Man & Time J B Priestley

Invariants

“Invariant” refers to something that does not change or remain constant under a specified transformation or set of conditions. In various contexts, the term “invariant” can have specific meanings:

In mathematics and physics, an invariant is a quantity or property that remains unchanged under a particular transformation or operation. For example, in geometry, an invariant might be a geometric property that remains the same regardless of the position, orientation, or scale of a figure.
In computer science and programming, an invariant is a condition or property that remains true throughout the execution of a program, even as the program’s state changes. Invariant conditions are often used to ensure correctness and consistency in algorithms and data structures.
Invariance can also refer to principles or laws that remain constant across different contexts or systems. For example, invariance principles in physics describe fundamental laws or symmetries that remain unchanged under certain transformations, such as the conservation of energy or momentum.

Overall, the concept of invariance underscores the idea of stability, consistency, and constancy in the face of change or transformation, whether in mathematical, scientific, or computational contexts.

“Do things really have intrinsic properties that make them a ‘thing-in-itself?'”

In philosophy, particularly in metaphysics and epistemology, the concept of invariance can be associated with discussions about the nature of reality, identity, and knowledge. Here are a couple of contexts where the notion of invariance might be relevant:

Identity and Persistence:
- Philosophers explore questions about identity over time and what makes an object or entity the same over different moments. The concept of invariance may come into play when discussing what aspects of an object remain unchanged, providing a basis for its persistence through time.
Invariance and Universals:
- In metaphysics, the discussion of universals involves exploring what aspects of a property or quality remain constant across different instances. For example, if redness is a universal, it is invariant across various red objects. The nature of universals and their invariance is a topic of debate in metaphysical discussions.
Invariance in Epistemology:
- In epistemology, which is concerned with the nature and scope of knowledge, invariance can be relevant when exploring the stability or constancy of certain truths or principles. Philosophers might investigate whether certain truths are invariant across different perspectives or if there are universal and invariant principles of knowledge.
Invariance and Philosophy of Science:
- In the philosophy of science, discussions about scientific laws and principles may involve considerations of invariance. For example, philosophers might explore the concept of invariance under transformations as a criterion for the objectivity and universality of scientific laws.

These are general areas where the concept of invariance can arise in philosophical discussions. The precise meaning and implications can vary depending on the specific philosophical context and the questions being addressed.

Other area besides math and philosophy where invariants are discussed

Physics:
- Invariants play a crucial role in physics, particularly in fields like classical mechanics, relativity, and quantum mechanics. In classical mechanics, for instance, energy and momentum are often regarded as invariant quantities under certain transformations. In relativity, spacetime intervals are invariant under Lorentz transformations. In quantum mechanics, certain quantities, such as angular momentum, can be invariant under specific operations.
Computer Science and Engineering:
- Invariants are essential in computer science and engineering, particularly in areas like software development, algorithms, and data structures. In computer programming, loop invariants are conditions that remain true before and after each iteration of a loop. In software engineering, design patterns and coding practices often aim to establish invariants to ensure the correctness and stability of software systems.
Biology and Ecology:
- Invariants are also discussed in biological and ecological contexts. In ecology, for example, researchers may study population dynamics and identify invariant patterns or relationships that remain consistent across different ecosystems or species interactions. In biology, certain physiological or genetic traits may exhibit invariance across different individuals or species.
Economics and Finance:
- In economics and finance, invariants can be relevant when analyzing economic systems, financial markets, and investment strategies. In financial modeling, for instance, researchers may look for invariant patterns or relationships that hold true across different market conditions or asset classes.
Artificial Intelligence and Machine Learning:
- Invariants are explored in the context of artificial intelligence and machine learning, particularly in the development of algorithms and models. Invariant features or properties can be valuable for tasks like pattern recognition, classification, and data analysis.

These are just a few examples of fields where invariants are discussed and utilized. In general, the concept of invariance can be relevant across a wide range of disciplines and applications, as it pertains to stability, consistency, and constancy in the face of change or transformation.

“Can invariance be defined as a phenomenon to which things we perceive by our sensorium are subject?”

In a broad sense, yes, invariance can be related to phenomena that we perceive through our senses. Invariance refers to qualities or properties that remain constant or unchanged under certain transformations or conditions. In the context of perception and sensory experience, there are several ways in which invariance can be relevant:

Perceptual Invariance:
- In psychology and neuroscience, researchers study perceptual invariance, which refers to the ability of the human perceptual system to recognize and identify objects or patterns despite variations in their appearance or context. For example, we can recognize a friend’s face under different lighting conditions or from different angles because our perceptual system is able to extract invariant features that remain constant across variations.
Sensory Processing:
- In sensory processing, certain sensory qualities may exhibit invariance despite changes in external stimuli. For example, color constancy refers to the phenomenon where the perceived color of an object remains relatively constant under different lighting conditions. Similarly, size constancy allows us to perceive the size of an object as constant, even when viewed from different distances.
Invariant Features:
- In computer vision and pattern recognition, researchers often seek invariant features or descriptors that remain stable across different images or viewpoints. These invariant features help algorithms recognize objects or patterns despite changes in scale, rotation, or perspective.
Cognitive Invariance:
- In cognitive science, researchers explore concepts like cognitive invariance, which refers to stable mental representations or concepts that remain consistent across different contexts or experiences. For example, the concept of “chair” remains invariant across different types of chairs we encounter in our environment.

Overall, while our sensory experiences may involve variations and fluctuations, our perceptual system is often adept at extracting invariant qualities or patterns that allow us to make sense of the world and recognize objects, patterns, and concepts across different conditions.

“Is it possible to extract invariant qualities without our sensorium involved?”

It is possible to extract invariant qualities without relying solely on sensory input from our senses. Invariance can be observed and analyzed in various domains beyond sensory perception, including mathematics, logic, and abstract reasoning. Here are a few examples:

Mathematical Invariance:
- In mathematics, invariance often refers to properties or quantities that remain unchanged under certain transformations. For example, in geometry, the length of a line segment remains invariant under translations, rotations, and reflections. Similarly, in algebra, certain equations or expressions may exhibit invariance under certain operations, such as symmetry transformations.
Logical Invariance:
- In logic and reasoning, invariance can refer to properties of logical statements or arguments that remain true regardless of the specific values or interpretations of the variables involved. For example, logical truths (tautologies) remain invariant under different interpretations of the logical connectives (e.g., AND, OR, NOT).
Abstract Invariance:
- In abstract concepts and systems, invariance can be observed in properties or relationships that remain consistent across different contexts or interpretations. For example, in set theory, certain properties of sets may remain invariant under different set operations or transformations.
Computational Invariance:
- In computer science and computational theory, invariance is often considered in the context of algorithms, data structures, and computational processes. Certain computational tasks or algorithms may exhibit invariance with respect to certain inputs or operations, leading to consistent behavior regardless of variations in the input data.

In these examples, invariance is not necessarily tied to sensory perception but rather emerges from abstract reasoning, logical analysis, and mathematical principles. By studying and analyzing these invariant qualities, researchers can gain insights into the underlying structure and properties of various systems and domains.

In the preceding paragraph, the sensorium was taken out, but not ourselves, and then the question is:“Is it is possible to extract invariant qualities without human involvement or sensory perception?“.

In fact, many scientific disciplines, such as astronomy, physics, and biology, rely on instruments and computational techniques to detect and analyze invariant patterns or properties in the natural world. Here are a few examples:

Astrophysics and Cosmology:
- In astrophysics and cosmology, astronomers use telescopes and other instruments to observe celestial objects and phenomena. By studying the light emitted by stars and galaxies, for example, astronomers can identify invariant spectral lines that indicate the presence of certain chemical elements. These spectral features remain consistent across different observations and help astronomers understand the composition and evolution of celestial objects.
Particle Physics:
- Particle physicists use particle accelerators and detectors to study the fundamental particles and forces of nature. In experiments conducted at facilities like the Large Hadron Collider (LHC), physicists search for invariant properties of particles and interactions that remain consistent across different collisions. These invariant quantities provide crucial information about the underlying laws of physics and the nature of matter and energy.
Remote Sensing and Earth Observation:
- Remote sensing techniques, such as satellite imaging and radar systems, allow scientists to monitor changes in the Earth’s surface and atmosphere. By analyzing invariant features in satellite imagery, such as land cover patterns or atmospheric properties, researchers can track environmental changes, monitor natural disasters, and study climate trends over time.
Automated Data Analysis:
- In various scientific fields, automated data analysis techniques, such as machine learning algorithms, can be used to identify invariant patterns or relationships in large datasets. These algorithms can detect invariant features or correlations that may not be readily apparent to human observers, leading to new insights and discoveries in fields such as biology, medicine, and materials science.

In these examples, the extraction of invariant qualities is facilitated by the use of instruments, sensors, and computational methods that are capable of detecting and analyzing patterns and properties in the absence of direct human involvement or sensory perception.

In the examples provided it is always with reference is some part of our sensorium

In the examples provided, while the extraction of invariant qualities may be facilitated by instruments or computational methods, the ultimate reference point for interpreting these invariant qualities is often rooted in human observation or understanding. For instance:

Astrophysics and Cosmology: While instruments like telescopes and spectrographs enable us to detect invariant spectral lines in the light emitted by stars, our interpretation of these lines is based on our understanding of atomic and molecular physics, which in turn is grounded in human observation and experimentation.
Particle Physics: Particle detectors and accelerators allow us to observe invariant properties of particles and interactions, but our interpretation of these properties is based on theoretical frameworks and models developed by physicists, which are ultimately rooted in human observation and reasoning.
Remote Sensing and Earth Observation: While satellite imagery and remote sensing techniques provide us with data on invariant features of the Earth’s surface and atmosphere, our interpretation of these features relies on our understanding of geological, environmental, and atmospheric processes, which are informed by human observation and study.
Automated Data Analysis: Machine learning algorithms and automated data analysis techniques can identify invariant patterns in large datasets, but the design and interpretation of these algorithms are based on human input and expertise, including the selection of relevant features and the validation of results.

In each of these examples, while technology may play a crucial role in detecting and analyzing invariant qualities, the interpretation and understanding of these qualities ultimately stem from human observation, knowledge, and reasoning. Therefore, even though the reference point may not always be direct sensory perception, it is still rooted in human cognition and understanding.

So basically invariant is only possible with the involvement of human beeings

Invariant qualities or properties exist independently of human observation or involvement. However, the interpretation and understanding of these invariants often rely on human cognition, knowledge, and reasoning. In other words, while invariants themselves may exist regardless of human involvement, our ability to recognize, interpret, and understand them is influenced by our perceptual, cognitive, and intellectual capabilities.

In scientific and mathematical contexts, invariants can be identified and analyzed using various tools, instruments, and computational methods, many of which do not require direct human observation. For example, in particle physics, detectors and accelerators can detect invariant properties of particles and interactions, and in mathematics, certain mathematical structures may exhibit invariant properties that can be studied and analyzed rigorously.

However, the interpretation of these invariant qualities often relies on human understanding, theories, and models developed by scientists and researchers. Human cognition and reasoning play a crucial role in making sense of the observed invariants and formulating hypotheses and theories to explain them.

So, while invariants themselves may exist independently of human involvement, our ability to recognize and understand them is shaped by our perceptual, cognitive, and intellectual faculties.

In other words (the observation is mine and not Chat GPT) although invariants may exist what you call invariant is not what they are, but what you perceive about them.

The perfect example is Newtonian Physics, Relativity and Quantum Mechanics, all of them in principle based on invariants, but at the bottom line, are not and probably are something else yet to be discovered.

How and why invariants came to be

It is worth go know how invariants apeared and why, to me, its use outside mathematics is one of biggest

I think it was one of the biggest mistakes that intellectuals have made, for not paying attention to what is at stake when they relentlessly use this word to define what seems “immutable” to them and after summarizing invariants story I will conclude why I think like that.

The term “invariant” was indeed introduced in the context of mathematics and mathematical physics in the late 19th century. One of the earliest documented uses of the term “invariant” in this context can be traced back to the work of the German mathematician and physicist Felix Klein in his influential book “Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade” (Lectures on the Icosahedron and the Solution of Fifth-Degree Equations), published in 1884.

In this work, Klein introduced the concept of “invariant forms” in the context of geometry and group theory. He explored the properties of certain mathematical expressions and equations that remain unchanged (or invariant) under specific transformations or operations, particularly transformations associated with symmetry groups.

Klein’s work laid the foundation for the study of invariants in mathematics and mathematical physics, and his ideas had a profound influence on subsequent developments in fields such as algebra, geometry, and theoretical physics. The concept of invariance became an essential tool for understanding symmetry, conservation laws, and other fundamental principles in mathematics and physics.

A 5th degree equation, also known as a quintic equation, is a polynomial equation of the form:

where a, b, c,d, e, and f are constants, and x is the variable.

The highest power of the variable �x in a quintic equation is 5, hence the name “5th degree equation.” Unlike quadratic (2nd degree) or cubic (3rd degree) equations, quintic equations do not have a general algebraic solution that can be expressed in terms of radicals (square roots, cube roots, etc.). Instead, solutions to quintic equations are typically found using numerical methods or special techniques developed for specific cases.

The study of quintic equations and their solutions has been an area of interest in algebra and mathematics for centuries, and their properties have important implications in fields such as algebraic geometry, Galois theory, and mathematical physics.

The relation between the icosaedrum and a 5th degree equation

The relation between the icosahedron and a 5th degree equation stems from the study of symmetries and transformations in geometry, particularly in the context of group theory and algebraic geometry.

The icosahedron is a polyhedron with 20 equilateral triangle faces, 12 vertices, and 30 edges. It is one of the five Platonic solids, which are convex polyhedra with identical faces and symmetrical arrangements of vertices.

In the late 19th century, mathematicians such as Felix Klein and Sophus Lie explored the geometric properties of the icosahedron and its connections to algebraic equations and group theory. They discovered that certain transformations of the icosahedron corresponded to solutions of algebraic equations of the 5th degree, known as quintic equations.

More specifically, the symmetries and transformations of the icosahedron can be described using a mathematical framework known as group theory. The group of symmetries of the icosahedron, denoted IℎIh, is isomorphic to the symmetric group S5S5, which is the group of permutations of 5 elements. This connection between the symmetries of the icosahedron and permutations of 5 elements is related to the fact that the solutions of a general quintic equation can be expressed in terms of permutations of its coefficients.

Furthermore, the study of the symmetries of the icosahedron and their algebraic representations led to insights into the structure of quintic equations and their solutions. For example, the study of Galois groups, which describe the symmetries of algebraic equations, is closely related to the symmetries of geometric objects such as the icosahedron.

Overall, the relation between the icosahedron and a 5th degree equation highlights the deep connections between geometry, algebra, and group theory, and it has important implications for understanding the structure and properties of mathematical objects and equations.

What is a platonic solid?

A Platonic solid, also known as a regular polyhedron, is a convex polyhedron whose faces are congruent regular polygons (i.e., polygons with equal side lengths and equal interior angles) and whose vertices are congruent regular polygons in the same arrangement.

There are five Platonic solids:

Tetrahedron: The tetrahedron has four faces, each of which is an equilateral triangle. It has four vertices and six edges.
Cube (or hexahedron): The cube has six square faces, four vertices, and twelve edges.
Octahedron: The octahedron has eight equilateral triangle faces, six vertices, and twelve edges.
Dodecahedron: The dodecahedron has twelve pentagonal faces, twenty vertices, and thirty edges.
Icosahedron: The icosahedron has twenty equilateral triangle faces, twelve vertices, and thirty edges.

Platonic solids have several remarkable properties, including:

Symmetry: Each face, vertex, and edge is symmetrically arranged around the solid.
Regularity: All faces and vertices are congruent to each other.
Euler’s Formula: For any Platonic solid, the number of faces (F), vertices (V), and edges (E) satisfies the formula V−E+F=2.

Platonic solids have been studied since antiquity and hold significance in mathematics, geometry, and philosophy due to their aesthetic beauty, symmetry, and mathematical properties. They also appear in various contexts in nature, art, and architecture.

Why they are called platonic?

Platonic solids are named after the ancient Greek philosopher Plato, who discussed them in his philosophical dialogue “Timaeus.” In this dialogue, Plato associated each of the five Platonic solids with one of the classical elements: fire, earth, air, water, and a fifth element called “aether” or “quintessence.”

Plato’s discussion of the Platonic solids was part of his broader exploration of geometry, mathematics, and metaphysics. He used the regular polyhedra as symbolic representations of fundamental elements and principles in his cosmology and philosophy. While Plato did not discover the Platonic solids himself, he played a significant role in popularizing and discussing them in philosophical and intellectual circles.

The term “Platonic solids” was later coined by the mathematician Euclid in his work “Elements,” where he described the properties of these regular polyhedra. The association with Plato’s philosophical ideas and discussions led to the adoption of the name “Platonic solids” to refer to these geometric objects.

The relation between platonic solids and Plato’s philosophy

The relationship between Platonic solids and Plato’s philosophy lies in Plato’s philosophical dialogue “Timaeus,” where he discusses these geometric shapes as symbolic representations of fundamental elements and principles in his cosmology and metaphysics.

