page 2: The impossible God of Catholicism
2.1: Introduction
This introduction is a condensed and simplified representation of cognitive cosmology.com the site in which I try to unite physics and theology as a step toward scientific theological study of our divine universe. The universe is a work of art which has created itself from a structureless initial singularity. This creation is described by the big bang theory of cosmogenesis. Big Bang - Wikipedia
Human artists may learn by studying this cosmic artistry. In particular, if we understand how the universe has made human beings out of fundamental particles, we will obtain precious clues about how to mould ourselves into a peaceful body politic.
This site is concerned with the political and moral consequences of the hypothesis that the universe is divine. I first published ideas developed here in a radio program in 1987. I have made some progress since then and intend to explain it in detail on this site. Jeffrey Nicholls (1987): A theory of Peace
2.2. From Aquinas via Lonergan to anew vision of God>/h5>
When I was 17 I decided to joined the Dominican Order. It was a difficult and painful decision, but my mother was a very devout Catholic and the priests surrounding us encouraged my decision. I was in effect bequeathed to the Church. I accepted it as a sacrifice necessary for my own salvation and my contribution to the salvation of the world.
I was entranced by the work of Thomas Aquinas and closely studied the model of God he presented in his Summa Theologiae. In particular wi spent a lot of time trying to understand his conception of the doctrine of the Trinity. The radical problem is to explain how the traditional unity of God is not compromised by the existence of three distinct persons each equally and identically divine. Aquinas;s work eventually became essential to my hypothesis that the universe, despite comprising a vast multitude of personalities, is nevertheless identical to God. I return to this question in the last section of this page after I have demonstrated that the standard monotheist model of God proposed by Aquinas is, from a logical and mathematical pint of view, self contradictory.
Aquinas introduces the study of God in the Preface to the first part of the Summa:
Quia igitur principalis intentio huius sacrae doctrinae est Dei cognitionem tradere, et non solum secundum quod in se est, sed etiam secundum quod est principium rerum et finis earum, et specialiter rationalis creaturae, ut ex dictis est manifestum; ad huius doctrinae expositionem intendentes, primo tractabimus de Deo; secundo, de motu rationalis creaturae in Deum; tertio, de Christo, qui, secundum quod homo, via est nobis tendendi in Deum. Consideratio autem de Deo tripartita erit. Primo namque considerabimus ea quae ad essentiam divinam pertinent; secundo, ea quae pertinent ad distinctionem personarum; tertio, ea quae pertinent ad processum creaturarum ab ipso. Circa essentiam vero divinam, primo considerandum est an Deus sit; secundo, quomodo sit, vel potius quomodo non sit; tertio considerandum erit de his quae ad operationem ipsius pertinent, scilicet de scientia et de voluntate et potentia. Circa primum quaeruntur tria. Primo, utrum Deum esse sit per se notum. Secundo, utrum sit demonstrabile. Tertio, an Deus sit. Aquinas, Summa, Part I: Translation of Question 2: Preface
The first step in theology is to establish the existence of its subject, God. At first I quite naturally accepted his proofs for the existence of God. Then I read Bernard Lonergan’s Insight. The core of Lonergan’s thesis is a division of knowledge into proportionate (things accessible to the human mind) and transcendent (things beyond our understanding). Thomas Aquinas, Summa, I, 2, 3: Does God exist?, Bernard Lonergan (1992): Insight: A Study of Human Understanding
To be a Catholic, one must accept this dichotomy, but his attempt to explain it seemed quite unsatisfactory. Being, he said, is completely intelligible. The world, however, is not completely intelligible because it contains empirical residue, that is meaningless and unintelligible facts.
I was an avid reader of Nature, Scientific American and the like, and this seemed wrong to me. First, why would God create such a world? And, more deeply, since the time of Darwin it has become clear that the world is created by evolution. Possibilities are explored by random variation and tested by natural selection. A close study of living physiology at the atomic and molecular level shows that almost every atom has an intelligible role that contributes to the life of its host.
Lonergan’s work led me to understand that the existence of God is a tautology. Since creation exists the creator, whatever it is, must exist. The arguments put forward by Aquinas and Lonergan merely support the contention that God and the Universe are distinct entities. It became obvious to me that God and the Universe are identical. I said this out loud. In the Church this is the worst heresy since it undermines the whole Catholic business plan. My solemn vows were annulled and I was expelled from the order. Jeffrey Nicholls (1967): How universal is the universe?
