Darwin (1859), Charles, The Origin of Species: By Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life, Cambridge University Press 1859, 2009 ' It's hard to talk about The Origin of Species without making statements that seem overwrought and fulsome. But it's true: this is indeed one of the most important and influential books ever written, and it is one of the very few groundbreaking works of science that is truly readable. . . . Darwin's friend and "bulldog" T.H. Huxley said upon reading the Origin, "How extremely stupid of me not to have thought of that." Alfred Russel Wallace had thought of the same theory of evolution Darwin did, but it was Darwin who gathered the mass of supporting evidence—on domestic animals and plants, on variability, on sexual selection, on dispersal—that swept most scientists before it.' Mary Ellen Curtin  Amazon   back

Einstein (1923), Albert, and Einstein, Lorentz, Minkowski, Weyl and Sommerfeld, The Principle of Relativity - A collection of original memoirs on the special and general theory of Relativity. With notes by A. Sommerfeld. Translated by W. Perrett and G. B. Jeffery, Methuen 1923 Minkowski: ' We can determine the ratio of the units of length and time beforehand in such a way that the natural limit of velocity becomes c = 1. If we introduce it = s in place of t the quadratic differential expression dτ² = - x² - y² - z² - s² thus becomes perfectly symmetrical in x, y, z, s; and this symmetry is communicated to any law which does not contradict the world postulate. Thus the essence of this postulate may be clothed in a very pregnant manner in the mystic formula 3.10⁵ = i seconds.'  Amazon   back

Feynman (2002), Richard, Feynman Lectures on Gravitation, Westview Press 2002 ' The Feynman Lectures on Gravitation are based on notes prepared during a course on gravitational physics that Richard Feynman taught at Caltech during the 1962-63 academic year. For several years prior to these lectures, Feynman thought long and hard about the fundamental problems in gravitational physics, yet he published very little. These lectures represent a useful record of his viewpoints and some of his insights into gravity and its application to cosmology, superstars, wormholes, and gravitational waves at that particular time. The lectures also contain a number of fascinating digressions and asides on the foundations of physics and other issues.' [zero-energy universe, pp 9 - 10]   Amazon   back

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.'  Amazon   back

Kolmogorov (1956), Andrey Nikolaevich, and Nathan Morrison (Translator) (With an added bibliography by A T Bharucha-Reid), Foundations of the Theory of Probability, Chelsea 1956 Preface: 'The purpose of this monograph is to give an axiomatic foundation for the theory of probability. . . . This task would have been a rather hopeless one before the introduction of Lebesgue's theories of measure and integration. However, after Lebesgue's publication of his investigations, the analogies between measure of a set and mathematical expectation of a random variable became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be in complete analogy with the corresponding properties of orthogonal functions . . .'  Amazon   back

Nielsen (2016), Michael A., and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2016 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002.  Amazon   back

von Neumann (2018), John, and Nicholas A. Wheeler (editor), Robert T Beyer (translator), The Mathematical Foundations of Quantum Mechanics, Princeton University Press 2018 ' Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics--a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. In this new edition of this classic work, mathematical physicist Nicholas Wheeler has completely reset the book in TeX, making the text and equations far easier to read. He has also corrected a handful of typographic errors, revised some sentences for clarity and readability, provided an index for the first time, and added prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson. The result brings new life to an essential work in theoretical physics and mathematics.'  Amazon   back

Albert Einstein (1915), The Field Equations of Gravitation, ' In two recently published papers I have shown how to obtain field equations of gravitation that comply with the postulate of general relativity, i.e., which in their general formulation are covariant under arbitrary substitutions of space-time variables. [. . .] With this, we have finally completed the general theory of relativity as a logical structure. The postulate of relativity in its most general formulation (which makes space-time coordinates into physically meaningless parameters) leads with compelling necessity to a very specific theory of gravitation that also explains the movement of the perihelion of Mercury. However, the postulate of general relativity cannot reveal to us anything new and different about the essence of the various processes in nature than what the special theory of relativity taught us already. The opinions I recently voiced here in this regard have been in error. Every physical theory that complies with the special theory of relativity can, by means of the absolute differential calculus, be integrated into the system of general relativity theory — without the latter providing any criteria about the admissibility of such physical theory' back

Aquinas, Summa, I, 10, 2, Is God eternal?, 'I answer that, The idea of eternity follows immutability, as the idea of time follows movement, as appears from the preceding article. Hence, as God is supremely immutable, it supremely belongs to Him to be eternal. Nor is He eternal only; but He is His own eternity; whereas, no other being is its own duration, as no other is its own being. Now God is His own uniform being; and hence as He is His own essence, so He is His own eternity.' back

Aquinas, Summa I, 25, 3, Is God omnipotent?, '. . . God is called omnipotent because He can do all things that are possible absolutely; which is the second way of saying a thing is possible. For a thing is said to be possible or impossible absolutely, according to the relation in which the very terms stand to one another, possible if the predicate is not incompatible with the subject, as that Socrates sits; and absolutely impossible when the predicate is altogether incompatible with the subject, as, for instance, that a man is a donkey.' 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, 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

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

Black hole - Wikipedia, Black hole - Wikipedia, the free encyclopedia, ' A black hole is a region of spacetime where gravity is so strong that nothing, including light and other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of no escape is called the event horizon. Although it has a great effect on the fate and circumstances of an object crossing it, it has no locally detectable features according to general relativity. In many ways, a black hole acts like an ideal black body, as it reflects no light. Moreover, quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is of the order of billionths of a kelvin for stellar black holes, making it essentially impossible to observe directly. ' back