In “Timaeus,” Plato presents a creation myth in which the universe is formed by the Demiurge, a divine craftsman. Plato associates each of the five Platonic solids with one of the classical elements—earth, water, air, fire, and a fifth element called “aether” or “quintessence.” According to Plato’s cosmology:

Tetrahedron (Fire): The tetrahedron, composed of four equilateral triangles, represents the element of fire. It is associated with the sharpness and intensity of fire.
Cube (Earth): The cube, composed of six square faces, represents the element of earth. It symbolizes stability, solidity, and materiality.
Octahedron (Air): The octahedron, composed of eight equilateral triangles, represents the element of air. It is associated with movement, breath, and the intangible aspects of existence.
Icosahedron (Water): The icosahedron, composed of twenty equilateral triangles, represents the element of water. It symbolizes fluidity, change, and the flowing nature of water.
Dodecahedron (Aether or Quintessence): The dodecahedron, composed of twelve pentagonal faces, represents the element of aether or quintessence. It symbolizes the celestial realm, the cosmos, and the divine order.

Plato used these geometric shapes as symbolic representations to convey his philosophical ideas about the nature of reality, the elements, and the structure of the universe. While the association between Platonic solids and Plato’s philosophy is primarily symbolic, it reflects Plato’s interest in geometry, mathematics, and metaphysics, and it has had a profound influence on subsequent philosophical and intellectual thought.

The word invariant didn’t exist before

The spread of the term “invariant” to many fields beyond mathematics and physics can be attributed to its fundamental conceptual importance and utility in various domains. While I’m not aware of a specific study focused solely on why the term spread to other fields, we can infer several reasons for its widespread adoption:

Conceptual Clarity: The concept of invariance provides a clear and precise way to describe properties or quantities that remain unchanged under specific transformations or conditions. This clarity makes it useful for communicating ideas across different disciplines.
Cross-Disciplinary Applicability: Invariance is a fundamental concept that applies not only to mathematics and physics but also to other scientific fields, engineering, computer science, and even areas like economics, linguistics, and social sciences. Many phenomena exhibit invariant properties, and the concept allows researchers to identify, analyze, and understand these properties across diverse contexts.
Interdisciplinary Research: As interdisciplinary research becomes more common, concepts and terminology from one field often spread to others. Researchers working at the intersection of multiple disciplines may find the concept of invariance useful for bridging different theoretical frameworks and methodologies.
Technological Advancements: Advances in technology, particularly in areas like data analysis, signal processing, and artificial intelligence, have led to increased interest in concepts related to invariance. For example, machine learning algorithms often rely on invariant features for tasks like pattern recognition and object detection.
Educational Influence: The concept of invariance is often introduced early in the education of scientists, mathematicians, and engineers. As students progress through their studies and enter various professions, they carry this conceptual framework with them, contributing to its widespread use and understanding.

While there may not be a single study specifically addressing why the term “invariant” spread to many fields, its adoption can be seen as a natural consequence of its conceptual importance, practical utility, and interdisciplinary relevance across diverse areas of research and practice.

Why I think its use is a misconception

While the term “invariant” is often used in the context of properties or quantities that remain unchanged under specific transformations or conditions, it’s important to note that not all properties or qualities can be considered invariant. In fact, many properties of objects or systems are inherently variable or contingent upon various factors.

Intrinsic properties, in particular, are characteristics that are essential or inherent to an object or system and are not dependent on external factors. However, even intrinsic properties can vary under certain conditions or when viewed from different perspectives.

For example, the mass of an object is often considered an intrinsic property, but it can vary depending on the object’s velocity relative to an observer (as described by special relativity) or in the presence of gravitational fields (as described by general relativity). Similarly, the color of an object may appear different under different lighting conditions or when viewed by individuals with different color perceptions.

Therefore, while the concept of invariance is useful for describing certain properties or quantities that remain constant under specific circumstances, it’s important to recognize that many properties are variable and contingent upon various factors. Intrinsic properties may not always be invariant, and the context in which a property is considered must be carefully considered when applying the concept of invariance.

Two examples to demonstrate the point

1-Is it correct to use the term invariant to the situation about a tree falling in Mars without any human hearing would not produce sound, which then would make the sound an invariant ?

In the context described, the term “invariant” may not be the most appropriate or accurate term to use. In physics and philosophy, an invariant typically refers to a property or quantity that remains unchanged under specific transformations or conditions. For example, invariance may refer to properties such as mass, energy, momentum, or certain mathematical relationships that hold true regardless of the observer’s frame of reference or the specific circumstances of a physical system.

The situation described about a tree falling on Mars without any human hearing it is more commonly discussed in the philosophical thought experiment known as “If a tree falls in a forest and no one is around to hear it, does it make a sound?” This thought experiment raises questions about perception, observation, and the nature of reality.

In this scenario, the term “sound” is not an invariant in the sense of physics or mathematics, because sound is a perceptual experience that typically requires an observer to perceive it. In other words, sound is a phenomenon that arises from the interaction between a vibrating object and a medium (such as air) that can transmit sound waves. Without an observer to perceive these sound waves, the experience of “hearing” does not occur.

Therefore, rather than describing sound as an invariant, it may be more accurate to say that sound is a phenomenon that depends on the presence of an observer capable of perceiving it. The situation raises philosophical questions about the nature of perception, reality, and the relationship between the observer and the observed.

2-In psychology the use of invariant to describe some pshycological traits is wrong?

In psychology, the term “invariant” is sometimes used to describe psychological traits or processes that remain consistent across different individuals, contexts, or time periods. However, it’s important to recognize that psychological traits and processes are often complex and multifaceted, and they can vary considerably among individuals and in different situations.

While some psychological traits may exhibit a degree of stability or consistency over time and across contexts, it’s rare for any trait to be completely invariant. Factors such as genetic predispositions, environmental influences, life experiences, and developmental processes can all contribute to variability in psychological traits and behaviors.

Additionally, the concept of invariance may not fully capture the dynamic and interactive nature of psychological processes. Psychological traits and behaviors can be influenced by numerous factors, and they may change over time in response to internal and external influences.

Therefore, while psychologists may use the term “invariant” to describe certain aspects of psychological functioning, it’s important to recognize that psychological traits and processes are often characterized by variability and change. Researchers in psychology often emphasize the importance of understanding the complexity and diversity of human behavior, rather than seeking to identify invariant traits or processes.

Conclusion: By extension isn’t it also wrong to associate the word invariant to intrinsic properties of things?

The conclusion is from Chat GPT, although it is the same I have.

Yes, you’re correct. While the term “invariant” is often used in the context of properties or quantities that remain unchanged under specific transformations or conditions, it’s important to note that not all properties or qualities can be considered invariant. In fact, many properties of objects or systems are inherently variable or contingent upon various factors.

Specific misuse of invariants

The specific misuse of the term “invariant” outside of mathematical contexts may not be as commonly discussed as broader issues of language use and misuse. However, there may still be instances where the term is misapplied or misunderstood in other domains, such as in scientific, technical, or philosophical discussions.

One potential area where the misuse of “invariant” could occur is in the interpretation of research findings in fields such as psychology, sociology, or biology, where concepts of stability or consistency are often discussed. For example, researchers may mistakenly use the term “invariant” to describe psychological traits or social phenomena that actually exhibit variability or change over time.

Additionally, in fields like engineering, computer science, or data analysis, where concepts of invariance play a crucial role in certain algorithms or models, there may be instances of misapplication or oversimplification of the concept.

While specific instances of misuse of “invariant” may not be extensively documented or studied, it’s important for researchers and practitioners in various fields to use terminology accurately and precisely to avoid misunderstandings and misinterpretations. Clear communication and conceptual clarity are essential for advancing knowledge and understanding in any domain.

The modern view of nature’s building blocks

Enormous progress has been made during the past generation in identifying increasingly detailed constituents of the fabric and behaviour of matter. In this article, a West African physicist explains our present understanding of the make-up of matter at the microscopic and even more infinitesimal levels. He accentuates the role of accelerators in the process and wonders how many more fundamental particles might exist.

As it was published by the Digital Library of UNESCO

D. A. Akyeampong has an interesting account on our present understanding of the make-up of matter at the microscopic and even more infinitesimal levels. He accentuates the role of accelerators in the process and wonders how many more fundamental particles might exist.

Daniel Afedzi Akyeampong obtained his Ph.D. in mathematical physics from the Imperial College of Science and Technology, London, in 1966. He is professor of mathematics at the University of Ghana, Legon, and was a visiting professor of mathematics at the Rivers State University of Science and Technology, Private Mail Bag 5080, Port Harcourt, Nigeria. The author was also Fellow of the Ghana Academy of Arts and Sciences, as well as senior associate at the International Centre for Theoretical Physics, Trieste (Italy). He has written numerous articles on the theory of elementary particles.

Introduction

The urge to be inquisitive is an ingrained human habit, and it is this insatiable desire that has led man for centuries to understand the world around and to think about the composition of matter. The pursuit of knowledge of the physical world on the smallest scales has a long history. In the fifth century B.C., Democritus and Leucippus suggested atomism, the word catom having been used less precisely than it is today. But because Aristotle favoured the four-elements theory of air, earth, water and fire, he used his enormous influence to discourage further study of atomism. It was only at the time of Galileo that the authority of science became sufficiently strong to challenge and defeat the Aristotelian conception of the universe.

The Democritean theory was revived in the eighteenth century, with Lavoisier‘s observation that all substances are composed of chemical elements. Dalton, Gay-Lussac, Avogadro and others followed in the nineteenth century with discoveries that these chemical elements are themselves composed of atoms and that each element has its own unique type of atom that can combine with other atoms to produce the wide variety of substances found in the world around us.

More progress in knowing the small-scale physical world has been made during this century than in any other. In 1911 Rutherford discovered that the atom of Dalton et al is not indivisible, but that it consists of a negatively charged electron orbiting about a relatively massive, positively charged nucleus.

But Rutherford’s model of the atom was not without problems for, according to classical physics, the atom should trace an elliptic path and radiate energy over a continuous range of frequencies. And yet, the hydrogen atom (for instance) does not lose energy and its electron does not fall into its nucleus. This is one of the crises referred to by Robert Oppenheimer in The Flying Trapeze: Three Crises for Physicists. (You can read it online) Niels Bohr—as we have already seen—was the first to provide an explanation of the atom’s stability; this contributed enormously towards the acceptance of quantum mechanics as the theoretical framework on which our understanding of microscopic physics today rests.

Were the electron and nucleus the ‘atoms’ of Democritus, or were they composite? Indications then and now are that the electron has no internal structure. But the nucleus is complex and breaks down into protons and neutrons having a measurable size of about 10 elevated to -13 cm. At least this was the simple picture of matter in the 1930s, but since then hundreds of related subatomic particles have been identified. The search for finer and finer matter continues, and our purpose here is to show how far physicists have got in finding the ultimate constituents of matter since Niels Bohr blazed the trail some sixty years ago.

Nature’s fundamental forces

Four basic forces in nature are believed to account for the observed actions of matter. These are usually called the strong nuclear, the electromagnetic, the weak nuclear and the gravitational forces.

The strong force is, as the name implies, the most powerful of these fundamental forces. Of extremely short range, its effects are felt over distances of only about 10-13 cm, roughly the diameter of a subatomic particle.

The next force, in order of strength, is the electromagnetic force, which is about one-hundredth (10-2) of the strong force. Its strength diminishes according to the well-known inverse square law, and its range is (in principle) unlimited. The electromagnetic force acts on all particles having an electric charge and involves the (uncharged) photon, the carrier of the electromagnetic force-field. This is the force binding electrons to the positively charged nucleus to form atoms and, further, binding atoms together to form molecules—and ‘thus in its manifold workings is responsible for all chemistry and biology’.

The next force downward is the weak nuclear force, having only about 10-13 of the strong force’s strength. Its real range is shorter than that of the electromagnetic force: two particles must approach to within 10-16 cm in order to feel this force. As far as we know, it cannot bind anything, but it is responsible for the decay of many subatomic particles, in particular for the decay of certain radioactive nuclei. And in contrast to the strong and electromagnetic forces, the weak nuclear force can distinguish between particles of left and right helicity. (Helicity is a basic variable used in quantum mechanics to describe the relative orientations of spin and linear momentum possessed by massless particles.)

Gravitational force is the fourth and weakest, and yet the most obvious, of the four forces. It influences all matter since it is always attractive and (like the electromagnetic force) its range extends to infinity. But on the atomic and nuclear scales, this force is very weak—about 10-39 times that of the strong force’s strength. Its effects on subatomic particles being extremely small, it was until recently ignored in theoretical investigations. The carriers of these fundamental forces are known collectively as gauge particles. We have already stated that the photon is one of these. The rest will be introduced below.

Classification of subatomic particles

All particles except those that are the transmitters of the fundamental forces are classified according to their response to the two nuclear forces. Those feeling the strong force are called hadrons (from the Greek hadros, stout or strong); those that do not feel the strong force but respond to the weak force are known as leptons (the Greek leptos means small or fine). Until recently, all the known leptons were particles of zero or very small mass. Particles belonging to these two families have properties that are quite different.

The hadrons are subdivided into two classes. Those with half odd-integer spin are called baryons because they are supposed to be relatively heavy (the proton and the neutron are the commonest); those with ‘integer spin’ are termed mesons. The masses of the mesons known some twenty years ago were between those of the leptons and baryons. The recent discovery of several mesons more massive than baryons indicates the inappropriateness of these terms, but they have come to stay. An example of a meson is Hideki Yukawa‘s pion.

Every subatomic particle, lepton or hadron, has a list of numbers identifying it uniquely and defining its behaviour. These are called the particle’s quantum numbers. All baryons, for instance, have a non-zero baryon quantum number and all mesons have a zero baryon quantum number. To every particle there is an antiparticle, and the quantum numbers of the latter are simply the additive inverses of those of the former. The electron’s antiparticle is called, for historical reasons, the positron. Generally, however, the antiparticles are identified by the prefix anti-, so that that of the proton is called the antiproton. The photon, like the pion, is its own antiparticle.

Well over two hundred hadrons have been discovered during the last few decades; it seems that many more exist, and these should be observed once larger accelerators become available. Such a plethora of ‘fundamental’ objects is unsatisfying, and serious doubts have been expressed as to whether they are truly elementary—that is, whether they are structureless ‘point particles‘. The apparent chaos existing in the subnuclear world became a matter of concern, so a search for a principle that would help bring order and beauty from this chaos led in the early 1960s to the ‘eightfold way‘.

Ordering the subnuclear world

Before the introduction of the eightfold way to particle physics, the hadrons were already organized into small families of particles called isotopic-spin (or I-spin) multiplets. The concept of I-spin, introduced by Werner Heisenberg, is analogous to that of ordinary-spin angular momentum—where, under an externally applied magnetic field, the electron (for example) can exist in two possible energy states that become indistinguishable in the absence of this field. We deduce from this that in the presence of a magnetic field the electron is a doublet.

The proton and neutron have the same spin, and nearly the same mass, but they have different charges. They interact strongly with about the same strength, however, suggesting that nuclear forces are independent of charge. By analogy with the previous example, if we could ‘turn off’ electromagnetism, then the proton and neutron would also degenerate into indistinguishability. Thus we can say that the two particles are the manifestations of a single state of matter, the nucleón. To distinguish between the two states of the nucleón, we introduce—in analogy to ordinary spin—the device of I-spin; this is conserved by strong interactions, but broken by electromagnetic forces when nucléons interact. We assign to the nucleón an I-spin of 1/2, so that its components (Iz) are given by ± 1/2. The proton and neutron are then distinguished from one another by assigning an Iz of + 1/2 to the former and —• 1/2 to the latter.

It then becomes a straightforward matter to extend this idea to all hadrons, leading to the observation that these objects occur as small families called I-spin multiplets, the particles in each multiplet having the same spin angular momentum and I-spin (but different Iz) and approximately the same mass (but different electric charges). The multiplets have one, two, three or four members, as, for example:

r¡’ = {r¡’}, N={p,n}; TC = {TT+, TI», TZ~}, N* = {N*++, N*+, N*°, N*~},

the superscripts denoting the electric charges carried by members of the family. The first has I-spin of o and is referred to as an I-spin singlet; the second with I-spin of 1/2 is a doublet; the third with /= 1 is a triplet; and so on. In strong interactions the members of each multiplet are all equivalent because electric charges does not play a role.

The eightfold way

In 1961, Murray Gell-Mann and Yuval Ne’eman independently proposed an extension of the idea that hadrons fall into I-spin multiplets by grouping them into larger multiplets involving eight quantum members. Gell-Mann called this the eightfold way, recalling an aphorism attributed to Buddha: ‘Now this, O monks! is noble truth that leads to the cessation of pain; this is the noble Eightfold Way, namely, right views, right intention, right speech, right action, right living, right effort, right mindfulness, right concentration.‘

Both I-spin and the eightfold way are based on a branch of mathematics called group theory, invented in the late nineteenth century by Sophus Lie, a Norwegian mathematician. The Lie ‘transformation’ generating I-spin is called SU(2) and the one generating the eightfold way SU(3), the terms standing for special unitary groups of 2 x 2 and 3×3 matrices, respectively. The groups are ‘special’ in the sense that a condition is imposed on the matrix elements, thereby reducing the number of independent elements in the two matrices from four to three in the case of SU(2) and from nine to eight in the case of SU(3).

The theory of the eightfold way requires that all hadrons be members of families (multiplets) corresponding to representations of the SU(3) group. Mathematically, the multiplets of SU(3) can thus have one, three, six, eight, ten or more members—with each multiplet sharing a common spin angular momentum. The multiplet with only one member is called a singlet, the three-member multiplet is a triplet, the eight-member one is an octet; the ten-member multiplet is known as a decuplet or decimet.

Physically, however, only those multiplets with one, eight or ten members are favoured. Specifically, the spin-o mesons compose a singlet and an octet; the spin-i mesons form an identical representation and so do the spin-1/2 baryons, while the spin-3/2 baryons form a decuplet. If the theory were exact, then all members of a given multiplet should have the same mass. This is not the case and, within a multiplet, there are significant differences in mass.

