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To return to the general analysis of the Rosicrucian outlook. Magic was a dominating factor, working as a mathematics-mechanics in the lower world, as celestial mathematics in the celestial world, and as angelic conjuration in the supercelestial world. One cannot leave out the angels in this world view, however much it may have been advancing towards the scientific revolution. The religious outlook is bound up with the idea that penetration has been made into higher angelic spheres in which all religions were seen as one; and it is the angels who are believed to illuminate man's intellectual activities.In the earlier Renaissance, the magi had been careful to use only the forms of magic operating in the elemental or celestial spheres, using talismans and various rituals to draw down favourable influences from the stars. The magic of a bold operator like Dee, aims beyond the stars, aims at doing the supercelestial mathematical magic, the angel-conjuring magic. Dee firmly believed that he had gained contact with good angels from whom he learned advancement in knowledge. This sense of close contact with angels or spiritual beings is the hallmark of the Rosicrucian. It is this which infuses his technology, however practical and successful and entirely rational in its new understanding of mathematical techniques, with an unearthly air, and makes him suspect as possibly in contact, not with angels, but with devils.
Frances A. Yates
The golden era of the golden number was the Italian renaissance. The expression divine proportion was coined by the great mathematician Luca Pacioli in his book 'De divina proportione', written in 1509.
Midhat Gazale
Two writings of al-Hassār have survived. The first, entitled Kitāb al-bayān wa t-tadhkār [Book of proof and recall] is a handbook of calculation treating numeration, arithmetical operations on whole numbers and on fractions, extraction of the exact or approximate square root of a whole of fractionary number and summation of progressions of whole numbers (natural, even or odd), and of their squares and cubes. Despite its classical content in relation to the Arab mathematical tradition, this book occupies a certain important place in the history of mathematics in North Africa for three reasons: in the first place, and notwithstanding the development of research, this manual remains the most ancient work of calculation representing simultaneously the tradition of the Maghrib and that of Muslim Spain. In the second place, this book is the first wherein one has found a symbolic writing of fractions, which utilises the horizontal bar and the dust ciphers i.e. the ancestors of the digits that we use today (and which are, for certain among them, almost identical to ours) [Woepcke 1858-59: 264-75; Zoubeidi 1996]. It seems as a matter of fact that the utilisation of the fraction bar was very quickly generalised in the mathematical teaching in the Maghrib, which could explain that Fibonacci (d. after 1240) had used in his Liber Abbaci, without making any particular remark about it [Djebbar 1980 : 97-99; Vogel 1970-80]. Thirdly, this handbook is the only Maghribian work of calculation known to have circulated in the scientific foyers of south Europe, as Moses Ibn Tibbon realised, in 1271, a Hebrew translation.[Mathematics in the Medieval Maghrib: General Survey on Mathematical Activities in North Africa]
Ahmed Djebbar
The impulse to all movement and all form is given by [the golden ratio], since it is the proportion that summarizes in itself the additive and the geometric, or logarithmic, series.
Schwaller de Lubicz
The focus of history and philosophy of science scholar Arthur Miller’s (2010) "137: Jung and Pauli and the Pursuit of Scientific Obsession" is Jung and Pauli’smutual effort to discover the cosmic number or fine structure constant, which is a fundamental physical constant dealing with electromagnetism, or, from a different perspective, could be considered the philosopher’s stone of the mathematical universe.This was indeed one of Pauli and Jung’s collaborative passions, but it was not the only concentration of their relationship. Quantum physics could be seen as the natural progression from ancient alchemy, through chemistry, culminating in the abstract world of subatomic particles, wave functions, and mathematics. [Ancient Egypt and Modern Psychotherapy]
Todd Hayen
Mathematics, which most of us see as the most factual of all sciences, constitutes the most colossal metaphor imaginable, and must be judged, aesthetically as well as intellectually in terms of the success of this metaphor.
Norbert Wiener
Myths, legends and stories are the signposts previous generations have left us so we don't have to figure out our own personal journey in solitude!They have to be metaphorical, because their interpretation will be different for each individual life!
Fred Van Lente
Arnold Sommerfeld generalized Bohr's model to include elliptical orbits in three dimensions. He treated the problem relativistically (using Einstein's formula for the increase of mass with velocity), ... According to historian Max Jammer, this success of Sommerfeld's fine-structure formula "served also as an indirect confirmation of Einstein's relativistic formula for the velocity dependence of inertia mass.