2.3: Theology, religion and war
That was more than fifty years ago. My expulsion was a shock, but I am back on an even keel now, and I can see clearly that the God of Aquinas that Lonergan tried to defend is self contradictory and cannot exist.
Christianity was built on the quasi mythological history recorded in the Hebrew Bible. Like Homer’s Iliad and John Milton’s Paradise Lost and Paradise Regain’d these and hundreds of similar classics are stories of origin often loosely based on memories of actual wars developed by imaginative authors into cosmic events. Hebrew Bible - Wikipedia
Religious war is a recurrent theme in human history. The Christian United States has built the world’s greatest war machine to control the non-Christian world. Russia’s Putin, advised by the Christian Patriarch Kirill, is pursuing a divinely mandated attempt to annihilate Ukraine, and so it goes. Niko Vorobyov (2022_03_28): Patriarch Kirill: Putin ally faces backlash after ‘blessing’ war
From a practical point of view, war is a combination of physics and theology. The physicists devise ever more effective weapons to support the theologians’ desire for hegemony. In Milton’s heavenly war, developed as a backstory to the legend of the Fall in Genesis, the Father deployed the Son to drive the daemons out of Heaven into their new home, Pandaemonium.
The theoretical key to war is the mathematical discipline know as cybernetics, described in Wiener’s book as Communication and Control in the Animal and the Machine. The purpose of politics is control. One alternative is ideology. Violence takes over where ideology fails. Constantine, Stalin, Hitler and Putin exemplify this progression. Norbert Wiener (1948, 1996)
The Prophet Isaiah billed the Messiah as the Prince of Peace. These words were generally interpreted to predict the advent of a military leader who would put the enemies of Israel to flight. There can be no doubt that Jesus of Nazareth, in his role as Son of God, planned to control the world. He started with ideology:
Then Jesus approached and said to them, “All power in heaven and on earth has been given to me. Go, therefore, and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the holy Spirit, teaching them to observe all that I have commanded you. And behold, I am with you always, until the end of the age.” Isaiah 9:6: 'Unto us a child is born . . . ', Matthew 28:18–20: All power is given to me . . .
Christianity spread quickly, assisted by easy communication within the Roman Empire. It sealed its hegemony by providing the theological foundation for the late Roman Empire through Constantine. The Western Roman empire was followed by the Holy Roman Empire. This empire, much diminished, remains with us as the Vatican. Although its territorial footprint is now tiny, Christianity remains at the religious heart of the dominant military and ideological powers of the world.
2.4: Where is God now?
Aquinas’ first proof for the existence of God comes almost verbatim from Aristotle’s argument for the unmoved mover. Like Aristotle, he concluded that God is pure action actus purus. He differed from Aristotle by accepting the Christian belief that God is outside the world. Aquinas, Summa, I, 2, 3: Does God exist?, Unmoved mover - Wikipedia
Aquinas then proceeds to derive the traditional properties of God, noting that the transcendent nature of God means that we cannot say what God is, only what they are not. His first step is to establishing that God is absolutely simple by denying them all forms of complexity found in the natural world. Aquinas, Summa, I, 3, 7: Is God altogether simple?, Apophatic theology - Wikipedia
2.5: The traditional God is ignorant and therefore powerless
Here we come to a major difficulty: how can an absolutely simple being be omniscient, that is be aware of every past, present and future real and possible event in the whole universe?
Aquinas argues for divine omniscience from the ancient theory of knowledge that equates intelligence with spirituality. Since God is maximally spiritual he says, they are therefore maximally knowing. Aquinas, Summa: I, 14, 1: Is there knowledge in God?
From a modern point of view, this argument carries no weight. A blank sheet of paper (like a blank computer screen) carries no information (except the fact that it exists). The actual information is carried by the marks on the screen, which may be quite complex, like an image with a million different pixels.
Claude Shannon adapted the thermodynamic concept of entropy to measure the amount of information carried by a set of marks. Information resolves uncertainty. The unit of information is the bit. One bit is the information required to resolve the uncertainty between two equiprobable states. A spinning fair coin may land heads or tails. While it spins, the observer sees one bit of uncertainty. When it lands and becomes stationary they receive one bit of information.