Within each multiplet, the members are distinguished from one another by two quantum members: Yz and hypercharge Y. Let us plot, for each multiplet, the particles Iz against their Y. The interesting result is that the hadrons form orderly arrays, as in Figures 1 and 2. Each octet forms a regular hexagon, with a particle at each vertex and two particles at the centre; the decuplet forms a triangle with a particle at each vertex, two particles equally spaced along the lines joining the vertices, and one particle at the interior point.

**Bottom:(c) Spin-0 octet (d) Spin-1 octe**t

FIG. I. Schematic diagrams of SU(3) multiplets of some mesons, showing their quark contents.

This led to the prediction of a new particle, the Ω -, the isospin singlet in the decuplet whose physical properties can be read directly from the diagram. This is a particle of electric charge —i, hypercharge —2 and mass of about 1,670 MeV. The discovery in 1964 of a particle having precisely these quantum numbers convinced physicists of the correctness of the theory: the known hadrons fit beautifully into the SU(3) representation without exception, mesons occurring only in multiplets of 1 and 8 and baryons in multiplets of 1,8 and 10. We have here an example of Eugene Wigner‘s dictum about the unreasonable effectiveness of mathematics in the description of the physical world.

Are hadrons fundamental?

The orderly arrays of the hadrons may be aesthetically satisfying, but it is at the same time puzzling that nature should appear to be favouring only three of the several possible representations of SU(3)\, Regularities of this sort cannot arise by accident, and it is clear that nature is trying to reveal to us some of its secrets. Gell-Mann and Zweig were the first to provide an explanation of this puzzle. They suggested that nature’s choice of the singlet, octet and decuplet representations could be understood by assuming that hadrons are not at all fundamental, but that they are constructed of more fundamental units of matter. These were called ‘quarks’ by Gell-Mann and ‘aces’ by Zweig, but only the first term gained acceptance in the physics community.

According to this suggestion, quarks are members of the simplets ‘non-trivial’ representation of the SU(3) group—a multiplet of three members. Quarks have spin angular momentum of 1/2 but, unlike the hadrons, they carry fractional charges. The simplest, non-trivial representation of SU(3) was chosen because all the hadrons then known could be constructed from only three quarks. We shall describe this model in some detail, since its generalization to cover other hadrons discovered later follows in a straightforward manner.

Following Gell-Mann, let us designate the three quarks as u, d and s for ‘cup’, ‘down’ and ‘strange’. The corresponding antiquarks will be designated as a, d and s. The quantum numbers of the u, d and Í quarks are summarized in Table 1. The corresponding antiquarks will have quantum numbers opposite to the ones listed. Note that these numbers are not independent; ‘for instance, Q = IZ + Y/2 and Y = B + S.

Baryons consist of three quarks bound together, and mesons of a quark and an antlquark. No other combination can exist as a hadron. According to the theory of angular momentum, therefore, baryons must have a half-odd integer spin and mesons an integer spin. Figures 1 and 2 show the subnuclear particles known in the 1960s, their quark composition being shown in parentheses. We notice in Figures 1(c) and 2(a) that the u and d quarks suffice to explain the structure of all the hadrons encountered in ordinary matter.

For example, the proton and neutron are made of the u and d quarks, the former being composed of two u quarks and a d quark (written uud) and the latter of one u quark and two d quarks {udd)—while the positive pion is composed of a M quark and a d anti-quark (ud).

Their quantum numbers are shown, by a simple calculation, to be in agreement with the known values. Thus, using Table 1, the proton’s charge is obtained as Q = 2/3 + 2/3 —1/3 = I, its baryon number B = 1/3 + 1/3 + 1/3—I, and the third component of its I-spin as ^ = 1/2 + 1/2—1/2 = 1/2. Other quantum numbers are similarly obtained.

A particle containing at least one s quark or s antiquark—such that its net strangeness quantum number S is non-zero—is called a strange particle. Examples of strange particles are A(uds), K°(ds) and E(dss). Another elementary calculation shows that the strangeness or S of A is —1, that of K” is I, while that of S is — 2.

The neutral baryons A+ and E° have the same quark composition, uds, but the structure of the neutral meson π° differs from its partner, n. For while the π5 is composed equally of uu and dd, the n includes a fraction of si in addition to the above. Thus the baryon octet scheme differs from that of the meson octet. The singlet meson n’ (or Xo) also contains equal contributions of uü, dd and ss. As can be seen from the figures, the spin I meson scheme is similar to that of spin o, except for the quark contents of the two I=0 members, φ(ss) and ω(uu + dd). The structure and properties of the other particles can be explained similarly, with the help of Table 1 and Figures 1 and 2. Through this procedure, the quark model correctly yields all the quantum numbers of the known hadrons.

Quarks have colour, too

Since quarks are spin-1/2 particles, they should obey Pauli’s exclusion principle, according to which no two such particles can be in the same quantum state. Particles with integral spin (mesons and the photon) do not respect this principle; arbitrarily large numbers of them can be collected in the same state. Particles obeying the principle are called fermions, and those which do not are termed bosons. Violation of Pauli’s principle by fermions has never been seen. Today, our understanding of the atom’s structure and of the periodic table of the elements is based on this exclusion principle.

The quarks in a meson satisfy the exclusion principle, since a quark and its antiquark cannot have identical quantum numbers. For baryons, however, if we accept the model as described above, then the principle is violated because we can identify some baryons such as N*++(uuu), N*+(ddd) and Ω-(sss), in which all a three quarks can have an identical quantum number.

To ensure that the three quarks inside a baryon obey Pauli’s principle, it will be necessary therefore to assign to each quark a new quantum number with three possible values (so that no two quarks can exist in the same quantum state). This new quantum number is called colour, although it has nothing to do with chromatic perception. The suggestion is that each triplet of quarks can appear in any of three ‘colours’—red, green, blue. Antiquarks possess the anti-colours of anti-red, anti-green and anti-blue. Baryons are now made up of three quarks, all of which have different colours and, as a result, the particles in a multiplet are colourless.

Similarly, mesons consist of a quark of one colour and the antiquark of the corresponding anti-colour, and the resulting particle is neutral with respect to the colour quantum-number. We believe that coloured particles (such as quarks) do not exist in a free state.

The introduction of colour increases the number of quarks known from three to nine: u(red), u(green), u(blue); d(red), d(green), d(blue); and s(red), s(green) and s(blue). But there is no corresponding increase in the number of hadrons

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Quarks and colour

The quark theory states that hadrons are not the ultimate building-blocks of matter, as originally believed; they are composites of more fundamental particles called quarks. Each quark exists in three states, distinguished by a property called colour, and all hadrons are colourless.

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Since each quark exists in three colour states, we can postulate the existence of another SU(3) symmetry group in hadrons. This is known as colour SU(3) or SUc(3); within this group, a blue quark, for instance, is transformed into a green one, or a red quark into blue. Compare this with the original SU(3) group of Gell-Mann and Ne’eman (involving I-spin and hypercharge), within which a u quark may be transformed into a d quark, or a d into an i. Because the two symmetry groups are not identical, we distinguish them by representing the u,d and s labels as the quark’s flavours—each quark flavour existing in three varieties identical in all their properties except that of colour. (As with colour, this ‘flavour’ has nothing to do with our gustatory taste.) The original SU(3) symmetry group is now referred to as SU(3) flavour or SUg(3).

High-energy inelastic electron-proton scattering experiments conducted at the Stanford Linear Accelerator Center (SLAC) in the late 1960s provided additional persuasive evidence of the spin half nature of the proton’s constituents.

The gluons

The evidence is persuasive that the force binding together the coloured quarks inside a hadron is the true, strong nuclear force (the one observed between hadrons being a vestige of the same fundamental force). Just as the photon is the carrier of the electromagnetic force, the strong nuclear force is transmitted by eight massless spin-I particles having zero charge: gluons, because they are supposed to ‘glue’ together the quarks. The gluon is a gauge particle, being neither a hadron nor a lepton. A quark emitting or absorbing a gluon has its colour changed, but its flavour remains unchanged. Thus, like the quarks, gluons carry the colour quantum-number and (therefore) should not exist in a free state. The distribution of hadrons observed at the PETRA electron-positron collider (Federal Republic of Germany) strongly suggests the existence of gluons.

The effect of the strong force on hadrons separated by subnuclear distance is important to note at this point. At short distances, hadrons appear to consist of non-interacting quarks, while at long distances (about 10-13 cm) they interact strongly. Isolated quarks, furthermore, have not been observed.

We conclude that the force between quarks is negligibly small when the particles are close together but becomes larger when they are farther apart. The force becomes so strong at large distances, in fact, that no external force (however a great) can isolate quarks from each other. Quarks as well as gluons are therefore believed to be permanently confined to the interiors of the particles they form.

Particles possessing charm

Until 1974 the properties of all the known hadrons could be explained in terms of the three quarks u, d, s and their antiquarks. The discovery later that year of the hadron F/Ω, a spin-I neutral particle whose structure could not be made out of the existing quark flavours, led to the belief that F/Ω is composed of a new quark flavour. For (or so went the reasoning) if quarks are the ultimate constituents of hadrons, then the picture of hadrons can only be complicated by the discovery of new flavours of quarks.

To explain the composition of F/Ω, therefore, a fourth coloured quark called the ‘charmed’ or c-quark with electric charge of 2/3 and carrying one unit of a new quantum number—c—was proposed. It now became easy to show that jf F/Ω is composed of a c-quark and a c antiquark (or cc), and so has hidden charm just as the φ meson has hidden strangeness.

Since then, several particles with a non-zero charm quantum number have been detected.

W and Z particles; top and bottom quarks

Remarkable progress has been made towards our understanding of the weak nuclear force. At present, we know of only six particles which feel the weak force as they approach each other. Known collectively as the leptons, these particles are the electron (e), the muon (μ), the tau (τ) and the neutrinos associated with each (symbolized by the Greek ν): νe, νμ, vτ.

While the first three are massive and carry —I unit of electric charge, their neutrinos are massless and electrically neutral. All the indications are that leptons have no internal structure and so are truly elementary. Unlike quarks, however, leptons are not subject to the strong nuclear force—although the charged ones interact electromagnetically.

By placing a left-handed electron and its associated neutrino in an SU(2) doublet and a right-handed electron in an SU(2) singlet, Abdus Salam and Steven Weinberg applied the mathematical concept of gauge invariance and a mechanism known technically as ‘spontaneous symmetry breaking’ to show that the electromagnetic and weak nuclear forces are different facets of a more basic short-range force now known as the electroweak force, whose effects can be felt over distances of less than 10-15 cm.

The minimal theory can easily be generalized to involve the observed leptons and quark flavours; it describes accurately the observed properties of the weak and electromagnetic interactions and (as with all good theories) makes several predictions. Perhaps the most important of these is that the carriers of the weak a force are the spin-I particles, W± and Z°. These three particles are, unlike the photon and gluons, massive, and are sometimes called the intermediate vector “*; bosons. They provide a link between quarks and leptons, changing the quarks flavour but not their colour during a scattering process, and decaying into leptons.

Discovery of the W particles in December 1982 and of the Z in May 1983 showed that theory and experiment are in perfect accord.

Theory also leads to the inference that quarks come in pairs, one with an electric charge of 2/3 units and the other of—1/3. To each quark pair is associated one lepton and its corresponding neutrino, forming a family (or generation) whose total electric charge is o. (Recall that each quark has three colours.) The members of the first family are u, d, e- and ve; the second family consists of c, s, u. and vμ. The tau and its neutrino must therefore be part of a third family of quarks and leptons. It was to complete this family that the top or t~ (charge 2/3) and bottom or b~ (charge —1/3) quarks were proposed.

A heavy meson (Y) discovered in 1977 was found to have the quark compo-sition bb. Evidence for the existence of t-flavoured hadrons has also emerged recently from experiments done at the European Laboratory for Particle Physics (CERN), but this remains to be confirmed. The masses of the quark-lepton families rise as the family increases—the lightest of the three being the first family (K, d, e, v„) (see Table 2).

A few conclusions

The look of the subatomic world several decades ago—in which all particles were elementary, but some were more elementary than others—has given way to a picture wherein the basic building-blocks of matter, on which nature’s four fundamental forces act, may be the three quark-lepton families:

with each of the quarks existing in three colours. The total electric charge in each family is o. And, unlike the leptons, which can exist in a free state, the quarks are permanently confined within the hadrons they form.

Then there are the carriers of the fundamental forces: The photon transmits the electromagnetic force. The W± and Z° particles transmit the weak nuclear force. The eight gluons transmit the strong nuclear force. The graviton, still a theoretical particle, carries the gravitational force.

Are these the ultimate, indivisible constituents of matter, the atoms of Democritus? That eighteen quarks and six leptons are the fundamental particles of nature may appeal to some physicists, one understands. But despite some attractive features, the theory leading to this structure of matter is considered too arbitrary by others. What, these ask, is the explanation for the repetition of families, and why is there no a priori reason for the quark and lepton charges to be related by the simple factor of 3? And then, inevitably, are quarks composed of still more fundamental particles? Theories have been proposed which attempt to answer some of these questions. None of these has, so far, experimental support. We may be at the beginning of the end of the search for the Democritean atom—if, indeed, the basic particles take this form of fermion families. It is also possible that we are now merely on another rung of the ladder. With ever more powerful accelerators currently in the design stage, we may not have to wait long for our answers.

A note about neutrinos

Thanks to the careful revision of Dr. Gary Stillwell, who has observed that along this explanation it was mentioned that neutrinos are massless, which is not true according to more recent findings. The question is the following:

According to the Standard Model of particle physics, neutrinos were originally considered to be massless particles. However, experiments conducted over the years have provided strong evidence that neutrinos do have mass, albeit very small.

The discovery of neutrino oscillation, which is the phenomenon where neutrinos change flavor (i.e., electron neutrinos, muon neutrinos, and tau neutrinos) as they travel through space, provided significant evidence for neutrino mass. Neutrino oscillation implies that neutrinos must have different mass eigenstates, and for this to occur, at least one of the neutrino flavors must have a non-zero mass.

The observation of neutrino oscillation has been confirmed by several experiments, including those conducted at the Super-Kamiokande detector in Japan, the Sudbury Neutrino Observatory in Canada, and the Daya Bay Reactor Neutrino Experiment in China.

While the precise masses of neutrinos are still not precisely known, experimental data indicate that they are much lighter than other known elementary particles, such as electrons or quarks. Neutrino masses are so tiny that they are difficult to measure directly, and current experiments are aimed at refining our understanding of their properties.

In summary, according to the most recent experimental evidence, neutrinos are not massless particles, as previously thought in the Standard Model, but they do have mass, although it is extremely small. This discovery has important implications for our understanding of particle physics and the fundamental nature of matter.

The Root of All Evil

Complementarity in Quantum Physics

Complementarity in quantum physics refers to a fundamental principle that describes the dual nature of certain physical properties, such as wave-particle duality, and the limitations of classical concepts in explaining quantum phenomena. This principle was first introduced by Danish physicist Niels Bohr as part of his interpretation of quantum mechanics.

At the heart of complementarity is the idea that certain pairs of physical properties, such as position and momentum, or energy and time, cannot be simultaneously precisely measured or known with arbitrary precision. This concept arises from the wave-particle duality inherent in quantum mechanics, which states that particles like electrons and photons exhibit both wave-like and particle-like behavior.

For example, in the famous double-slit experiment, where particles such as electrons or photons are sent through two narrow slits and observed on a screen behind them, the particles exhibit interference patterns characteristic of waves when not observed, but behave as individual particles when observed. This illustrates the complementary nature of wave and particle behavior.

In a broader sense, complementarity in quantum physics suggests that different experimental setups or measurements may reveal different aspects of a quantum system, and no single measurement or observation can fully capture all aspects simultaneously. This challenges the classical intuition that physical properties have well-defined values independent of observation and underscores the inherently probabilistic nature of quantum mechanics.

Overall, complementarity highlights the need for a more nuanced understanding of physical reality beyond classical concepts, and it remains a central concept in the interpretation of quantum mechanics.

Max Born

Max Born was born in Breslau, Germany (now Wroclaw, Poland), where his father was a professor of anatomy. Born studied at universities in Breslau, Heidelberg, Zurich and Göttingen, where he received his doctorate in 1906. After serving in the army during the First World War, he became a professor at the University of Frankfurt-on-Main in 1919 and at the University of Göttingen in 1921. After the Nazis seized power in 1933, he moved to Cambridge in United Kingdom. Beginning in 1936, he served as a professor at the University of Edinburgh. Max Born was married and had three children.

In Niels Bohr’s theory of the atom, electrons absorb and emit radiation of fixed wavelengths when jumping between orbits around a nucleus. The theory provided a good description of the spectrum created by the hydrogen atom, but needed to be developed to suit more complicated atoms and molecules. Following Werner Heisenberg’s initial work around 1925, Max Born contributed to the further development of quantum mechanics. He also proved that Schrödinger’s wave equation could be interpreted as giving statistical (rather than exact) predictions of variables.

Einstein had an issue with statistical definition which I summarize at the introduction of God does not play dice with the Universe.