Stephen G. Brush
The theoretical determination of the fine structure constant is certainly the most important of the unsolved problems of modern physics. We believe that any regression to the ideas of classical physics (as, for instance, to the use of the classical field concept)cannot bring us nearer to this goal. To reach it, we shall, presumably, have to pay with further revolutionary changes of the fundamental concepts of physics with a still farther digression from the concepts of the classical theories.
Wolfgang Pauli
But some numbers, called dimensionless numbers, have the same numerical value no matter what units of measurement are chosen. Probably the most famous of these is the "fine-structure constant," .... Physicists love this number not just because it is dimensionless, but also because it is a combination of three fundamental constants of nature.
John Archibald Wheeler
Following the path of earlier unificationists, one of Eddington's aims was to reduce the contingencies in the description of nature, for example, by explaining the fundamental constants of physics rather than accepting them as merely experimental data. One of these constants was the fine-structure constant ..., which entered prominently in Dirac's theory and was known to be about 1/137.
Helge Kragh
Some astrophysicists have convinced themselves that the fifth significant figure of the fine structure constant has changed over the past ten billion years.
Sheldon L. Glashow
As Sommerfeld said in his famous text "Spectral Lines and Atomic Constitution," on which a generation of physicists learned the subject, "In the fine structure constant e is the representative of the electron theory, h the appropriate representative of the quantum theory, c comes from relativity and characterizes it in contrast to classical theory.
Emilio Segrè
Dirac's equation not only accounted for the spin of the electron and its observed magnetic moment, but also correctly explained the fine structure of the hydrogen atom. If the derivation of the Sommerfeld-like formula for the spectrum of the hydrogen atom was one of the striking successes of the Dirac equation, some of its other features were very troublesome.
Silvan S. Schweber
God is a pure mathematician!' declared British astronomer Sir James Jeans. The physical Universe does seem to be organised around elegant mathematical relationships. And one number above all others has exercised an enduring fascination for physicists: 137.0359991.... It is known as the fine-structure constant and is denoted by the Greek letter alpha (α).
Paul Davies
The bridge between the electron and the other elementary particles is provided by the fine structure constant. ... An expanded form of the constant leads to equations that define the transformation of electromagnetic energy into electron mass/energy, ...
Malcolm H. Mac Gregor
In his first philosophical lecture on modern physics that Pauli gave in November 1934 to the Zurich Philosophical Society he said that only a formulation of quantum theory would be satisfactory which expresses the relation between the value of [the fine structure constant] and charge conservation in the same complementary was as that between the space-time description and energy-momentum conservation.
Charles P. Enz
... it should be remembered that the atomicity of electric charge has already found its expression in the specific numerical value of the fine structure constant, a theoretical understanding of which is still missing today.
Wolfgang Pauli
True, the Standard Model does explain a very great deal. Nevertheless it is not yet a proper theory, principally because it does not satisfy the physicists naive faith in elegance and simplicity. It involves some 17 allegedly fundamental particles and the same number of arbitrary and tunable parameters, such as the fine-structure constants, the muon-electron mass ratio and the various mysterious mixing angles.
Sheldon L. Glashow
To calculate 'the' fine structure constant, 1/137, we would need a realistic model of just about everything, and this we do not have. In this talk I want to return to the old question of what it is that determines gauge couplings in general, and try to prepare the ground for a future realistic calculation.
Steven Weinberg
In short, the idea dawns that the one universal principle which possibly ... between force and structure, the embodiment of the Principle of Least Action and the (unknown) force, which in mathematics is known as the attractor which pulls ... in the direction of the most optimal and relatively stable self-organized criticality, could very well be the Golden Ratio dynamic. the universal principle which as the balance between finiteness and infinity, stability and flexibility underlies self-similar fractal forms emerging at the 'edge of chaos' indeed seems to be the Golden Ratio Spiral.
Marja de Vries
The unsolved problems of the physical world now seem even more formidable than those solved in the twentieth century. Though in application it works splendidly, we do not even understand the physical meaning of quantum mechanics, much less how it might be united with general relativity.We don't know why the dimensionless constants (ratios of masses of elementary particles, ratios of strength of gravitational to electric forces, fine structure constant, etc.) have the values they do, unless we appeal to the implausible anthropic principle, which seems like a regression to Aristotelian teleology.
