Some particular aspects on the study of competition in moderna and archaïc societies and groups.

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

In her provocative discussion of the challenge posed to the traditional impartialist, justice-focused conception of morality by the new-wave care perspective in ethics, Annette Baier calls for ‘a “marriage” of the old male and newly articulated female... moral wisdom,’ to produce a new ‘cooperative’ moral theory that ‘harmonize[s] justice and care.’ I want in this paper to play matchmaker, proposing one possible conjugal bonding: a union of two apparently dissimilar modes of what Nel Noddings calls ‘meeting the other morally,’ (...) a wedding of respect and care. (shrink)

Over the past few decades, scholars have reassessed the role of amour-propre in Rousseau’s thought. While it was once believed that he had an entirely negative valuation of the emotion, it is now widely held that he finds it useful and employs it to strengthen moral attachments, conjugal love, civic virtue and moral heroism. At the same time, scholars are divided as to whether this positive amour-propre is an antidote to the negative or dangerous form. Some scholars are confident (...) that ‘inflamed’ amour-propre can be overcome while others adopt a more fatalistic view. While mindful of Rousseau’s pessimism in his most famous works, this essay seeks to identify a middle position. By contending Rousseau’s discussion of amour-propre is largely concerned with the problems surrounding identity construction in commercial, urban societies, it will be argued that amour-propre can be lessened to manageable levels in more rural societies, that is, agrarian provincial life. (shrink)

El propósito de Levinas coincide con el intento moderno de recuperación de la verdad y del sentido aunque en una dirección y contenidos distintos. Si en Hegel la Aufhebung tendía a la Totalidad y lo Mismo , para Husserl será esencial la apertura de Mundo que tiene lugar ya en la experiencia de conciencia del ego trascendental, mientras que Heidegger, por su parte, primará la pregunta por el Ser. El intento de Levinas, en cambio, no será recomponer la relación entre (...) el yo, por un lado, y el mundo, lo absoluto, las cosas o el ser, por el otro, sino la recuperación de la relación entre yo-y-otro. No es un simple cambio en la dirección o en el contenido del sentido de la reflexión filosófica, sino un intento serio de encontrar una nueva significación, «otra manera que ser» que no termine siendo otro proyecto más de integración y síntesis. Lo que propone Levinas es una auténtica salida para la que traza el itinerario que va del ser al otro, recurriendo sencillamente a la experiencia que cotidianamente se nos impone a cada uno de nosotros con un peso incontestable, a saber: la presencia de las diferencias, de lo asimétrico, en definitiva, la manifestación del otro en tanto que otro. Es esta experiencia heterónoma ordinaria, esta vivencia diaria de la alteridad como dato primordial del fenómeno de la intersubjetividad el ámbito que ha intentado explorar nuestro autor. ¿Acaso es esta responsabilidad así sentida conjugable con una experiencia filosófica universal? ¿La responsabilidad puede llevarse hasta el límite de la substitución por el otro, hasta la de-posición del Yo sin identidad? ¿Qué tipo de relación puede darse con algo absolutamente asimétrico, exterior, previo e irreductible? ¿De dónde viene esa asignación apremiante de responsabilidad que llega hasta arrojarme en la obsesión y el asedio? ¿Cómo puede ser éticamente plausible un mandato tan traumatizante y violento que termina por convertir al sujeto en rehén, sustituido ya por los otros? ¿Es posible conciliar la libertad y la autónoma decisión del sujeto con una consideración de la subjetividad como «heme aquí», absoluta pasividad expuesta a los otros y vulnerabilidad de una piel que se ofrece al ultraje y la herida?. En definitiva: ¿es la subjetividad algo de lo que partimos o a lo que llegamos? (shrink)

