Paradise Regained: Thirteen steps to a divine world
An Introduction to the commentary on the Home Page
In scientific investigations . . . it is permitted to invent any hypothesis, and if it explains various large and independent classes of facts, it rises to the rank of a well grounded theory. Charles Darwin (1998): The Variation of Animals and Plants Under Domestication
Perhaps now is the time to widen the quest for understanding still further, to expand the intellectual effort beyond conventional science—to engage the larger non-scientific communities of philosophers, theologians and others who often resonate with the cosmic-evolutionary theme even if not in name, all in an ambitious effort to construct a millennial world view of who we are, where we came from, and how we fit into the cosmic scheme of things as wise, ethical, human beings. Eric J. Chaisson (2002): Cosmic Evolution: The Rise of Complexity in Nature, page 211
When God began to create heaven and earth, and the earth then was welter and waste and darkness over the deep and God’s breath hovering over the waters, God said, “let there be light.” And there was light. And God saw the light, that it was good and God divided the light from the darkness. And God called the light Day, and the darkness he called Night. And it was evening and it was morning, first day. Robert Alter (2004): The Five Books of Moses:A Translation with Commentary (Genesis I_1-5
Here and elsewhere we shall not obtain the best insights into things until we actually see them grow from the beginning (Aristotle quoted in Jaeger). Werner Wilhelm Jaeger (1997): Aristotle: Fundamentals of the history of his development
Here we begin the interesting task of outlining the creation of the universe from almost nothing. We must begin with the principle ex nihilo nihil fit “nothing comes from nothing”. This implies that the origin of the universe, whatever it it, is eternal, without a beginning in time.
At least since the origin of our species Homo sapiens, billions of people in many thousands of languages and cultures have developed stories to explain our condition, how we came to be here and sometimes where we are going. Long oral traditions, art, writing and archaeology give us growing insight into what our ancestors were doing and thinking. Physical objects like weapons, pottery, burials, canals, roads buildings, sculpture and finally writing show how our ancestors lived and give us some insight into what they were thinking. Mahabharata - Wikipedia
An important channel for information about ancient theology, religion and politics is the relationship between astrology and astronomy. Implicit in astrology is the belief that influences originating in the heavens shape life on Earth. Different traditions intermingled the work of intelligent invisible anthropomorphic beings like gods, goddesses and angels with the apparent physical influences of the visible sun, stars, planets and the moon. This slowly led to the development of measuring instruments ranging from monoliths to protractors, compasses and telescopes and to the emergence of scientific astronomy driven and often paid for by the astrological desire for clear pictures of heavenly motions and their roles in human affairs.
Tensions developed between astronomical observations and traditional beliefs in sixteenth century Italy. The instrument maker, Galileo Galilei, began to make empirical studies of physical phenomena and realized that many of the beliefs attributed to Aristotle were false, particularly the idea that the planet Earth was at the centre of reality and the Sun revolved around it.
Studies and observations by Tycho Brahe, Copernicus, Kepler and others were questioning this belief. After Galileo learnt of the existence telescopes and built a series of improved models for himself he was able to observe the moons of Jupiter and the phases of Venus. These observations convinced him that the Earth could be orbiting the Sun. He published his opinion and came into conflict with the Church, the Galileo affair. Galileo affair - Wikipedia
The five books of Moses provide foundation story for the Hebrew people as they moved out of the ancient Egyptian theocracy, became the nation of Israel and fought their way into the territory we now call the Holy Land. There, during a Roman military occupation, their Judaic religion metamorphosed into Christianity. In the next three hundred years the new religion far outgrew its parent. Robert Alter (2004): op.cit, Keith Hopkins (2001): A World Full of Gods: The Strange Triumph of Christianity
In the fourth century Christianity was appropriated by the Emperor Constantine to become the Roman Catholic Church and the Holy Roman Empire. This theocratic culture ruled Europe until the modern era and is still followed by millions of people in the European diaspora throughout the world. Constantine the Great and Christianity - Wikipedia, Holy Roman Empire - Wikipedia, Theocracy - Wikipedia
The Book of Joshua records an incident in which the God of Israel, Yahweh, provided physical astronomical assistance to their followers. Book of Joshua - Wikipedia
12 At that time Joshua spoke to the LORD in the day when the LORD gave the Amorites over to the sons of Israel, and he said in the sight of Israel, "Sun, stand still at Gibeon, and moon, in the Valley of Aijalon.”
