Inventors

"The function just found cannot, it is true, express rigorously the probabilities of the errors: for since the possible errors are in all cases confined within certain limits, the probability of errors exceeding those limits ought always to be zero, while our formula always gives some value. However, this defect, which every analytical function must, from its nature, labor under, is of no importance in practice, because the value of our function decreases so rapidly... that it can safely be considered as vanishing. Besides, the nature of the subject never admits of assigning with absolute rigor the limits of error."

"Mathematics is the queen of the sciences."

"I will add that I have recently received from Hungary a little paper on non-Euclidean geometry in which I rediscover all my own ideas and results worked out with great elegance... The writer is a very young Austrian officer, the son of one of my early friends, with whom I often discussed the subject in 1798, although my ideas were at that time far removed from the development and maturity which they have received through the original reflections of this young man. I consider the young geometer J. Bolyai a genius of the first rank."

"To praise it would amount to praising myself. For the entire content of the work … coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years."

"We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori."

"I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where ½ proof = 0, and it is demanded for proof that every doubt becomes impossible."

"Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density."

"Less depends upon the choice of words than upon this, that their introduction shall be justified by pregnant theorems."

"In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere, which are the end points of the radii drawn parallel to the lines. The centre and the radius of this auxiliary sphere are here quite arbitrary. The radius may be taken equal to unity. This procedure agrees fundamentally with that which is constantly employed in astronomy, where all directions are referred to a fictitious celestial sphere of infinite radius. Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present."

"It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. [Wahrlich es ist nicht das Wissen, sondern das Lernen, nicht das Besitzen sondern das Erwerben, nicht das Da-Seyn, sondern das Hinkommen, was den grössten Genuss gewährt.] When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again. The never-satisfied man is so strange; if he has completed a structure, then it is not in order to dwell in it peacefully, but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others."

"The enchanting charms of this sublime science reveal themselves in all their beauty only to those who have the courage to go deeply into it. But when a person of that sex, that, because of our mores and our prejudices, has to encounter infinitely more obstacles and difficulties than men in familiarizing herself with these thorny research problems, nevertheless succeeds in surmounting these obstacles and penetrating their most obscure parts, she must without doubt have the noblest courage, quite extraordinary talents and superior genius."

"But in our opinion truths of this kind should be drawn from notions rather than from notations."

"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."

"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."

"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."

"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."

"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."

"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."

"Almost everything which you needed to know in your daily life was written down somewhere. And at the time, in the 1980s, it was almost certainly written down on a computer somewhere. It was very frustrating that people's effort in typing it in was not being used when, in fact, if it could only be tied together and made accessible, everything would be so much easier for everybody."

"Now, if someone tries to monopolize the Web, for example pushes proprietary variations on network protocols, then that would make me unhappy."

"Anyone who has lost track of time when using a computer knows the propensity to dream, the urge to make dreams come true and the tendency to miss lunch."

"Web 1.0 was all about connecting people. It was an interactive space, and I think Web 2.0 is of course a piece of jargon, nobody even knows what it means. If Web 2.0 for you is blogs and wikis, then that is people to people. But that was what the Web was supposed to be all along."

"I don't believe in the sort of eureka moment idea. I think it's a myth. I'm very suspicious that actually Archimedes had been thinking about that problem for a long time. And it wasn't that suddenly it came to him."

"The fact that we're all connected, the fact that we've got this information space — does change the parameters. It changes the way people live and work. It changes things for good and for bad. But I think, in general, it's clear that most bad things come from misunderstanding, and communication is generally the way to resolve misunderstandings — and the Web's a form of communications — so it generally should be good. But I think, also, we have to watch whether we preserve the stability of the world — like we don't want to watch this phenomenon like the stock market becoming unstable when it became computerized, for example. We need to look at the whole society and think, "Are we actually thinking about what we're doing as we go forward, and are we preserving the really important values that we have in society? Are we keeping it democratic, and open, and so on?""

"He is a great visionary, but not actually always that good at explaining it … He is very technical, and always happiest when talking to other techies. All he really wants to do is write code, but now he has to go and meet world leaders and business people. I don't think he realised what they were doing at CERN would change the world this much. I think this is as big, if not bigger, than the printing press."

"The trick... is to make sure that each limited mechanical part of the Web, each application, is within itself composed of simple parts that will never get too powerful."

"In an extreme view, the world can be seen as only connections, nothing else. We think of a dictionary as the repository of meaning, but it defines words only in terms of other words. I liked the idea that a piece of information is really defined only by what it's related to, and how it's related. There really is little else to meaning. The structure is everything. There are billions of neurons in our brains, but what are neurons? Just cells. The brain has no knowledge until connections are made between neurons. All that we know, all that we are, comes from the way our neurons are connected."

"At CERN there was a credo meant to avoid unnecessary labors, it said that when acquiring new technology: Buy, Don't Build. There were several commercial hypertext editors and I thought we could just add some internet code, so that the hypertext documents could then be sent over the internet. I thought the companies engaged in the then fringe field of hypertext would immediately grasp the possibilities of the web. Unfortunately, their reaction was quite the opposite... it seemed that explaining the vision of the web was exceedingly difficult without a web browser in hand, people had to be able to grasp the web in full, which meant imagining a whole world populated with websites and browsers. It was a lot to ask. Despite the buy don't build credo I came to the conclusion that I was going to have to create the web on my own."

"The web is more a social creation than a technical one. I designed it for a social effect — to help people work together — and not as a technical toy. The ultimate goal of the Web is to support and improve our weblike existence in the world. We clump into families, associations, and companies. We develop trust across the miles and distrust around the corner."

"This snoopers charter has no place in a modern democracy - it undermines our fundamental rights online. The bulk collection of everyone's internet browsing data is disproportionate, creates a security nightmare for the ISPs who must store the data - and rides roughshod over our right to privacy. Meanwhile, the bulk hacking powers in the Bill risk making the internet less safe for everyone"

"When somebody has learned how to program a computer … You're joining a group of people who can do incredible things. They can make the computer do anything they can imagine."

"Aaron is dead. Wanderers in this crazy world, we have lost a mentor, a wise elder. Hackers for right, we are one down, we have lost one of our own. Nurtures, careers, listeners, feeders, parents all, we have lost a child. Let us all weep."

"We’ve lost a fighter. We’ve lost somebody who put huge energy into righting wrongs. There are people around the world who take it on themselves to just try to fix the world but very few of them do it 24/7 like Aaron. Very few of them are as dedicated. So of the people who are fighting for right, and what he was doing up to the end was fighting for right, we have lost one of our own. … We’ve lost a great person."