Religion has a considerable influence over the public’s attitudes towards science and technologies. The objective of the paper is to understand the ethical and religious problems concerning the use of embryo for research in assisting conception for infertile couples from the perspective of Catholic Christians. This paper seeks to explain our preliminary reflections on how religious communities particularly the Catholic Christian communities respond to and assess the ethics of reproductive technologies and embryo research. Christianity as a whole lacks a unified (...) and definitive statement on when an embryo becomes a person, although fundamentalist Christians tend to be opposed to embryo experimentation. Roman Catholics tend to believe that the embryo should be treated as human life from the moment of conception or fertilisation. As opposed to this preconception I have tried to point out that a foetus is a clump of cells and lacks individuality as a conscientious human being and thus can be used for research for therapeutic reason. The paper concluded that the Church accepts techniques on embryo that respect their life. So they would allow procedures that are akin with healing and improvement of life without involving undue risks. The Church feels children should arise out of act of love between man and his wife in co-operation with God. In this regard, it may be pointed out though the creation of a child through a conjugal act in a wed lock is the preferred method since it is the most natural, least expensive one. But that does not mean, it should be the only acceptable means to conception. To state a child born using ARTs would be less perfect compared to a child born through conjugal act of husband and wife is absurd one to be mentioned. (shrink)

The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the violations of (...) energy conservation in a “safe”, maximally remote point in the alleged “beginning of the universe”. On the contrary, an omnipresent and omnitemporal medium obeying quantum information conservation rather than energy conservation permanently generates action and thus the physical world. The utilization of that creation “ex nihilo” is accessible to humankind, at least theoretically, as long as one observes the physical laws, which admit it in their new and wider generalization. One can oppose Hilbert mathematics to Gödel mathematics, which can be identified as all the standard mathematics until now featureable by the Gödel dichotomy of arithmetic to set theory: and then, “dialectic”, “intuitionistic”, and “Gödelian” mathematics within the former, according to a negative, positive, or zero value of the distance between finiteness and infinity. A mapping of Hilbert mathematics into pseudo-Riemannian space corresponds, therefore allowing for gravitation to be interpreted purely mathematically and ontologically in a Pythagorean sense. Information and quantum information can be involved in the foundations of mathematics and linked to the axiom of choice or alternatively, to the field of all rational numbers, from which the pair of both dual and anti-isometric Peano arithmetics featuring Hilbert arithmetic are immediately inferable. Noether’s theorems (1918) imply quantum information conservation as the maximally possible generalization of the pair of the conservation of a physical quantity and the corresponding Lie group of its conjugate. Hilbert mathematics can be interpreted from their viewpoint also after an algebraic generalization of them. Following the ideas of Noether’s theorem (1918), locality and nonlocality can be realized both physically and mathematically. The “light phase of the universe” can be linked to the gap of mathematics and physics in the Cartesian organization of cognition in Modernity and then opposed to its “dark phase”, in which physics and mathematics are merged. All physical quantities can be deduced from only mathematical premises by the mediation of the most fundamental physical constants such as the speed of light in a vacuum, the Planck and gravitational constants once they have been interpreted by the relation of locality and nonlocality. (shrink)

The analysis of the reversibility of quantum mechanics depends upon the choice of the time reversal operator for quantum mechanical states. The orthodox choice for the time reversal operator on QM states is known as the Wigner operator, T*, where * performs complex conjugation. The peculiarity is that this is not simply the unitary time reversal operation, but an anti-unitary operator, involving complex conjugation in addition to ordinary time reversal. The alternative choice is the Racah operator, which is simply ordinary (...) time reversal, T. Orthodox treatments hold that it is either logically or empirically necessary to adopt the Wigner operator, and the Racah operator has received little attention. The basis for this choice is analysed in detail, and it is concluded that all the conventional arguments for rejecting the Racah operator and adopting the Wigner operator are mistaken. The additional problem of whether the deterministic part of quantum mechanics should be judged to be reversible or not is also considered. The adoption of the Racah operator for time reversal appears prima facie to entail that quantum mechanics is irreversible. However, it is concluded that the real answer to question depends upon the choice of interpretation of the theory. In any case, the conventional reasons for claiming that quantum mechanics is reversible are incorrect. (shrink)

