Inventors

"Cardan was the most distinguished astrologer of his time, and when he settled in Rome he received a pension in order to secure his services as astrologer to the papal court. This proved fatal to him for, having foretold that he should die on a particular date, he felt obliged to commit suicide in order to keep up his reputation—so at least the story runs."

"He states that the root of x^3 + 6x = 20 is{{center|1=x = \sqrt[3]{\sqrt{108} + 10} - \sqrt[3]{\sqrt{108} - 10}.}}"

"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."

"Jerome Cardan is... the founder of the higher algebra; for, whatever he may have borrowed from others, we derive the science from his Ars Magna, published in 1545. It contains many valuable discoveries; but that which has been most celebrated is the rule for the solution of cubic equations, generally known by Cardan's name, though he had obtained it from a man of equal genius in algebraic science, Nicolas Tartaglia. The original inventor appears to have been Scipio Ferreo, who, about 1505, by some unknown process, discovered the solution of a single case; that of x3 + px = q. Ferreo imparted the secret to one Fiore, or Floridus, who challenged Tartaglia to a public trial of skill, not unusual in that age. Before he heard of this, Tartaglia, as he assures us himself, had found out the solution of two other forms of cubic equation; x3 + px2 = q, and x3 - px2 = q. When the day of trial arrived, Tartaglia was able, not only to solve the problems offered by Fiore, but to baffle him entirely by others which resulted in the forms of equation, the solution of which had been discovered by himself. This was in 1535; and, four years afterwards, Cardan obtained the secret from Tartaglia under an oath of secrecy. In his Ars Magna, he did not hesitate to violate this engagement; and, though he gave Tartaglia the credit of the discovery, revealed the process to the world."

"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."

"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."

"Every medieval and Renaissance court had a royal astrologer who advised the duke or prince he served. ...Men such as Roger Bacon, who even in the thirteenth century was a clear and outspoken champion of the experimental method in science, and Jerome Cardan, one of the foremost mathematicians and physicians of the sixteenth century, subscribed to astrology."

"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."

"It appears... from this short chapter [Ars Magna, lib x. ch. 1], that he had discovered most of the principal properties of the roots of equations, and could point out the number and nature of the roots, partly from the signs of the terms, and partly from the magnitude and relations of the co-efficients."

"He... gave thirteen forms of the cubic which have positive roots, these having already been given by Omar Kayyam."

"I have not lost my faith; and this I must attribute more to a miracle than to my own wisdom; more to Divine Providence than to my own virtue. Steadfastly, in fact from my earliest childhood, I have made this my prayer, "Lord God... grant me long life, and wisdom, and health of mind and body.""

"My father, in my earliest childhood, taught me the rudiments of arithmetic, and about that time made me acquainted with the arcana; whence he had come by this learning I know not. This was about my ninth year. Shortly after, he instructed me in the elements of the astronomy of Arabia, meanwhile trying to instill in me some system of theory for memorizing, for I had been poorly endowed with the ability to remember. After I was twelve years old he taught me the first six books of Euclid, but in such a manner that he expended no effort on such parts as I was able to understand by myself. This is the knowledge I was able to acquire and learn without any elementary schooling..."

"Since this art surpasses all human subtelty and the perspecuity of mortal talent and is truly a celestial gift and a very clear test of the capacity of man's minds, whoever applies himself to it will believe that there is nothing that he cannot understand."

"What if one should address a word to the kings of the earth and say, "Not one of you but eats lice, flies, bugs, worms, fleas—nay the very filth of your servants! With what an attitude would they listen to such statements, though they be truths? What is this complacency then but an ignoring of conditions, a pretense of not being aware of what we know exists, or a will to set aside a fact by force? And so it is with everything else foul, vain, confused and untrue in our lives."

"I have accustomed my features always to assume an expression quite contrary to my feelings; thus I am able to feign outwardly, yet within know nothing of dissumulation. This habit is easy if compared to the practice of hoping for nothing, which I have bent my efforts toward acquiring for fifteen successive years, and have at last succeeded."

