementary experience.
A postulationalist treatment of numbers makes them simply objects to be arranged in a beforeand-after relation so that if a is before b and b is before c, a is before c, and every number other than o has another number immediately before it, and so on. These are some of the postulates in such a treatment of the number system. In the constructionalist treatment of numbers, a unit set is all of which are the same. The number. A diad is a set of entities is not a unit set but which becomes a unit set on the.
Three is the set of all triads. In this way, and by the. To the layman all of this will perhaps sound rather like empty logic chopping. Have we not in fact used the numbers i, 2, and 3 in only a slightly obscured form when we built up these definitions of the earlier. I had indeed already written two or three essays in the application of this technique to the construction of certain elementary mathematical situations. Postulationalism in particular is shared by physics.
Nevertheless, the cold, hard medium of logic, like the cold hard medium of marble, imposes a certain internal. When I looked for a French scholar with whom to study, I looked for one whose work might embody one or both of these two directions of thought. As far as these demands were concerned, Frchet had no rival among French mathematicians. So far I have spoken of the new direction of thought largely from the Anglo-American point of view. In Germany, too, there had been some early exponents both of postulationalism and of constructionalism, and here the leading and most original names were those of G.
Frege and Schroder. France, on the other hand, was rather late to adopt these newer habits of thought, but, as far as France had gone in postulationalism, Fr6chet was the unquestioned leader. I myself had made one or two not completely unsuccessful attempts to supplement Fr6chet's postulationalism as a tool for the study of new and more complicated spaces of curves by means of a construedition.
His first plans had been to spend his holidays in B6arn, on the Spanish border. Later, however, he changed his mind and invited me to come and work with him, first in Strasbourg, and then in a little country village in Lorraine which has the German name of Dagsburg and the French. However, the gin-soaked twenties were already upon us, and I found that my friends' ideas of what was becoming on an ocean voyage were incompatible with my rather puritanical personal habits. I had never been a teetotaler. I enjoyed the wine we had with our meals on the boat, which I diluted plentifully with water.
On the other hand, I did not like distilled liquors, and I protested vigorously against the convention under which my ac-. Thus, I was not happy on the boat and I made no friends. I was eager to land and to get away from my. But before we landed we had an interesting and not altogether pleasant experience of another sort.
It had been an overcast voyage, and we were unable to shoot the sun for several days. We were going full speed ahead by dead reckoning, for these were the days in which wireless was simply a means of communication rather than an aid to navigation through an. The engines were set full speed accurate system of cross bearings. Water came in to the steerage compartment. I am told that there were the beginnings of a panic. This was controlled by the ship's officers together with a French prize-fighter passenger whose prestige was enough to keep order.
We were all sent down to our quarters to put on our life belts. It was not pleasant coming up on deck again in the midst of the milling crowd.
- El retorno de los soldados (Fantasía) (Spanish Edition);
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- Detlev Wulf Bronk | Biographical Memoirs: V | The National Academies Press.
- Creative Writing Prompts to Feed the Imagination.
I felt that I would like to be on deck as. I forced myself to. The ship's so that they did in fact hold throughout our trip across the channel to Le Havre. But still we were ordered to spend the. I remember that somebody dropped a bottle by my head as I slept. There was mail awaiting me on shore. I learned that Frechet. At Cambridge I found some old friends waiting for me. I stayed with Dr.
Bernard Muscio, a couple of Aus-. I looked up a number of other acquaintances, including Hardy, who was about to leave Camtralian psychologists. I had not reception been matriculated at Cambridge, as I had gone there on the basis of a special arrangement with Harvard University, per-. Under the circumstances, she said, the best that I could call mitting I. At any rate, I have found Alma Mater more than ready to accept her by-blow into the family. After a few days I left for Paris, where I stayed in a cheap hotel with unbelievably bad sanitary accommodations near the Louvre.
I did not find my vegetarianism much in my way in. France, for there was a wealth of cheap restaurants with good and appetizing vegetable dishes. I had no friends in Paris, nor was my French at that time more than barely usable. Moreover, the Paris caf6 and street life shocked my youthful puritanism, and I was profoundly homesick and unhappy. It seemed to me as if the house doors of a great city were. He was a mustached, sinewy, athletic man of medium height.
He had served in the French army as an interpreter for the British, and he was as enthusiastic for walks and tours as I was. I found my friends in their fine old house in Louvain, which had just been restored from the disorder and filth in which it had been left by the German officers who occupied it during the war, but my trip was badly settle.
