Physicians From Italy

"The first epoch-making algebra to appear in print was the Ars Magna of Cardan (1545). This was devoted primarily to the solution of algebraic equations. It contained the solution of the cubic and biquadratic equations, made use of complex numbers, and in general may be said to have been the first step toward modern algebra."

"Most of his analysis of cubic equations seems to have been original; he shewed that if the three roots were real, Tartaglia's solution gave them in a form which involved imaginary quantities. Except for the somewhat similar researches of Bombelli a few years later, the theory of imaginary quantities received little further attention from mathematicians until John Bernoulli and Euler took up the matter after the lapse of nearly two centuries. Gauss first put the subject on a systematic and scientific basis, introduced the notation of complex variables, and used the symbol i, which had been introduced by Euler in 1777, to denote the square root of (-1): the modern theory is chiefly based on his researches."

"The Ars Magna is a great advance on any algebra previously published. Hitherto algebraists had confined their attention to those roots of equations which were positive. Cardan discussed negative and even complex roots, and proved that the latter would always occur in pairs, though he declined to commit himself to any explanation as to the meaning of these "sophistic" quantities which he said were ingenious though useless."

"In 1570 he was imprisoned for heresy on account of his having published the horoscope of Christ, and when released he found himself... generally detested..."

"After spending a year or so in France, Scotland, and England, he returned to Milan as professor of science, and shortly afterward was elected to a chair at Pavia. Here he divided his time between debauchery, astrology, and mechanics. His two sons were as wicked and passionate as himself: the elder was in 1560 executed for poisoning his wife, and about the same time Cardan in a fit of rage cut off the ears of the younger who committed some offence; for this scandelous outrage he suffered no punishment, as Pope Gregory XIII granted him protection."

"His career is an account of the most extraordinary and inconsistent acts. A gambler, if not a murderer, he was an ardent student of science, solving problems which had long baffled all investigation; at one time in his life he was devoted to intrigues which were a scandal even in the sixteenth century, at another he did nothing but rave on astrology, and yet at another he declared that philosophy was the only subject worthy of a man's attention. His was the genius that was closely allied to madness."

"Anticipations of Cardan are more truly wonderful when we consider that the symbolical language of algebra, that powerful instrument not only expediting the processes of thought, but in suggesting general truths to the mind, was nearly unknown in his age. Diophantus, Fra Luca, and Cardan make use occasionally of letters to express indefinite quantities besides the res or cosa, sometimes written shortly, for the assumed unknown number of an equation. But letters were not yet substituted for known quantities. Michael Stifel, in his Arithmetics Integra, Nuremberg, 1544, is said to have first used the signs + and -, and numeral exponents of powers. It is very singular that discoveries of the greatest convenience, and apparently, not above the ingenuity of a village schoolmaster, should have been overlooked by men of extraordinary acuteness like Tartaglia, Cardan, and Ferrari; and hardly less so, that by dint of this acuteness they dispensed with the aid of these contrivances, in which we suppose that so much of the utility of algebraic expression consists."

"The task of the educator of young children lies in seeing that the child does not confound good with immobility, and evil with activity."

"Never help a child with a task at which he feels he can succeed."

"One who has drunk at the fountain of spiritual happiness says good-by of his own accord to the satisfactions that come from a higher professional status … What is the greatest sign of success for a teacher thus transformed? It is to be able to say, "The children are now working as if I did not exist.""

"The child is truly a miraculous being, and this should be felt deeply by the educator."

"We teachers can only help the work going on, as servants wait upon a master. We then become witnesses to the development of the human soul; the emergence of the New Man who will no longer be the victim of events but, thanks to his clarity of vision, will become able to direct and to mold the future of mankind."

"If help and salvation are to come they can only come from the children, for the children are the makers of men. The child is endowed with unknown powers, which can guide us to a radiant future. If what we really want is a new world, then education must take as its aim the development of these hidden possibilities."

"If education is always to be conceived along the same antiquated lines of a mere transmission of knowledge, there is little to be hoped from it in the bettering of man's future."

