Inventors

"In the History of Mathematics it is generally stated that the higher analysis took its rise in the method of indivisibles of Cavalieri (1635). This assertion... is erroneous. ...Leibniz was led to his invention of the algorithm of the higher analysis by a study of the writings of Pascal, more than by anything else."

"The German idealist philosophical tradition from which Hayek emerged is usually held to begin with Gottfried Leibniz, who wrote mostly during the second half of the seventeenth century. Leibniz put forward the idea of “monads,” a starkly idealist conception. Essentially, “each monad is a soul,” in the words of Bertrand Russell. Leibniz reversed the traditional conception of mind and matter by applying attributes of matter (in terms of sensory experience) to mind. Mind is what it experiences. Every mind or soul becomes an independent attribute of the universe, divinely ordered or arranged. Leibniz’s focus truly was mind. […] Leibniz was born at the end of the Thirty Years’ War. Religious struggles, such as the Thirty Years’ War, are often protracted and intense because they concern fundamental individual beliefs and values to which compromise is not always applicable. Chaos and disorder reigned in the larger society from which Leibniz emerged. It is not surprising that his philosophy moved in the direction of mind from a strictly sociological perspective, for the world was too hard to bear."

"Perhaps never has a man read as much, studied as much, meditated more, and written more than Leibniz… What he has composed on the world, God, nature, and the soul is of the most sublime eloquence. If his ideas had been expressed with the flair of Plato, the philosopher of Leipzig would cede nothing to the philosopher of Athens."

"When one compares the talents one has with those of a Leibniz, one is tempted to throw away one's books and go die quietly in the dark of some forgotten corner."

"The manuscripts of Leibniz... show, perhaps more clearly than his published work, the great importance which Leibniz attached to suitable notation in mathematics and... in logic generally. He was perhaps the earliest to realize fully and correctly the important influence of a calculus [some mindless method of calculation] on discovery. ...There is a frivolous objection... to the effect that such economy of thought is an attempt to substitute unthinking mechanism for living thought. This contention fails... through the simple fact that this economy is only used in certain circumstances. In no science do we try to make subject to a mechanical calculus any trains of reasoning except such that have not been the object of careful thought many times previously. ...this reasoning has been universally recognized as valid, and we do not wish to waste energy of thought in repeating it when so much remains to be discovered by means of this energy. Since the time of Leibniz, this truth has been recognized, explicitly or implicitly, by all the greatest mathematical analysts."

"The main ideas of his philosophy are to be attributed to his mathematical work, and not vice versa."

"Leibniz was certainly not alone among great men in presenting in his early work almost all the important mathematical ideas contained in his mature work."

"In the interval of 200 years between Kepler and Gauss there arose no great mathematician in Germany excepting Leibniz."

"[T]he program which Immanuel Kant proposed back in the 1760s... was this: our knowledge of the outside world depends on our modes of perception... Unfortunately, a great revolution took place in or about the year 1768, when he read a paper by Euler which intended to show that space was indeed absolute as Newton had suggested and not relative as Leibnitz suggested. (...in the eighteenth century the question of whether Newton's... or Leibnitz's view of the world was right profoundly affected all philosophy.) After reading Euler's argument... Kant... for the first time proposed that... we must be conscious of [absolute space] a priori. ...Kant died in 1804, long before new ideas about space... had been published... And since one of the things that happened in [our] lifetime has been the substitution of... a Leibnitz universe, the universe of relativity, for Newton's universe... we should think that out again."

"Gottfried Leibniz is famous... for his slogan Calculemus, which means "Let us calculate." He envisioned a formal language to reduce reasoning to calculation, and he said that reasonable men, faced with a difficult question of philosophy or policy, would express the question in a precise language and use rules of calculation to carry out precise reasoning. This is the first reduction of reasoning to calculation ever envisioned. ...he actually designed and built a working calculating machine, the Stepped Reckoner ...inspired by the somewhat earlier work of Pascal, who built a machine that could add and subtract. Leibniz's machine could add, subtract, divide, and multiply, and was apparently the first machine with all four arithmetic capabilities."

"Ainsi on peut dire que non seulement l'âme, miroir d'un univers indestructible, est indestructible, mais encore l'animal même, quoique sa machine périsse souvent en partie, et quitte ou prenne des dépouilles organiques."

"Thus there is nothing waste, nothing dead in the universe; no chaos, no confusions, save in appearence. We might compare this to the appearence of a pond in the distance, where we can see the confused movement and swarming of the fish, without distinguishing the fish themselves. Thus we are that each living body has a dominante entelechy, which in case of an animal is the soul, but the members of this living body are full of other living things, plants and animals, of which each has in turn ita dominant entelechy or soul."