Gerald Holton
The power of the deductive network produced in physics has been illustrated in a delightful article by Victor F. Weisskopf. He begins by taking the magnitudes of six physical constants known by measurement: the mass of the proton, the mass and electric charge of the electron, the light velocity, Newton's gravitational constant, and the quantum of action of Planck. He adds three of four fundamental laws (e.g., de Broglie's relations connecting particle momentum and particle energy with the wavelength and frequency, and the Pauli exclusion principle), and shows that one can then derive a host of different, apparently quite unconnected, facts that happen to be known to us by observation separately ....
Gerald Holton
Highly complex numbers like the Comma of Pythagoras, Pi and Phi (sometimes called the Golden Proportion), are known as irrational numbers. They lie deep in the structure of the physical universe, and were seen by the Egyptians as the principles controlling creation, the principles by which matter is precipitated from the cosmic mind.Today scientists recognize the Comma of Pythagoras, Pi and the Golden Proportion as well as the closely related Fibonacci sequence are universal constants that describe complex patterns in astronomy, music and physics. ...To the Egyptians these numbers were also the secret harmonies of the cosmos and they incorporated them as rhythms and proportions in the construction of their pyramids and temples.
Jonathan Black
Since ancient times artists and architects have seen in the golden mean the most aesthetically satisfying geometric ratio.
Stephen M. Barr
The prime number 137 had continuously occupied Pauli's mind. It is an approximate value for a constant appearing in the fine structure theory of atomic spectra which in its theoretical expression ties together electromagnetism, relativity and quantum theory. Pauli saw the fine structure theory of spectra as a key in understanding the deepest contemporary problems of theoretical physics. For that reason the number 137 possessed a mysterious attraction for him.
K. V. Laurikainen
The water beneath the Temple was both actual and metaphorical, existing as springs and streams, as spiritual energy, and as a symbol of the receptive or lunar aspect of nature. The meaning of that principle is too wide and elusive for it to be given any one name, so in the terminology of ancient science it was given a number, 1,080. Its polar opposite, the positive, solar force in the universe, was also referred to as a number 666. These two numbers, which have an approximate golden-section relationship of 1:1.62, were at the root of the alchemical formula that expressed the supreme purpose of the Temple. Its polar opposite, the positive, solar force in the universe, was also referred to as a number 666. Not merely was it used to generate energy from fusion of atmospheric and terrestrial currents, but it also served to combine in harmony all the correspondences of those forces on every level of creation.
John Michell
Science does nothing for man spiritually, and organized religion demands blind faith in illogical liturgy that was never meant to be taken literally!
Fred Van Lente
And, if you'll investigate the history of science, my dear boy, I think you'll find that most of the really big ideas have come from intelligent playfulness. All the sober, thin-lipped concentration is really just a matter of tidying up around the fringes of the big ideas.
Kurt Vonnegut Jr.
The strength of the familiar electromagnetic force between two electrons, for example, is expressed in physics in terms of a constant known as the fine structure constant. The value of this constant, almost exactly 1/137, has puzzled many generations of physicists. A joke made about the famous English physicist Paul Dirac (1902-1984), one of the founders of quantum mechanics, says that upon arrival to heaven he was allowed to ask God one question. His question was: "Why 1/137?
Mario Livio
Not enough books focus on how a culture responds to radically new ideas or discovery. Especially in the biography genre, they tend to focus on all the sordid details in the life of the person who made the discovery. I find this path to be voyeuristic but not enlightening. Instead, I ask, After evolution was discovered, how did religion and society respond? After cities were electrified, how did daily life change? After the airplane could fly from one country to another, how did commerce or warfare change? After we walked on the Moon, how differently did we view Earth? My larger understanding of people, places and things derives primarily from stories surrounding questions such as those.
Neil deGrasse Tyson
According to Thoth, because of the placement of the Great Pyramid on the Earth connecting into the Earth's huge geometrical field - specifically the octahedral field of the Earth, which is equivalent to our own fields - and because of the pyramid's mass and the geometries used in it, the white-light energy field spirals upward and becomes extremely strong, stretching all the way out to the center of the galaxy. The dark-light energy comes in from above, spirals through zero point and connects with the center of the Earth. In this way the Great Pyramid connects the center of the Earth to the center of our galaxy.
Drunvalo Melchizedek
While twentieth-century physicists were not able to identify any convincing mathematical constants underlying the fine structure, partly because such thinking has normally not been encouraged, a revolutionary suggestion was recently made by the Czech physicist Raji Heyrovska, who deduced that the fine structure constant, ...really is defined by the [golden] ratio ....