"This is our mission: to cast a ray of light and pass on. I compare the effects of these first lessons the impressions of a solitary wanderer who is walking serene and happy in a shady grove, meditating; that is leaving his inner thought free to wander. Suddenly a church bell pealing out nearby recalls to himself; then he feels more keenly that peaceful bliss which had already been born, though dormant, within him. To stimulate life, leaving it free, however, to unfold itself, that is the first duty of the educator. For such a delicate mission great art is required to suggest the right moment and to limit intervention, last one should disturb or lead astray rather than help the soul which is coming to life and which will live by virtue of its own efforts. This art must accompany the scientific method, because the simplicity of our lessons bears a great resemblance to experiments in experimental psychology."

"The best instruction is that which uses the least words sufficient for the task."

"Rewards and punishments, to speak frankly, are the desk of the soul, that is, a means of enslaving a child's spirit, and better suited to provoke than to prevent deformities."

"If a child finds no stimuli for the activities which would contribute to his development, he is attracted simply to 'things' and desires to possess them."

"Adults have not understood children or adolescents and they are, as a consequence, in continual conflict with them. The remedy is not that adults should gain some new intellectual knowledge or achieve a higher standard of culture. No, they must find a different point of departure. The adult must find within himself the still unknown error that prevents him from seeing the child as he is."

"Let us picture to ourselves a clever and proficient workman, capable, not only of producing much and perfect work, but of giving advice in his workshop, because of his ability to control and direct the general activity of the environment in which he works. The man who is thus master of his environment will be able to smile before the anger of others, showing that great mastery of himself which comes from consciousness of his ability to do things. We should not, however, be in the least surprised to know that in his home this capable workman scolded his wife if the soup was not to his taste, or not ready at the appointed time. In his home, he is no longer the capable workman; the skilled workman here is the wife, who serves him and prepares his food for him. He is a serene and pleasant man where he is powerful through being efficient, but is domineering where he is served. Perhaps if he should learn how to prepare his soup he might become a perfect man! The man who, through his own efforts, is able to perform all the actions necessary for his comfort and development in life, conquers himself, and in doing so multiplies his abilities and perfects himself as an individual. We must make of the future generation, powerful men, and by that we mean men who are independent and free."

"The peril of servilism and dependence lies not only in that "useless consuming of life," which leads to helplessness, but in the development of individual traits which indicate all too plainly a regrettable perversion and degeneration of the normal man. I refer to the domineering and tyrannical behaviour with examples of which we are all only too familiar. The domineering habit develops side by side with helplessness. It is the outward sign of the state of feeling of him who conquers through the work of others. Thus it often happens that the master is a tyrant toward his servant. It is the spirit of the task-master toward the slave."

"We give the name scientist to the type of man who has felt experiment to be a means guiding him to search out the deep truth of life, to lift a veil from its fascinating secrets, and who, in this pursuit, has felt arising within him a love for the mysteries of nature, so passionate as to annihilate the thought of himself. The scientist is not the clever manipulator of instruments, he is the worshipper of nature and he bears the external symbols of his passion as does the follower of some religious order. To this body of real scientists belong those who, forgetting, like the Trappists of the Middle Ages, the world about them, live only in the laboratory, careless often in matters of food and dress because they no longer think of themselves; those who, through years of unwearied use of the microscope, become blind; those who in their scientific ardour inoculate themselves with tuberculosis germs; those who handle the excrement of cholera patients in their eagerness to learn the vehicle through which the diseases are transmitted; and those who, knowing that a certain chemical preparation may be an explosive, still persist in testing their theories at the risk of their lives. This is the spirit of the men of science, to whom nature freely reveals her secrets, crowning their labours with the glory of discovery. There exists, then, the "spirit" of the scientist, a thing far above his mere "mechanical skill," and the scientist is at the height of his achievement when the spirit has triumphed over the mechanism. When he has reached this point, science will receive from him not only new revelations of nature, but philosophic syntheses of pure thought."

"In the vivid description of the Gospel, it would seem that we must help the Christ hidden in every poor man, in every prisioner, in every sufferer. But if we paraphrased the marvelous scene and applied it to the child, we should find that Christ goes to help all men in the form of the child."