Thus my entertainment was largely a matter for the children, and in particular for a young son of the family who had just completed a year at the Harvard Law School. He took me about the burned and ruined town and showed me the remains of the library, the town hall, and the nave of the church, half blocked with scaffolding. He also took me on various walks about the countryside and gave me his Harvard and.
He did not like the case system. I settled in. In the co-ordinate representation of space, any two points at the ends of a line interval are measured by the difference between corresponding numbers at one terminus and at the other. In ordinary geometry of two or of three dimensions, this method of representing a line segment is known as its vector tried to extend. Frechet's treatment of. For example, given one point in three-dimensional space, I can locate another with respect to it by saying. The theory of vectors is not new in mathematics.
For well over a century and a half it has been known that an ordinary space of three dimensions contains in itself directed quantities which can be added. It is beside the point here like arrows,. Frechet's generalized theory of limits and of differentials vector spaces, but is applies to many sorts of spaces, including not necessarily confined to those spaces in which the elements.
This was the task which I had performed. It was very closely allied to the theory of the combination of successive transformations which is known as group of theory, and in fact it constitutes a significant chapter that theory. But then, a few weeks later, he became quite excited when he saw an article published by Stefan Banach in a Polish mathematical journal which contained results practically identical with those I had given, neither more nor less general.
Banach's conception of his ideas and his publication of them were both a few months earlier than my own. There had, however, been no chance for communication between us, and the. Thus the two pieces of work, Banach's and my own, came for a time to be known as the theory of Banach-Wiener spaces. For has remained a popular direction of work. For a short while I kept publishing a paper or two on this topic, but I gradually left the field. At present these spaces are quite justly.
There were several motives which led me to abandon this brain child, of whom I was at least one of the parents. The first was that I did not like to be hurried or to watch the literature day by day in order to be sure that neither Banach nor one of. All mathematical work is done under sufficient pressure, and its increase by such a fortuitous competitive element is intolerable to me.
But the important reasons for my accepting or rejecting any specific piece of work have to do with the much-neglected field of mathematical aesthetics. To ask exactly what I mean by this.
Classics in the History of Psychology -- Washburn ()
I shall have to tell him my reasons for rejecting certain problems which have proved interesting to other people for a considerable number of years but do not seem to me to offer the. This leads to a problem which must be faced in one form or other by any autobiographer who has done significant work in. The writer or the painter is no less involved in he problem goes in for autobiography. He may seem to address himself to the educated layman who can appreciate the results of his creative work.
However, he has not completely performed the task of the autobiographer unless at the same time he has managed to express himself concerning those tasks of writing and of painting which can be fully appreciated only by the man who himself has faced them on a high professional cal composition. He is further aided by the fact that,. If the general public ever thinks of mathematics, it sees it at best as a tool for the physicist.
Hardly any non-mathematician will admit that mathematics has a cultural and aesthetic appeal, that it has anything to do with beauty or power or emotion. I categorically. To other mathematimatics. To be free to do. It is quite possible to imagine a community of musical composers whose primary sat-. They might well be relatively indifferent to the performance of these scores at concerts attended by those capable of understanding them only through the vaguer isfaction will arise.
That the mathematician displays this aloofness from his is. At least part of my motive in writing this book is to call the attention of the public at large to the existence of this more limited public of amateur mathematisufficient. Nowadays of the theory of Banach space are taking on a sufficiently rich texture and have been endowed with a sufficiently unobvious it. By this I do not mean to reproach the work of Banach himself but rather that of the many inferior writers,. Differential space, the space of the Brownian motion, is itself in fact a sort of vector space, very close to the Banach spaces, and it presented itself as a successful rival for my attentions because it had a physical character most gratifying to me.
In addition, it. I do not believe that Fr6chet appreciated the importance of. Polytechnique, then the most promising young probabilitytheory man in France, whose work and mine have exerted a mutual influence on each other up to the present time. It cost. He was to become one of my closest friends and supporters. Curiously enough, another colleague whose work has always been in the closest relation with Levy's and mine was the Swedish mathematician Cramer, whom I had met during my stay in England as another house guest at the Muscios' that summer. For some time my mathematical interests made me oblivious.
When I came to sufficiently to think my environment, I found that I was lonely at my boardingwho had come over with who had no high opinion of me. I wanted this composer to like me, but I had started off on the wrong foot. My fellow passenger of La Touraine certainly did nothing to help.
