Non Fiction Authors

"Barely a hundred and fifty years had passed since Galileo's experiment at Pisa had ushered in the new order of things; a mere instant as compared with the previous life of the race. Yet, this brief span had witnessed a complete shift in the outlook of the intellectual leaders of humanity: from blind adherence to authority and dogma towards a healthy habit of facing facts and an enlightened faith in the efficacy of reason. Few doubted that this buoyancy and self-reliance of the leaders would eventually reach the masses, thus causing a profound metamorphosis in the attitude of the common man towards his own life and the destinies of his race. ...Led by thinkers, and under the banners of liberty, happiness, and truth, humanity was to emerge into a Golden Age, free from oppression and strife. Alas! The French Revolution... resembled more a convention of inquisitors and hangmen than it did an assembly of enlightened emancipators. ...After twenty years of adventure, the humanitarian aspirations bequeathed by the Encyclopedists, tattered and trampled first by a bloody republic, then by a still bloodier empire, were finally declared dead by the Holy Alliance."

"Poincaré's mind was not subject to hysteresis or hibernation. He had the unique faculty of dismissing an idea from his mind, the instant the stimulus was gone, and to supplant it immediately with another creative idea."

"He was an iconoclast. But even in this category he defies classification. For, he fits no pattern, and is beyond all norm. He sought no followers, he shunned confederates, he hewed no tablets to replace those which he had shattered."

"The evolution of scientific thought is inseparable from the history of man's efforts to resolve the perplexities of his own existence."

"One part of the dreams of the eighteenth century intellectuals was realized: the resources of nature did yield a magnificent harvest. But the thinkers who helped to tap these resources... failed to attend, detained in their studies and laboratories, lost in their dreams and calculations, seeking new fields, co-ordinating old and new, spinning abstract theories... the thinkers were unequal to the task of developing these vast resources, most of which they had themselves uncovered. The shrewd declassés, who had... the world to gain, pioneered this development and took possession of the earth."

"Science... may be viewed as man's supreme effort to find himself in that perplexing pattern which he calls Nature. ...Has he succeeded in achieving some measure of harmony with Nature? Or has he merely managed to transfer to Nature the irreconcilable duality within himself?"

"The Industrial Revolution, too, failed to introduce a reign of freedom and happiness: it converted the medieval serf into an industrial slave; replaced the feudal baron by the industrial mogul, created in its wake an ever-growing, ever-shifting class of declassés, who had neither pride of ancestry nor love of tradition... The age of machine and competition, of capital, class-struggle, and demagogy was upon man."

"There exists among the most primitive tribes of Australia and Africa a system of numeration which has neither 5, 10, nor 20 for base. It is a binary system, i.e., of base two. These savages have not yet reached finger counting. They have independent numbers for one and two, and composite numbers up to six. Beyond six everything is denoted by “heap.”"

"‘…the transition [to the Hindu number system], far from being immediate, extended over long centuries. The struggle between the Abacists, who defended the old traditions, and the Algorists, who advocated the reform, lasted from the eleventh to the fifteenth century and went through all the usual stages of obscurantism and reaction. In some places, Arabic numerals [more precisely, Hindu numerals] were banned from official documents; in others, the art was prohibited altogether. And, as usual, prohibition did not succeed in abolishing, but merely served to spread bootlegging, ample evidence of which is found in the thirteenth century archives of Italy, where, it appears, merchants were using the Arabic numerals as a sort of secret code.’"

"The preface to the French edition of that work contains the following passage: "To me the French edition of my work is not a mere translation, but a transcription of ideas into a language in which it should have been written in the first place... I proudly acknowledge... my master. His words are among the most brilliant recollections of my youth; his piercing wisdom and potent prose have inspired my efforts of a riper age. To the memory of Henri Poincaré, the intellectual giant who was the first to recognize the role which the idiosyncrasies of the race play in the evolution of scientific ideas, I dedicate this book."

"Between the philosopher's attitude towards the issue of reality and that of the mathematician there is this essential difference: for the philosopher the issue is paramount; the mathematician's love for reality is purely platonic."

"The arithmetization of mathematics... which began with Weierstrass... had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics. These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought."

"But how can we avoid the use of human language? The... symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic."

"To describe means to classify, and the man Poincaré defies classification, as does indeed his philosophy."

"The progress of mathematics has been most erratic, and... intuition has played a predominant rôle in it. ...It was the function of intuition to create new forms; it was the acknowledged right of logic to accept or reject these new forms, in whose birth in had no part. ...the children had to live, so while waiting for logic to sanctify their existence, they throve and multiplied."

"In the history of mathematics, the "how" always preceded the "why," the technique of the subject preceded its philosophy."

"Greek thought was essentially non-algebraic, because it was so concrete. The abstract operations of algebra, which deal with objects that have been purposely stripped of their physical content, could not occur to minds which were so intently interested in the objects themselves. The symbol is not a mere formality; it is the very essence of algebra. Without the symbol the object is a human perception and reflects all the phases under which the human senses grasp it; replaced by a symbol the object becomes a complete abstraction, a mere operand subject to certain indicated operations."

"The great Cartesian invention had its roots in those famous problems of antiquity which originated in the days of Plato. In endeavoring to solve the problems of the trisection of an angle, of the duplication of the cube and of the squaring of the circle, the ruler and compass having failed them, the Greek geometers sought new curves. They stumbled on the conic sections...There we find the nucleus of the method which Descartes later erected into a principle. Thus Apollonius referred the parabola to its axis and principal tangent, and showed that the semichord was the mean propotional between the latus rectum and the height of the segment. Today we express this relation by x2 = Ly, calling the height the ordinate (y) and the semichord the abscissa (x); the latus rectum being... L. ...the Greeks named these curves and many others... loci... Thus the ellipse was the locus of a point the sum of the distances of which from two fixed points was constant. Such a description was a rhetorical equation of the curve..."