13 And the sun stood still, and the moon stopped, until the nation took vengeance on their enemies.' The Book of Joshua 10:12-13
Two thousand years later the Holy Inquisition claimed that this ancient text proves that the Sun orbits Earth rather that vice versa. They charged Galileo with vehement suspicion of heresy for which the punishment, if “proven”, was death. Galileo knew without doubt that the Earth orbited the Sun. He had used his telescope to observe the phases of Venus, which orbits the Sun inside the orbit of Earth. He recanted to save his life but the evidence shows that the Church was wrong and many thought Galileo had been abused. Galileo Galilei (1633): Recantation of Galileo (June 22, 1633)
On the centenary of Einstein’s birth on 10 November 1979 the Roman Pope John Paul II foreshadowed a modern study of this “Galileo Affair”. The Papal Academy of Science established a Study Commission for this purpose on 3 July 1981. The Pope announced the conclusions of this study in an address to a Plenary Session of the Academy on 31 October 1992:
4. [. . .] One might perhaps be surprised that, at the end of the Academy’s study week on the subject of the emergence of complexity in the various sciences, I am returning to the Galileo case. Has not this case long been shelved and have not the errors committed been recognised?
That is certainly true. However, the underlying problems of this case concern both the nature of science and the message of faith. It is therefore not to be excluded that one day we shall find ourselves in a similar situation, one which will require both sides to have an informed awareness of the field and of the limits of their own competencies. Saint John Paul II (1992_10_31): Address to the Plenary Session on ‘The Emergence of Complexity in Mathematics, Physics, Chemistry and Biology’
Throughout his discussion of the Church’s treatment of Galileo the Pope sticks firmly to the ecclesiastical dichotomy between revelation and science. He explains:
12. [. . .] There exist two realms of knowledge, one which has its source in Revelation and one which reason can discover by its own power. To the latter
belong especially the experimental sciences and philosophy. The distinction
between the two realms of knowledge ought not to be understood as opposition.
The two realms are not altogether foreign to each other; they have points of
contact. The methodologies proper to each make it possible to bring out different aspects of reality [. . .].
14. Humanity has before it two modes of development. The first involves
culture, scientific research and technology, that is to say whatever falls within the horizontal aspect of man and creation, which is growing at an impressive rate.
[. . .] The second mode of development involves what is deepest in the human
being, when, transcending the world and transcending himself, man turns to the
One who is the Creator of all. It is only this vertical direction which can give full meaning to man’s being and action, because it situates him in relation to his origin and his end.
We may argue against this splitting on two grounds. The first, following the idea from Aristotle displayed at the beginning of this page, is to go back to the beginning and postulate an initial singularity which embraces both realms of knowledge, constrained only by local consistency. This is an analogue of the current big bang theory. Rather than choosing something like a black hole, as suggested by Hawking and Ellis, we use the Christian model of God, developed by Aquinas from the work of Aristotle, joined with Einstein’s model of the universe to provide an initial singularity which is eternal, omnipotent and totally without structure. This entity is described in Commentary page 1: The omnipotent Aquinas–Einstein initial singularity. Hawking & Ellis (1975): The Large Scale Structure of Space-Time
The second is to show that Darwin’s theory of evolution is an explanation of creation that takes care of all aspects of the both humanity and the universe, from the beginning to any conceivable end. Because the initial singularity is omnipotent, it acts. Because it has no structure it acts at random, thus implementing the creative input to evolution, variation.
