On Mysticism IV: Science & Mysticism II

"Science destroys poetry until the heart bursts into mysticism, and out of science brings poetry again, asserting a wonder and a vague mystery of life and feeling, beneath and beyond all science, and proclaiming the wonderfulness and mystery of that which we seem most familiarly to understand. (Frederick W Robertson, "The Influence of Poetry on the Working Classes", 1852)

 "Science will, in all probability, be increasingly impregnated by mysticism." (Pierre Teilhard de Chardin, "My Universe", 1924)

"To be a scientist - it is not just a different job so that a man should choose between being a scientist and being an explorer or a bond-salesman or a physician or a king or a farmer. It is a tangle of very obscure emotions, like mysticism, or wanting to write poetry; it makes its victim all different from the good natural man." (Sinclair Lewis, "Arrowsmith", 1925)

"When science starts to be interpretiveit is more unscientific even than mysticism." (David H Lawrence, Pansies: Poems, 1929)

"Our only way of avoiding the extremes of materialism and mysticism is the never ending endeavor to balance analysis and synthesis." (Niels Bohr, 1968)

"The three attributes of commitment, imagination, and tenacity seem to be the distinguishing marks of greatness in a scientist. A scientist must be as utterly committed to the pursuit of truth as the most dedicated of mystics; he must be as pertinacious in his struggle to advance into uncharted country as the most indomitable pioneers; his imagination must be as vivid and ingenious as a poet’s or a painter’s. Like other men, for success he needs ability and some luck; his imagination may be sterile if he has not a flair for asking the right questions, questions to which nature’s reply is intelligible and significant." (Alfred M Taylor, "Imagination and the Growth of Science", 1970)

"[...] one extreme is the idea of an objective world, pursuing its regular course in space and time, independently of any kind of observing subject; this has been the guiding image from modern science. At the other extreme is the idea of a subject, mystically experiencing the unity of the world and no longer confronted by an object or by any objective world; this has been the guiding image of Asian mysticism. Our thinking moves somewhere in the middle, between these two limiting conceptions; we should maintain the tension resulting from these opposites." (Werner K Heisenberg, "Across the Frontiers", 1974)

"Mystics understand the roots of the Tao but not its branches; scientists understand its branches but not its roots. Science does not need mysticism and mysticism does not need science; but man needs both." (Fritjof Capra, "The Tao of Physics", 1975)

"Science is a way to call the bluff of those who only pretend to knowledge. It is a bulwark against mysticism, against superstition, against religion misapplied to where it has no business being." (Carl Sagan, "Demon-Haunted World: Science as a Candle in the Dark", 1995)

"The mystic is content to bask in the wonder and revel in a mystery that we were not 'meant' to understand. The scientist feels the same wonder but is restless, not content; recognizes the mystery as profound, then adds, 'But we’re working on it.'" (Richard Dawkins, "Unweaving the Rainbow: Science, Delusion and the Appetite for Wonder", 1998)

On Mysticism VI: Trivia

"The whole secret of mysticism is this: that man can understand everything by the help of something he cannot understand." (Gilbert K Chesterton, "Orthodoxy", 1908)

"Mysticism is, in essence, little more than a certain intensity and depth of feeling in regard to what is believed about the universe." (Bertrand Russell, "Mysticism and Logic: And Other Essays", 1910)

"Mysticism is the art of union with Reality. The mystic is a person who has attained that union in greater or less degree; or who aims at and believes in such attainment." (Evelyn Underhill, "Practical Mysticism", 1914)

"Mysticism, according to its historical and psychological definitions, is the direct intuition or experience of God; and a mystic is a person who has, to a greater or less degree, such a direct experience -- one whose religion and life are centered, not merely on an accepted belief or practice, but on that which the person regards as first hand personal knowledge." (Evelyn Underhill, "Mystics of the Church" , 1925)

"[...] sometimes, through the strangely compelling experience of mystical insight, a man knows beyond the shadow of a doubt, that he has been in touch with a reality that lies behind mere phenomena. He himself is completely convinced, but he cannot communicate the certainty. It is a private revelation. He may be right, but unless we share his ecstasy we cannot know." (Edwin P Hubble, "The Nature of Science and Other Lectures", 1954)

"Life, this anti-entropy, ceaselessly reloaded with energy, is a climbing force, toward order amidst chaos, toward light, among the darkness of the indefinite, toward the mystic dream of Love, between the fire which devours itself and the silence of the Cold. Such a Nature does not accept abdication, nor skepticism." (Albert Claude, [Nobel lecture] 1974)