This paper aims to show issues raised by lacanian psychoanalyses concerning the reasons of the phenomenon of aggressiveness, mainly due to the frequency of this phenomenon in education. In this paper, it was intended to highlight the philosophical dimension of the problem, since we are using basically the dissertative method. Lacan takes Hegelian and Marxist legacy to develop the thesis of aggressiveness as realization of a dynamic introduced from the gaze and that has its modus operandi in the movements of (...) alienation and non-alienation. The aggressiveness illustrated, for example, by the injuries suffered by teachers shows itself as a tentative to cause the fall of the Other, this fall is considered as the object a of which its appearance is regulated by the Oedipus Complex. Namely, both the way how the parental authority figures are inscribed in the significant chains that compose the individual and how this inscription shapes the existential possibilities of interaction with the opposite sex would be the key to foresee the extent the individual makes use of aggressiveness. In this way, the Oedipus complex, reinvested by the event of puberty would be responsible for the displacement of the libido one time to the ´Other´ and other time to the own subject. The Other, in the theoretical development of Lacan that follows the decade of 1960, comprehends the identifier choices and also what escapes from any identification. The Other, as a teacher, has the role of positioning itself to generate intuitively one process of identification and has the delicate function of sustain the dialectic that emerges in the moment where the Other falls, moment which usually comes after the identification and that happens with a joy capable of unveiling the object a. Although the role of education is not to maintain an auscultation to this object, the education can influence its nonexclusion and make this object be contoured with the advent of singularities. In this moment, the explicitness of the rules which education constitutes itself as well as the empathy from the educator can be a fundamental instrument in education like the subject to be taught. From the text, we can conclude that: we need to put the aggressiveness in our speech as via of achievement of the non-alienation process conjugated with the possibility to support the desire. (shrink)

En 1968 ocurrieron dos hechos sobre los cuales cabe hacer una reflexión orientada por la bioética: la llamada Revolución del 68 y la aparición de la Carta encíclica Humanae Vitae. El Concilio Vaticano II, que fue presentado como una actualización de la Iglesia católica al mundo moderno, fue el escenario de los estudios previos a la redacción del documento pontificio, donde Pablo VI dejó clara la postura del Magisterio de la Iglesia sobre la moral sexual y anticipa los errores prácticos (...) que se seguirían a planteamientos conceptuales antropológicos erróneos o equivocados sobre esa temática. Hay necesidad de rehabilitar la Humanae vitae para volver a percibir el acto conyugal en su “verdad inalterable”, donde no se puede separar el bien y la belleza de la donación mutua de los cónyuges, que redunda en el bien común de la sociedad para defender su célula básica y nuclear que es la familia. In 1968, two events occurred on which it is worth reflecting on bioethics: the so-called Revolution of 1968 and the appearance of the Encyclical Letter Humanae Vitae. The Second Vatican Council, which was presented as an update of the Catholic Church to the modern world, was the scene of the studies prior to the drafting of the pontifical document, where Paul VI made clear the position of the Magisterium of the Church on sexual morality and it anticipates the practical errors that would follow erroneous or mistaken anthropological conceptual approaches on this subject. There is a need to rehabilitate Humanae vitae in order to re-perceive the conjugal act in its "unalterable truth", where good and beauty cannot be separated from the mutual donation of the spouses, which results in the common good of society to defend its basic and nuclear cell which is the family. (shrink)

The label `semiotic grammar' captures a fundamental property of the grammars of human languages: not only is language a semiotic system in the familiar Saussurean sense, but its organizing system, its grammar, is also a semiotic system. This proposition, explicated in detail by William McGregor in this book, constitutes a new theory of grammar. Semiotic Grammar is `functional' rather than `formal' in its intellectual origins, approaches, and methods. It demonstrates, however, that neither a purely functional nor a purely formal account (...) of language is adequate, given the centrality of the sign as the fundamental unit of grammatical analysis. The author distinguishes four types of grammatical signs: experiential, logical, interpersonal, and textural. The signifiers of these signs are syntagmatic relationships of the following types, respectively: constituency, dependency, conjugational and linking. McGregor illustrates and exemplifies the theory with data from a variety of languages including English, Acehnese, Polish, Finnish, Japanese, Chinese, and Mohawk; and from his pioneering research on Gooniyandi and Nyulnyul, two languages of the Kimberleys region of Western Australia. (shrink)

From Chernobyl to Fukushima, it became clear that the technology is a system evolutionary factor, and the consequences of man-made disasters, as the actualization of risk related to changes in the social heredity (cultural transmission) elements. The uniqueness of the human phenomenon is a characteristic of the system arising out of the nonlinear interaction of biological, cultural and techno-rationalistic adaptive modules. Distribution emerging adaptive innovation within each module is in accordance with the two algorithms that are characterized by the dominance (...) of vertical (transgenerational) and horizontal (infection, contagion) adaptive streams of information, respectively. Evolutionary risk is the result of an imbalance of autonomous adaptive systems have an essential attribute of adaptibe strategy of Homo. Technological civilization inherent predisposition to overcome their dependence on biological and physical components. This feature serves as an enhancer of the evolutionary generating conjugate with the scientific and technological development risk We can assume the existence of an intention of Western mentality to a high priority (positive or negative) of technological modifications micro-social environment and post- Soviet (East Slavic) mentality to modification of macro-social system. (shrink)