Shannon models a communication as the exchange of information between two sources connected by a channel. A source or a person is any entity that can transmit and receive information. Here you and I are the sources and the array of physical machinery connecting us is the channel.
A source A is described mathematically by an alphabet of i symbols ai each with a probability of emission pi. The source entropy per symbol is then given (in bits) by the equation
HA = − Σi pi log2 pi
given that the pi are normalized:
Σi pi = 1.
The total entropy of a message of n symbols from a source (like this page) is nHA and the information transmitted between us by this text is also nHA. Claude Shannon (1949): Communication in the Presence of Noise
This measure of information information enables us to state the cybernetic principle of requisite variety. Simply put, if one system is to control another, an essential pre-requisite is that the controller must have equal or greater entropy than the system to be controlled. The controller must have an an adequate response to every move the controlled system can make. In wrestling terms, it must be able to pin it. W. Ross Ashby (1964): An Introduction to Cybernetics
Clearly if Aquinas is right and God is absolutely simple, God is equivalent to a blank page. Their entropy is zero. Since the entropy of the Universe is quasi-infinite, such a God can neither know nor control the universe. The Thomistic idea that God has immediate providence over everything must therefore be false. Aquinas, Summa, I, 22, 3: Does God have immediate providence over everything?
2.6: Theology and religion are real, embedded in human minds, art and architecture since antiquity.
God and religion are facts of human life which have been ubiquitous throughout our history. Atheists are swimming against a powerful empirical tide. How do we resuscitate the idea of God and establish its consistency with modern science, politics and morality?
The key, I feel, is to go back to the beginning. Penrose, Hawking and Ellis showed that Einstein’s theory of relativity predicts the existence of a structureless initial singularity. The big bang theory of cosmic evolution proposes that this singularity is the source of the current universe. It is, in effect, the creator. Hawking & Ellis (1975): The Large Scale Structure of Space-Time
Einstein’s theory is classical and we assume that the ultimate theory of the universe will be quantum mechanical. We therefore replace this classical initial singularity with a quantum initial singularity which is formally identical to the definition of God proposed by Aristotle and Aquinas: God is pure action actus purus and altogether simple omnino simplex. General relativity - Wikipedia
As noted above, this god cannot be omniscient, but we can imagine it to be energetic, capable of repeated action. Its nature is to act. It is inherently omnipotent. In quantum mechanics, energy is identical to the rate of repetition of action, E = hf. Planck-Einstein relation - Wikipedia
This replicates the Trinity, the central dogma of Catholic theology. The Father begets the Son and the Spirit proceeds from the Father and the Son together, all three being identically God. Catholic dogma limits this process to three persons or sources. Here we assume divine procession to be analogous to Peano’s axioms, generating an infinite sequence of distinct agents (sources or persons) which may be represented by orthogonal vectors in Hilbert space. Catholic Catechism §234: In the name of the Father . . . , Peano axioms - Wikipedia, Hilbert space - Wikipedia
This action is necessarily uncontrolled since at any point in time the agent is of lower entropy than the outcome. This establishes the first prerequisite for creative evolution, variations or random events.
God is omnipotent, which means, in Thomistic terms, that they can do anything that does not involve contradiction. This is natural selection. It explains the scientific faith that apparent contradictions in the universe may always be resolved with further investigation. Systems which are internally consistent and consistent with their environment, on the other hand, are capable of continued existence.