"The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. ...The conic sections, invented in an attempt to solve the problem of doubling the alter of an oracle, ended by becoming the orbits followed by the planets... The imaginary magnitudes invented by Cardan and Bombelli describe... the characteristic features of alternating currents. The absolute differential calculus, which originated as a fantasy of Riemann, became the mathematical model for the theory of Relativity. And the matrices which were a complete abstraction in the days of Cayley and Sylvester appear admirably adapted to the... quantum of the atom."

"His essays on the foundations of science are cases in point. They strike one as extemporaneous speeches rather than edited articles. ...those who knew him best insisted that he rarely, if ever, would revise a manuscript, even if he was fully aware of its stylistic shortcomings."

"The mathematical activity of Ancient Greece reached its peak during the glorious era of Euclid, Eratosthenes, Archimedes and Apollonius, a time when Greek letters, art and philosophy were already on the decline. ...it was not Greece proper but its outposts in Asia Minor, in Lower Italy, in Africa that had contributed most to the development of mathematics."

"Poincaré was an artist par excellence. Estheticism with him was not a mere creed: it was a way of life."

"Politeness is the art of choosing among one's real thoughts."

"Psychologically and spiritually, whether one calls them complexes or spiritual beings, they can be either upbuilding, creative forces, or negative and destructive influences."

"Religious practice provides three... mythological methods of coming to terms with spiritual reality and finding the treasure within it. One way is to study the myth in its historical context... And for modern Christians this means trying to see the psychological meaning of myth in the development of human consciousness. A second way is through ritual in which the mythological story is acted out... And third, he can sometimes step into the myth imaginatively through meditation, actually entering the spiritual world... and becoming active and effective in it."

"In the early years of Christianity the Church was known to be a place to bring those who were sick, either mentally or physically... A vital Christianity still has this power."

"Almost any reality which we fail to confront and deal with in some way, will try to possess us. This is as true of autonomous complexes or spirits as of germs and bacteria."

"Myth can act almost like throwing open a window to reveal reality that is not being touched by the rational, Aristotelian approach."

"The problem confronting the modern church is... to discover this new, and yet very old way of looking at reality mythologically. This is the Platonic, the psychological, the Christian way of expressing spiritual reality, through images and symbols, and it is the only way of approaching this realm as a living reality. Otherwise it must be broken down into elements and is dead."

"Myth and ritual act as transformers in bringing people the value of spiritual reality, just as an electrical transformer... The dream also provides the same kind of stepped-down encounter."

"The greater the man, the more subject he is to the ravaging effects of the negative side of this reality."

"There is no painless way of coming into contact with spiritual reality."

"How seldom do we look at the mythological pattern as it moves deep within the lives of individuals, prompting them to meet fate, to meet events following almost exactly the meaning outlined by the myth."

"Protestants have tried to make their religion completely logical and sensible... The result is that the average Western Protestant, completely cut off from his own myth, turns to the Vedas or theosophy, to Masonry, or to a struggle for power, or even war, to give him mythological symbols which his faith does not encompass."

"Even the church, which in ages past was custodian of man's myths, has turned its back upon myth, has forgotten its meaning, and has lost the ability to interpret and use it."

"Morton Kelsey, the most prolific writer among twentieth century Christian mystics."

"As Jung worked with patients from all over the world, he began to study the mythologies of different peoples... Folklore and mythology... appeared as the collective dreams of a people, expressing for the group what poetic imagination, phantasies, visions and dreams express for the individual. Both the individual and collective types of experience are vital to human life."

"One interesting confirmation of this viewpoint comes from the widespread dream research of William Dement... Not only did these subjects who were deprived of their dreams step up the frequency of their attempts to dream, but if they continued to be cut off from completing their dreams, they soon began to show signs of nervous breakdown."

"Man cannot remain well psychologically, let alone socially, if he loses contact with the unconscious and its symbolic and mythological life."

"The unconscious reveals its meaning imaginatively, through symbols and images, and it speaks... a basically mythological language."

"Western man, religious or not, came to believe that he was nothing but a shell of mechanically functioning matter, built to house his rational consciousness. ...Strangely enough, just as people were trying to get used to that kind of world, science began to see it differently. ...the scientific truths they had once considered universal and absolutely certain were only partly true."

"The Eastern or Greek Orthodox tradition has never turned its back upon the dream or the myth. ...it has continued to believe that spiritual reality is mediated to men through mythological images in story and actions, and in the pictorial representation of the icon."

"One of the most important ways of understanding the unconscious—indeed, as Freud saw it, the royal road to discovering the nature of its contents—is the dream. And what is a dream but a series of images that tell a story?"

"The success of a ministry depends more upon one's capacity to relate and to care, than [on] one's theological background."

"The inner journey is as individual as our thumbprint. We need to guide others on their way and never impose our way upon them."

"I learned that all people can be touched, with genuine caring and understanding."

"If humankind is open to another dimension of reality, then the dream may be one of the most common avenues through which God reaches out to us."

"The neurotic, it has been said, worries about castles in the air, while the psychotic lives in them. ...The hysterical person can copy reliably nearly any disease syndrome. ...Destructive emotional causes or influences may play a part in any disease, whatever the class or immediate cause."

"People always knock what's new but I love the modern Internet, where cleverness is currency. Social media is a cleverness meritocracy. We're living in it."

"The highest privilege of being a writer is being able to say, "open your mind to me and I'll take you to another world.""