A very serious error espoused by the Catholic Church based on its two truth model is the assertion that women are not sufficiently human to becomes priests. This assertion alone nullifies any claim the Church may have to be a religion for all of us. Another assertion sailing in the face of science is the claim that evolution cannot be the source of the human spirit. Pope Paul VI (1976_10_15): Inter Insigniores: On the question of admission of women to the ministerial priesthood, Pope John Paul II (22 October 1996): Address to Plenary Session on 'The Origins and Early Evolution of Life'
The selective limits on both divinity and creation are set by the principle of noncontradiction, the logical foundation of the ontological test of survival. This situation is illustrated by a standing problem in the science of computation known as P versus NP. P describes the power of a deterministic universal Turing machine. NP describes a potentially more powerful process that arrives at conclusions by random action. P versus NP problem - Wikipedia, Turing machine - Wikipedia
Here we guess that random chance can take us to places where logic cannot go. Someday someone may prove or disprove this conjecture. Nevertheless, we feel that the results of chance can be tested by a deterministic P process. In evolution, a rabbit may be designed by an NP process, but the reliable reproduction of rabbits, and therefore their survival, must depend on P processes
Evolution is made possible by the duality, first noted by Aristotle, with the help of his teacher Plato, between matter and form. Each of us carries two copies of ourselves, one formal and genetic, coded in a few gigabytes of DNA and the other our actual self, tens of trilllions of living cells whose growth and structure is guided by the genetic code. The key to evolution is changes in the DNA, which comes about by sexual mating and by chance.
On this site we assume that there is quantum mechanical evolution analogous to genetic evolution. Once again we rely on a random process to generate variety and selective processes to pick out those stable variants that can reproduce themselves and so become relatively permanent fixtures in the nature of the world. In biology living structures are defined by genes. In this deeper view of the world, quantum formalism defines the elementary particles from which every other body in the world is constructed.
The world is founded on Hilbert space, the world of waves from infinite monotones to the most complex sounds of speech and orchestra to the structure of the universe a superposition of a countable infinity of frequencies into a Cantorian transfinity of unbounded detail, a divinity of which our own bodies and minds and cultures are the elements closest to us, children of god. Pina Bausch:The Rite of Spring, Hilbert space - Wikipedia, Transfinite numbers - Wikipedia
The choreography of Hilbert music is visible to us in Minkowski space at scales ranging from the photon, the proton and the electron to the universe as a whole. Minkowski space - Wikipedia
Choreography uses energy to make form concrete. The key to this is the quantum of action, the logical element of energy which processes a wave to a reality by a series of quanta of action analogous to the stepwise operation of a Turing machine running up and down on its memory tape, reading and writing. Passionate execution of Stravinsky’s music created in his mind, itself a Minkowski representation of logical process, embedded in neurons, synapses and electrical connections.
As we go along we will show how the divine world, like the traditional gods, supports human life and welfare: long life, happiness and peace on Earth. We no longer postulate heaven for the good and hell for the bad but a route to an enjoyable life for everyone. We must learn from the nature of the world to restrain our greed and pride to honour the system that created us.
This website is a sequel to my book Cognitive Cosmogenesis: a systematic integration of physics and theology. There I propose that we must accept the physical nature of the world as the true source of theology. Physics, in all its dimensions, is God’s body language. We must learn to read it instead of killing it and burning it down. Jeffrey Nicholls (2025); Cognitive Cosmogenesis: A systematic integration of physics and theology
Here I condense the enormous complexity of modern physics to produce a simple physical story to explain the creation and nature of the world. This possible because the world started, as Aquinas explains, very simply as a pure structureless action whose essence is to be.
I summarize this story on the home page. I expand it in this commentary. As the site grows I will add more and more detail, eventually arriving at an extended treatment of the divine lust for life that created the magnificent universe.
One might thinks that this story must be too good to be true, but there can be no doubt that the universe started from something like the Aquinas–Einstein symmetry and evolved itself by a combination of random choice driven by fixed point theory and selected by consistency, the key to omnipotence, to get us to the world we have now. Brouwer fixed-point theorem - Wikipedia
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Notes and references
Further readingBooks
Alter (2004), Robert, The Five Books of Moses, W. W.Norton 2004 ' Through a distinguished career of critical scholarship and translation, Robert Alter has equipped ua to read thr Hebrew Bible as a powerful cohesive work of literature. In this landmark work, Alter's masterly translation and probing commentary combine to give contemporary readers the definitive edition of the Five Books of Moses.
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Chaisson (2002), Eric J., Cosmic Evolution: The Rise of Complexity in Nature, Harvard University Press 2002 ' In Cosmic Evolution Chaisson addresses some of the most basic issues we can contemplate: the origin of matter and the origin of life, and the ways matter, life, and radiation interact and change with time. Guided by notions of beauty and symmetry, by the search for simplicity and elegance, by the ambition to explain the widest range of phenomena with the fewest possible principles, Chaisson designs for us an expansive yet intricate model depicting the origin and evolution of all material structures. He shows us that neither new science nor appeals to nonscience are needed to understand the impressive hierarchy of the cosmic evolutionary story, from quark to quasar, from microbe to mind.'