I repeat here what I already said there, because I will elaborate here this perspective in more detail:

In his Nobel lecture he reflected on the philosophical implications of his work, “The statistical interpretation of quantum mechanics:

born-lecture Download

Max Born was perhaps the phisycist which most expanded his concerns with methaphysics, under the following notions (and others):

Ontology: Ontology is the branch of metaphysics concerned with the study of being, existence, and reality. It explores questions such as: What exists? What is the nature of existence? What are the fundamental categories of being?
Cosmology: Cosmology deals with the study of the universe as a whole, including its origins, structure, and ultimate fate. It explores questions about the nature of space, time, causality, and the fundamental laws governing the universe.
Epistemology: Epistemology is the branch of philosophy concerned with the nature, scope, and limits of knowledge. It explores questions such as: What is knowledge? How do we acquire knowledge? What are the criteria for determining truth and justification?
Philosophy of mind: The philosophy of mind explores questions about the nature of consciousness, mental phenomena, and the relationship between the mind and the body. It addresses issues such as the nature of perception, cognition, intentionality, and free will.
Metaphysics of religion: The metaphysics of religion examines questions about the nature of God, the existence of the soul, and the ultimate meaning and purpose of life. It explores metaphysical concepts related to religious beliefs and experiences.
Philosophy of science: The philosophy of science investigates the nature, methods, and assumptions of scientific inquiry. It explores questions about the nature of scientific theories, the relationship between theory and observation, and the status of scientific laws and explanations.
Philosophy of language: The philosophy of language explores questions about the nature of language, meaning, reference, and communication. It addresses issues such as the relationship between language and reality, the nature of linguistic representation, and the limits of language in expressing metaphysical concepts.

His ideas can be summarized in his famous statement:

“I believe that ideas such as absolute certitude, absolute exactness, final truth, etc. are figments of the imagination which should not be admissible in any field of science. On the other hand, any assertion of probability is either right or wrong from the standpoint of the theory on which it is based. This loosening of thinking (Lockerung des Denkens) seems to me to be the greatest blessing which modern science has given to us. For the belief in a single truth and in being the possessor thereof is the root cause of all evil in the world.”

He exchanged letters with Einstein telling him about his interpretation long before Einstein would have his famous dispute with the letter which I introduce the subject with the other side opposite to Born and those who had the same idea and that Einstein contradicted with the famous phrase, which I explore in detail in the other entry.

Determinism and Reality

Max Born in his Nobel Lecture raises a very interesting point about Determinism and Reality and I quote, becauxe it closes full circle with the introduction of this post which is Complementarity:

“The determinism of classical physics turns out to be an illusion, created by overrating mathematico-logical concepts. It is an idol, not an ideal in scientific research and cannot, therefore, be used as an objection to the essentially indeterministic statistical interpretation of quantum mechanics.

Much more difficult is the objection based on reality. The concept of a particle, e.g. a grain of sand, implicitly contains the idea that it is in a definite position and has definite motion. But according to quantum mechanics it is impossible to determine simultaneously with any desired accuracy both position and velocity (more precisely : momentum, i.e. mass times velocity) .

Thus two questions arise: what prevents us, in spite of the theoretical assertion, to measure both quantities to any desired degree of accuracy by refined experiments? Secondly, if it really transpires that this is not feasible, are we still justified in applying to the electron the concept of particle and therefore the ideas associated with it?

Referring to the first question, it is clear that if the theory is correct – and we have ample grounds for believing this – the obstacle to simultaneous measurement of position and motion (and of other such pairs of so-called conjugate quantities) must lie in the laws of quantum mechanics themselves. In fact, this is so. But it is not a simple matter to clarify the situation.

Niels Bohr himself has gone to great trouble and ingenuity to develop a theory of measurements to clear the matter up and to meet the most refined and ingenious attacks of Einstein, who repeatedly tried to think out methods of measurement by eans of which position and motion could be measured simultaneously and accurately.

The following emerges: to measure space coordinates and instants of time, rigid measuring rods and clocks are required. On the other hand, to measure momenta and energies, devices are necessary with movable parts to absorb the impact of the test object and to indicate the size of its momentum. Paying regard to the fact that quantum
mechanics is competent for dealing with the interaction of object and apparatus, it is seen that no arrangement is possible that will fulfil both requirements simultaneously. There exist, therefore, mutually exclusive though complementary experiments which only as a whole embrace everything which can be experienced with regard to an object.
This idea of complementarity is now regarded by most physicists as the key to the clear understanding of quantum processes.

Bohr has generalized the idea to quite different fields of knowledge, e.g. the connection between consciousness and the brain, to the problem of free will, and other basic problems of philosophy.

To come now to the last point: can we call something with which the concepts of position and motion cannot be associated in the usual way, a thing, or a particle? And if not, what is the reality which our theory has been invented to describe?

The answer to this is no longer physics, but philosophy, and to deal with it thoroughly would mean going far beyond the bounds of this lecture. I have given my views on it elsewhere. Here I will only say that I am emphatically in favour of the retention of the particle idea. Naturally, it is necessary to redefine what is meant. For this, well-developed concepts are available which appear in mathematics under the name of invariants in transformations. Every object that we perceive appears in innumerable aspects. The concept of the object is the invariant of all these aspects. From this point of view, the present universally used system of concepts in which particles and waves appear simultaneously, can be completely justified.

The latest research on nuclei and elementary particles has led us, however, to limits beyond which this system of concepts itself does not appear to suffice. The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road.”

Note on the concept of the object as the invariante of all its aspects

The concept of the object as invariant of all its aspects refers to the idea that, despite the many different ways in which we perceive and experience an object, there exists an underlying essence or identity that remains unchanged. In other words, while our perception of an object may vary depending on factors such as our perspective, sensory modalities, and contextual cues, the object itself maintains a consistent identity or “sameness” across these variations.

This concept is related to philosophical and psychological notions of object permanence and object constancy. Object permanence refers to the understanding that objects continue to exist even when they are not directly perceived, while object constancy refers to the ability to recognize and maintain a stable representation of an object despite changes in its appearance or context.

From a philosophical perspective, the concept of the object as invariant reflects the idea of a “thing-in-itself,” as posited by philosophers such as Immanuel Kant. According to this view, there is a reality or existence independent of our perceptions and experiences, and objects possess intrinsic properties that remain constant regardless of how they are perceived or interacted with.

In psychology, the concept of object constancy is often studied in the context of cognitive development and perceptual processes. For example, infants gradually develop the ability to recognize objects as stable and consistent entities, even when they are obscured from view or undergo transformations in appearance.

Overall, the concept of the object as invariant highlights the fundamental nature of objects as enduring and stable entities, despite the many ways in which they may be perceived or experienced by observers. It underscores the importance of recognizing the underlying unity and identity of objects, even amidst their diversity of appearances and manifestations.

Natural Complements

In this article, K. C. Cole (Karen Christine Cole), who was trained in the humanities, and is a writer associated with the monthly journal of science popularization, Discover, explores the concept which allowed Quantum Mechanics to come of age.

“Because one can describe a phenomenon in different terms, what makes sense in a given context fails to do so in another. Complementarity was badly needed sixty years ago in order to accommodate the seeming contradictions of quantum physics. The action of light waves could not be reconciled with the motion of electron-like particles, and it was Niels Bohr’s idea of complementarity that showed us that the other side of truth—in science—is not perforce heresy. “

There is an oft-repeated story among physicists about a conversation that took place many years ago between Nobel Prize winners Felix Bloch and Werner Heisenberg. The two famous physicists were walking along a beach while Bloch lectured to Heisenberg on the significance of a new theory on the mathematical structure of space. At length, Heisenberg responded: ‘Space is blue and birds fly in it!’

The story is popular because it illustrates what many physicists believe to be the most profound contribution of quantum theory. This contribution was not a discovery in the normal sense: not a particle, not a new kind of extraterrestrial object or event, not even a theory or an equation. It was, rather, a philosophical outlook that allowed scientists to make sense of the mass of paradoxes that seemed to be making modern physics all but impenetrable.

It was the notion of complementarity.

And if nothing else, the story of Heisenberg and Block captures the essence of complementarity: that one can talk about the same subject in two very different kinds of terms, and that what makes good sense in one context can make absolutely no sense in another.

Complementarity was a concept sorely needed to accommodate the contradictions introduced in the 1920s by the new ideas of quantum physics. Light waves were particle-like, and particles like electrons were known to behave like waves. You could pinpoint the position of a particle, but only at the expense of losing track of its motion; you could track its motion only by blurring its position. All the stable forms of matter in the universe took their shapes from indivisible bits of vibrating energy known as quanta—and yet if you tried to probe such a quantum to see how it was made, it would melt as surely as a snowflake in the palm of your hand.

It was the physicist Niels Bohr who came up with complementarity as a way of taming these inherent contradictions. He said that the reality of nature required complementary descriptions—more than one point of view. It didn’t matter that you could not measure both the motion and position of a particle at the same time; you cannot see both sides of a coin at the same time either.

Complementary descriptions are required for a full spectrum of understanding, just as a full array of colours is required to produce pure white. Complements are the yin and yang of science. Or, as the physicist Emilio Segré wrote, ‘It is one of the special beauties of science that points of view which seem diametrically opposed turn out later, in a broader perspective, to be both right.’

Complementarity is far more than just the physicists’ fancy version of ‘on one hand/on the other hand’. It not only says that two opposing views can be correct; it also says that two correct views can be mutually exclusive. Anyone can see that waves and particles, for example, are mutually exclusive concepts. A particle is like a bullet: a patently material, finite object that occupies a defined place in space and time. A wave is more like a motion: a continuous, abstract form. A wave has no more in common with a particle than the waves of the sea have with a school of fish swimming underneath. Yet experiments confirm that elementary particles have aspects of both—something that moved one physicist to remark that nature behaved according to quantum theory (like particles) on Mondays, Wednesdays and Fridays, and wave theory on Tuesdays, Thursdays and Saturdays. The trick to complementarity is knowing when which view is appropriate. Indeed, as physicist J. Robert Oppenheimer pointed out, ‘the more nearly appropriate the first way of thinking is to a situation, the more wholly inappropriate is the second’.

The statement that ‘space is blue’ is hardly an appropriate way of expressing a mathematical relationship, but then an equation would hardly be an adequate way of describing one’s sense of the sky during a stroll on the beach on a summer’s day. The more a particle acts like a particle, the less it behaves like a wave—just as the clearer the position of a particle becomes, the more fuzzy its motion becomes (and vice versa).

The term complementarity comes, of course, from colours. Blue and orange are complementary because they add up to white—the full spectrum. They are also mutually exclusive. Blue is a colour that contains no orange, just as orange contains no blue. If you subtract blue from white, the leftover light is orange.

A complement is a kind of shadow.

Night is both the shadow and the complement of day. In the most extreme cases, focusing sharply on one aspect of a situation can actually destroy the other. Bohr must have been a skier, for he compared this to trying to analyse in minute detail the motions that make up a Christiana, or parallel turn. As soon as you try, ‘it will evanesce and become an ordinary stem turn, just as the quantum state turns into classical motion when analysed by sharp observation’. A quantum state, like a ballerina’s arabesque or a bird’s song, only retains its character as long as it remains whole. This is not to say that you cannot break down these things into their individual notes and motions and molecules: only that watching an animal in the wild and dissecting it in a laboratory are complementary ways of exploring nature.

MIT professor of computer science Joseph Weizenbaum said much the same thing recently in speaking about, of all things, the dangers of over-reliance on computers. ‘Consider the utility of a microscope,’ he said. It magnifies to a very large degree, but essentially it also shuts out the rest of the world. Now there are times when you can’t see both: to see the detail, you have to sacrifice the view of the whole organism. But even then it wouldn’t make sense to say that what you’re seeing in any way resembles the essence of the organism itself.

Weizenbaum, who wrote Computer Power and Human Reason, is afraid that society’s love affair with computers is a symptom that the scientific mode of thinking is becoming ‘imperialistic’. Not that scientific thinking is bad—only that it is dangerous when it overwhelms all other approaches. If you wanted to understand the Great Depression of the 1930s and you only looked at Department of Labor statistics and you didn’t read novels by people like John Dos Passos because novels are not scientific, then that’s bad—because in a very deep way you can learn more by reading the novels.

Weizenbaum’s worry is hardly new. Nobel Prize winner Max Born carried on a long and well known correspondence with Albert Einstein over several of the perplexing implications of the new physics—specifically whether the notion of cause and effect could survive quantum theory, or whether, as Einstein refused to concede, it meant that ‘God plays dice with the universe’. Born concluded that the trouble lay in the inclination of philosophy and also science toward ‘final, categorical statements’. He wrote: If quantum theory has any philosophical importance at all, it lies in the fact that it demon-strates the necessity of dual aspects and complementary considerations. Much futile controversy could be avoided in this way.

For centuries, people argued over whether light was essentially a wave or essentially a particle. Today, this seems as superfluous as arguing about whether space is blue or whether it has mathematical properties. Each, in its proper context, is true. This doesn’t imply that the ‘whole truth’ lies somewhere in between the two viewpoints: complementarity is not a compromise. It is rather like the sides of a box, or the facets of a problem. What you see depends on what side of the box you look at—which is why light and in fact all energy and matter show up as clumps or quanta in some experiments, and behave like waves in others. Accepting complementarity merely means accepting that the other side of truth is not necessarily heresy. Bora’s answer to Einstein’s complaint that quantum theory left nature to chance was essentially that the absence of complete predictability did not imply that nature was random: the laws of chance are laws of nature, too. It seems absurd today that people confined by religious rigidity once considered it a heresy to believe that the sun was the centre of the solar system. But scientists like Weizenbaum are now afraid that people may be getting so caught up in their new-found scientific perspectives that they are treating emotional and moral perspectives as heretical. They may be forgetting—or at least dismissing—the fact that space is blue. If they are, this would be profoundly ironic, for as Born wrote: This loosening of the rules of thinking seems to me the greatest blessing which modern science has given us. The belief that there is only one truth and that oneself is in possession of it seems to me the deepest root of all the evil that is in the world.

Take a look at: The modern view of nature’s building blocks

Sto. Agostinho sobre a natureza humana

Jan Edward Garrett

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Agostinho tirou de Platão a visão de que o eu humano é uma alma imaterial que pode pensar. Platão sustentava que após a morte as almas daqueles que mais amam as formas subiriam para contemplar as verdades eternas, uma espécie de céu além do espaço e do tempo. Agostinho disse que essas formas eram ideias na mente do Deus eterno e perfeito. Ele disse que o que era necessário era que amássemos o Deus eterno e perfeito.

Enquanto Platão enfatizou a importância de aperfeiçoar a razão e segui-la, Agostinho enfatizou a importância da vontade, a capacidade de escolher entre o bem e o mal. O dever religioso fundamental é amar e servir a Deus; se conseguirmos isso, também escolheremos o bem e evitaremos o mal.

A natureza humana, tal como foi criada por Deus, é boa, e o livre arbítrio que Ele originalmente nos deu nos coloca numa posição mais elevada na escala metafísica dos seres do que os animais ou plantas não-humanos. (Os anjos e, claro, o próprio Deus estão acima de nós.)

Originalmente, segundo Agostinho, éramos igualmente livres para escolher o bem ou o mal. Mas os humanos são agora constantemente atraídos pelo mal, isto é, pela satisfação excessiva dos nossos desejos inferiores por coisas materiais e prazeres. (Conforme ele explica, isso decorre do fato de termos herdado o pecado original de nossos primeiros pais. Adão e Eva desobedeceram a Deus quando comeram o fruto proibido no Jardim do Éden.) Só podemos escapar da pecaminosidade herdada se recebermos a graça de Deus e não há como ganhar tal graça, ou forçar Deus a concedê-la a nós sendo bons.

Esta é uma visão que combina uma opinião bastante baixa da natureza humana com uma crença na imortalidade da alma. Portanto, materialistas como Thomas Hobbes ou Sigmund Freud não são os únicos pensadores que têm uma opinião negativa sobre a humanidade em geral.

É verdade que Agostinho acredita que existem humanos santos. Esses humanos amam as coisas que deveriam amar. Eles usam a razão corretamente. Mas sem a graça que recebem de Deus, e que não podem merecer, não seriam bons nem capazes de raciocinar corretamente.

A visão de Agostinho era que Deus seleciona apenas algumas pessoas para receberem graça e serem salvas. O resto da humanidade continuará a pecar e a não se arrepender, e então será punida por isso após a morte no fogo do inferno.

Agostinho foi profundamente educado na literatura da Roma pagã e na filosofia pré-cristã. Nos seus últimos anos, ele chegou a pensar que a maior parte desta literatura valia muito pouco, e preferiu discutir e citar as Escrituras em vez de autores pagãos. Ele pensava que a filosofia neoplatónica – uma escola filosófica pré-cristã baseada nas obras de Plotino (século III d.C.) e indirectamente em Platão (séculos V e IV a.C.) – por vezes antecipava as percepções cristãs e por isso não os rejeitou totalmente. Mas estudar autores pagãos não era garantia da bondade de uma pessoa. Pode até contribuir para a vaidade de uma pessoa. Agostinho pode ter pensado que a graça de Deus poderia operar em nós através do nosso encontro com as Sagradas Escrituras, mas mesmo aqui a salvação não era automática: nenhuma quantidade de recitação ou mesmo estudo das Sagradas Escrituras poderia garantir que uma pessoa receberia ou teria recebido a graça.

Para mais informações sobre a visão de Agostinho sobre o pecado original no contexto de uma discussão de visões filosóficas sobre a natureza de Deus, consulte Visões Filosóficas de Deus.

Nem todos os cristãos seguem Agostinho ao aceitar a ideia do pecado original herdado. Aqueles que, como o ministro e escritor unitarista do século XIX, William Ellery Channing , rejeitam a noção de pecado original, muitas vezes dizem que é contrário à bondade de Deus. Além disso, universalistas como Hosea Ballou , contemporâneo de Channing , afirmam que ninguém está destinado à condenação eterna e que todos, mais cedo ou mais tarde, serão reconciliados com Deus.