2.7: General covariance and quantum theory
Einstein’s general theory is based on the principle of general covariance. This meant, to Einstein, that the processes of nature are in no way affected by human observation. When we observe a particular phenomenon using different frames of reference, these frame must be covariant, meaning that observations taken with one frame can be transformed identically into the observations taken with another, thus neutralizing the role of the frames of reference. General covariance - Wikipedia
This principle cannot be reconciled with quantum mechanics, which is why Einstein, until his death, rejected with quantum theory. What Einstein overlooked is that an observation is also a natural interaction. One cannot be seen without acting. I see you because you are emitting photons which enter my eyes. At the quantum level, observation changes reality. Measurement in quantum mechanics - Wikipedia
2.8: Communication, love and uncertainty
A most appropriate ancient definition says God is love. As in the Trinity, the structure of divinity is defined by communication. My hypothesis that the universe is divine is built around the observation that love operates throughout the universe. Because love is communication it involves the meeting of two distinct beings who may never have interacted before. There is therefore always a a certain amount uncertainty in their meeting. 1 John 4:7-21: God is love
Meetings occur at all scales, which explains the spectrum of uncertainty from quantum mechanics to global politics. When two electrons meet, there is an infinite spectrum of possible outcomes. This introduces a troublesome infinity of possibilities into quantum field theory. Quantum field theory - Wikipedia
Every meeting changes both agents. As soon as we see each other millions of synapses in our minds are transformed to represent the new feelings our meeting induces in us.
2.8: Omniscience and omnipotence are not enough to guarantee determinism
How does the traditional omnipotent and omniscient Christian god behave? The evidence suggests that this being is a vicious killer just like any other warlord. A minor infraction at the beginning was punished with universal death. Given their amazing powers we should expect that they should have treated us much better. Could they not have created a world for us as good and perfect as traditional theology says they are themself? Aquinas, Summa, I, 6, 2: Is God the supreme good?
Why do they give us a such hard time? Because they think we are sinners and deserve punishment? The New Testament tells us that they had their own Son murdered to give themself satisfaction for the original sin committed by some angels and people. God set humanity up to fail and sent Satan, a very persuasive serpent, to make sure. Every one of us is punished with death, pain and work. Fall of Man - Wikipedia,
The real reason for evil in our divine world arises from evolution by reproduction with variation and selection. The exponential growth resulting from chain reactions like reproduction, nuclear fission and cell division eventually exhaust any finite system of resources. The result is a zero sum situation: I can only win if you lose, I can only life if you die. At the human social and economic scale, this is the cause of war and many other evils arising from real or perceived conflicts of interest.
We might suppose that an omnipotent and omniscient being could avoid such zero sum situations by a well informed application of prudence.
Here we hit another obstacle. The tradition mathematical process of proof works within the bounds of requisite variety. Gregory Chaitin interpreted Gödel’s incompleteness theorem to imply the cybernetic principle of requisite variety: no proof (ie no deterministic computation) can produce a result of higher entropy than its input.
This implies that consistent mathematics is not necessarily deterministic. Since the second law of thermodynamics tells us that the entropy of the Universe (that is to say, the entropy of God) is always increasing. Consequently an evolving God, even though omnipotent (ie able to anything that does not involve a contradiction) cannot control the future with certainty. There is a limit to providence. Gödel's incompleteness theorems - Wikipedia, Computability - Wikipedia
2.9: From Catholic mythology to scientific theology
Catholic dogma has enjoyed no real theoretical development since Aquinas incorporated Aristotelian science into theology in the thirteenth century. It currently bears the same relationship to a possible modern scientific theology as medieval physiology and health care compare to modern medicine. Our health care is based on enormously detailed knowledge of physiology and pathology to diagnose and treat the wide spectrum of disease that affect us.
The medievals knew next to nothing about the underlying relationships between physiology and disease. Modern theologians, trapped by powerful institutional inertia and in may cases deluded by the arbitrary power of an allegedly infallible autocracy, know no more about the real divinity than their medieval peers. There is a vast sphere of development open to scientific theology. Medieval medicine of Western Europe - Wikipedia
For most of their history Christian churches has used the standard (and current) imperial methods of deception, propaganda, war, torture and murder to maintain orthodoxy. More recently, as in my case, they simply deprive dissidents of a living. The abusive effects of Christianity in the spheres of gender and sexuality have come into prominence and are being subjected to correction. The next major issue to be addressed is the total failure of most religions to keep pace with modern developments in empirical science, democratic politics, human rights, ethics, and the value of truth.
We need to change just one bit of information to initiate the modernization of theology. The proposition God is not an observable reality needs to be changed to God is an observable reality . Once one has made this change of perspective, all else follows.
2.10: My motivation
You might ask why I find necessary to accuse the Church in such harsh tones. The answer lies in personal experience. I was born, baptized and raised as a Catholic. I went to Catholic schools and ultimately entered a Catholic religious order, the Order of Preachers.