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Darwin (1998), Charles, and Harriet Ritvo (Introduction), The Variation of Animals and Plants Under Domestication (Foundations of Natural History), Johns Hopkins University Press 1883, 1998 Introduction, page 9: "In scientific investigations is it permitted to invent any hypothesis, and if it explains vsarious large and independent classes of facts it rises to the rank of a well-grounded theory". [Reproduced from the 1883 edition (which was revised from its original publication in 1868), this was Darwin's follow-up to his On the Origin of Species, written in response to criticisms that his theory of evolution was unsubstantiated.]
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Hawking (1975), Steven W, and G F R Ellis, The Large Scale Structure of Space-Time, Cambridge UP 1975 Preface: Einstein's General Theory of Relativity . . . leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.'
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Hopkins (2001), Keith, A World Full of Gods: The Strange Triumph of Christianity, Penguin Random House 2001 ' In this provocative, irresistibly entertaining book, Keith Hopkins takes readers back in time to explore the roots of Christianity in ancient Rome. Combining exacting scholarship with dazzling invention, Hopkins challenges our perceptions about religion, the historical Jesus, and the way history is written. He puts us in touch with what he calls “empathetic wonder”—imagining what Romans, pagans, Jews, and Christians thought, felt, experienced, and believed-by employing a series of engaging literary devices. These include a TV drama about the Dead Sea Scrolls; the first-person testimony of a pair of time-travelers to Pompeii; a meditation on Jesus’ apocryphal twin brother; and an unusual letter on God, demons, and angels.'
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Jaeger (1997), Werner Wilhelm, Aristotle: Fundamentals of the history of his development, Oxford University Press 1997 Jacket: '"Aristotle was the first thinker to set up along with his philosophy a conception of his own position in history; he thereby created a new kind of philosophical consciousness, more responsible and inwardly complex. He was the inventor of the notion of intellectual development in time . . . ." In this classic study, Professor Jaeger profoundly altered the general view of Aristotle among philosophers and classical scholars. He showed that Aristotle was not uncompromisingly opposed to Plato, that he developed gradually, applying step by step his particular genius to the problems of his age.'
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Nicholls (2025), Jeffrey, Cognitive Cosmogenesis: A systematic unification of physics and theology, Austin Macauley Publishers 12025 ' This book is a personal narrative of those events and a defense of the belief that the universe itself is divine. The central argument is that by embracing this reality and abandoning notions of supernatural deities, humanity can resolve its problems. The universe, it is argued, is self-creating, and a proper understanding of physics leads to a plausible scientific theology. The natural intelligence inherent in the universe, from cellular organization to ecosystems, far surpasses any artificial intelligence. Comprehending this natural order, the author suggests, would make achieving world peace relatively straightforward.
The book contends that modern theologians should recognize the physical world, rather than ancient texts, as the foundation for credible theology. It also addresses the historical entanglement of religion and politics, asserting that the model of creation presented herein fundamentally rejects the imperialistic ambitions that have fueled genocidal holy wars.'