"My personal affairs are not as highly esteemed as men commonly value their own interests—vain, empty affairs like those great clouds seen in the wake of the sunset which are meaningless and soon pass away."

"Although a long series of rules might be added and a long discourse given about them, we conclude our detailed consideration with the cubic, others being merely mentioned, even if generally, in passing. For as positio refers to a line, quadratum to the surface, and cubum to a solid body, it would be very foolish for us to go beyond this point. Nature does no permit it."

"This I recognize as unique and outstanding among my faults—the habit...of preferring to say above all things what I know to be displeasing to the ears of my hearers. ...I keep it up wilfully, in no way ignorant of how many enemies it makes for me. ...Yet I avoid this practice in the presence of my benefactors and of my superiors. It is enough not to fawn upon these, or at least not to flatter them."

"Among other myseries what I pray you tá be greater than whē a man riseth frō bed in the morning, to be incertaine of his returne to rest againe. or being in bed, whether his life shall continue tyll he ryse. besydes that, what labour, what hazard & care, are men constrained to abyde with these our brittle bodies, our feeble force, and incertayne lyfe: so as no nacion I thinke a man better or more fitlye named than the Spaniard, who in their language do terme a man shadow. And sure ther is nothing to be found of lesse assurance or soner passed than the lyfe of man, no... may more rightly be resembled to a shadow."

"From these beginnings, as it were, have issued bitterness, contentious obstinancy, lack of amenity, hasty judgement, anger, and an intense desire for revenge—to say nothing of headstrong will; that which many damn, by word at least, was my delight."

"I am cold of heart, warm of brain, and given to never-ending meditation; I ponder over ideas, many and weighty, and even over things which can never come to pass."

"So shall we voyd of all craft and sail, with true reason declare how much each man erreth in life, judgement, opinion, and will. Some things there are that so wel do prove themselves, as besides nature nede no profe at all."

"Cardano reasoned that the end of man is to know God and to mediate between the divine and the mortal. The is immortal and when permeated with is inseparable from God. True wisdom is gained from and by mathematics, as God has subjected the world to mathematical law."

"Better it is to have the worst, than none at all. for example we see, that houses are nedefull, such as can not possese & stately pallaces of stone, do persuade themselves to dwell in houses of timber and clap, and wanting them, are contented to inhabite the simple cotage, yea rather than not to be housed at all refuse not the pore cabbon, and most beggerly cave. So necessarie is this gift of consolacion, as there livith no man, but that hathe cause to embrace it. for in these things better is it to have any than none at al."

"And wel we see ther is none alive that in every respect may be accompted happie, yea though mortall men were free from all calamities, yet the torments & feare of death should stil attend them But b:sides them, behold, what, and how manye evilles there bee, that unlesse the cloude of error bee removed, impossible it is to see the truth, or receive allay of our earthly woes."

"I am able to admit two distinct trains of thought to my mind at the same time."

"You troubled mindes with tormentes loste that sighes and sobs consumes: (Who breathes and puffes from burning breast, both smothring smoke and fumes.) Come reade this booke that freelye bringes, a boxe of balme full swete, An oyle to noynt the brused partes, of everye heavye spirete. ...The lame whose lack of legges is death, unto a loftye mynde, Wyll kiss his crotche and creepe on knees,Cardanus workes to fynde."

"The greatest advantage in gambling lies in not playing at all."

"Der Glaube an eine bestimmte Idee gibt dem Forscher den Rückhalt für seine Arbeit. Ohne diesen Glauben wäre er verloren in einem Meer von Zweifeln und halbgültigen Beweisen."

"Only too often the inventor is the idealist who, like Mephisto, tries to improve the world, only to be crushed by harsh realities. If he wants to carry through his ideas, he is forced to do business with the wielders of power, whose sense of reality is sharper and more developed."