A visão de Agostinho (brevemente resumida)

A natureza (por trás da qual, é claro, está Deus) nos dá uma noção geral de nossos deveres. As instituições sociais moldam-nos para promover hábitos “socialmente úteis”, como a justiça. Mas estes esforços não são verdadeiramente suficientes para nos tornar bons.
A parte mais importante de uma pessoa é a pessoa interior, ou seja, a mente.
Eticamente, a parte mais importante da mente não é o intelecto (ou a razão), mas a vontade.
A orientação da vontade determina se amamos os bens inferiores (como os bens corporais, a riqueza e a reputação) ou os bens superiores (a virtude e, acima de tudo, Deus).
Embora originalmente não fosse nem boa nem má, a vontade humana tornou-se corrompida, de modo que, na maioria dos casos, está inclinada a amar os bens inferiores em vez dos bens superiores.
Pessoas boas são aquelas cuja vontade e razão estão subordinadas à fé em Deus e à devoção à vontade de Deus (ou seja, que devemos viver em retidão).
A fé é um dom da graça que não podemos ordenar, mas só recebemos quando chega.
No entanto, as ações perversas de pessoas sem fé, que violam os princípios básicos da justiça, vêm de dentro delas e, portanto, merecem punição proporcional por parte das autoridades humanas.
A graça de Deus pode operar em nós quando estudamos as Escrituras, mas o estudo das Escrituras, não importando o quanto, não é garantia que isto ocorra

Bênção do giz, teofania e outros sacramentais

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postado por Roque E. de Campos 12 de Janeiro de 2024

Sacramentos e Sacramentais

Sacramentos: Ritos centrais e primários instituídos por Cristo para conferir graças específicas direta e visivelmente. São um ritual ou cerimônia sagrada estabelecida por Cristo como meio de receber a graça de Deus. Na teologia católica, existem sete sacramentos: Batismo, Confirmação, Eucaristia, Penitência (Reconciliação), Unção dos Enfermos, Ordem Sagrada e Matrimônio. Cada sacramento é considerado um sinal externo instituído por Cristo para conferir graça ao destinatário. Os sacramentos são centrais para a fé católica e acredita-se que transmitem a presença e a ação de Deus de uma forma tangível.
Sacramentais: Rituais, objetos ou ações secundárias que visam preparar os indivíduos para a graça, santificar vários aspectos da vida e promover a devoção sem conferir o mesmo nível de graça que os sacramentos. São sinais, objetos ou ações sagradas que a Igreja Católica utiliza para preparar as pessoas para receber a graça e para santificar diferentes circunstâncias da vida. Ao contrário dos sacramentos, os sacramentais não conferem o mesmo nível de graça que os sacramentos. Exemplos de sacramentais incluem bênçãos, água benta, medalhas, crucifixos, escapulários e orações. O objetivo deles é atrair os indivíduos para uma conexão mais profunda com Deus, promover a devoção e fornecer uma maneira de buscar ajuda espiritual em vários aspectos da vida.

Bênção do giz e teofania

**Mosaico dos Três Reis Magos, Sant’Apollinare Nuovo em Ravenna, Itália**

A bênção do giz da Teofania é sacramental. Em muitos lugares é chamada de Epifania, mas na verdade é uma Teofania, que é uma palavra grega que significa a “aparição de Deus” ou a “manifestação de Deus”. Nas tradições cristãs, a Teofania refere-se à manifestação de Deus no mundo, particularmente a manifestação de Jesus Cristo em eventos como o Batismo no Rio Jordão.

A bênção do giz da Epifania é um ritual associado à Festa da Teofania, também conhecida como Epifania nas tradições cristãs ocidentais. Durante esse ritual, o giz é abençoado por um sacerdote e depois usado para marcar a entrada das casas. As marcações normalmente incluem o ano e as iniciais dos Reis Magos (Três Reis Magos) – Caspar, Melchior e Balthazar. Esta prática simboliza a proteção do lar e de seus habitantes através da manifestação da presença de Deus. O termo “Teofania” enfatiza a revelação do divino neste ritual.

A Epifania, celebrada no dia 6 de janeiro, marca a visita dos Reis Magos (Três Reis Magos ou Três Reis Magos) ao menino Jesus.

A tradição envolve uma cerimônia onde um giz especial é abençoado por um padre e depois usado para escrever uma inscrição acima da porta de entrada de uma casa. A inscrição normalmente inclui o ano e as iniciais dos nomes tradicionais dos Magos – Caspar, Melchior e Balthazar. O formato geralmente é: 20+C+M+B+21.

As letras têm significados religiosos e simbólicos:

C: Significa Caspar, um dos Magos.
M: Significa Melchior, outro dos Magos.
B: Significa Balthazar, o terceiro Mago.
A cruz (+): Representa a fé cristã.
Os números: Representam o ano (neste caso, 2024).

A inscrição é uma forma de os cristãos buscarem a bênção e a proteção de Deus para seus lares e para aqueles que neles habitam. Serve como um lembrete da visitação dos Reis Magos e da revelação de Jesus como o Salvador, não apenas para o povo judeu, mas para todas as nações.

O giz é frequentemente distribuído nas igrejas durante a Missa da Epifania, junto com a bênção do padre. Famílias ou indivíduos então usam o giz para marcar o batente da porta, oferecendo uma oração pela orientação, proteção e bênçãos de Deus no próximo ano. A inscrição permanece na porta como um sinal visível de fé e uma lembrança da época da Epifania.

Esta tradição como “GMB” e relacionada ao nome dos três magos, em muitos lugares as iniciais seriam na verdade “CMB”, que poderia vir em referência aos nomes dos Reis Magos, ou poderia significar “ Christus Mansionem Benedicat” que significa “Cristo abençoe esta casa”. Talvez se refira a ambos ou talvez represente variações locais desse costume.

Origens da epifania do giz

Deuteronômio 6:6-8 é uma passagem da Bíblia Hebraica (Antigo Testamento) que faz parte do Shemá , uma oração central e fundamental no Judaísmo:

“E estas palavras que hoje te ordeno estarão no teu coração. Tu as ensinarás diligentemente a teus filhos, e delas falarás sentado em tua casa, e andando pelo caminho, e ao deitar-te, e ao levantar-te. Você os amarrará como um sinal em sua mão, e eles serão como frontais entre seus olhos”.

Esta passagem enfatiza a importância de guardar os mandamentos de Deus no coração e transmiti-los às gerações futuras através do ensino diligente e da lembrança constante. É um elemento central da oração Shemá no Judaísmo.

Embora obviamente os judeus não aceitem o Cristo da mesma forma que os cristãos, é impossível não relacionar o que está embutido no Sharma e na Teofania do Giz, que é um relato de como o mundo, através dos Maggi, reconhece e aceita Jesus. como o Senhor com o mesmo espírito que os judeus enfatizam em seu Shemá.

A Mezuzá

Por que os judeus esfregam o batente da porta ao entrar em uma casa?

Na verdade, eles estão pegando uma pequena caixa (que é chamada mezuzá) contendo um pergaminho inscrito com versículos da Torá, afixado no umbral da porta, e é uma tradição judaica. A mezuzá serve como símbolo e lembrete da presença e dos mandamentos de Deus. Quando os judeus entram ou saem de um quarto ou casa, é um costume comum tocar a mezuzá e depois beijar os dedos que a tocaram em sinal de reverência.

A base bíblica para a mezuzá é encontrada na Torá, especificamente nos versos da oração Shemá do Livro de Deuteronômio (Deuteronômio 6:4-9 e 11:13-21). A porção relevante inclui a ordem de escrever as palavras de Deus nas ombreiras das casas e nos portões:

Deuteronômio 6:4-9 (ESV): “Ouve, ó Israel: O Senhor nosso Deus, o Senhor é o único. Amarás o Senhor teu Deus de todo o teu coração, de toda a tua alma e de todas as tuas forças. E estas palavras que hoje te ordeno estarão no teu coração. Tu as ensinarás diligentemente a teus filhos, e delas falarás sentado em tua casa, e andando pelo caminho, e ao deitar-te, e ao levantar-te. Você os amarrará como um sinal na sua mão, e eles serão como frontais entre os seus olhos. Você as escreverá nos umbrais de sua casa e nos seus portões”.

A mezuzá é uma expressão tangível deste mandamento, e o ato de tocá-la e beijá-la é uma forma de os indivíduos afirmarem sua conexão com os mandamentos de Deus e buscarem Suas bênçãos ao entrar ou sair de um espaço. É um ritual rico em simbolismo e serve como um lembrete diário da importância de viver de acordo com os ensinamentos da Torá.

A Mezuzá e o Shemá

A mezuzá em si não faz parte da oração Shemá, mas a prática de afixar uma mezuzá no batente da porta está enraizada nos mandamentos bíblicos encontrados no Shemá. Os versículos relevantes do Shemá enfatizam a importância de inscrever as palavras de Deus nas ombreiras das casas e nos portões. A mezuzá serve como uma expressão tangível deste mandamento.

A oração Shemá é uma declaração central da unidade de Deus e o mandamento de amar a Deus com todo o coração, alma e poder. É encontrado na Torá, no Livro de Deuteronômio, particularmente em Deuteronômio 6:4-9. O mandamento de escrever as palavras de Deus nos umbrais das portas faz parte desta passagem mais ampla.

Embora o conteúdo específico do Shemá não esteja escrito no pergaminho dentro da mezuzá, a própria mezuzá serve como um símbolo e um lembrete dos ensinamentos do Shemá. Muitos lares judaicos têm uma mezuzá afixada nas ombreiras das portas, e as pessoas costumam tocar e beijar a mezuzá como um ato de reverência e uma forma de cumprir o mandamento mencionado no Shemá.

Religiões Abraâmicas

As religiões abraâmicas são fés monoteístas que traçam a sua linhagem espiritual até ao patriarca Abraão . Estas religiões partilham elementos comuns de crença, particularmente no conceito de um Deus único. As três principais religiões abraâmicas são:

Judaísmo:
- O Judaísmo é uma das religiões monoteístas mais antigas e é a fé do povo judeu. Os textos fundamentais do Judaísmo incluem a Torá , que consiste nos primeiros cinco livros da Bíblia Hebraica (Gênesis, Êxodo, Levítico, Números e Deuteronômio).
Cristandade:
- O Cristianismo emergiu como uma tradição religiosa distinta seguindo os ensinamentos de Jesus Cristo, a quem os cristãos acreditam ser o Messias e o Filho de Deus. O texto central do Cristianismo é a Bíblia, que inclui o Antigo Testamento (compartilhado com o Judaísmo) e o Novo Testamento, contendo os ensinamentos e a vida de Jesus.
Islamismo:
- O Islã foi fundado no século 7 dC pelo profeta Maomé na Arábia. O principal texto sagrado do Islã é o Alcorão , considerado pelos muçulmanos como a palavra literal de Deus revelada a Maomé. O Hadith, uma coleção de ditos e ações do Profeta Muhammad, também tem uma importância significativa.

Essas religiões compartilham elementos comuns, como a crença em um único Deus, princípios éticos e uma conexão com a aliança abraâmica. No entanto, eles também têm crenças, práticas e interpretações distintas de seus textos sagrados. As religiões abraâmicas desempenharam um papel profundo na formação das culturas, histórias e civilizações do mundo.

Ritual romano

O Ritual Romano ( latim : Rituale Romanum ) é um dos livros litúrgicos oficiais do Rito Romano da Igreja Latina da Igreja Católica . Contém todos os serviços que um sacerdote ou diácono pode realizar; e não estão contidos no Missale Romanum , Pontificale Romanum ou Caeremoniale Episcoporum , mas por conveniência incluem alguns rituais que esses livros contém.

Desde 1969, o Ritual Romano é dividido em diferentes volumes por assunto, para uso padrão na Igreja Latina , ainda assim os padres e comunidades que celebram rituais pré – Concílio Vaticano II ainda usam a edição de 1952.

A mais utilizada é a versão original em latim de 1925 , mas nos Estados Unidos existe uma versão traduzida para o inglês, que pode ser vista em Rituale Romanum Index e em Português não encontrei algo semelhante, mas pode fazer o down load de <

Uma palavra sobre o compartilhamento dessas tradições por parte dos judeus

O lar hebreu foi abençoado, falando livremente, de diversas maneiras diferentes. Uma das mais dramáticas foi a aspersão do sangue do cordeiro pascal na verga e nas laterais da porta para afastar o Anjo da Morte durante a primeira Páscoa (Ex 12,1-14). Outra tinha a ver com obedecer ao mandamento de Deuteronômio 6:9, “escrever na entrada e nas portas da tua casa” o grande mandamento, ou Shema Yisrael : “Ouve, ó Israel, o Senhor nosso Deus é o único Senhor. “Amarás o Senhor teu Deus de todo o teu coração, e de toda a tua alma, e de todas as tuas forças.” (Deut. 6,4-5) Judeus piedosos cumpriram esta ordem (e ainda o fazem) com o uso de uma mezuzá, um pequeno cilindro contendo as palavras do Shema Yisrael que está pregado na lateral da porta.

Além do Missal e do Breviário, o Rituale Romanum está entre os livros litúrgicos mais importantes do rito romano tradicional. Codificado pela primeira vez em 1614 e editado pela última vez em 1953, o Ritual contém uma bênção sacerdotal para quase todas as ocasiões, do berço ao túmulo e para quase todos os objetos, sagrados e profanos. Além de bênçãos para todos os tipos concebíveis de cinto, escapulário e rosário (você sabia que existem rosários especiais de Nosso Senhor, do Preciosíssimo Sangue, da Santíssima Trindade, das Sete Dores e de São José?), também existem bênçãos para abelhas e cerveja, vinho e mulheres, equipamentos de alpinismo, ferrovias e sismógrafos. Várias destas bênçãos foram anteriormente reservadas a ordens e congregações religiosas específicas, mas hoje podem ser usadas por qualquer sacerdote validamente ordenado.

O valor dessas bênçãos é imenso. As bênçãos há muito que ocupam uma posição apreciada na vida católica pelos benefícios específicos que conferem ao corpo e à alma, mas também desempenham funções adicionais que conduzem ao bem da Igreja. Uma maneira de apreciar esses benefícios adicionais é ver as bênçãos do Ritual através do prisma da declaração de Cristo no Sermão da Montanha de que Ele veio não para abolir a Lei, mas para cumpri-la nos seus mínimos detalhes, até mesmo em seus “jotas”. e “tils”. (Mateus 5,17-18)[2]

Há um relato interessante e detalhado sobre o que está por trás ou sob o Rituale Romanum que pode ser visto em< de onde tirei as notas acima, e me vem à mente que a ideia toda não é apenas enfrentar Deus após nossa queda do Paraíso como diz a tradição e o pecado original e a saga de Cristo para nos salvar: tem como objetivo e visa transformar-nos em seres civilizados.

O valor corporativo e social do ritual

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Estamos agora em melhor posição para apreciar alguns dos valores ocultos nas bênçãos do Rituale Romanum . Mesmo além do seu bem mais óbvio – que é a bênção, seja ela constitutiva ou invocativa, de pessoas e objetos – as cerimônias contidas no Rituale também apresentam outras vantagens.

Primeiro, a relação clara que muitas, se não a maioria, das suas bênçãos têm com a Lei Antiga destaca apropriadamente as raízes judaicas da fé cristã. É verdade que existe o perigo de minimizar as diferenças entre o Judaísmo e o Cristianismo ou de misturá-las, como vemos nas heresias dos Ebionitas e dos Nazarenos – seitas antigas que, parafraseando São Jerônimo, ao quererem ser ao mesmo tempo judeus e Os cristãos não eram nenhum dos dois.[14] Mas também existe o perigo de esquecer ou depreciar essas raízes, como deixa claro a heresia do Marcionismo. “Espiritualmente”, declarou o Papa Pio XI, “somos todos semitas.”[15] À sua maneira modesta, as bênçãos do Rituale lembram-nos corretamente como proceder.

Em segundo lugar, as bênçãos do Rituale são particularmente úteis num mundo onde o ritual partilhado e significativo está em declínio. Esta é uma tendência perturbadora, pois é uma indicação de uma barbárie crescente.Segundo Confúcio, é o respeito e a observância dos rituais tradicionais que separa o civilizado do selvagem.[16] Embora seja verdade que o propósito da Igreja Católica é produzir santos em vez de senhoras e senhores, dificilmente seria lamentável se ela produzisse ambos. Certamente este duplo objectivo esteve por detrás de muitos dos esforços dos educadores, alguns dos quais são agora santos canonizados, que fundaram escolas, colégios e universidades católicas tanto no Velho como no Novo Mundo.

Em segundo lugar, o bom ritual promove nos homens e nas mulheres um padrão civilizador de comportamento que os Padres Latinos da Igreja chamavam de humanitas , que denota não apenas humanidade ou natureza humana, mas uma cordialidade refinada e cortesia.

E terceiro, um avanço na humanitas genuína é um avanço na pietas , pois, como deixam claro as primeiras linhas das Confissões de Santo Agostinho , somos mais autenticamente humanos quando louvamos e damos graças a Deus todo-poderoso. Josef Pieper, em seu encantador livro In Tune with the World: A Theory of Festivity, escreve que o cerne da festividade consiste “na expressão física dos homens de sua concordância com tudo o que existe” e que “o festival ritual é a forma mais festiva que a festividade pode possivelmente aceitar.”[17] “A única maneira adequada de responder ao dom” de nossa existência, Pieper acrescenta mais tarde, é “pelo louvor a Deus na adoração ritual”[18] – até mesmo nos festivais seculares modernos, que muitas vezes são distorções e repúdios à fé cristã, têm “suas raízes nos rituais de adoração”.