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Links
Aline Sanford (2016_11_21), A Brief Analysis of Augustine of Hippo’s Studies and the Impact of the Doctrine of Original Sin Across Religions, ' Augustine of Hippo also known as Saint Augustine, Doctor of Grace among many other names, was a Christian theologian and philosopher who lived 354–430 CE. He influenced western Christianity with his teachings. He was baptized in 386 CE and after that developed how own approach to Christianity and the philosophy within the matter. Within the catholic church Augustine is considered a Saint although Eastern orthodox churches have also used his teaching as bases for their own studies and illustrations of their faith. Among many of Augustine’s studies and works there is his contemplation of the Doctrine of Original Sin. Original sin, also called ancestral sin, is the Christian doctrine of humanity’s state of sin resulting from the fall of man, stemming from Adam and Eve’s rebellion in Eden, namely the sin of disobedience in consuming from the tree of knowledge of good and evil.' back |
Book of Joshua - Wikipedia, Book of Joshua - Wikipedia, the free encyclopedia, 'The Book of Joshua . . . is the sixth book in the Hebrew Bible and of the Old Testament. Its 24 chapters tell of the entry of the Israelites into Canaan, their conquest and division of the land under the leadership of Joshua, and of serving God in the land. Joshua forms part of the biblical history of the emergence of Israel which begins with the exodus of the Israelites from slavery in Egypt, continues with their conquest of Canaan under their leader Joshua (the subject matter of the book of Joshua), and culminates in Judges with the settlement of the tribes in the land.' back |
Brouwer fixed-point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, 'Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f mapping a nonempty compact convex set to itself, there is a point x0 such that f(x0) = x0. The simplest forms of Brouwer's theorem are for continuous functions from a closed interval I in the real numbers to itself or from a closed disk D to itself. A more general form than the latter is for continuous functions from a nonempty convex compact subset K of Euclidean space to itself.' back |
Constantine the Great and Christianity - Wikipedia, Constantine the Great and Christianity - Wikipedia, the free encyclopedia, ' During the reign of the Roman Emperor Constantine the Great (AD 306–337), Christianity began to transition to the dominant religion of the Roman Empire. Historians remain uncertain about Constantine's reasons for favoring Christianity, and theologians and historians have often argued about which form of early Christianity he subscribed to. . . . Constantine's decision to cease the persecution of Christians in the Roman Empire was a turning point for early Christianity, sometimes referred to as the Triumph of the Church, the Peace of the Church or the Constantinian shift. In 313, Constantine and Licinius issued the Edict of Milan decriminalizing Christian worship. The emperor became a great patron of the Church and set a precedent for the position of the Christian emperor within the Church and raised the notions of orthodoxy, Christendom, ecumenical councils, and the state church of the Roman Empire declared by edict in 380. He is revered as a saint and is apostolos in the Eastern Orthodox Church, Oriental Orthodox Church, and various Eastern Catholic Churches for his example as a "Christian monarch”.' back |
Galileo affair - Wikipedia, Galileo affair - Wikipedia, the free encyclopedia, ' The Galileo affair (Italian: il processo a Galileo Galilei) began around 1610 and culminated with the trial and condemnation of Galileo Galilei by the Roman Catholic Inquisition in 1633. Galileo was prosecuted for his support of heliocentrism, the astronomical model in which the Earth and planets revolve around the Sun at the centre of the Solar System. ' back |
Galileo Galilei (1633), Recantation of Galileo (June 22, 1633), ' Therefore, desiring to remove from the minds of your Eminences, and of all faithful Christians, this vehement suspicion, justly conceived against me, with sincere heart and unfeigned faith I abjure, curse, and detest the aforesaid errors and heresies, and generally every other error, heresy, and sect whatsoever contrary to the said Holy Church, and I swear that in the future I will never again say or assert, verbally or in writing, anything that might furnish occasion for a similar suspicion regarding me; ' back |
God helps those who help themselves - Wikiepedia, God helps those who help themselves - Wikiepdia, the free encyclopedia, ' The phrase "God helps those who help themselves" is a motto that emphasizes the importance of self-initiative and agency. The phrase originated in ancient Greece as "the gods help those who help themselves" and may originally have been proverbial. It is illustrated by two of Aesop's Fables and a similar sentiment is found in ancient Greek drama. Sophocles used it in the form of "No good e'er comes of leisure purposeless; And heaven ne'er helps the men who will not act", while Euripides portrays Orestes saying, "I think that Fortune watcheth o'er our lives, surer than we. But well said: he who strives will find his gods strive for him equally." Ovid's version of the phrase is "divinity helps those who dare" (audentes deus ipse iuvat). back |
Gregor Mendel - Wikipedia, Gregor Mendel - Wikipedia, the free encyclopedia, ' Gregor Johann Mendel, OSA was a biologist, meteorologist, mathematician, Augustinian friar and abbot of St. Thomas' Abbey in Brünn (Brno), Margraviate of Moravia. Mendel was born in a German-speaking family in the Silesian part of the Austrian Empire (today's Czech Republic) and gained posthumous recognition as the founder of the modern science of genetics. Though farmers had known for millennia that crossbreeding of animals and plants could favour certain desirable traits, Mendel's pea plant experiments conducted between 1856 and 1863 established many of the rules of heredity, now referred to as the laws of Mendelian inheritance.' back |
Hilbert space - Wikipedia, Hilbert space - Wikipedia, the free encyclopedia, ' In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that induces a distance function for which the space is a complete metric space. A Hilbert space is a special case of a Banach space. ' back |
Holy Roman Empire - Wikipedia, Holy Roman Empire - Wikipedia, the free encyclopedia, ' The Holy Roman Empire, also known as the Holy Roman Empire of the German Nation after 1512, was a polity in Central and Western Europe, usually headed by the Holy Roman Emperor. It developed in the Early Middle Ages, and lasted for a millennium until its dissolution in 1806 during the Napoleonic Wars. Initially, it comprised three constituent kingdoms—Germany, Italy, and, from 1032, Burgundy—held together by the emperor's overlordship. By the 15th century, imperial governance became concentrated in the Kingdom of Germany, as the empire's effective control over Italy and Burgundy had largely disappeared.