The musician regarded me as heavy-handed and Philistine. This was partly because of my actual social ineptitude and bad manners, but it was also due to the fact that he considered that mathematics by arts. Later on hate initially disposed an we got into explicit quarrel, in which we really said the un-. The landlord and landlady of my inn were very considerate. I did occasional jobs of wood chopping and the like for them. I felt at home in the countryside, among the crowing of. I enjoyed the sound of the water trickling down the village street to the place where the.
Three young American friends of mine came for the meeting. We put them up in my boardinghouse, two to a room. One was Forrest Murray of Harvard, vague and amiable, with whom I had often played tennis, and who had been a friend of our. Walsh accompanied him. Joe, who was about my age, is still a professor in the Harvard mathematics department.
He is tall and genial, and in those days his blond hair stood almost erect on his high forehead. He seemed family for. He intended to stay in France for a year of postdoctoral study. His deep, booming. The fourth of our group was James S. Taylor, then like my-. Barnum and was himself an enthusiastic showman of parlor tricks. The four of us have gone very different ways since, but at that time we were all united by youth, and we were tasting this youth to the full. The congress guests began to roll in.
From America there came Eisenhart from Princeton, with his beautiful young wife; Leonard Eugene Dickson, the number theorist of Chicago, famous as an enthusiast for France and the French, and a past master at bridge; and Solomon Lefschetz of Kansas, who had conquered the effects of a terrible industrial accident which he had suffered as engineer with the Westinghouse Company at Pittsburgh and had entered upon the new career in mathematics which was to take him to the leadership of the mathe-.
There were several of the older people at the meeting whom connecting us with the great past of mathemat-. Sturdy old Sir George Greenhill represented Woolwich.
Camille Jordan, who for all his ninety years accompanied us on. His recollections dated back to the great days. When Jordan died, two years later, we all felt his death as a break in the continuity of the mathematical tradition. Professor Jacques Hadamard, of Paris, played a great part at the congress. He was then only in his middle fifties, but his reputation had been well established before the end of the. Small, bearded, very Jewish-looking in the fin. French way, he occupied a unique position in the affections of younger colleagues.
English mathematics belongs to Oxford and Cambridge, where there are ample bonds between the undergraduate and the don; while German mathematics is characterized by the his. The official discussion of a scientific paper is followed by a procession across the university town to a beer garden, where the great and the little alike talk over the latest results in mathematics as well as the trivial pleasures of life. French mathematics, however, has followed a. To this withdrawn existence, Hadamard forms an exception, for he is genuinely interested in his students and has always been accessible to them.
He has considered it an important largely official course,. Under his personal influence, the present generation of French mathematicians, for all the tradition of a barrier between the younger and the older. There was no reason why Hadamard should have paid any I. The French soldiers took us there in army trucks, but on the way back the trucks broke down and we had a long and tedious wait.
Thus, when. We had to sip these as a matter of courtesy. I will not deny that the wine was excellent, but two glasses on an empty stomach represent a severe ordeal, and new wine has a potency of its own. As we continued to Strasbourg by truck and by train, some staid souls were a bit less inhibited than was their wont. Soon the meeting was over and the four of us went back to Paris. Taylor was to return to America with me, but my other two American friends had decided to spend a year studying in Paris.
They were eager to immerse themselves in a thoroughly French environment, and they made it quite clear that we should confer on them no favor by continuing to forgather with. The remaining two of us found ourselves without return accommodations. La Touraine, on which I had come to France and on which we had intended to return, had not yet recovered from its near shipwreck, so all through a very autumnal September and part of October we waited in vain for the resumption of service, believing to the very last that we should be back for the beginning of the M.
This however was impossible. We haunted the shipping agencies and finally heard of tardiness. The passenger list was small and interesting and con-. The travelers Osa Johnson and her husband were on board, together with a tame orangutan that they had brought from Indonesia. This orangutan contrasted pleasantly in its cultured behavior with a demon child who insisted on scattering the chessmen with which we were playing in the smoking room. I came back from Europe with renewed and enlarged inFor all of the defects of I had lived in my French, spiration. France and had for the first time established a contact with my French colleagues.
Both in France and in England I had found that I occupied a more important position than at home, and I had work pending which seemed at least to myself, if to few others , the promising beginning of a career in mathesisted largely of old globe-trotters. I had, however, become aware that the European spirit had greater possibilities of recuperation than I had previously assumed. Notwithstanding the war in the West, the defection of Russia from the European camp, and the news of battles in Poland, I.