Carl Johan Calleman
Fine Structure Constant: Fundamental numerical constant of atomic physics and quantum electrodynamics, defined as the square of the charge of the electron divided by the product of Planck's constant and the speed of light.
Steven Weinberg
Plato, Socrates, Aristotle and many more great minds laid the groundwork for the development of modern science. Over the foundation of philosophy, history witnessed the daring ventures of human excellence by both philosophical and scientific geniuses, such as Leonardo-da-Vinci, Copernicus, Galileo, Kepler, Bacon, Darwin, Newton and so on. And the chain of reaction they triggered with their extraordinarily abnormal thinking, given their surrounding ignorance and fundamentalism, resulted into the evolution of our modern science.
Abhijit Naskar
The fine-structure constant is ubiquitous throughout physics. I’ve already noted its connection to the electromagnetic interaction. In atomic physics, the binding energy, fine-structure splitting, and Lamb shift are all proportional to powers of α. In condensed matter physics, α characterizes Josephson junction oscillations and quantum Hall resistance steps. In addition, α is an important component of our system of fundamental constants. [Physics Today]
Gerald Gabrielse
It's true. I doubt. I doubt because I seek the truth. Doubt has served me well.
Bradley Steffens
A number of years ago, when I was a freshly-appointed instructor, I met, for the first time, a certain eminent historian of science. At the time I could only regard him with tolerant condescension.I was sorry of the man who, it seemed to me, was forced to hover about the edges of science. He was compelled to shiver endlessly in the outskirts, getting only feeble warmth from the distant sun of science- in-progress; while I, just beginning my research, was bathed in the heady liquid heat up at the very center of the glow.In a lifetime of being wrong at many a point, I was never more wrong. It was I, not he, who was wandering in the periphery. It was he, not I, who lived in the blaze.I had fallen victim to the fallacy of the 'growing edge;' the belief that only the very frontier of scientific advance counted; that everything that had been left behind by that advance was faded and dead.But is that true? Because a tree in spring buds and comes greenly into leaf, are those leaves therefore the tree? If the newborn twigs and their leaves were all that existed, they would form a vague halo of green suspended in mid-air, but surely that is not the tree. The leaves, by themselves, are no more than trivial fluttering decoration. It is the trunk and limbs that give the tree its grandeur and the leaves themselves their meaning., 'it is because I have stood on the shoulders of giants.
Isaac Asimov
Plato, Socrates, Aristotle and many more great minds laid the groundwork for the development of modern science. Over the foundation of philosophy, history witnessed the daring ventures of human excellence by both philosophical and scientific geniuses, such as Leonardo-da-Vinci, Copernicus, Galileo, Kepler, Bacon, Darwin, Newton and so on. And the chain of reaction they triggered with their extraordinarily abnormal thinking, given their surrounding ignorance and fundamentalism, resulted into the evolution of our modern science.
Abhijit Naskar
The fine-structure constant is ubiquitous throughout physics. I’ve already noted its connection to the electromagnetic interaction. In atomic physics, the binding energy, fine-structure splitting, and Lamb shift are all proportional to powers of α. In condensed matter physics, α characterizes Josephson junction oscillations and quantum Hall resistance steps. In addition, α is an important component of our system of fundamental constants. [Physics Today]
Gerald Gabrielse
It's true. I doubt. I doubt because I seek the truth. Doubt has served me well.
Bradley Steffens
A number of years ago, when I was a freshly-appointed instructor, I met, for the first time, a certain eminent historian of science. At the time I could only regard him with tolerant condescension.I was sorry of the man who, it seemed to me, was forced to hover about the edges of science. He was compelled to shiver endlessly in the outskirts, getting only feeble warmth from the distant sun of science- in-progress; while I, just beginning my research, was bathed in the heady liquid heat up at the very center of the glow.In a lifetime of being wrong at many a point, I was never more wrong. It was I, not he, who was wandering in the periphery. It was he, not I, who lived in the blaze.I had fallen victim to the fallacy of the 'growing edge;' the belief that only the very frontier of scientific advance counted; that everything that had been left behind by that advance was faded and dead.But is that true? Because a tree in spring buds and comes greenly into leaf, are those leaves therefore the tree? If the newborn twigs and their leaves were all that existed, they would form a vague halo of green suspended in mid-air, but surely that is not the tree. The leaves, by themselves, are no more than trivial fluttering decoration. It is the trunk and limbs that give the tree its grandeur and the leaves themselves their meaning., 'it is because I have stood on the shoulders of giants.
Isaac Asimov
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