On 25 December 800, Pope Leo III crowned the Frankish king Charlemagne Roman emperor, reviving the title more than three centuries after the fall of the Western Roman Empire in 476.' back |
Lamarckism - Wikipedia, Lamarckism - Wikipedia, the free encyclopedia, ' Lamarckism, also known as Lamarckian inheritance or neo-Lamarckism, is the notion that an organism can pass on to its offspring physical characteristics that the parent organism acquired through use or disuse during its lifetime. It is also called the inheritance of acquired characteristics or more recently soft inheritance. The idea is named after the French zoologist Jean-Baptiste Lamarck (1744–1829), who incorporated the classical era theory of soft inheritance into his theory of evolution as a supplement to his concept of orthogenesis, a drive towards complexity.' back |
Mahabharata - Wikipedia, Mahabharata - Wikipedia, the free encyclopedia, ' The Mahābhārata is one of the two major Sanskrit epics of ancient India, the other being the Rāmāyaṇa. It narrates the struggle between two groups of cousins in the Kurukshetra War and the fates of the Kaurava and the Pāṇḍava princes and their successors.
It also contains philosophical and devotional material, such as a discussion of the four "goals of life" or puruṣārtha (12.161). Among the principal works and stories in the Mahābhārata are the Bhagavad Gita, the story of Damayanti, the story of Shakuntala, the story of Pururava and Urvashi, the story of Savitri and Satyavan, the story of Kacha and Devayani, the story of Rishyasringa and an abbreviated version of the Rāmāyaṇa, often considered as works in their own right.' back |
Minkowski space - Wikipedia, Minkowski space - Wikipedia, the free encyclopedia, ' By1908 Minkowski realized that the special theory of relativity, introduced by his former student Albert Einstein in 1905 and based on the previous work of Lorentz and Poincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which time and space are not separated entities but intermingled in a four-dimensional space–time, and in which the Lorentz geometry of special relativity can be effectively represented using the invariant interval x2 + y2 + z2 − c2 t2.' back |
National Human Genome Research Institute, Genome Timeline, ' Because of a lapse in government funding, the information on this website may not be up to date, transactions submitted via the website may not be processed, and the agency may not be able to respond to inquiries until appropriations are enacted. The NIH Clinical Center (the research hospital of NIH) is open. For more details about its operating status, please visit cc.nih.gov. Updates regarding government operating status and resumption of normal operations can be found at opm.gov. back |
P versus NP problem - Wikipedia, P versus NP problem - Wikipedia, the free encyclopedia, ' The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified (technically, verified in polynomial time) can also be solved quickly (again, in polynomial time).
The underlying issues were first discussed in the 1950s, in letters from John Forbes Nash Jr. to the National Security Agency, and from Kurt Gödel to John von Neumann. The precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in his seminal paper " The complexity of theorem proving procedures" and is considered by many to be the most important open problem in the field.' back |
Petite messe solennelle - Wikipedia, Petite messe solennelle - Wikipedia, the free encyclopedia, ' Gioachino Rossini's Petite messe solennelle (Little Solemn Mass) was written in 1863, possibly at the request of Count Alexis Pillet-Will for his wife Louise, to whom it is dedicated. The composer, who had retired from composing operas more than 30 years before, described it as "the last of my péchés de vieillesse" (sins of old age).