I was indoctrinated into the Catholic story since birth, long before I developed any critical intelligence. I had no choice but to believe. I accepted, with considerable pain, that I was an evil little masturbator and that only a serious act of supererogation could save me. So I gave my life to "God".
In the monastery, my eyes were opened. I became a lifelong fan of Saint Thomas Aquinas, not least because he writes in limpidly simple Latin that I could (and can) read fluently. Thomas showed me, above all, that we should think about our faith. To him, a child of the Middle Ages, faith and reality blend perfectly. Using Aristotle, he united physics and theology.
I think I was dismissed unfairly, and have been making my case in my mind ever since. I was being groomed to be a Catholic intellectual, a theologian in an Order that prides itself on a strong theological tradition, founded on Albert the Great and Thomas Aquinas. I was powerless then, but nearly fifty years later I still think I was right and they were wrong. Hence my effort to drag theology from mythology to science.
The Roman Catholic Church sponsors many good works at its lower levels, but its management is rotten, eaten away by the myth of infallible autocracy and a long history of violent imperial politics. From my point of view it is a relic of an imperial age in which emperors hated their people, enslaved them and treated them as cannon fodder with no rights. They placated the noisy ones either by promising eternal bliss in some unknown future or torturing them to death as a lesson to the others.
So much of this is captured in the Christian aspirations of Stalin’s child Vladimir Putin, whose only route to satisfaction is mindless destruction. Everywhere around the world see instances of religious autocracy, modelled on the imperial soul of ancient Rome embedded in the Vatican. Camila Vergara (2022_10_27): Opinion: How Christian Nationalism is taking Root Across the World
Jeffrey Nicholls
PO Box 13002, University of Adelaide, North Terrace, 5005
+61 0423 472 342
theologyco@gmail.com
The reason for this is that, as Alan Turing proved, there exist incomputable functions, paths which deterministic computation cannot follow. The only way to move from an initial state to a final state with which is has no deterministic computable connection is is by random motion. Alan Turing (1936): On Computable Numbers, with an application to the Entscheidungsproblem
It may be possible, however, to find a deterministic path back the other way. This is the essence of the P versus NP problem in computer science. A P process is a path from some initial state to a final state in which the computer halts with an answer. It has decided. An NP process, on the other hand, is generally considered to be incomputable (although this result has not been proven) but can be achieved by a machine which has random choices to make its next step. In the context of evolution, we may consider the random element in reproduction to be an NP process. A grain of pollen, blowing on the wind, finds a suitable seed to fertilize.
This sets a reproductive process in motion, which is a P process, a sequence of well controlled steps which leads to the emergence of a new living plant. Natural selection picks the defined P processes to check and exploit the random NP processes, thus acting as a sort of rachet which fixes certain outcomes of random behaviour to reproduce themselves. Carlson, Jaffe & Wiles (2006): The Millennium Prize Problems
This is the way the universe has created itself. It is the way of science, randomly generated hypotheses being subjected to testing to find the ones that match reality. Here we take the view that a similar process lies behind the development of language, culture, law, politics and all the more complex layers of structure whose ingredients are human individuals.
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Notes and references
Further reading
Books
Ashby (1964), W Ross, An Introduction to Cybernetics, Methuen 1956, 1964 'This book is intended to provide [an introduction to cybernetics]. It starts from common-place and well understood concepts, and proceeds step by step to show how these concepts can be made exact, and how they can be developed until they lead into such subjects as feedback, stability, regulation, ultrastability, information, coding, noise and other cybernetic topics.'
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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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Lonergan (1992), Bernard J F, Insight: A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '. . . Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding'
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Wiener (1996), Norbert, Cybernetics or Control and Communication in the Animal and the Machine, MIT Press 1996 The classic founding text of cybernetics.