"Contrary to the strict division of the activity of the human spirit into separate departments - a division prevailing since the nineteenth century - I consider the ambition of overcoming opposites, including also a synthesis embracing both rational understanding and the mystical experience of unity, to be the mythos, spoken and unspoken, of our present day and age." (Wolfgang Pauli, "Writings on Physics and Philosophy", 1994)

"The idea of philosophy is a mysterious tradition. Philosophy is, in all, the problem of knowing. It is an undefined Science of the Sciences, a mysticism of the desire for knowledge; it is the very Spirit of the Sciences, and consequently unrepresentable, either in form or application, in the perfect representation of a special science." (Novalis)

"What I see in Nature is a grand design that we can understand only imperfectly, one with which a responsible person must look at with humility. This is a genuine religious feeling and has nothing to do with mysticism." (Albert Einstein)

On Mysticism V: Mathematics & Mysticism II

"In order to know the curvature of a curve, the determination of the radius of the osculating circle furnishes us the best measure, where for each point of the curve we find a circle whose curvature is precisely the same. However, when one looks for the curvature of a surface, the question is very equivocal and not at all susceptible to an absolute response, as in the case above. There are only spherical surfaces where one would be able to measure the curvature, assuming the curvature of the sphere is the curvature of its great circles, and whose radius could be considered the appropriate measure. But for other surfaces one doesn’t know even how to compare a surface with a sphere, as when one can always compare the curvature of a curve with that of a circle. The reason is evident, since at each point of a surface there are an infinite number of different curvatures. One has to only consider a cylinder, where along the directions parallel to the axis, there is no curvature, whereas in the directions perpendicular to the axis, which are circles, the curvatures are all the same, and all other oblique sections to the axis give a particular curvature. It’s the same for all other surfaces, where it can happen that in one direction the curvature is convex, and in another it is concave, as in those resembling a saddle." (Leonhard Euler, "Recherches sur la courbure des surfaces", 1767)

"A circle no doubt has a certain appealing simplicity at the first glance, but one look at a healthy ellipse should have convinced even the most mystical of astronomers that that the perfect simplicity of the circle is akin to the vacant smile of complete idiocy. Compared to what an ellipse can tell us, a circle has nothing to say." (Eric T Bell, "The Handmaiden of the Sciences", 1937)

"Here, then, in mathematics we have a universal language, valid, useful, intelligible everywhere in place and in time - in banks and insurance companies, on the parchments of the architects who raised the Temple of Solomon, and on the blueprints of the engineers who, with their calculus of chaos, master the winds. Here is a discipline of a hundred branches, fabulously rich, literally without limit in its sphere of application, laden with honors for an unbroken record of magnificent accomplishment. Here is a creation of the mind, both mystic and pragmatic in appeal. Austere and imperious as logic, it is still sufficiently sensitive and flexible to meet each new need." (Edward Kasner & James R Newman, "Mathematics and the Imagination", 1940)

"[...] I find both a special pleasure and constraint in describing the progress of mathematics, because it has been part of so much speculation: a ladder for mystical as well as rational thought in the intellectual ascent of man." (Jacob Bronowski, "The Ascent of Man", 1973)

"[...] mathematics and poetry move together between two extremes of mysticism, the mysticism of the commonplace where ideas illuminate and create facts, and the mysticism of the extraordinary where God, the Infinite, the Real, poses the riddles of desire and disappointment, sin and salvation, effort and failure, question and paradoxical answer [...]" (Scott Buchanan, "Poetry and Mathematics", 1975)

"[The Riemann] zeros did not appear to be scattered at random. Riemann’s calculations indicated that they were lining up as if along some mystical ley line running through the landscape."  (Marcus du Sautoy, "The Music of the Primes", 2003)

"Until [the RH is proved], we shall listen enthralled by this unpredictable mathematical music, unable to master its twists and turns. The primes have been a constant companion in our exploration of the mathematical world yet they remain the most enigmatic of all numbers. Despite the best efforts of the greatest mathematical minds to explain the modulation and transformation of this mystical music, the primes remain an unanswered riddle. We still await the person whose name will live for ever as the mathematician who made the primes sing." (Marcus du Sautoy, "The Music of the Primes", 2003)

On Mysticism III: Physics & Mysticism I

"It is in fact wonderful how physics - as soon as it is concerned not with technical purposes but with general results - without knowing it gets into cosmogony, astrology, theosophy, or whatever you wish to call it, in short, into a mystic discipline of the whole." (K W Friedrich Schlegel, "Dialogue on Poetry and Literary Aphorisms", cca. 1797–1800)