The extended work is a missa solemnis (solemn Mass), but Rossini ironically labeled it petite (little). He scored it originally for twelve singers, four of them soloists, two pianos and harmonium. The mass was first performed on 14 March 1864 at the couple's new home in Paris. Rossini later produced an orchestral version, including an additional movement, a setting of the hymn "O salutaris hostia" as a soprano aria. This version was not performed during his lifetime because he was unable to obtain permission to have female singers in a church. It was finally performed at the Salle Ventadour in Paris by the company of the Théâtre-Italien on 24 February 1869, three months after his death.' back |
Pina Bausch, The Rite of Spring, Music: Igor Fedorovich Stravinsky performed by Pierre Boulez and The Cleveland Orchestra
I'll never forget the first time that we did a whole run-through of The Rite. Up until then Pina had been rehearsing the role of the 'chosen' separately in her office.
None of us had any idea how the 'chosen' would dance in order to die. At the time Marlis was dancing her. The choreography unfolded and there we were, sweaty and breathless, the whole room trembling as we watched Marlis fighting against death. It was extraordinary; it was so terrifying that I could barely watch it. I said to myself that she really was going to die. I then had to come downstage, alone. My feet were like lead. My eyes were fixed on Marlis. Then, at the end, she fell down, dead. Who knows whether she wasn't really dead? I couldn't bear it and I ran off stage sobbing – that's how extraordinary it was. The Rite is absolutely unique. [. . .] Jo Ann Endicott
Excerpt from Je suis une femme respectable, published by L’Arche (Paris), in 1999, translated into English by Miriam Heard. back |
Pope John Paul II (22 October 1996), Address to Plenary Session on 'The Origins and Early Evolution of Life', ' John Paul II refers to Pius XI’s hope that the Academy would become a Senatus scientificus. In relation to the origins of life and the universe the Pope asks: ‘How do the conclusions reached by the various scientific disciplines coincide with those contained in the message of Revelation? And if, at first sight, there are apparent contradictions, in what direction do we look for their solution?’ John Paul II surveys the Magisterium’s comments on the theory of evolution and adds that ‘to tell the truth, rather than the theory of evolution, we should speak of several theories of evolution’. Those theories of evolution which ‘consider the mind as emerging from the forces of living matter’ are ‘incompatible with the truth about man’. The human being, indeed, is ‘called to enter into eternal life’.' back |
Pope Paul VI (1976_10_15), Inter Insigniores: On the question of admission of women to the ministerial priesthood , '. . . in execution of a mandate received from the Holy Father and echoing the declaration which he himself made in his letter of 30 November 1975, the Sacred Congregation for the Doctrine of the Faith judges it necessary to recall that the Church, in fidelity to the example of the Lord, does not consider herself authorized to admit women to priestly ordination.' back |
Qubit - Wikipedia, Qubit - Wikipedia, the free encyclopedia, 'A quantum bit, or qubit . . . is a unit of quantum information. That information is described by a state vector in a two-level quantum mechanical system which is formally equivalent to a two-dimensional vector space over the complex numbers.
Benjamin Schumacher discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in a state, and storing the information on a smaller number of states. This is now known as Schumacher compression. In the acknowledgments of his paper (Phys. Rev. A 51, 2738), Schumacher states that the term qubit was invented in jest, during his conversations with Bill Wootters.' back |
Saint John Paul II (1992_10_31), Saint John Paul II (1992_10_31): Address to the Plenary Session on ‘The Emergence of Complexity in Mathematics, Physics, Chemistry and Biology’, ' However, the underlying problems of [the Galileo] case concern both the nature of science and the message of faith. It is therefore not to be excluded that one day we shall find ourselves in a similar situation, one which will require both sides to have an informed awareness of the field and of the limits of their own competencies. The approach provided by the theme of complexity could provide an illustration of this.
5. A twofold question is at the heart of the debate of which Galileo was the centre.
The first is of the epistemological order and concerns biblical hermeneutics. In this regard, two points must again be raised. In the first place, like most of his adversaries, Galileo made no distinction between the scientific approach to natural phenomena and a reflection on nature, of the philosophical order, which that approach generally calls for. . . .
Secondly, the geocentric representation of the world was commonly admitted in the culture of the time as fully agreeing with the teaching of the Bible, of which certain expressions, taken literally, seemed to affirm geocentrism. The problem posed by theologians of that age was, therefore, that of the compatibility between heliocentrism and Scripture.