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Links
1 John 4:7-21, God is love, ' 8. He that loveth not knoweth not God; for God is love.' back |
Apophatic theology - Wikipedia, Apophatic theology - Wikipedia, the free encyclopedia, 'Apophatic theology (from Greek ἀπόφασις from ἀπόφημι - apophēmi, "to deny")—also known as negative theology or via negativa (Latin for "negative way")—is a theology that attempts to describe God, the Divine Good, by negation, to speak only in terms of what may not be said about the perfect goodness that is God. It stands in contrast with cataphatic theology.' back |
Aquinas Summa I, 2, 3, Does God exist?, 'I answer that, The existence of God can be proved in five ways. The first and more manifest way is the argument from motion. . . . ' back |
Aquinas, Summa, I, 2, 3, Does God exist?, ' I answer that the existence of God can be proved in five ways. The first and more manifest way is the argument from motion. . . . The second way is from the nature of the efficient cause. . . . The third way is taken from possibility and necessity . . . The fourth way is taken from the gradation to be found in things. . . . The fifth way is taken from the governance of the world.' back |
Aquinas, Summa, I, 22, 3, Does God have immediate providence over everything?, ' I answer that, Two things belong to providence—namely, the type of the order of things foreordained towards an end; and the execution of this order, which is called government. As regards the first of these, God has immediate providence over everything, because He has in His intellect the types of everything, even the smallest; and whatsoever causes He assigns to certain effects, He gives them the power to produce those effects. Whence it must be that He has beforehand the type of those effects in His mind. As to the second, there are certain intermediaries of God's providence; for He governs things inferior by superior, not on account of any defect in His power, but by reason of the abundance of His goodness; so that the dignity of causality is imparted even to creatures.' back |
Aquinas, Summa, I, 3, 7, Is God altogether simple?, 'I answer that, The absolute simplicity of God may be shown in many ways. First, from the previous articles of this question. For there is neither composition of quantitative parts in God, since He is not a body; nor composition of matter and form; nor does His nature differ from His "suppositum"; nor His essence from His existence; neither is there in Him composition of genus and difference, nor of subject and accident. Therefore, it is clear that God is nowise composite, but is altogether simple. . . . ' back |
Aquinas, Summa, I, 6, 2, Is God the supreme good?, ' I answer that, God is the supreme good simply, and not only as existing in any genus or order of things. For good is attributed to God, as was said in the preceding article, inasmuch as all desired perfections flow from Him as from the first cause. They do not, however, flow from Him as from a univocal agent, as shown above (I:4:2); but as from an agent which does not agree with its effects either in species or genus. Now the likeness of an effect in the univocal cause is found uniformly; but in the equivocal cause it is found more excellently, as, heat is in the sun more excellently than it is in fire. Therefore as good is in God as in the first, but not the univocal, cause of all things, it must be in Him in a most excellent way; and therefore He is called the supreme good. ' back |
Aquinas, Summa: I, 14, 1, Is there knowledge in God?, ' I answer that, In God there exists the most perfect knowledge. . . . it is clear that the immateriality of a thing is the reason why it is cognitive; and according to the mode of immateriality is the mode of knowledge. Hence it is said in De Anima ii that plants do not know, because they are wholly material. But sense is cognitive because it can receive images free from matter, and the intellect is still further cognitive, because it is more separated from matter and unmixed, as said in De Anima iii. Since therefore God is in the highest degree of immateriality as stated above (Question 7, Article 1), it follows that He occupies the highest place in knowledge.' back |
Big Bang - Wikipedia, Big Bang - Wikipedia, the free encyclopedia, ' The Big Bang theory is the prevailing cosmological model explaining the existence of the observable universe from the earliest known periods through its subsequent large-scale evolution. The model describes how the universe expanded from an initial state of high density and temperature, and offers a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. ' back |
Catholic Catechism §234, In the name of the Father and of the Son and of the Holy Spirit, ' 234 The mystery of the Most Holy Trinity is the central mystery of Christian faith and life. It is the mystery of God in himself. It is therefore the source of all the other mysteries of faith, the light that enlightens them. It is the most fundamental and essential teaching in the "hierarchy of the truths of faith". The whole history of salvation is identical with the history of the way and the means by which the one true God, Father, Son and Holy Spirit, reveals himself to men "and reconciles and unites with himself those who turn away from sin".' back |