As to Russia and the incipient iron curtain, the great body of Russians of the time were not merely prerevolutionary but. In one way or another, my taste for European contacts had grown with its own satisfaction. I was eagerly awaiting my next opportunity to see something more of the mother continent of. I showed my results to Professor E. Wilson, of the Massachusetts Institute of. Professor Wilson, who is now retired from teaching but still active in scientific administration, had been a pupil of Cibbs at Yale and had taught mathematics for some years at M.
There he was teaching physics in , and ultimately he came to be the mathematical specialist at the Harvard School of Another direction from which I received much encouragement was that of the department of electrical engineering, where Professor Dugald C. Jackson was head.
I had known Professor Jackson and his son as neighbors when both of us had. Jackson had an engineer with mathematical sense, or for a mathematician with engineering sense, to resolve. Most of the types of electrical generators, motors, and transformers which now exist were already thoroughly understood by that date; and the present trend towards the fractional horsepower motor and the separately motored machine were well under way. What progress has been. The great power nets in the United States. As to communication engineering, the situation was stabilized much later.
Wireless had been an established art for twenty years, but for the most part this was wireless in the limited original sense in which Marconi had conceived it. Broadcasting was yet to come on a national scale, and the few. The electronic valve had indeed arrived, but there. Television was not a new concept, for people had talked of television even before the beginning of the cenin which it was tury, but it was just emerging from the stage conceived in terms of the selenium.
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The telephone, indeed, was triumphant everywhere, and was extending around the world the tentacles of a tight communication net. In the United States the A. It was of course understood that speech is carried on a telephone line by a fluctuating current whose. The great problem to understand the full implications of the theory of fluc-. For several decades, the theory of fluctuating currents and voltages had dominated not only communication engineering. The ordinary direct, continuous current is rather intractable. There are no simple means to step its voltage.
This brilliant and eccentric Yugoslav and converted engineer worked for the Westinghouse people current not in a continuous them to the policy of generating. It can be used in various types of motors, including certain sorts of induction motors entirely free from sliding elecit. As a matter of fact, in certain forms of the induc-. The electrical current which magnetizes the iron of the rotor is produced by the simultaneous action of the rotor and the fixed part, or stator, as an electromagnetic transformer.
Such a piece. This quarrel had as one of its consequences the fact. This was the result of a deal put through the legislature in order to give a bad name to the more. Before long, however, the quarrels between the two schools of electrical engineering.
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This brilliant little. The reason for introducing complex numbers into the engineering of alternating currents is that each complex number really consists of a pair of real. For many years the theory of alternating-current engineering has been pretty complete, at least as far as concerns currents and voltages of fixed frequency, such as sixty-cycle currents.
In telephone and other communication engineeralso deal with a sort of alternating current, but this ing alternating current is far more complicated because its fre-. A telephone line carries at the same time frequencies of something like twenty per second and frequencies of three thousand. It is precisely this variability and multiplicity of frequency which makes the telephone line an effective vehicle of information. The line must be able to carry everything from a groan to a squeak. Here we are concerned with one of the most ancient branches of mathematics, the theory of the vibrating string, which has its roots in the ideas of the Greek mathematician Pythagoras.
To what extent the Greeks were aware that a single string can vibrate in several. Let us now consider more complicated curves, made up by adding sinusoids. It is possible to add curves to one another by adding their displacements, that is to say, by combining two tuning forks of different rates of oscillation so that they both act on the same straw as it traces its path along a drum of. The study of how to break up various sorts of curves into such sums of sinusoids is called harmonic analysis. There is a fundamental theorem that says that if we have a curve which repeats the same form indefinitely it can be broken this.
While results of this sort were. French Academy of Sciences who accompanied Napoleon on his expedition to Egypt. Fourier's name is also connected with other. We may indeed have to add a curve, mass of sinusoids which is entirely too dense to be arranged in. In both cases the mathematician is forced to use the sophisticated methods of adding quantities to which we have already referred under the name of Lebesgue integration.
Moreover, the sort of phenomenon in which the engineer is chiefly interested had almost entirely escaped the treatment of the pure mathematicians. The Fourier series,. The standard form of the theory of the Fourier integral, as developed by Plancherel and others, concerns curves which are small in the remote past and are destined to become small in the remote future. In other words, the standard theory of the Fourier integral deals with phe-.
The sort of continuing phenomenon that we find in a noise or a beam of light had been completely neglected by the professional mathematician, and had been left to such mathemati-. I came to understand that the various demands made on me by Professor Jackson concerning the proper foundation of com-. What the communication engineers actually did was to use a formal calculus of communication theory which had been developed. This Heaviside calculus had not as yet been given a thoroughly rigorous justification, but it had worked for Heaviside and for those of his followers who had absorbed the spirit of his theory sufficiently to use.