Mas disto segue-se uma conclusão preocupante: “Não pode haver destruição mais mortal e mais implacável da festividade do que a recusa do louvor ritual.”[20] Pieper até sugere que a noção de pureza ritual, no sentido de preparar-se para uma festa , “deveria ser repensado e recapturado.”[21] Obviamente, ter uma rica lista de rituais específicos como aqueles que examinamos neste ensaio empalidece em comparação com o culto ritual central da Igreja, a celebração da Eucaristia: a bênção de o vinho no dia de São João Evangelista, por exemplo, é trivial quando comparado à consagração do vinho no Cálice Precioso. No entanto, mesmo as coisas triviais, mesmo os “jotas e tils”, têm o seu lugar na constelação cristã de sinais e não devem, por esse motivo, ser desconsideradas ou suprimidas.

Como tudo isso se tornou a raiz e a estrutura da educação como principal fator do advento da civilização

É muito difícil, se não impossível, expressar em palavras e de forma razoável como estes elementos se tornaram a raiz e a estrutura da educação, mas vamos tentar.

Tenha em mente que estamos pensando nas tradições ocidentais e num período de cerca de 2.000 anos, desde o aparecimento de Cristo e no início deste século XXI.

Numa breve pincelada, o cristianismo, especialmente a igreja católica, foi no seu início um influenciador muito forte e com o passar do tempo perdeu força, mas sempre esteve presente nas épocas seguintes:

Antiguidade Clássica (c. 800 AC – 476 DC):
- Este período inclui as civilizações da Grécia Antiga e Roma. Lançou as bases para a filosofia, arte, literatura e pensamento político ocidentais. O declínio do Império Romano em 476 dC é frequentemente usado como um marcador para o fim da Antiguidade Clássica.
Primeira Idade Média (c. 476 – 1000):
- Também conhecido como Idade das Trevas, este período testemunhou o declínio da autoridade romana centralizada e a ascensão do feudalismo. A difusão do cristianismo tornou-se uma força unificadora na Europa e o monarquismo desempenhou um papel crucial na preservação do conhecimento.
Alta Idade Média (c. 1000 – 1300):
- Esta era viu o renascimento do comércio e das atividades culturais. A ascensão das universidades medievais, a arquitetura gótica e o crescimento das cidades e do comércio caracterizaram este período. Também testemunhou as Cruzadas e o estabelecimento de monarquias feudais.
Final da Idade Média (c. 1300 – 1500):
- O final da Idade Média incluiu a Peste Negra, que teve profundas consequências demográficas e económicas. A Guerra dos Cem Anos, o Papado de Avignon e o Grande Cisma também foram eventos significativos. O período terminou com o Renascimento, marcado por um interesse renovado pela arte clássica, literatura e humanismo.
Renascença (séculos XIV-XVII):
- O Renascimento foi um período de grande crescimento cultural e intelectual. Viu avanços na arte, ciência, filosofia e literatura. A redescoberta de textos e ideias clássicas teve um impacto transformador no pensamento europeu.
Reforma e Contra-Reforma (século XVI):
- A Reforma Protestante, liderada por figuras como Martinho Lutero e João Calvino, desafiou a autoridade da Igreja Católica. Este período também testemunhou a Contra-Reforma Católica em resposta à propagação do Protestantismo.
Período Moderno (séculos XVII a XVIII):
- O início do período moderno incluiu a revolução científica, o Iluminismo e a Era da Exploração ou descobertas marítimas. Marcou uma mudança em direção à razão, ao empirismo e ao secularismo no pensamento ocidental.
Revolução Industrial (séculos XVIII a XIX):
- A Revolução Industrial trouxe avanços tecnológicos significativos, mudanças econômicas e urbanização. Transformou sociedades agrárias em industriais e teve profundos impactos sociais e económicos.
Século XIX e Nacionalismo:
- O século XIX viu a ascensão do nacionalismo, a difusão dos ideais democráticos e a industrialização das sociedades ocidentais. Também testemunhou mudanças políticas e sociais significativas, incluindo revoluções e a unificação de vários estados europeus.
Século XX e Era Contemporânea:
- O século 20 trouxe duas guerras mundiais, a Guerra Fria, avanços tecnológicos significativos e mudanças culturais. A última parte do século XX viu o colapso da União Soviética, a ascensão da globalização e a revolução digital. O século 21 foi marcado por contínuas mudanças tecnológicas, políticas e sociais.

Como a religião esteve presente em todos esses períodos?

Novamente, falando em termos gerais e de forma muito resumida:

Dogmas e credos

Dogmas e credos no catolicismo representam crenças fundamentais que são consideradas divinamente reveladas e não estão sujeitas a alterações ou debates dentro dos ensinamentos oficiais da Igreja. Servem como elementos fundamentais da fé, fornecendo uma estrutura doutrinária para a teologia católica. Ao praticar o catolicismo, espera-se que os adeptos aceitem e afirmem estes dogmas e credos como expressões das verdades essenciais da fé. Os mais importantes são:

Infalibilidade: A Igreja Católica ensina a infalibilidade de certos dogmas, o que significa que são considerados isentos de erros e irreformáveis. A infalibilidade é atribuída à autoridade docente da Igreja quando esta define solenemente uma doutrina relativa à fé ou à moral.
Credo Niceno e Credo Apostólico: O Credo Niceno e o Credo Apostólico são dois dos credos mais conhecidos do catolicismo. Esses credos expressam sucintamente crenças fundamentais sobre a Trindade, a Encarnação e o papel da Igreja.
Estabilidade Doutrinária: Dogmas e credos proporcionam estabilidade à doutrina católica, garantindo continuidade e consistência no ensino de verdades essenciais ao longo do tempo.
Uso Litúrgico: Credos, como o Credo Niceno, são regularmente recitados durante a liturgia, enfatizando o seu papel central na vida de culto da Igreja.

Rituais e práticas litúrgicas

O “ Rituale Romanum ” desempenha um papel significativo na orientação dos rituais e práticas litúrgicas da Igreja Católica. Este livro litúrgico fornece aos sacerdotes as rubricas, orações e instruções cerimoniais para vários sacramentos e sacramentais. Os rituais descritos no “ Rituale Romanum ” cobrem uma ampla gama de cerimônias e ritos religiosos, incluindo:

Sacramentos: O “ Rituale Romanum ” inclui os rituais para a administração dos sacramentos, como o batismo, a confirmação, a penitência, a unção dos enfermos, as ordens sagradas e o matrimônio.
Sacramentais: Inclui várias bênçãos, consagrações e rituais associados a objetos, lugares e eventos. Exemplos de sacramentais incluem a bênção de água benta, a consagração de uma igreja ou altar e a bênção de artigos religiosos.
Exorcismos: O “ Rituale Romanum ” contém orações e rituais para o rito solene de exorcismo, usado nos casos em que a Igreja determina que uma pessoa pode ser afligida por influência demoníaca.
Ritos Funerários: O livro fornece as instruções litúrgicas e orações para os ritos fúnebres, incluindo a celebração da missa pelos falecidos e a encomenda da alma a Deus.
Várias Bênçãos: O “ Rituale Romanum ” contém bênçãos para diversas situações e objetos, como bênçãos para um casal recém-casado, uma casa, colheitas e medalhas religiosas.

Em essência, o “ Rituale Romanum ” serve de guia para os sacerdotes na administração dos sacramentos e sacramentais da Igreja, garantindo que estes rituais sejam realizados de acordo com as tradições e ensinamentos da Igreja Católica. Ele fornece as palavras, ações e sequências prescritas a serem seguidas durante esses ritos sagrados.

Dogmas e credos não são objeto de discussão na prática do catolicismo, o que realmente aparece são as práticas rituais e litúrgicas e o cotidiano do crente é formado por isso, que independe de pensamentos sobre dogmas e crenças

Como, então, o ritual “promove nos homens e nas mulheres um padrão civilizatório de comportamento que os Padres Latinos da Igreja chamavam de humanitas , que denota não apenas humanidade ou natureza humana, mas uma cordialidade refinada e cortesia.“?

Humanitas, pietas, Trivium e Quadrivium

Humanitas como um avanço na pietas , nas primeiras linhas das Confissões de Santo Agostinho deixa claro, afirmando que somos mais autenticamente humanos quando louvamos e damos graças a Deus Todo-Poderoso.

A isto devem ser acrescentadas as ideias de Santo Agostinho sobre a natureza humana

Tudo isso foi dito por Santo Agostinho por volta dos séculos IV e V e demoraria um pouco para se tornar padrão, embora de uma forma muito mais ampla e secular na idade média que era o Trivium e o Quadrivium.

Trivium e Quadrivium foram componentes-chave do sistema educacional clássico que influenciou a educação medieval. Estes termos descrevem dois conjuntos de disciplinas fundamentais que formaram a base da educação em artes liberais durante a Idade Média:

Trivium:
- O Trivium consiste em três assuntos centrais que foram considerados essenciais para o desenvolvimento de um indivíduo completo e educado. Os três componentes do Trivium são:
  - Gramática: No contexto do Trivium, a gramática não se refere apenas à estrutura da língua, mas abrange o estudo do latim e o uso correto da língua. Forneceu a base para a compreensão e interpretação de textos escritos.
  - Retórica: A retórica concentra-se na arte da comunicação persuasiva, tanto na forma escrita quanto falada. Os alunos do Trivium aprenderam como se expressar de forma eficaz, argumentar de forma persuasiva e participar no discurso público.
  - Lógica: A lógica envolve o estudo do raciocínio e da argumentação. Os alunos aprenderam os princípios do raciocínio sólido, do pensamento crítico e como construir e analisar argumentos lógicos.
- O Trivium teve como objetivo dotar os alunos das ferramentas intelectuais necessárias para uma comunicação eficaz, pensamento crítico e interpretação de textos.
Quadrívium:
- O Quadrivium baseia-se no Trivium e consiste em quatro disciplinas adicionais, concentrando-se mais em matemática e ciências. Os quatro componentes do Quadrivium são:
  - Aritmética: O estudo de números e operações matemáticas básicas.
  - Geometria: O estudo das formas, tamanhos e propriedades do espaço.
  - Música: No contexto do Quadrivium, o estudo da música envolve a compreensão dos princípios matemáticos subjacentes à harmonia e composição musical.
  - Astronomia: O estudo dos corpos celestes e seus movimentos.
- O Quadrivium teve como objetivo proporcionar aos alunos uma compreensão mais profunda dos princípios matemáticos e científicos que governam o mundo natural.

Estas sete artes liberais, conhecidas coletivamente como as “sete artes liberais e ciências”, formavam o currículo básico da educação medieval. Eles foram considerados fundamentais para o cultivo de um indivíduo completo e intelectualmente competente. Enquanto o Trivium se concentrava mais nas habilidades linguísticas e de comunicação, o Quadrivium enfatizava a alfabetização matemática e científica. Juntos, lançaram as bases para a educação de estudiosos, teólogos e intelectuais durante o período medieval.

Escrevi um artigo no jornal local da minha cidade natal onde tento conectar tudo isso com a realidade do século XXI:

“A educação voltada para as “Artes Liberais”, ou “humanidades” deriva da expressão latina renascentista studia humanitatis , que significa “estudo do humano”, visando a cultura, o refinamento, a educação e, especificamente, uma “educação condizente com um homem culto” . No início do século XV, os studia humanitatis eram compostos pelo Trivium (3) e pelo Quaddrivium (4). 3 + 4 = Sete Artes Liberais. Gramática, Lógica e Retórica eram as artes liberais centrais (o Trivium), Aritmética, Geometria, Teoria Musical e Astronomia (Quadrivium) desempenhavam um papel um pouco menor. Até o final da Idade Média, eram estudados como “modos de fazer as coisas”. Uma grande mudança ocorreu com o Humanismo Renascentista do século XV através do surgimento das línguas modernas, quando as Humanidades começaram a ser consideradas como assunto de estudo e não de prática, especialmente em campos tradicionais como literatura e história,

A ciência levaria 15 séculos para ser considerada válida e poder sentar-se à mesa dos cultos, isso aconteceu através da introdução de Galileu, ao propor pela primeira vez (junto com o vernáculo italiano) o que se tornaria o padrão para o pensamento científico, ou seja, sua tese medindo o Inferno de Dante. A matemática, na época, não era considerada digna de figurar no que pensava a elite da época. Ao fazê-lo, Galileu abandonou as ferramentas matemáticas da Ciência como forma válida de pensar e anunciou a separação da Ciência da Religião. O pensamento “científico” foi completado pela influência de Descartes, com a introdução do seu método e prevaleceu até o início do século XX.

No século XX, esta visão foi desafiada pelo movimento pós-modernista, que procurou redefinir as Humanidades em termos igualitários adequados para uma sociedade democrática, uma vez que as sociedades grega e romana em que as Humanidades se originaram não eram democráticas. Esta mudança de foco estava de acordo com a visão dos pós-modernistas de si mesmos como o ápice da história. Talvez o preconceito de que as humanidades eram dispensáveis se deva ao fato de o movimento pós-modernista do final do século XX querer redefinir a Cultura em termos utilitários e democráticos, uma vez que até então era privilégio da elite. Há muita gente na Academia que parou por aí, ignorando que o mundo mudou mais nos últimos 30 anos do que em todo o século anterior… Tudo isto é agravado pelo fato de a Ciência, não por si, mas por quem a utiliza , ter sido determinada como a forma correta de compreender e interpretar a realidade. Completado pela percepção no primeiro mundo de que quem se forma em Ciências Humanas está desempregado ou subempregado e quem estuda Ciências Exatas não precisa de Ciências Humanas. Isto deve mudar porque o trabalho tal como Marx o percebeu, que claramente sempre exigiu contingentes de pessoas instruídas e focadas nas ciências exatas, está prestes a desaparecer devido à entrada dos Robôs e da Inteligência Artificial. Isto está a dar lugar a uma vasta rede de serviços, para a qual a educação na área das humanidades é sinequanon. Até o final deste século, alguém questionará por que alguém em algum momento pensou em dispensar as indispensáveis “Humanidades”, ou melhor ainda, por que alguém tem que entendê-las exatamente, quando tudo o que precisa fazer é aprender como usá-las com a ajuda de um computador, algo que eu mesmo percebi nos anos 2000, quando dava aulas, levando em conta o que os computadores pessoais já faziam e o que os iPhones faziam a partir de 2007.

Conclusão ou observações finais

Fechando o círculo, que eu diria que começou com Confúcio há cerca de 2.600 anos, transcrevo suas palavras dos Analectos:

Analectos 1:12, 2:7, 3:8, 16:13, 17:19. onde, a cosmovisão confucionista chega ao ponto de considerar o Estado de direito uma medida necessária apenas para os bárbaros. Os seres humanos civilizados não precisam da força da lei, apenas dos costumes e dos rituais ancestrais.

A concepção de que o Estado de Direito é necessário apenas para os seres humanos bárbaros e civilizados não precisaria da força da lei, apenas do costume e do ritual ancestral, que está presente nos ensinamentos encontrados nos Analectos de Confúcio. Embora seja importante notar que a tradução e interpretação dos textos confucionistas podem variar, o sentimento geral alinha-se com a ideia de que a conduta ética, guiada pelo ritual e pela tradição, deve ser uma parte internalizada do caráter de um indivíduo numa sociedade bem ordenada . (Eu não poderia ter uma definição melhor de educação)

Em diversas passagens dos Analectos, Confúcio enfatiza a importância do cultivo moral, da virtude e da internalização de princípios éticos. Os costumes (ou rituais, “li” em chinês) desempenham um papel significativo na formação do comportamento e espera-se que os indivíduos adiram a uma conduta adequada com base nestas práticas tradicionais.

Analectos 2:7:
- “O Mestre disse: ‘Não é um prazer, tendo aprendido algo, experimentá-lo na prática? Não é uma alegria ter amigos vindos de longe? Não é cavalheiresco não se ofender quando os outros não apreciam suas habilidades? Não é cavalheiresco não se ofender quando os outros não apreciam seus talentos? Não é cavalheiresco não se ofender quando os outros não reconhecem os seus méritos? Não é cavalheiresco não ser impaciente com outros que não têm a sua habilidade? Não é cavalheiresco não se preocupar com um problema que os outros não veem? Não é cavalheiresco não ficar agitado quando outros não conseguem compreender os méritos de suas realizações? Não é cavalheiresco ter força para esperar pacientemente quando os outros demoram para entender?’”
Analectos 12:1:
- “O Mestre disse: ‘O cavalheiro é aberto e direto, enquanto o homem pequeno é argumentador e tendencioso.’”
Analectos 12:22:
- “O Mestre disse: ‘Em uma linguagem que é firme, mas educada, e em um rosto que é amigável, mas imponente, raramente há qualquer falha no comportamento.’”

Estas passagens, entre outras, destacam a ênfase de Confúcio no cultivo de virtudes morais, na prática de conduta adequada e na incorporação das qualidades de um verdadeiro cavalheiro (Junzi). A ideia subjacente é que, numa sociedade onde os indivíduos incorporam valores éticos e propriedade ritual, a necessidade de força externa, como regulamentações legais estritas, é minimizada. A ênfase está na internalização de princípios morais por meio da educação, ritual e reflexão pessoal.