Black hole thermodynamics - Wikipedia, Black hole thermodynamics - Wikipedia, the free encyclopedia, 'In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. Much as the study of the statistical mechanics of black body radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle.' back

Boson - Wikipedia, Boson - Wikipedia, the free encyclopedia, 'In particle physics, bosons are particles with an integer spin, as opposed to fermions which have half-integer spin. From a behaviour point of view, fermions are particles that obey the Fermi-Dirac statistics while bosons are particles that obey the Bose-Einstein statistics. They may be either elementary, like the photon, or composite, as mesons. All force carrier particles are bosons. They are named after Satyendra Nath Bose. In contrast to fermions, several bosons can occupy the same quantum state. Thus, bosons with the same energy can occupy the same place in space.' back

Brouwer fixed point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, 'Among hundreds of fixed-point theorems] Brouwer's is particularly well known, due in part to its use across numerous fields of mathematics. In its original field, this result is one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem, the invariance of dimension and the Borsuk–Ulam theorem. This gives it a place among the fundamental theorems of topology.' back

Determinism - Wikipedia, Determinism - Wikipedia, the free encyclopedia, ' Determinism is the philosophical view that all events in the universe, including human decisions and actions, are causally inevitable.[1] Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and considerations. Like eternalism, determinism focuses on particular events rather than the future as a concept. The opposite of determinism is indeterminism, or the view that events are not deterministically caused but rather occur due to chance.' back

Eigenvalue algorithm - Wikipedia, Eigenvalue algorithm - Wikipedia, the free encyclopedia, ' In numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors.' back

Fermion - Wikipedia, Fermion - Wikipedia, the free encyclopedia, 'In particle physics, fermions are particles with a half-integer spin, such as protons and electrons. They obey the Fermi-Dirac statistics and are named after Enrico Fermi. In the Standard Model there are two types of elementary fermions: quarks and leptons. . . . In contrast to bosons, only one fermion can occupy a quantum state at a given time (they obey the Pauli Exclusion Principle). Thus, if more than one fermion occupies the same place in space, the properties of each fermion (e.g. its spin) must be different from the rest. Therefore fermions are usually related with matter while bosons are related with radiation, though the separation between the two is not clear in quantum physics. 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

Laplace's demon - Wikipedia, Laplace's demon - Wikipedia, the free encyclopedia, ' We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.' A Philosophical Essay on Probabilities, Essai philosophique dur les probabilites introduction to the second edition of Theorie analytique des probabilites based on a lecture given in 1794. 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

Ousia - Wikipedia, Ousia - Wikipedia, the free enxcycxlopedia, 'Ousia (Ancient Greek: οὐσία) is a philosophical and theological term, originally used in ancient Greek philosophy, then later in Christian theology. It was used by various ancient Greek philosophers, like Plato and Aristotle, as a primary designation for philosophical concepts of essence or substance. In contemporary philosophy, it is analogous to English concepts of being, and ontic. In Christian theology, the concept of θεία ουσία (divine essence) is one of the most important doctrinal concepts, central to the development of trinitarian doctrine.] The Ancient Greek term θεία ουσία (theia ousia; divine essence) was translated in Latin as essentia or substantia, and hence in English as essence or substance. . . . Some modern authors also suggest that the Ancient Greek term οὐσία is properly translated as essentia (essence), while substantia has a wider spectrum of meanings.' back

Planck constant - Wikipedia, Planck constant - Wikipedia, the free encyclopedia, ' Since energy and mass are equivalent, the Planck constant also relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to replacing the metal cylinder, called the International Prototype of the Kilogram (IPK), that had defined the kilogram since 1889. . . . For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.626 070 150 × 10-34 J⋅s exactly. ' back

Second law of thermodynamics - Wikipedia, Second law of thermodynamics - Wikipedia - The free encyclopedia, 'The second law of thermodynamics states that in a natural thermodynamic process, there is an increase in the sum of the entropies of the participating systems. The second law is an empirical finding that has been accepted as an axiom of thermodynamic theory. back

Stockholm Resilience Center, The nine planetary boundaries, ' Founded in 2007 A joint initiative between Stockholm University and the Beijer Institute of Ecological Economics at The Royal Swedish Academy of Sciences. Approximately 140 members of staff The mission of the centre is to advance research for governance and management of social-ecological systems to secure ecosystem services for human well-being and resilience for long-term sustainability ' back

Variety (cybernetics) - Wikipedia, Variety (cybernetics) - Wikipedia, the free encyclopedia, 'The term Variety was introduced by W. Ross Ashby to denote the count of the total number of states of a system. The condition for dynamic stability under perturbation (or input) was described by his Law of Requisite Variety. Ashby says: Thus, if the order of occurrence is ignored, the set {c, b, c, a, c, c, a, b, c, b, b, a} which contains twelve elements, contains only three distinct elements- a, b, c. Such a set will be said to have a variety of three elements. He adds The observer and his powers of discrimination may have to be specified if the variety is to be well defined. Variety can be stated as an integer, as above, or as the logarithm to the base 2 of the number i.e. in bits.' back

Zero-energy universe - Wikipedia, Zero-energy universe - Wikipedia, the free encyclopedia, 'The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly cancelled out by its negative energy in the form of gravity. . . . The zero-energy universe theory originated in 1973, when Edward Tryon proposed in the journal Nature that the universe emerged from a large-scale quantum fluctuation of vacuum energy, resulting in its positive mass-energy being exactly balanced by its negative gravitational potential energy.' back