Claude Shannon (1949), Communication in the Presence of Noise, 'A method is developed for representing any communication system geometrically. Messages and the corresponding signals are points in two “function spaces,” and the modulation process is a mapping of one space into the other. Using this representation, a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect. Formulas are found for the maximum rate of transmission of binary digits over a system when the signal is perturbed by various types of noise. Some of the properties of “ideal” systems which transmit at this maximum rate are discussed. The equivalent number of binary digits per second for certain information sources is calculated.' [C. E. Shannon , “Communication in the presence of noise,” Proc. IRE, vol. 37, pp. 10–21, Jan. 1949.] back |
Computability - Wikipedia, Computability - Wikipedia, the free encyclopedia, ' Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem. The most widely studied models of computability are the Turing-computable and μ-recursive functions, and the lambda calculus, all of which have computationally equivalent power. Other forms of computability are studied as well: computability notions weaker than Turing machines are studied in automata theory, while computability notions stronger than Turing machines are studied in the field of hypercomputation.' back |
Fall of Man - Wikipedia, Fall of Man - Wikipedia, the free encyclopedia, 'In Christian doctrine, the fall of man, or simply the fall, was the transition of the first humans from a state of innocent obedience to God to a state of guilty disobedience to God. Though not named in the Bible, the concept for the Fall comes from Genesis chapter 3. Adam and Eve live at first with God in a paradise, but the serpent tempts them into eating the fruit from the tree of knowledge of good and evil, which God forbade. After doing so they become ashamed of their nakedness and God consequently expelled them from paradise. Many Christian denominations believe that the fall corrupted the entire natural world, including human nature, causing people to be born into original sin, a state from which they cannot attain eternal life without the gracious intervention of God.' back |
General covariance - Wikipedia, General covariance - Wikipedia, the free encyclopedia, In theoretical physics, general covariance (also known as diffeomorphism covariance or general invariance) is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws.' back |
General relativity - Wikipedia, General relativity - Wikipedia, the free encyclopedia, 'General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics. General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.' back |
Gödel's incompleteness theorems - Wikipedia, Gödel's incompleteness theorems - Wikipedia, 'Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (i.e., any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.' back |
Hebrew Bible - Wikipedia, Hebrew Bible - Wikipedia, the free encyclopedia, The Hebrew Bible . . . is a term referring to the books of the Jewish Bible as originally written mostly in Biblical Hebrew with some Biblical Aramaic. The term closely corresponds to contents of the Jewish Tanakh and the Protestant Old Testament (see also Judeo-Christian) but does not include the deuterocanonical portions of the Roman Catholic or the Anagignoskomena portions of the Eastern Orthodox Old Testaments. The term does not imply naming, numbering or ordering of books, which varies (see also Biblical canon).' back |
Hilbert space - Wikipedia, Hilbert space - Wikipedia, the free encyclopedia, ' The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is a vector space equipped with an inner product, an operation that allows defining lengths and angles. Furthermore, Hilbert spaces are complete, which means that there are enough limits in the space to allow the techniques of calculus to be used.' back |
Isaiah 9:6, 'Unto us a child is born . . . ', 'For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counseller, The mighty God, The everlasting Father, The Prince of Peace.' back |
Jeffrey Nicholls (1967), How universal is the universe?, ' 61 The future is beyond our comprehension, but we can get an idea of it and speed its coming by studying what we already have. Contemplating the size and wonder of the universe as it stands in the light of its openness to the future must surely be a powerful incentive to men to love God. We have come a long way since the little world of St Thomas. Ours is open to all things, even participating in god. This is what I mean by universal. ' back |
Jeffrey Nicholls (1987), A theory of Peace, ' The argument: I began to think about peace in a very practical way during the Viet Nam war. I was the right age to be called up. I was exempted because I was a clergyman, but despite the terrors that war held for me, I think I might have gone. It was my first whiff of the force of patriotism. To my amazement, it was strong enough to make even me face death. |
Matthew 28:18–20, The Great Commission, ' Then Jesus approached and said to them, “All power in heaven and on earth has been given to me. Go, therefore, and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the holy Spirit, teaching them to observe all that I have commanded you. And behold, I am with you always, until the end of the age".' back |