Assim, quando escrevemos com giz acima da porta de entrada de nossa casa a Teofania, celebrando o aparecimento do Deus único mais reverenciado pela humanidade, não pelo poder da força, mas pelo amor e pela transmissão de Seus ensinamentos, que estão embutidos para tornar o mundo civilizado da maneira que foi mal discutida aqui (minhas desculpas).

Theophany Chalk Blessing and other Sacramentals

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Sacraments and Sacramentals

Sacraments: Central and primary rites instituted by Christ to confer specific graces directly and visibly. They are a sacred ritual or ceremony established by Christ as a means of receiving God’s grace. In Catholic theology, there are seven sacraments: Baptism, Confirmation, Eucharist, Penance (Reconciliation), Anointing of the Sick, Holy Orders and Matrimony. Each sacrament is considered an outward sign instituted by Christ to confer grace upon the recipient. The sacraments are central to the Catholic faith and are believed to convey the presence and action of God in a tangible way.
Sacramentals: Secondary rituals, objects, or actions that are meant to prepare individuals for grace, sanctify various aspects of life, and foster devotion without conferring the same level of grace as sacraments. They are sacred signs, objects, or actions that the Catholic Church uses to prepare people to receive grace and to sanctify different circumstances in life. Unlike sacraments, sacramentals do not confer the same level of grace as the sacraments. Examples of sacramentals include blessings, holy water, medals, crucifixes, scapulars, and prayers. They are meant to draw individuals into a deeper connection with God, foster devotion, and provide a way to seek spiritual help in various aspects of life.

Theophany chalk blessing

**Mosaic of the Three Magi, Sant’Apollinare Nuovo in Ravenna, Italy**

Theophany chalk blessing is a sacramental. In many places it is called Epiphany, but actually it is a Theophany, which is a Greek word that means the “appearance of God” or the “manifestation of God.” In Christian traditions, Theophany refers to the manifestation of God in the world, particularly the manifestation of Jesus Christ in events such as the Baptism in the Jordan River.

The Epiphany chalk blessing is a ritual associated with the Feast of Theophany, which is also known as Epiphany in Western Christian traditions. During this ritual, chalk is blessed by a priest and then used to mark the entrance of homes. The markings typically include the year and the initials of the Magi (Three Wise Men) – Caspar, Melchior, and Balthazar. This practice symbolizes the protection of the home and its inhabitants through the manifestation of God’s presence. The term “Theophany” emphasizes the revelation of the divine in this ritual.

The Epiphany, celebrated on January 6th, marks the visit of the Magi (Three Wise Men or Three Kings) to the infant Jesus.

The tradition involves a ceremony where a special chalk is blessed by a priest and then used to write an inscription above the entrance door of a home. The inscription typically includes the year and the initials of the traditional names of the Magi—Caspar, Melchior, and Balthazar. The format is often: 20+C+M+B+21.

The letters have both religious and symbolic meanings:

C: Stands for Caspar, one of the Magi.
M: Stands for Melchior, another of the Magi.
B: Stands for Balthazar, the third Magi.
The cross (+): Represents the Christian faith.
The numbers: Represent the year (in this case, 2024).

The inscription is a way for Christians to seek God’s blessing and protection on their homes and those who dwell within. It serves as a reminder of the visitation of the Wise Men and the revelation of Jesus as the Savior not only for the Jewish people but for all nations.

The chalk is often distributed in churches during the Epiphany Mass, along with a blessing from the priest. Families or individuals then use the chalk to mark the doorframe, offering a prayer for God’s guidance, protection, and blessings in the coming year. The inscription remains on the door as a visible sign of faith and a reminder of the Epiphany season.

This tradition as “GMB” and related to the name of the three magi, in many places the initials would actually be “CMB”, which could come in reference to the names of the Magi, or it could mean “Christus Mansionem Benedicat” which means “Christ bless this house.” Perhaps it comes in reference to both or perhaps this represents local variations on this custom.

Origins of the chalk epiphany

Deuteronomy 6:6-8 is a passage from the Hebrew Bible (Old Testament) that is part of the Shema, a central and foundational prayer in Judaism:

“And these words that I command you today shall be on your heart. You shall teach them diligently to your children, and shall talk of them when you sit in your house, and when you walk by the way, and when you lie down, and when you rise. You shall bind them as a sign on your hand, and they shall be as frontlets between your eyes.”

This passage emphasizes the importance of keeping God’s commandments in one’s heart and passing them on to future generations through diligent teaching and constant remembrance. It is a central element of the Shema prayer in Judaism.

Although obviously the Jews do not accept the Christ the same way as Christians do, it is impossible not to relate what is embedded in the Sharma and the Chalk Theophany, which is an account on how the world, through the Maggi, recognize and accepts Jesus as the Lord with the same spirit that the Jews emphasize in their Shema.

The Mezuzah

Why do Jews rub the doorpost when entering a house?

Actually, they are reaching for a small box (which is called mezuzah) containing a parchment inscribed with verses from the Torah, affixed to the doorpost, and it is a Jewish tradition. The mezuzah serves as a symbol and a reminder of God’s presence and commandments. When Jews enter or exit a room or a house, it’s a common custom to touch the mezuzah and then kiss the fingers that touched it as a sign of reverence.

The scriptural basis for the mezuzah is found in the Torah, specifically in the verses of the Shema prayer from the Book of Deuteronomy (Deuteronomy 6:4-9 and 11:13-21). The relevant portion includes the command to write the words of God on the doorposts of one’s house and gates:

Deuteronomy 6:4-9 (ESV): “Hear, O Israel: The Lord our God, the Lord is one. You shall love the Lord your God with all your heart and with all your soul and with all your might. And these words that I command you today shall be on your heart. You shall teach them diligently to your children, and shall talk of them when you sit in your house, and when you walk by the way, and when you lie down, and when you rise. You shall bind them as a sign on your hand, and they shall be as frontlets between your eyes. You shall write them on the doorposts of your house and on your gates.”

The mezuzah is a tangible expression of this commandment, and the act of touching and kissing it is a way for individuals to affirm their connection to God’s commandments and seek His blessings upon entering or leaving a space. It’s a ritual that is rich in symbolism and serves as a daily reminder of the importance of living in accordance with the teachings of the Torah.

The mezuzah and Shema

The mezuzah itself is not part of the Shema prayer, but the practice of affixing a mezuzah to the doorpost is rooted in the scriptural commandments found in the Shema. The relevant verses from the Shema emphasize the importance of inscribing the words of God on the doorposts of one’s house and gates. The mezuzah serves as a tangible expression of this commandment.

The Shema prayer is a central declaration of the oneness of God and the commandment to love God with all one’s heart, soul, and might. It is found in the Torah in the Book of Deuteronomy, particularly in Deuteronomy 6:4-9. The commandment to write God’s words on the doorposts is part of this broader passage.

While the specific content of the Shema is not written on the parchment inside the mezuzah, the mezuzah itself serves as a symbol and a reminder of the Shema’s teachings. Many Jewish homes have a mezuzah affixed to the doorposts, and individuals often touch and kiss the mezuzah as an act of reverence and a way to fulfill the commandment mentioned in the Shema.

Abrahamic Religions

The Abrahamic religions are monotheistic faiths that trace their spiritual lineage to the patriarch Abraham. These religions share common elements of belief, particularly in the concept of one God. The three major Abrahamic religions are:

Judaism:
- Judaism is one of the oldest monotheistic religions, and it is the faith of the Jewish people. The foundational texts of Judaism include the Torah, which consists of the first five books of the Hebrew Bible (Genesis, Exodus, Leviticus, Numbers, and Deuteronomy).
Christianity:
- Christianity emerged as a distinct religious tradition following the teachings of Jesus Christ, whom Christians believe is the Messiah and the Son of God. The central text of Christianity is the Bible, which includes the Old Testament (shared with Judaism) and the New Testament, containing the teachings and life of Jesus.
Islam:
- Islam was founded in the 7th century CE by the Prophet Muhammad in Arabia. The primary sacred text of Islam is the Quran, believed by Muslims to be the literal word of God as revealed to Muhammad. The Hadith, a collection of sayings and actions of Prophet Muhammad, also holds significant importance.

These religions share common elements, such as belief in one God, ethical principles, and a connection to the Abrahamic covenant. However, they also have distinct beliefs, practices, and interpretations of their sacred texts. The Abrahamic religions have played a profound role in shaping the cultures, histories, and civilizations of the world.

Rituale Romanum

The Roman Ritual (Latin: Rituale Romanum) is one of the official liturgical books of the Roman Rite of the Latin Church of the Catholic Church. It contains all of the services that a priest or deacon may perform; and are not contained in the Missale Romanum, Pontificale Romanum, or Caeremoniale Episcoporum, but for convenience does include some rituals that one of these books contains.

Since 1969, the Roman Ritual is divided into different volumes by subject, for standard use in the Latin Church, yet priests and communities that celebrate pre–Second Vatican Council rituals still use the edition of 1952

The most commonly used is the original Latin version from 1925, but in the United States there is a translated version to English, which can be seen at Rituale Romanum Index

A word about the sharing of these traditions from the Jews

The Hebrew home was blessed, loosely speaking, in a number of different ways. One of the most dramatic was the sprinkling of the blood of the Paschal lamb on the lintel and sides of the door to avert the Angel of Death during the first Passover (Ex 12,1-14). Another had to do with obeying the commandment of Deuteronomy 6:9, “to write in the entry, and on the doors of thy house” the great commandment, or Shema Yisrael: “Hear, O Israel, the LORD our God is one LORD. Thou shalt love the LORD thy God with thy whole heart, and with thy whole soul, and with thy whole strength.” (Deut. 6,4-5) Pious Jews complied with this command (and still do) with use of a mezuzah, a small cylinder containing the words of the Shema Yisrael that is nailed to the side of the door.

In addition to the Missal and the Breviary, the Rituale Romanum is among the most important liturgical books of the traditional Roman rite. First codified in 1614 and last edited in 1953, the Ritual contains a priestly blessing for almost every occasion from the cradle to the grave and for almost every object, sacred and profane. In addition to blessings for every conceivable kind of cincture, scapular, and rosary (did you know that there are special rosaries of Our Lord, the Precious Blood, the Holy Trinity, the Seven Sorrows, and St. Joseph?), there are also benedictions for bees and beer, wine and women, mountain-climbing equipment, railroads, and seismographs. Several of these blessings were formerly reserved to particular religious orders and congregations, but today they can be used by any validly ordained priest.

The value of these blessings is immense. Blessings have long held a cherished position in Catholic life for the specific benefits they bestow on body and soul, but they also serve additional functions that are conducive to the good of the Church. One way to appreciate these additional benefits is to view the blessings of the Ritual through the prism of Christ’s statement in the Sermon on the Mount that He came not to abolish the Law but to fulfill it in its most minute details, even its “jots” and “tittles.” (Matt. 5,17-18)[2]

There is an interesting and detailed account on what is behind or under the Rituale Romanum which can be seen at from which I took the notes above, and it comes to mind that the whole idea is not only to come to grips with God after our fall form Paradise as the tradition says and the original sin and the saga of Christ to save us: It is meant and aimed at transforming us into civilized beings.

The Corporate, Social Value of the Ritual

See it in detail at

We are now in a better position to appreciate some of the hidden value in the blessings of the Rituale Romanum. Even aside from their most obvious good—which is the blessing, be it constitutive or invocative, of people and objects—the ceremonies contained in the Rituale have other advantages as well.

First, the clear relation that many if not most of its blessings have to the Old Law aptly highlights the Jewish roots of the Christian faith. It is true that there is a danger in minimizing the differences between Judaism and Christianity or in mixing them, as we see in the heresies of the Ebionites and the Nazarenes—ancient sects that, to paraphrase St Jerome, in wanting to be both Jews and Christians were neither.[14] But there is also a danger in forgetting or deprecating those roots, as the heresy of Marcionism makes clear. “Spiritually,” Pope Pius XI declared, “we are all Semites.”[15] In their modest way, the blessings of the Rituale correctly remind us how.

Second, the Rituale’s blessings are particularly helpful in a world where shared, meaningful ritual is on the decline. This is a disturbing trend, for it is an indication of increasing barbarism. According to Confucius, it is respect for and observance of traditional ritual that separates the civilized from the savage.[16] Although it is true that the purpose of the Catholic Church is to produce saints rather than ladies and gentlemen, it would hardly be lamentable if she produced both. Surely this twin goal was behind many of the efforts of the educators, some of whom are now canonized saints, who founded Catholic schools, colleges, and universities in both the Old and New Worlds.

Second, good ritual fosters in men and women a civilizing pattern of behavior that the Latin Fathers of the Church called humanitas, which denotes not simply humanity or human nature but a refined warmth and courtesy.

And third, an advance in genuine humanitas is an advance in pietas, for as the opening lines of St Augustine’s Confessions makes clear, we are most authentically human when we praise and give thanks to almighty God. Josef Pieper, in his delightful book In Tune with the World: A Theory of Festivity, writes that the heart of festivity consists “in men’s physically expressing their agreement with everything that is” and that “ritual festival is the most festive form that festivity can possibly take.”[17] “The only fitting way to respond to the gift” of our existence, Pieper adds later, is “by praise of God in ritual worship”[18]—even modern secular festivals, which are often distortions and repudiations of the Christian faith, have “their roots in the rituals of worship.”[19]

But from this follows a sobering conclusion: “There can be no deadlier, more ruthless destruction of festivity than refusal of ritual praise.”[20] Pieper even suggests that the notion of ritual purity, along the lines of making oneself ready for a feast, “should be rethought and recaptured.”[21] Obviously, having a rich roster of specific rituals like those we have examined in this essay pales in comparison to the central ritual worship of the Church, the celebration of the Eucharist: the blessing of wine on St John the Evangelist’s Day, for example, is trivial when compared to the consecration of wine in the Precious Chalice. Yet even trivial things, even jots and tittles, have their place in the Christian constellation of signs and should not on that account be disregarded or suppressed.

How all that became the root and frame of education as the main factor of the advent of civilization

It is very difficult, if not impossible to express in words and in a reasonble way how these elements became the root and frame of education, but let’s try.

Bear in mind that we are thinking western traditions and a time span of some 2000 years, since the Christ appeared and in the beginning of this 21rst century.

In a very brief stroke, christianism, specially the catholic church was at its inception a very strong influencer and with the time elapsing, lost its strenght, but has been alwasys present in the following eras:

Classical Antiquity (c. 800 BCE – 476 CE):
- This period includes the civilizations of Ancient Greece and Rome. It laid the foundations for Western philosophy, art, literature, and political thought. The decline of the Roman Empire in 476 CE is often used as a marker for the end of Classical Antiquity.
Early Middle Ages (c. 476 – 1000):
- Also known as the Dark Ages, this period witnessed the decline of centralized Roman authority and the rise of feudalism. The spread of Christianity became a unifying force in Europe, and monasticism played a crucial role in preserving knowledge.
High Middle Ages (c. 1000 – 1300):
- This era saw the revival of trade and cultural activities. The rise of medieval universities, the Gothic architecture, and the growth of towns and commerce characterized this period. It also witnessed the Crusades and the establishment of feudal monarchies.
Late Middle Ages (c. 1300 – 1500):
- The Late Middle Ages included the Black Death, which had profound demographic and economic consequences. The Hundred Years’ War, the Avignon Papacy, and the Great Schism were also significant events. The period ended with the Renaissance, marked by renewed interest in classical art, literature, and humanism.
Renaissance (14th – 17th centuries):
- The Renaissance was a period of great cultural and intellectual growth. It saw advancements in art, science, philosophy, and literature. The rediscovery of classical texts and ideas had a transformative impact on European thought.
Reformation and Counter-Reformation (16th century):
- The Protestant Reformation, led by figures like Martin Luther and John Calvin, challenged the authority of the Catholic Church. This period also witnessed the Catholic Counter-Reformation in response to the spread of Protestantism.
Early Modern Period (17th – 18th centuries):
- The Early Modern Period included the scientific revolution, the Enlightenment, and the Age of Exploration. It marked a shift toward reason, empiricism, and secularism in Western thought.
Industrial Revolution (18th – 19th centuries):
- The Industrial Revolution brought about significant technological advancements, economic changes, and urbanization. It transformed societies from agrarian to industrial and had profound social and economic impacts.
19th Century and Nationalism:
- The 19th century saw the rise of nationalism, the spread of democratic ideals, and the industrialization of Western societies. It also witnessed significant political and social changes, including revolutions and the unification of several European states.
20th Century and Contemporary Era:
- The 20th century brought two world wars, the Cold War, significant technological advancements, and cultural shifts. The latter part of the century saw the collapse of the Soviet Union, the rise of globalization, and the digital revolution. The 21st century has been marked by ongoing technological, political, and social changes.

How religion was present during all these periods?

Again, broadly speaking and in a very summarized way:

Dogmas and creeds

Dogmas and creeds in Catholicism represent core beliefs that are considered divinely revealed and are not subject to change or debate within the official teachings of the Church. They serve as foundational elements of the faith, providing a doctrinal framework for Catholic theology. When practicing Catholicism, adherents are expected to accept and affirm these dogmas and creeds as expressions of the essential truths of the faith. The most important are:

Infallibility: The Catholic Church teaches the infallibility of certain dogmas, which means that they are considered free from error and irreformable. The infallibility is attributed to the teaching authority of the Church when it solemnly defines a doctrine concerning faith or morals.
Nicene Creed and Apostles’ Creed: The Nicene Creed and the Apostles’ Creed are two of the most well-known creeds in Catholicism. These creeds succinctly express fundamental beliefs about the Trinity, the Incarnation, and the role of the Church.
Doctrinal Stability: Dogmas and creeds provide stability to Catholic doctrine, ensuring continuity and consistency in the teaching of essential truths over time.
Liturgical Use: Creeds, such as the Nicene Creed, are regularly recited during the liturgy, emphasizing their central role in the worship life of the Church.