"Or, comme il y a une infinité d'univers possibles dans les idées de Dieu, et qu'il n'en peut exister qu'un seul, il faut qu'il y ait une raison suffisante du choix de Dieu qui le détermine à l'un plutôt qu'à l'autre. Et cette raison ne peut se trouver que dans la convenance, dans les degrés de perfection que ces mondes contiennent, chaque possible ayant droit de prétendre à l'existence à mesure de la perfection qu'il enveloppe."

"Et comme tout présent état d'une substance simple est naturellement une suite de son état précédent, tellement, que le présent y est gros de l'avenir."

"On est obligé d’ailleurs de confesser que la Perception et ce qui en dépend, est inexplicable par des raisons mécaniques, c’est-à-dire par les figures et par les mouvements. Et feignant qu'il y ait une Machine, dont la structure fasse penser, sentir, avoir perception ; on pourra la concevoir agrandie en conservant les mêmes proportions, en sorte qu’on y puisse entrer, comme dans un moulin. Et cela posé, on ne trouvera en la visitant au dedans, que des pièces, qui poussent les unes les autres, et jamais de quoi expliquer une perception. Ainsi c'est dans la substance simple, et non dans le composé, ou dans la machine qu’il la faut chercher."

"The love of God consists in an ardent desire to procure the general welfare, and reason teaches me that there is nothing which contributes more to the general welfare of mankind than the perfection of reason."

"We never have a full demonstration, although there is always an underlying reason for the truth, even if it is only perfectly understood by God, who alone penetrated the infinite series in one stroke of the mind."

"Ce miracle de l'Analyse, prodige du monde des idées, objet presque amphibie entre l'Être et le Non-être, que nous appelons racine imaginaire."

"De quelque manière que Dieu aurait créé le monde, il aurait toujours été régulier et dans un certain ordre général. Mais Dieu a choisi celui qui est le plus parfait, c’est-à-dire celui qui est en même temps le plus simple en hypothèses et le plus riche en phénomènes..."

"Although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough, if, using reason well, we were never deceived by it."

"cur aliquid potius extiterit quam nihil"

"J'ay marqué plus d'une fois, que je tenois l'espace pour quelque chose de purement relatif, comme le temps; pour un ordre des coëxistences, comme le temps est un ordre des successions."

"It is an extremely useful thing to have knowledge of the true origins of memorable discoveries, especially those that have been found not by accident but by dint of meditation. It is not so much that thereby history may attribute to each man his own discoveries and others should be encouraged to earn like commendation, as that the art of making discoveries should be extended by considering noteworthy examples of it."

"Musica est exercitium arithmeticae occultum nescientis se numerare animi."

"Il y a deux labyrinthes fameux où notre raison s’égare bien souvent : l'un regarde la grande question du libre et du nécessaire, surtout dans la production et dans l'origine du mal ; l'autre consiste dans la discussion de la continuité et des indivisibles qui en paraissent les éléments, et où doit entrer la considération de l'infini."

"My philosophical views approach somewhat closely those of the late Countess of Conway, and hold a middle position between Plato and Democritus, because I hold that all things take place mechanically as Democritus and Descartes contend against the views of Henry More and his followers, and hold too, nevertheless, that everything takes place according to a living principle and according to final causes — all things are full of life and consciousness, contrary to the views of the Atomists."

"I have seen something of the project of M. de St. Pierre, for maintaining a perpetual peace in Europe. I am reminded of a device in a cemetery, with the words: Pax perpetua; for the dead do not fight any longer: but the living are of another humor; and the most powerful do not respect tribunals at all."

"[The consequences of] beliefs that go against the providence of a perfectly good, wise, and just God, or against that immortality of souls which lays them open to the operations of justice.... I even find that somewhat similar opinions, by stealing gradually into the minds of men of high station who rule the rest and on whom affairs depend, and by slithering into fashionable books, are inclining everything toward the universal revolution with which Europe is threatened, and are completing the destruction of what still remains in the world of the generous Greeks and Romans who placed love of country and of the public good, and the welfare of before fortune and even before life."

"La nature ne fait jamais des sauts."

"When Sir A. Fountaine was at Berlin with Leibnitz in 1701, and at supper with the Queen of Prussia, she asked Leibnitz his opinion of Sir Isaac Newton. Leibnitz said that taking mathematicians from the beginning of the world to the time when Sir Isaac lived, what he had done was much the better half; and added that he had consulted all the learned in Europe upon some difficult points without having any satisfaction, and that when he applied to Sir Isaac, he wrote him in answer by the first post, to do so and so, and then he would find it."

"Il y a jusque dans les exercices des enfants ce qui pourrait arrêter le plus grand Mathématicien."

"Pour ce qui est des connaissances non-écrites qui se trouvent dispersées parmi les hommes de différents professions, je suis persuadé qu’ils passent de beaucoup tant à l'égard de la multitude que de l'importance, tout ce qui se trouve marqué dans les livres, et que la meilleure partie de notre trésor n'est pas encore enregistrée."