"The idea of an atom has been so constantly associated with incredible assumptions of infi nite strength, absolute rigidity, mystical actions at a distance and indivisibility, that chemists and many other reasonable naturalists of modern times, losing all patience with it, have dismissed it to the realms of metaphysics, and made it smaller than 'anything we can conceive'." (William T Kelvin, "On the Size of Atoms", Nature Vol. 1, 1870)

"[...] in the present-day reconstruction of physics, fragments of the Newtonian concepts are stubbornly retained. The result is to reduce modern physics to a sort of mystic chant over an unintelligible universe." (Alfred N Whitehead, "Modes of Thought", 1938)

"Whenever the Eastern mystics express their knowledge in words - be it with the help of myths, symbols, poetic images or paradoxical statements-they are well aware of the limitations imposed by language and 'linear' thinking. Modern physics has come to take exactly the same attitude with regard to its verbal models and theories. They, too, are only approximate and necessarily inaccurate. They are the counterparts of the Eastern myths, symbols and poetic images, and it is at this level that I shall draw the parallels. The same idea about matter is conveyed, for example, to the Hindu by the cosmic dance of the god Shiva as to the physicist by certain aspects of quantum field theory. Both the dancing god and the physical theory are creations of the mind: models to describe their authors' intuition of reality." (Fritjof Capra, "The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism", 1975)

"The conceptual framework of quantum mechanics, supported by massive volumes of experimental data, forces contemporary physicists to express themselves in a manner that sounds, even to the uninitiated, like the language of mystics." (Gary Zukav, "The Dancing Wu Li Masters", 1979)

"An aura of mysticism still surrounds the concept that has since been called 'imaginary numbers', and anyone who encounters these numbers for the first time is intrigued by their strange properties. But 'strange' is relative: with sufficient familiarity, the strange object of yesterday becomes the common thing of today." (Eli Maor, "e: The Story of a Number", 1994)

"The universe of Eastern mysticism is an illusion, A physicist who attempts to link it with his own work has abandoned physics." (Stephen Hawking)

On Mysticism II: Science & Mysticism I

"So, the vast results obtained by Science are won by no mystical faculties, by no mental processes, other than those which are practised by every one of us, in the humblest and meanest affairs of life." (Thomas H Huxley, "Science and Education", 1891)

"Metaphysics, or the attempt to conceive the world as a whole by means of thought, has been developed, from the first, by the union and conflict of two very different human impulses, the one urging men towards mysticism, the other urging them towards science." (Bertrand Russell, "Mysticism and Logic: And Other Essays", 1919)

"One has to recognize that science is not metaphysics, and certainly not mysticism; it can never bring us the illumination and the satisfaction experienced by one enraptured in ecstasy. Science is sobriety and clarity of conception, not intoxicated vision." (Ludwig Von Mises, "Epistemological Problems of Economics", 1933)

"It is his intuition, his mystical insight into the nature of things, rather than his reasoning which makes a great scientist." (Karl R Popper, "The Open Society and Its Enemies", 1945)

"To be a scientist - it is not just a different job so that a man should choose between being a scientist and being an explorer or a bond-salesman or a physician or a king or a farmer. It is a tangle of very obscure emotions, like mysticism, or wanting to write poetry; it makes its victim all different from the good natural man." (Sinclair Lewis, "Arrowsmith", 1952)

"Nominally a great age of scientific inquiry, ours has actually become an age of superstition about the infallibility of science; of almost mystical faith in its nonmystical methods; above all [...] of external verities; of traffic-cop morality and rabbit-test truth." (Louis Kronenberger, "Company Manners: A Cultural Inquiry into American Life", 1954)

"The experience of science - to stub your toe hard and then notice that it was really a rock on which you stubbed it - this experience is something that is hard to communicate by popularization, by education, or by talk. It is almost as hard to tell a man what it is like to find out something new about the world as it is to describe a mystical experience to a chap who has never had any hint of such an experience." (J Robert Oppenheimer, "The Open Mind", 1955)

"Science does not need mysticism and mysticism does not need science, but man needs both. Mystical experience is necessary to understand the deepest nature of things, and science is essential for modern life. What we need, therefore, is not a synthesis, but a dynamic interplay between mystical intuition and scientific analysis." (Fritjof Capra, "The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism", 1975)

"There is no such thing as a Scientific Mind. Scientists are people of very dissimilar temperaments doing different things in very different ways. Among scientists are collectors, classifiers and compulsive tidiers-up; many are detectives by temperament and many are explorers; some are artists and others artisans. There are poet-scientists and philosopher-scientists and even a few mystics. What sort of mind or temperament can all these people be supposed to have in common? Obligative scientists must be very rare, and most people who are in fact scientists could easily have been something else instead." (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)