Measurement in quantum mechanics - Wikipedia, Measurement in quantum mechanics - Wikipedia, the free encyclopedia, 'The framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus.' back |
Medieval medicine of Western Europe - Wikipedia, Medieval medicine of Western Europe - Wikipedia, the free encyclopedia, ' Medieval medicine is widely misunderstood, thought of as a uniform attitude composed of placing hopes in the church and God to heal all sicknesses, while sickness itself exists as a product of destiny, sin, and astral influences as physical causes. On the other hand, medieval medicine, especially in the second half of the medieval period (c. 1100–1500 AD), became a formal body of theoretical knowledge and was institutionalized in the universities.' back |
Niko Vorobyov (2022_03_28), Patriarch Kirill: Putin ally faces backlash after ‘blessing’ war, ' On March 16, Pope Francis held a video meeting with Patriarch Kirill, the 75-year-old leader of the Russian Orthodox Church and a longtime ally of President Vladimir Putin. The head of the Catholic church warned the Russian patriarch against hiding behind religion to justify armed aggression and conquest. “Once upon a time there was also talk in our churches of holy war or just war,” the pope said, according to the Vatican press office. “Today we cannot speak like this.” Ten days earlier, in a sermon, Patriarch Kirill appeared to endorse Moscow’s so-called “special peacekeeping operation,” as the war on Ukraine is officially called in Russia. “We have entered into a struggle that has not a physical, but a metaphysical significance,” the patriarch said.' back |
Peano axioms - Wikipedia, Peano axioms - Wikipedia - the free encyclopedia, 'In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of whether number theory is consistent and complete.' back |
Planck-Einstein relation - Wikipedia, Planck-Einstein relation - Wikipedia, the free encyclopedia, 'The Planck–Einstein relation. . . refers to a formula integral to quantum mechanics, which states that the energy of a photon (E) is proportional to its frequency (ν). E = hν. The constant of proportionality, h, is known as the Planck constant.' back |
Quantum field theory - Wikipedia, Quantum field theory - Wikipedia, the free encyclopedia, 'Quantum field theory (QFT) provides a theoretical framework for constructing quantum mechanical models of systems classically described by fields or (especially in a condensed matter context) of many-body systems. . . . In QFT photons are not thought of as 'little billiard balls', they are considered to be field quanta - necessarily chunked ripples in a field that 'look like' particles. Fermions, like the electron, can also be described as ripples in a field, where each kind of fermion has its own field. In summary, the classical visualisation of "everything is particles and fields", in quantum field theory, resolves into "everything is particles", which then resolves into "everything is fields". In the end, particles are regarded as excited states of a field (field quanta). back |
Rolf Landauer (1999), Information is a Physical Entity, 'Abstract: This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that on the ultimate nature of the laws of physics are included.' back |
Thomas Aquinas, Summa Theologiae - Home, ' Because the doctor of Catholic truth ought not only to teach the proficient, but also to instruct beginners (according to the Apostle: As unto little ones in Christ, I gave you milk to drink, not meat—1 Corinthians 3:1-2), we purpose in this book to treat of whatever belongs to the Christian religion, in such a way as may tend to the instruction of beginners. We have considered that students in this doctrine have not seldom been hampered by what they have found written by other authors, partly on account of the multiplication of useless questions, articles, and arguments, partly also because those things that are needful for them to know are not taught according to the order of the subject matter, but according as the plan of the book might require, or the occasion of the argument offer, partly, too, because frequent repetition brought weariness and confusion to the minds of readers. Endeavouring to avoid these and other like faults, we shall try, by God's help, to set forth whatever is included in this sacred doctrine as briefly and clearly as the matter itself may allow.' back |
Unmoved mover - Wikipedia, Unmoved mover - Wikipedia, the free encyclopedia, ' The unmoved mover (Ancient Greek: ὃ οὐ κινούμενον κινεῖ, romanized: ho ou kinoúmenon kineî, lit. 'that which moves without being moved'] or prime mover (Latin: primum movens) is a concept advanced by Aristotle as a primary cause (or first uncaused cause) or "mover" of all the motion in the universe. As is implicit in the name, the unmoved mover moves other things, but is not itself moved by any prior action. In Book 12 (Greek: Λ) of his Metaphysics, Aristotle describes the unmoved mover as being perfectly beautiful, indivisible, and contemplating only the perfect contemplation: self-contemplation. He equates this concept also with the active intellect. This Aristotelian concept had its roots in cosmological speculations of the earliest Greek pre-Socratic philosophers and became highly influential and widely drawn upon in medieval philosophy and theology. St. Thomas Aquinas, for example, elaborated on the unmoved mover in the Quinque viae. ' back |