For several years the chief demand made on me at M. Other people were doing the same thing at the same time in other countries, although I do not think that any of these treatments were more satisfactory than the one which I ultimately gave. In performing this task, I had to study harmonic analysis on an extremely general basis, and I found out that Heaviside's work could be translated. Previous to my work there had been no thoroughly satisfactory example given of the sort of motion that would correspond to sound or light with a continuous spectrum that In.
The harmonic analysis which had already been given corresponded more closely to what one sees when one examines the light of sodium vapor than what one sees when one examines sunlight. The light of sodium vapor is concentrated in a number of bright lines, whereas sunlight has a continuous distribution in color and is,. In Chapter i I pointed out my work on the mathematics and physics of the discrete, and in particular of the Brownian motion, in which.
In other it. Now, almost thirty years later, communication theory is thoroughly statistical, and this can be traced directly back to my work of that time. There were other problems which occupied me, some intensively and some in a more or less desultory way.
Aberdeen Proving Ground days. Kellogg of Harvard concerning problems of possible interest on which I might do research. I did not realize at that time how carefully many professors conserve problems for their own graduate students and how sharply they regard proprietary rights in new problems. I had been used to the freer atmosphere of England and to the lavish manner in which my father had scattered the I. It would be of no to the problem here explicitly, but it is quite possistate point ble to tell the layman what sort of a problem it is. There are tribution. The temperature in a room is such a quantity, and there are certain other similar quantities.
Ever since the time of Leibnitz it has been well known that there are quantities distributed both in time and in space; and that they have space rates of change as well quantities fall off in different directions. Again, if water is flowing downhill, the steeper the. Many quantities thus distributed in space and in time are of great engineering importance. It is the rate at which the local electromotive force. The study of the tricity. In that part of a room. However, when we come to the immediate neighbor-. Near these regions, which are known.
In the case of the electrostatic potential, one particular boundary phenomenon is exhibited by the sharp-pointed conductor, such as the lightning rod. Around such a sharply-pointed conductor projecting into a region in which there are electric. The electric field will not. Many sailors. It is through this corona effect that a lightning rod relaxes.
The ability to stand up to these stresses is known as the dielectric strength. So far I have been stating the problem of the pointed conductor in a physical way, depending on the specific dielectric strengths of the different media into which the conductor may be pointed. There are however closely related problems of a. We here come to one of those mathematical situations in which there is a close relation between mathematical and physical ideas but in which the correspondence between the two not precise.
All physically pointed objects are like the point of a needle that is very slightly rounded off at the end. It is is. Impossible as it is to realize such a figure physically, its conception offers no mathematical difficulty whatsoever. It is even possible to consider an electrical potential distributed about such a re-entrant spike and to ask how such a potential would behave near the very.
It will be found that there are cases where the mathematical behavior of potential around this ideal spike will be strongly suggested by the actual behavior of potential about a very sharp physical spike. In the physical case the strains become so great that the matter in the field breaks down.
In the mathemat-. It was this phenomenon which I started to investigate at Kellogg's suggestential at the point of the spike. Polish mathematician by the name of Zaremba had obtion. In this intermediate field Professor Kellogg had done vitally important work, and two of his young friends were writing doctoral dissertations on the subject at Princeton. Alterations in the respiratory enzyme of the mitochondria of growing and resting yeast. In: Aspects of Yeast Metabolism, ed. Mills, pp. Oxford: Blackwell Scientific Publications. The regulation of glycolysis and gluconeo- genesis in animal tissues.
In: Current Topics in Cellular Regulation, vol. Horecker and E. Stadt- man, pp. New York: Academic Press. Rose, E. O'Connell, P. Noce, H. Wood, I. Wil- lard, T. Cooper, and M. Stereochemistry of the. Irias and M. Revers- ible inactivation by cold. FEES Symp. In: Citric Acid Cycle, ed. Low- enstein, pp. New York: Marcel Dekker. Pyruvate carboxylase from bakers' yeast. The presence of bound zinc. Possible control mechanisms of liver Pyruvate carboxylase.
Regulation of gluconeogenesis, 9th Conf. Soling and B. Willms, pp. Fung, and M. Pyruvate car- boxylase from chicken liver. Steady state kinetic studies indicate a "two-site" ping pony mechanism. With B. Taylor and R. Identification of the reacting form of Pyruvate carboxylase. Formation of oxalacetate by CO2 fixa- tion on phosphoenolpyruvate.