I examine Bernard Lonergan's approach to the problem of evil. I look to determine whether his solution, which is based on the conjugate forms of faith, hope, and charity, and culminates in a heuristic where forgiveness plays an essential role in moving beyond the problem of evil is adequate. I examine the distinction between basic sin, moral evil, and physical evil as well as his claim that from the viewpoint of the unrestricted act of understanding the non-systematic vanishes.

Quantum complementarity is interpreted in terms of duality and opposition. Any two conjugates are considered both as dual and opposite. Thus quantum mechanics introduces a mathematical model of them in an exact and experimental science. It is based on the complex Hilbert space, which coincides with the dual one. The two dual Hilbert spaces model both duality and opposition to resolve unifying the quantum and smooth motions. The model involves necessarily infinity even in any finitely dimensional subspace of the complex (...) Hilbert space being due to the complex basis. Furthermore, infinity is what unifies duality and opposition, universality and openness, completeness and incompleteness in it. The deduced core of quantum complementarity in terms of infinity, duality and opposition allows of resolving a series of various problems in different branches of philosophy: the common structure of incompleteness in Gödel’s (1931) theorems and Enstein, Podolsky, and Rosen’s argument (1935); infinity as both complete and incomplete; grounding and self-grounding, metaphor and representation between language and reality, choice and information, the totality and an observer, the basic idea of philosophical phenomenology. The main conclusion is: Quantum complementarity unifies duality and opposition in a consistent way underlying the physical world. (shrink)

As a philosophical paradigm, differential heterogenesis offers us a novel descriptive vantage with which to inscribe Deleuze’s virtuality within the terrain of “differential becoming,” conjugating “pure saliences” so as to parse economies, microhistories, insurgencies, and epistemological evolutionary processes that can be conceived of independently from their representational form. Unlike Gestalt theory’s oppositional constructions, the advantage of this aperture is that it posits a dynamic context to both media and its analysis, rendering them functionally tractable and set in relation to other (...) objects, rather than as sedentary identities. Surveying the genealogy of differential heterogenesis with particular interest in the legacy of Lautman’s dialectic, I make the case for a reading of the Deleuzean virtual that departs from an event-oriented approach, galvanizing Sarti and Citti’s dynamic a priori vis-à-vis Deleuze’s philosophy of difference. Specifically, I posit differential heterogenesis as frame with which to examine our contemporaneous epistemic shift as it relates to multi-scalar computational modeling while paying particular attention to neuro-inferential modes of inductive learning and homologous cognitive architecture. Carving a bricolage between Mark Wilson’s work on the “greediness of scales” and Deleuze’s “scales of reality”, this project threads between static ecologies and active externalism vis-à-vis endocentric frames of reference and syntactical scaffolding. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine – (...) Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

A cognitive science perspective of yoga system of thought will be developed in conjugation with the Samkhya Darsana. This development will be further advanced using Advaita Vedanta and will be translated into modern scientific terms to arrive at an idea about cognition process. The stalling of the cognitive process and stilling the mind will be critically discussed in the light of this perspective. This critical analysis and translation into cognitive science and modern scientific terms will be presented together with its (...) implications and applications to the disciplines of mind-machine modeling, natural language comprehension branch of artificial intelligence and physiological psychology. (shrink)

Christopher Bennett has argued that state support of conjugal relationships can be founded on the unique contribution such relationships make to the autonomy of their participants by providing them with various forms of recognition and support unavailable elsewhere. I argue that, in part because a long history of interaction between two people who need each other’s validation tends to produce less meaningful responses over time, long-term conjugal relationships are unlikely to provide autonomy-enhancing support to their participants. To the (...) extent that intimate relationships can provide a unique form of reciprocal support, Bennett fails to show that couples have an advantage over multiple-partner arrangements in doing so. (shrink)