"[...] in science there are collectors, classifiers, compulsory tidiers-up and permanent contesters, detectives, some artists and many artisans, there are poet-scientists and philosophers and even a few mystics." (Rolf M Zinkernagel, [Nobel lecture] 1996)

On Mysticism I: Mathematics & Mysticism I

"All things began in order, so shall they end, and so shall they begin again; according to the ordainer of order and mystical mathematics of the city of heaven." (Sir Thomas Browne, "The Garden of Cyrus", 1658)

"There is a famous formula, perhaps the most compact and famous of all formulas developed by Euler from a discovery of de Moivre: It appeals equally to the mystic, the scientist, the philosopher, the mathematician." (Edward Kasner & James R Newman, "Mathematics and the Imagination", 1940)

"The word ‘imaginary’ is the great algebraical calamity, but it is too well established for mathematicians to eradicate. It should never have been used. Books on elementary algebra give a simple interpretation of imaginary numbers in terms of rotations. […] Although the interpretation by means of rotations proves nothing, it may suggest that there is no occasion for anyone to muddle himself into a state of mystic wonderment over nothing about the grossly misnamed ‘imaginaries’." (Philip E B Jourdain, "The Nature of Mathematics" in [James R Newman, “The World of Mathematics” Vol. I, 1956])

"A real number that satisfies (is a solution of) a polynomial equation with integer coefficients is called algebraic. […] A real number that is not algebraic is called transcendental. There is nothing mystic about this word; it merely indicates that these numbers transcend (go beyond) the realm of algebraic numbers."  (Eli Maor, "e: The Story of a Number", 1994)

"An aura of mysticism still surrounds the concept that has since been called 'imaginary numbers', and anyone who encounters these numbers for the first time is intrigued by their strange properties. But 'strange' is relative: with sufficient familiarity, the strange object of yesterday becomes the common thing of today." (Eli Maor, "e: The Story of a Number", 1994)

"In many ways, the mathematical quest to understand infinity parallels mystical attempts to understand God. Both religions and mathematics attempt to express the relationships between humans, the universe, and infinity. Both have arcane symbols and rituals, and impenetrable language. Both exercise the deep recesses of our mind and stimulate our imagination. Mathematicians, like priests, seek ‘ideal’, immutable, nonmaterial truths and then often try to apply theses truth in the real world." (Clifford A Pickover, "The Loom of God: Mathematical Tapestries at the Edge of Time", 1997)

"The primes have been a constant companion in our exploration of the mathematical world yet they remain the most enigmatic of all numbers. Despite the best efforts of the greatest mathematical minds to explain the modulation and transformation of this mystical music, the primes remain an unanswered riddle." (Marcus du Sautoy, "The Music of the Primes", 2003)

"To survive, mathematical ideas must be beautiful, they must be seductive, and they must be illuminating, they must help us to understand, they must inspire us. […] Part of that beauty, an essential part, is the clarity and sharpness that the mathematical way of thinking about things promotes and achieves. Yes, there are also mystic and poetic ways of relating to the world, and to create a new math theory, or to discover new mathematics, you have to feel comfortable with vague, unformed, embryonic ideas, even as you try to sharpen them."  (Gregory Chaitin, "Meta Math: The Quest for Omega", 2005)

"Mathematical language is littered with pejorative and mystical terms - such as irrational, imaginary, surd, transcendental - that were once used to ridicule supposedly impossible objects. And these are just terms applied to numbers. Geometry also has many concepts that seem impossible to most people, such as the fourth dimension, finite universes, and curved space - yet geometers (and physicists) cannot do without them. Thus there is no doubt that  mathematics flirts with the impossible, and seems to make progress by doing so." (John Stillwell, "Yearning for the Impossible: The Surprising Truths of Mathematics", 2006)

"Zero is not a point of non-existence. Zero is always a balance point of existents. The human understanding of 'zero' must undergo the most radical of all transformations. Most people, especially scientists, associate it with absolute nothingness, with non-existence. This is absolutely untrue. Or, to put it another way, we can define it in two ways: 1) nothing as non-existence, in which case it has absolutely no consequences but leads to all manner of abstract paradoxes and contradictions, or 2) nothing as existence, in which case it is always a mathematical balance point for somethings. It is purely mathematical, not scientific, or religious, or spiritual, or emotional, or sensory, or mystical. It is analytic nothing and whenever you encounter it you have to establish the exact means by which it is maintaining its balance of zero." (Thomas Stark, "God Is Mathematics: The Proofs of the Eternal Existence of Mathematics", 2018)