The Enzymes, 6: The removal of nucleic acids from microbial extracts by precipitation with lysozyme. Taylor and S. The control of the synthesis of Pyruvate carboxylase in Pseudomonas citronellolis. Decarboxylation of oxalacetate to pyruvate by pur- ified avian liver phosphoenolpyruvate carboxykinase. Taylor, F. Isohashi, W. Frey II, G. Zan- der5 and J. Structural properties of pyruvate carbox- ylase from chicken liver and other sources.
USA, 72 Barden and B. Pyruvate carboxylase: An eval- uation of the relationships between structure and mechanism and between structure and catalytic activity. Barritt and G. The regulation of pyruvate carboxylase activity in gluconeogenic tissues. In: Gluconeogene- sis, ed. The biochemistry of manganese. Frey II. Binding of acetyl-CoA to chicken liver pyru- vate carboxylase. O'Brien, D. Chuang, and B. Novel enzymic machinery for the metabolism of oxalacetate, phosphoenolpy- ruvate and pyruvate in Pseudomonas citronellolis.
Gluconeogenesis as a compartmentalized ac- tivity. Swack and G. Use of avidin-sepharose to iso- late and identify biotin polypeptides from crude extracts. Leiter, M. Weinberg, and F. Relationship be- tween phosphorylation and activity of pyruvate dehydrogenase in rat liver mitochondria and the absence of such a relationship for pyruvate carboxylase. Taylor, W. Frey II, and M. The use of. Atkin and M. Pyruvate carboxylase and phosphoenolpyruvate carboxykinase activity in leukocytes and fibroblasts from a patient with pyruvate carboxylase deficiency. Atkins, M.
Buist, and A. Pyruvate carbox- ylase deficiency in a retarded child without Leigh's Syndrome. With N. Cohen, H. Beegen, and N. A re-examina- tion on the electron microscopic appearance of pyruvate car- boxylase from chicken liver. Cohen, N. Wrigley, and A. Quaternary structure of yeast pyruvate carboxylase: Biochemical and elec- tron microscopic studies. Cohen, I. Duc, and H. Quaternary structure of pyruvate carboxylase from Pseudomonas citronellolis. Eject of thyroid hormone on the turnover of rat liver pyruvate carboxylase and pyruvate dehydrogenase.
I Biol. Structural and regulatory properties of pyru- vate kinase from Pseudomonas citronellolis. Introduction of pyruvate carboxylase apoen- zyme and holoenzyme in 3T3-L1 cells during differentiation. USA, EEect of streptozotocin-induced diabetes mellitis on the turnover of rat liver pyruvate carboxylase and pyruvate dehydrogenase. Biochemical mechanisms of biotin and thiamin action and relationships to genetic disease. Desnick, pp. New York: Alan R. Liss, Inc. Prass and F. Purification and characterization of an extramitochondrial acetyl-coenzyme A hydrolase from rat liver.
Sheu and C. Pyruvate dehydrogenase com- plex activity in normal and deficient fibroblasts. With S. Freytag and M. Regulation of the synthe- sis and degradation of pyruvate carboxylase in animal tissue. Baltimore: University Park Press. Goss and N. Characterization of the subunit structure of pyruvate carboxylase from Pseudomonas citronellolis. Watford, Y. Hod, Y. Chiao, and R. The unique role of the kidney in gluconeogenesis in the chicken. The significance of a cytosolic form of phosphoenolpyruvate carboxykinase.
The enzymatic synthesis of some potential pho- toaffinity analogs of benzoyl-coenzyme A. Hod and R. The mitochondrial and cytosolic forms of avian phosphoenolpyruvate carboxykinase GTP are encoded by different messenger RNAs. Hu and M. Induction of pyruvate dehydro- genase in 3T3-L1 cells during differentiation. Regulation of the synthesis and degradation of pyruvate carboxylase in 3T3-L1 cells.
Myers and B. Activation of yeast pyruvate car- boxylase: Interactions between acyl coenzyme A compounds,. Sheu, H. Ho, L. Nolan, P. Markovitz, l. Richard, and P. Stereochemical course of thiophosphoryl group transfer catalyzed by mitochondrial phosphoenolpyruvate car- boxykinase. Biographic Memoirs Volume 56 contains the biographies of deceased members of the National Academy of Sciences and bibliographies of their published works.
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