Schrödinger’s equation says that the Hamiltonian is the generator of time translations. This seems to imply that any reasonable definition of time operator must be conjugate to the Hamiltonian. Then both time and energy must have the same spectrum since conjugate operators are unitarily equivalent. Clearly this is not always true: normal Hamiltonians have lower bounded spectrum and often only have discrete eigenvalues, whereas we typically desire that time can take any real value. Pauli concluded that constructing a general a (...) time operator is impossible. Here we show how the Pauli argument fails when one uses an external system to track time, so that time arises as correlations between the system and the clock. In this case, the time operator is conjugate to the clock Hamiltonian and not to the system Hamiltonian, but its eigenvalues still satisfy the Schrödinger equation for arbitrary system Hamiltonians. (shrink)

If this can be seen as a long way from the beginning of the ancient history, where humans have envisioned different new things and then invented them to make their life’s working smoother and easier, then it can be found that they have attributed their discoveries to various aspects and names of Gods and tried to signify their belief in the form of portraying the God’s powers through the nature of their discovery. Rather, in much modern times, when humans have (...) developed the natural insights and prorated those in the form of a much more logically biased discovery, then, the atheists have started to dominate the scientific arena for their foreplay in the work of their discoveries. However, as time passes by, five special types of research communities have gathered to allocate their discovered data’s in the respective norms as such, i) Atheists to whom, there is in essence no God and nothing in this universe can be attributed to them. ii) Believer of only one God as a whole, where the principle of religious biasing is effluent and supreme in their regards of the physical laws associated with the life and stimuli, iii) Believer of multiple God’s as a whole which poses no such scientific evaluation but can be thought of as a conjugate mechanism for the creator of the universe, iv) A divine supreme, where there is exactly no God, but the whole universe is a manifestation of the nature, where nature indirectly focuses the presence of God’s or the supreme creator that maintains symmetry and working of the universe, v) The not-so-sure about mechanism of the God’s presence, where the researcher sometimes tends to belief in God when something magical happens and attribute all to their divine grace, or in times of failures where they accused them for not being philosophically intrinsic as to their own needs, and in times with the believe that, ‘we won’t believe what we can’t see!’, either in the middle of the good or bad moments or in general in a casual and carefree mode. But, this should be kept in mind, that, the Eastern mysticism has always signifies God’s action in terms of every scientific actions with a proper mythological essence which when accompanied by knowledge produces something so scientific in the ancient of the days, that modern day researchers also have had no options left than to attribute affirmation to the fantastic achievements in the ‘so’ ancient times discovery with a strict modern effluence. Therefore, to model this paper, I have gathered data’s and ideas from researchers of various fields mostly (PhDs) in their respective discipline, so as to emulate their minds in the norms of God and its associated beliefs. (shrink)

To evaluate an innovative sonopelvimetry method for early prediction of obstructed labour. Methods: A prospective study was conducted in two centers.GPS-based sonopelvimetry, laborProTM (Trig Medical Inc., Yoqneam Ilit, Israel) devise, was used prior to labour in nulliparous women at 39 - 42 weeks gestation remote from labor. Maternal pelvic parameters, including inter-iliac transverse diameter, obstetric conjugate and interspinous diameter were evaluated. Fetal parameters included head station, biparietal diameter and occipitofrontal diameter. Data on delivery and outcome were collected from the electronic (...) files. Results: The innovative use of sonopelvimetry was applied to 154 consecutive women, none of the participants complained of discomfort or complications observed. The mean time of examination was 15 + 2 minutes. Mean time of examination to delivery interval was 4.8 days (range 0 - 16 days). Small interspinous diameter and high head station were the best predictors for obstructed labour. Analysis indicated 87% sensitivity and 61% specificity for birth weight fetal head station and ISD combined in predicting obstructed labour with an area under the curve of 0.77. Conclusions: Our results indicate that GPS-based sonopelvimetry combined with fetal estimated weight is a valuable tool in the risk assessment of obstructed labour. Parameters obtained by sonopelvimetry combined with birth weight may be useful. (shrink)

During 17th century a scientific controversy existed on the derivation of Snell’s laws of reflection and refraction. Descartes gave a derivation of the laws, independent of the minimality of travel time of a ray of light between two given points. Fermat and Leibniz gave a derivation of the laws, based on the minimality of travel time of a ray of light between two given points. Leibniz’s calculus method became the standard method of derivation of the two laws. We demonstrate in (...) this article that Snell’s law of reflection follows from simple results of geometry. We do not use the concept of motion or the time of travel in our demonstration. That is, time plays no role in our demonstration. (shrink)