"Undecided about whether to pursue art or engineering, he pursued engineering, but with a continued interest in design—for his senior school project, he had designed a city of the future (à la Fritz Lang's Metropolis) based on a hexagonal grid. Like Alan Turing, Zuse was educated in a system that focused on a child's emotional and philosophical life as well as his intellectual life, and at the end of school, like Turing, Zuse found himself to be something of an outsider—to the disappointment of his very conventional parents, he no longer believed in God or religion."

"The rattling of the relays of the Z4 was the only interesting thing to be experienced in Zurich's night life!"

"After the war Zuse constructed the Z4 computer, which became the world’s first commercially used computer. Zuse is also credited with writing the first programming language for his computers: Plankalkül, meaning calculus for programs. As an engineer by trade, Zuse was mainly focused on building a working machine that could perform calculations. He was not at all concerned with the theory of computation, which at that time was explored by renowned mathematicians in the academic world like Schönfinkel, Church, Post, Kleene, and Turing. Because of this, Zuse was not an established name in the academic community as a theoretical computer scientist. It is known however, that Turing and Zuse were familiar with each other’s work (Zenil, 2012). Although Zuse has always been more characterized as an engineer than a theorist. This is perhaps one of the reasons why his main work on computation in physics has been relatively unnoticed in the academic community for so long."

"The microphone-amplifier-loudspeaker combination is having an enormous effect on our civilization. Not all of it is good! Consider to what heights of impudence and tyranny, and to what depths of moral depravity, has radio broadcasting and the loudspeaker attained in that recent monstrosity, Transit Radio, Inc. Almost incredible is the loathsome fact that already in 21 cities bus riders must listen to never-ending, blatant advertising and unwelcome jitterbug and bop music."

"I foresee great refinements in the field of short-pulse microwave signaling, whereby several simultaneous programs may occupy the same channel, in sequence, with incredibly swift electronic communication; vastly important developments in microwave technique, whereby present clumsy connecting leads between wall or floor sockets and electric devices like toasters and vacuum sweepers may become unnecessary; gigantic magnetrons and klystrons, or their successors, will generate megawatts in microwaves; living rooms and their occupants will be heated by high-frequency waves from walls or ceilings; short waves will be generally used in the kitchen for roasting and baking, almost instantaneously"

"To place a man in a multi-stage rocket and project him into the controlling gravitational field of the moon where the passengers can make scientific observations, perhaps land alive, and then return to earth—all that constitutes a wild dream worthy of Jules Verne. I am bold enough to say that such a man-made voyage will never occur regardless of all future advances."

"So I repeat that while theoretically and technically television may be feasible, yet commercially and financially, I consider it an impossibility; a development of which we need not waste little time in dreaming."

"The children of the white families in town were not permitted to associate with me, because my father was committing the then unpardonable crime, in Southern eyes, of educating negroes."

"Unwittingly then had I discovered an Invisible Empire of the Air, intangible, yet solid as granite, whose structure shall persist while man inhabits the planet."

"The actual poetry of this engineering triumph was first brought stunningly upon me in 1915 when I sat in an audience in San Francisco and heard the breaking of the surf upon the far Atlantic shore."

"To be and not to be, that is the answer."

"We shall have to evolve problem-solvers galore — since each problem they solve creates ten problems more."

"Men, said the Devil, are good to their brothers: they don’t want to mend their own ways, but each other's."

"The human spirit sublimates the impulses it thwarts; a healthy sex life mitigates the lust for other sports."

"Love while you've got love to give. Live while you've got life to live."

"Foes of what's cooking see no worth behind it. Those that are looking for nothing — will find it."

"if you possess more than just eight things then y o u are possessed by t h e m"

"Experts have their expert fun ex cathedra telling one just how nothing can be done."

"Giving in is no defeat. Passing on is no retreat. Selves are made to rise above. You shall live in what you love."

"Co-existence or no existence."