"To prepare teachers in the method of the experimental sciences is not an easy matter. When we shall have instructed them in anthropometry and psychometry in the most minute manner possible, we shall have only created machines, whose usefulness will be most doubtful. Indeed, if it is after this fashion that we are to initiate our teachers into experiment, we shall remain forever in the field of theory. The teachers of the old school, prepared according to the principles of metaphysical philosophy, understood the ideas of certain men regarded as authorities, and moved the muscles of speech in talking of them, and the muscles of the eye in reading their theories. Our scientific teachers, instead, are familiar with certain instruments and know how to move the muscles of the hand and arm in order to use these instruments; besides this, they have an intellectual preparation which consists of a series of typical tests, which they have, in a barren and mechanical way, learned how to apply. The difference is not substantial, for profound differences cannot exist in exterior technique alone, but lie rather within the inner man. Not with all our initiation into scientific experiment have we prepared new masters, for, after all, we have left them standing without the door of real experimental science; we have not admitted them to the noblest and most profound phase of such study, — to that experience which makes real scientists."

"Freedom without organization of work would be useless. The child left free without means of work would go to waste, just as a new-born baby, if left free without nourishment, would die of starvation.The organization of the work, therefore, is the cornerstone of this new structure of goodness [in education], but even that organization would be in vain without the liberty to make use of it."

"The child is essentially alien to this society of men and might express his position in the words of the Gospel: My kingdom is not of this world"

"We have in ourselves tendencies that are not good and which flourish like weeds in a field. (Original sin). These tendencies are many; they fall into seven groups, known of old as the Seven deadly sins. All deadly sins tend to separate us from the child; for the child compared to us, is not only purer but has mysterious qualities, which we adults as a rule cannot perceive, but in which we must believe with faith, for Jesus spoke to them so clearly and insistently that all the Evangelists recorded His words: Unless ye be converted and become as little children, ye shall nor enter into the Kingdom of Heaven. That which the educator must seek is to be able to see the child as Jesus saw him. It is with this endeavour, thus defined and delimited, that we wish to deal."

"It seems as though a new epoch were in preparation, a truly human epoch, and as though the end had almost come of those evolutionary periods which sum up the history of the heroic struggles of humanity; an epoch in which an assured peace will promote the brotherhood of man, while morality and love will take their place as the highest form of human superiority. In such an epoch there will really be superior human beings, there will really be men strong in morality and in sentiment. Perhaps in this way the reign of woman in approaching, when the enigma of her anthropological superiority will be deciphered. Woman was always the custodian of human sentiment, morality and honour, and in these respects man always has yielded women the palm."

"Maria Montessori, busy giving lectures in various cities, committed herself to raising public awareness of “modern charity,” where the theme of the “new woman” emerged. She became a champion of women's emancipation and ideals of peace. In March 1896, she became co-founder and deputy secretary of a Roman women's association and in 1899 she joined the Maternal Union. She took up the women's cause in international forums, such as the Women's Congress in London in 1899, where she was approached by Guido Baccelli (1830-1916), who had experienced the barricades that defended the Roman Republic from the assault of French troops in 1849 and was seven times Minister of Education. Also in 1899, Montessori joined the Theosophical Society, founded in 1875 in New York for the study and dissemination of theosophy (divine wisdom) and esoteric sciences. Adhering to the Masonic principle of “universal brotherhood,” theosophy was based on the motto “there is no religion higher than truth.” No specific profession of faith was required of its members. This institution and its official organ, The Theosophist (1879), were founded by Helena Blavatsky (1831-1891), a Russian-born American philosopher, theosophist, occult essayist, and medium, and Colonel Henry Steel Olcott (1832-1907) ."

"If a teacher can discern what a child is trying to do in his informational interaction with the environment, and if that teacher can have on hand materials relevant to that intention, if he can impose a relevant challenge with which the child can cope, supply a relevant model for imitation, or pose a relevant question the child can answer, that teacher can call forth the kind of accommodative change that constitutes psychological development or growth."