"TO LOVE is to find pleasure in the happiness of others. Thus the habit of loving someone is nothing other than BENEVOLENCE by which we want the good of others, not for the profit that we gain from it, but because it is agreeable to us in itself. CHARITY is a general benevolence. And JUSTICE is charity in accordance with wisdom. … so that one does not do harm to someone without necessity, and that one does as much good as one can, but especially where it is best employed."

"As regards the objection that possibles are independent of the decrees of God I grant it of actual decrees (although the Cartesians do not at all agree to this), but I maintain that the possible individual concepts involve certain possible free decrees; for example, if this world was only possible, the individual concept of a particular body in this world would involve certain movements as possible, it would also involve the laws of motion, which are the free decrees of God; but these, also, only as possibilities. Because, as there are an infinity of possible worlds, there are also an infinity of laws, certain ones appropriate to one; others, to another, and each possible individual of any world involves in its concept the laws of its world."

"Chaque substance est comme un monde à part, indépendant de toute autre chose, hors de Dieu..."

"Omne possibile exigit existere."

"To love is to be delighted by the happiness of someone, or to experience pleasure upon the happiness of another. I define this as true love."

"Nam filum labyrintho de compositione continui deque maximo et minimo ac indesignabili at que infinito non nisi geometria praebere potest, ad metaphysicam vero solidam nemo veniet, nisi qui illac transiverit."

"Theologus: Amare autem? Philosophus: Felicitate alterius delectari."

"Languages are the best mirror of the human mind [and] the most ancient monu­ments of peoples."

"quando orientur controversiae, non magis disputatione opus erit inter duos philosophos, quam inter duos computistas. Sufficiet enim calamos in manus sumere sedereque ad abacos, et sibi mutuo (accito si placet amico) dicere: calculemus"

"Chemistry, in its application to animals and vegetables. Endeavours jointly with physiology to enlighten us respecting the mysterious processes and sources of organic life."

"To investigate the essence of a natural phenomenon, three conditions are necessary: We must first study and know the phenomenon itself, from all sides; we must then determine in what relation it stands to other natural phenomena; and lastly, when we have ascertained all these relations, we have to solve the problem of measuring these relations and the laws of mutual dependence—that is, of expressing them in numbers. In the first period of chemistry, all the powers of men's minds were devoted to acquiring a knowledge of the properties of bodies; it was necessary to discover, observe, and ascertain their peculiarities. This is the alchemistical period. The second period embraces the determination of the mutual relations or connections of these properties; this is the period of phlogistic chemistry. In the third period, in which we now are, we ascertain by weight and measure and express in numbers the degree in which the properties of bodies are mutually dependent. The inductive sciences begin with the substance itself, then come just ideas, and lastly, mathematics are called in, and with the aid of numbers, complete the work."

"The acquisition of a new truth is like the acquisition of a new sense, which renders a man capable and recognizing a large number of phenomena that are hidden from another, as they were from him originally."

"The final result of our researches has widened the class of substances sensitive to light vibrations, until we can propound the fact of such sensitiveness being a general property of all matter."

"he was the type of inventor whose interest flags when he has solved his problem. Let somebody else take care of the development. He would be off on a new voyage of discovery."

"Mr. Watson — Come here — I want to see you."

"At that time Mr. Bell was giving his nights to trying to "make iron talk"...He was up and began his day around four to six. Often there were guests for dinner, for everybody of note the world over who came to Washington wanted to meet him. On Wednesdays after dinner there usually gathered a group of scientists and public men to talk things over. Mr. Bell was something to see at these dinners and gatherings, the finest social impresario I ever saw in action, so welcoming, appreciative, eager, receptive. I thought then I had never seen anybody so generous about what others were doing. He loved to draw out great stories of adventure and discovery and would silence all talkers when once such narrating was started."

"Years later I told Alexander Graham Bell of my introduction to the telephone. "Nobody," he said, "can estimate what the teachers of science in colleges and high schools were doing in those days not only to spread knowledge of the telephone but to stir youth to tackle the possibilities in electricity." What I best remember is not the telephone but Professor Tingley's amazing enthusiasm for the telephone. This revelation of enthusiasm, its power to warm and illuminate was one of the finest and most lasting of my college experiences. The people I had known, teachers, preachers, doctors, business men, all went through their day's work either with a stubborn, often sullen determination to do their whole duty, or with an undercurrent of uneasiness, if they found pleasure in duty. They seemed to me to feel that they were not really working if they were not demonstrating the Puritan teaching that labor is a curse. It had never seemed so to me, but I did not dare gloat over it. And here was a teacher who did gloat over his job in all its ramifications. Moreover, he did his best to stir you to share his joy."

"Bell had his own theories about the threat that people with disabilities represented to the future of the species. His mother and wife had both been born deaf, and in 1883 he warned the National Academy of Sciences that unless the use of sign language was vigorously discouraged in schools for the deaf, society ran the risk of engendering "a race of deaf-mutes.""