6. From this we can now draw our first conclusion. The birth of a new way of approaching the study of natural phenomena demands a clarification on the part of all disciplines of knowledge. . . .
9. . . . The majority of theologians did not recognise the formal distinction between Sacred Scripture and its interpretation, and this led them unduly to transpose into the realm of the doctrine of the faith a question which in fact pertained to scientific investigation. . . .
12. . . .There exist two realms of knowledge, one which has its source in Revelation and one which reason can discover by its own power. To the latter belong especially the experimental sciences and philosophy. The distinction between the two realms of knowledge ought not to be understood as opposition. The two realms are not altogether foreign to each other; they have points of contact. The methodologies proper to each make it possible to bring out different aspects of reality. . .
14. Humanity has before it two modes of development. The first involves culture, scientific research and technology, that is to say whatever falls within the horizontal aspect of man and creation, which is growing at an impressive rate. In order that this progress should not remain completely external to man, it presupposes a simultaneous raising of conscience, as well as its actuation. The second mode of development involves what is deepest in the human being, when, transcending the world and transcending himself, man turns to the One who is the Creator of all. It is only this vertical direction which can give full meaning to man’s being and action, because it situates him in relation to his origin and his end. In this twofold direction, horizontal and vertical, man realises himself fully as a spiritual being and as homo sapiens. But we see that development is not uniform and linear, and that progress is not always well ordered. This reveals the disorder which affects the human condition. The scientist who is conscious of this twofold development and takes it into account contributes to the restoration of harmony.
Those who engage in scientific and technological research admit, as the premise of its progress, that the world is not a chaos but a ‘cosmos’; that is to say, that there exist order and natural laws which can be grasped and examined, and which, for this reason, have a certain affinity with the spirit. Einstein used to say: ‘What is eternally incomprehensible in the world is that it is comprehensible’.9 This intelligibility, attested to by the marvellous discoveries of science and technology, leads us, in the last analysis, to that transcendent and primordial Thought imprinted on all things.' back |
Science - Wikipedia, Science - Wikipedia, the free encyclopedia, ' Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into two – or three – major branches: the natural sciences, which study the physical world, and the social sciences, which study individuals and societies. While referred to as the formal sciences, the study of logic, mathematics, and theoretical computer science are typically regarded as separate because they rely on deductive reasoning instead of the scientific method as their main methodology. Meanwhile, applied sciences are disciplines that use scientific knowledge for practical purposes, such as engineering and medicine.' back |
The Book of Joshua 10:12-13, Chapter 10, 12-13, ' 12 At that time Joshua spoke to the LORD in the day when the LORD gave the Amorites over to the sons of Israel, and he said in the sight of Israel, "Sun, stand still at Gibeon, and moon, in the Valley of Aijalon.”
13 And the sun stood still, and the moon stopped, until the nation took vengeance on their enemies.' back |
Theocracy - Wikipedia, Theocracy - Wikipedia, the free encyclopedia, ' Theocracy is a form of government in which one or more deities are recognized as supreme ruling authorities, giving divine guidance to human intermediaries who manage the government's daily affairs.. . .
The term was initially coined by Flavius Josephus in the first century AD to describe the characteristic government of the Jews. . . . according to Josephus, the government of the Jews was unique. Josephus offered the term theocracy to describe this polity in which a god was sovereign and the god's word was law. . .
Iran has been described as a "theocratic republic" by the CIA World Factbook, and its constitution has been described as a "hybrid" of "theocratic and democratic elements" by Francis Fukuyama. Like other Islamic states, it maintains religious laws and has religious courts to interpret all aspects of law. According to Iran's constitution, "all civil, penal, financial, economic, administrative, cultural, military, political, and other laws and regulations must be based on Islamic criteria". ' back |
Transfinite numbers - Wikipedia, Transfinite numbers - Wikipedia, the free encyclopedia, ' Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were nevertheless not finite. Few contemporary workers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as "infinite". However, the term "transfinite" also remains in use.' back |
Turing machine - Wikipedia, Turing machine - Wikipedia, the free encyclopedia, ' A Turing machine is a hypothetical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a computer.
The "machine" was invented in 1936 by Alan Turingwho called it an "a-machine" (automatic machine). The Turing machine is not intended as practical computing technology, but rather as a hypothetical device representing a computing machine. Turing machines help computer scientists understand the limits of mechanical computation.' back |
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