Rituals and liturgical practices

The “Rituale Romanum” plays a significant role in guiding the rituals and liturgical practices of the Catholic Church. This liturgical book provides priests with the rubrics, prayers, and ceremonial instructions for various sacraments and sacramentals. The rituals outlined in the “Rituale Romanum“ cover a wide range of religious ceremonies and rites, including:

Sacraments: The “Rituale Romanum” includes the rituals for administering the sacraments, such as baptism, confirmation, penance, the anointing of the sick, holy orders, and matrimony.
Sacramentals: This includes various blessings, consecrations, and rituals associated with objects, places, and events. Examples of sacramentals include the blessing of holy water, the consecration of a church or altar, and the blessing of religious articles.
Exorcisms: The “Rituale Romanum” contains prayers and rituals for the solemn rite of exorcism, used in cases where the Church determines that a person may be afflicted by demonic influence.
Funeral Rites: The book provides the liturgical instructions and prayers for funeral rites, including the celebration of Mass for the deceased and the commendation of the soul to God.
Various Blessings: The “Rituale Romanum” contains blessings for diverse situations and objects, such as blessings for a newly married couple, a house, crops, and religious medals.

In essence, the “Rituale Romanum” serves as a guidebook for priests in the administration of the Church’s sacraments and sacramentals, ensuring that these rituals are performed in accordance with the traditions and teachings of the Catholic Church. It provides the prescribed words, actions, and sequences to be followed during these sacred rites.

Dogmas and creed are not subject of discussion when practicing catholicism, what really shows up are the ritual and liturgical practices and the everyday life of the believer is formed by this, which does not depend on thoughts about dogmas and beliefs

How, then, the ritual ” fosters in men and women a civilizing pattern of behavior that the Latin Fathers of the Church called humanitas, which denotes not simply humanity or human nature but a refined warmth and courtesy.“?

Humanitas, pietas, Trivium and Quadrivium

Humanitas as an advance in pietas, in the opening lines of St Augustine’s Confessions makes clear, stating that we are most authentically human when we praise and give thanks to almighty God.

To this it should be added St. Augustine’s ideas about human nature

All that was said by St. Augustine around the 4th and 5th century and it would take a while to become standard, although in a much broader and secular way in the middle ages which was the Trivium and Quadrivium.

Trivium and Quadrivium were key components of the classical education system that influenced medieval education. These terms describe two sets of foundational subjects that formed the basis of liberal arts education during the Middle Ages:

Trivium:
- The Trivium consists of three core subjects that were considered essential for developing a well-rounded and educated individual. The three components of the Trivium are:
  - Grammar: In the context of the Trivium, grammar refers not only to language structure but encompasses the study of Latin and the correct usage of language. It provided the foundation for understanding and interpreting written texts.
  - Rhetoric: Rhetoric focuses on the art of persuasive communication, both in written and spoken form. Students of the Trivium learned how to express themselves effectively, argue persuasively, and engage in public discourse.
  - Logic: Logic involves the study of reasoning and argumentation. Students learned the principles of sound reasoning, critical thinking, and how to construct and analyze logical arguments.
- The Trivium aimed to equip students with the intellectual tools necessary for effective communication, critical thinking, and the interpretation of texts.
Quadrivium:
- The Quadrivium builds on the foundation of the Trivium and consists of four additional subjects, focusing more on mathematics and the sciences. The four components of the Quadrivium are:
  - Arithmetic: The study of numbers and basic mathematical operations.
  - Geometry: The study of shapes, sizes, and properties of space.
  - Music: In the context of the Quadrivium, the study of music involves understanding the mathematical principles underlying musical harmony and composition.
  - Astronomy: The study of celestial bodies and their movements.
- The Quadrivium aimed to provide students with a deeper understanding of the mathematical and scientific principles that govern the natural world.

These seven liberal arts, collectively known as the “seven liberal arts and sciences,” formed the core curriculum of medieval education. They were considered foundational for the cultivation of a well-rounded and intellectually competent individual. While the Trivium focused more on language and communication skills, the Quadrivium emphasized mathematical and scientific literacy. Together, they laid the groundwork for the education of scholars, theologians, and intellectuals during the medieval period.

I wrote an article in the local newspaper of my hometown where I try to connect all that with our 21rst century reality:

“Education focused on “Liberal Arts”, or “humanities” derives from the Renaissance Latin expression studia humanitatis, which means “study of the human”, aiming at culture, refinement, education and, specifically, an “education befitting a cultivated man”. At the beginning of the 15th century, the studia humanitatis was composed of the Trivium (3) and the Quaddrivium, (4). 3 + 4 = Seven Liberal Arts. Grammar, Logic and Rhetoric were the central liberal arts (the Trivium), Arithmetic, Geometry, Music Theory and Astronomy (Quadrivium) played a somewhat lesser role. Until the end of the Middle Ages, they were studied as “ways of doing things”. A major change occurred with the Renaissance Humanism of the 15th century through the emergence of modern languages, when the Humanities began to be considered as subject to study rather than practice, especially in traditional fields such as literature and history,

Science would take 15 centuries to be considered valid and be able to sit at the table of the educated, happening through the introduction by Galileo, when proposing for the first time (along with the Italian vernacular) what would become the standard for scientific thought, or that is, his thesis measuring Dante’s Inferno. Mathematics, at the time, was not considered worthy of appearing in what the elite of the time thought. In doing so, Galileo abandoned the mathematical tools of Science as a valid way of thinking and announced the separation of Science from Religion. “Scientific” thinking was completed by the influence of Descartes, with the introduction of his method and prevailed until the beginning of the 20th century.

In the 20th century, this view was challenged by the postmodernist movement, which sought to redefine the Humanities in egalitarian terms suitable for a democratic society, since the Greek and Roman societies in which the Humanities originated were not democratic. This shift in focus was in line with postmodernists’ view of themselves as the culmination of history. Perhaps the bias that humanities were dispensable is because the postmodernist movement at the end of the 20th century wanted to redefine Culture in utilitarian and democratic terms, since until then it was the privilege of the elite. There are many people in the Academy who stopped there, ignoring that the world has changed more in the last 30 years than in the entire previous century… All this is aggravated by the fact that Science, not by itself, but by those who use it, has determined itself as the correct way to understand and interpret reality. Completed by the perception in the first world that those educated in Humanities are unemployed or underemployed and those who study Exact Sciences do not need Humanities. This must change because work as Marx perceived it, which clearly always required contingents of educated people focused on exact sciences, is about to disappear due to the entry of Robots and Artificial Intelligence. This is giving way to a vast network of services, for which an education in the humanities is sinequanon. Until the end of this century, someone will question why anyone at any point thought of dispensing with the indispensable “Humanities”, or better yet, why someone has to understand them exactly, when all they need to do is learn how to use them with the help of a computer, something that I myself realized in the 2000s, when I taught classes, taking into account what personal computers were already doing and what iPhones were doing from 2007 onwards.”

Conclusion or final remarks

Going full circle, which I would say started with Confucius some 26 hundred years ago, I transcribe his words from the Analects:

Analects 1:12, 2:7, 3:8, 16:13, 17:19. where, the Confucian worldview goes so far as to consider the rule of law a measure necessary only for the barbaric. Civilized human beings do not need the force of law, only custom and ancestral ritual.

The concept that the rule of law is necessary only for the barbaric and civilized human beings would not need the force of law, only custom and ancestral ritual, whicch is present in the teachings found in the Analects of Confucius. While it’s important to note that the translation and interpretation of Confucian texts may vary, the general sentiment aligns with the idea that ethical conduct, guided by ritual and tradition, should be an internalized part of an individual’s character in a well-ordered society. (I could not have a better definition of education)

In several passages from the Analects, Confucius emphasizes the importance of moral cultivation, virtue, and the internalization of ethical principles. Custom (or ritual, “li” in Chinese) plays a significant role in shaping behavior, and it is expected that individuals adhere to proper conduct based on these traditional practices.

Analects 2:7:
- “The Master said, ‘Is it not a pleasure, having learned something, to try it out in practice? Is it not a joy to have friends come from afar? Is it not gentlemanly not to take offense when others fail to appreciate your abilities? Is it not gentlemanly not to take offense when others fail to appreciate your talents? Is it not gentlemanly not to take offense when others fail to recognize your merits? Is it not gentlemanly not to be impatient with others who lack your ability? Is it not gentlemanly not to have a mind for a problem that others do not see? Is it not gentlemanly not to be agitated when others fail to grasp the merits of your achievements? Is it not gentlemanly to have the strength to wait patiently when others take time to catch on?'”
Analects 12:1:
- “The Master said, ‘The gentleman is open and straightforward, while the small man is quibbling and biased.'”
Analects 12:22:
- “The Master said, ‘In language that is firm yet polite, and in a face that is friendly yet imposing, there is seldom any failure in demeanor.'”

These passages, among others, highlight Confucius’s emphasis on cultivating moral virtues, practicing proper conduct, and embodying the qualities of a true gentleman (Junzi). The underlying idea is that, in a society where individuals embody ethical values and ritual propriety, the need for external force, such as strict legal regulations, is minimized. The emphasis is on the internalization of moral principles through education, ritual, and personal reflection.

So, when we chalk write above the entrance door of our home the Theophany, celebrating the appearance of the one God most revered by the human kind, not by power of force, but by love and the bringing of His teachings, which are embedded in turning the world civilized in the way that was poorly discussed here,(my apologies).

Envelhecimento

See it in English

O envelhecimento é o efeito da passagem do tempo sobre tudo que existe, especialmente sobre os seres vivos.

Pássaros idosos – pressione e veja o video

Pássaros idosos não voam e não existem casas de repouso para pássaros. Portanto, os passarinhos mais jovens os alimentam. Essa é uma EXPRESSA mensagem para que seres humanos, senão conseguirem ser humanos, pelo menos exercitem o mesmo tipo de cuidado, como o fazem outros seres vivos ditos “inferiores”, que carregam em suas células Amor, Compaixão, Respeito, Fraternidade, União e Amor digno de um Cristão e que formam o eixo de uma atitude adequada.

Como e o que fazer seguindo o exemplo da natureza

Idosos

No nosso pais, legalmente, o idoso é que atinge 60 anos e embora nossa preocupação no que vai ser discutido aqui sejam pessoas com mais de 80 anos, é interessante ter em mente o Estatuto da Pessoa Idosa, sancionado através da LEI Nº 14.423, DE 22 DE JULHO DE 2022, que pode ser vista em detalhe neste documento oficial.

Deste Estatuto, os seguintes itens vão servir de base para estabelecermos como podemos enfrentar este problema dentro da nossa comunidade, especialmente a nível Municipal.

Conforme reza o conteúdo do Estatuto, os seguintes assuntos eventualmente serão resolvidos se conseguirmos uma solução adequada para o que nos propomos r

Cadastramento da população idosa em base territorial

II – atendimento geriátrico e gerontológico em ambulatórios;
III – unidades geriátricas de referência, com pessoal especializado nas áreas de geriatria e gerontologia social;

Conselho Municipal da Pessoa Idosa;

IV – Conselho Estadual da Pessoa Idosa;
V – Conselho Nacional da Pessoa Idosa.

Essência do Estatuto do Idoso

“Art. 20. A pessoa idosa tem direito a educação, cultura, esporte, lazer, diversões, espetáculos, produtos e serviços que respeitem sua peculiar condição de idade.” (NR)

“Art. 21. O poder público criará oportunidades de acesso da pessoa idosa à educação, adequando currículos, metodologias e material didático aos programas educacionais a ela destinados.

§ 1º Os cursos especiais para pessoas idosas incluirão conteúdo relativo às técnicas de comunicação, computação e demais avanços tecnológicos, para sua integração à vida moderna.

§ 2º As pessoas idosas participarão das comemorações de caráter cívico ou cultural, para transmissão de conhecimentos e vivências às demais gerações, no sentido da preservação da memória e da identidade culturais.” (NR)

“Art. 22. Nos currículos mínimos dos diversos níveis de ensino formal serão inseridos conteúdos voltados ao processo de envelhecimento, ao respeito e à valorização da pessoa idosa, de forma a eliminar o preconceito e a produzir conhecimentos sobre a matéria.” (NR)

‘Art. 46. A política de atendimento à pessoa idosa far-se-á por meio do conjunto articulado de ações governamentais e não governamentais da União, dos Estados, do Distrito Federal e dos Municípios.’ (NR)

O que diz o Estatuto para o Grupo que nos interessa, i.e., incapazes de cuidar de si mesmos

IV – serviço de identificação e localização de parentes ou responsáveis por pessoas idosas abandonados em hospitais e instituições de longa permanência;

V – proteção jurídico-social por entidades de defesa dos direitos das pessoas idosas;

VI – mobilização da opinião pública no sentido da participação dos diversos segmentos da sociedade no atendimento da pessoa idosa.’

Não existe nem pode existir Conselho Tutelar para Idosos

O Estatuto originado pela lei teve em mente a integração do Idoso na sociedade sem discriminação e com facilidades para facilitarem seus problemas naturais e existe um parecer do Conselho Nacional do Idoso esclarecendo isso, do qual extraimos:

O Estatuto do Idoso, em seu art. 7.°, prevê que os Conselhos Nacional, Estaduais, do Distrito Federal e Municipais do Idoso previstos na Lei n.° 8.842, de 04 de janeiro de 1994, que dispõe sobre a Política Nacional do Idoso, por sua vez, atribui aos Conselhos do Idoso a supervisão, o acompanhamento, a fiscalização e a avaliação da Política Nacional do Idoso nas respectivas instâncias administrativas, zelarão pelo cumprimento dos direitos do idoso.

Ao contrário, toda política do idoso e todas as reinvindicações dos movimentos de pessoas idosas são voltadas ao protagonismo e à autonomia da pessoa idosa. Por sinal, a 4.ª Conferência Nacional dos Direitos da Pessoa Idosa, realizada de 24 a 27 de abril de 2016, teve justamente o tema “Empoderamento e Protagonismo da Pessoa Idosa”. Portanto, a reinvindicação do segmento idoso não é de “tutela” ou “guarda”, e sim de reconhecimento e implementação de direitos.

Malgrado fato de o idoso não ser posto sob tutela, cabe esclarecer que, se o idoso, por causa transitória ou permanente, não puder exprimir sua vontade, ele deverá ser declarado Nota oficial de esclarecimento CNDI 0231616 SEI 00005.214336/2016-83 / pg. 2 relativamente incapaz, nos termos do art. 4.°, III, do Código Civil. Tal declaração somente poderá se dar em processo judicial de interdição, no qual é assegurado o direito de defesa. Se ao final do processo de interdição o juiz considerar o idoso relativamente incapaz, nomeará curador para o idoso e estabelecerá os limites da curatela.

Em suma: a tutela nunca se aplica à pessoa idosa. A pessoa idosa mantém sua capacidade civil. Caso a pessoa idosa não tenha condições de expressar sua vontade, deverá ser interditada e posta sob curatela, nos limites fixados pelo juiz.

O que acontece na prática

Os municípios criam

Fundo Municipal do Idoso	Conselho Municipal do Idoso

Lista completa para os Municípios do Estado de São Paulo, salientando S.João da Boa Vista e Vargem Grande do Sul

Vargem Grande do Sul

Criado em 2010 e não tem Fundo do Idoso

Endereço: Rua Major Correa, nº 485 – Centro CEP: 13.880-000
Telefone: (19) 3641-5509 Email: socialvgsul@gmail.com

Sao Joao da Boa Vista

Criado em 2014 tem fundo do Idoso

Endereço: Rua General Carneiro, 344 Centro CEP: 13.870-000
Telefone: (19) 3631-0301 R 213 Email: cmi@saojoao.sp.gov.br

Fundo do Idoso

Fundo Estadual do Idoso

O que é? O Fundo Estadual do Idoso se destina a financiar programas e ações voltadas à pessoa idosa, com o objetivo de assegurar os seus direitos sociais e criar condições para promover sua autonomia, integração e participação efetiva na sociedade.

Fundo Municipal do Idoso

O Fundo Municipal dos Direitos da Pessoa Idosa será gerenciado pela Secretaria Municipal a que se vincula o Conselho Municipal dos Direitos do Idoso, sendo de competência deste a deliberação sobre a aplicação dos recursos em programas, projetos e ações voltados à pessoa idosa. Existem muitos incentivos, principalmente sob o Imposto de Renda legalmente disponiveis.

Vargem Grande do Sul tem que promulgar a seguinte Lei para se beneficiar deste mecanismo

MINUTA DE LEI MUNICIPAL INSTITUIDORA DO FUNDO MUNICIPAL DOS DIREITOS DA PESSOA IDOSA

Cadastrar para poder fazer jus aos repasses vinculados as doacoes com uso do Imposto de Renda

Ter CNPJ com natureza jurídica de Fundo Público e situação cadastral ativa. Estar vinculado ao CNPJ com endereço do município ao qual está subscrito. Contar com uma conta bancária aberta em instituição financeira pública e associada ao CNPJ informado.

Plano Inicial para Solucionar o Problema

Criar um grupo “Ad Hoc” sob o Conselho Municipal do Idoso de Vargem Grande do Sul, que deve ficar sob o Departamento de Ação Social, mas que poderia ter uma existência independente como o fez o Município de Vargem Grande Paulista

Ad hoc significa “para esta finalidade“,“para isso” ou “para este efeito“. É uma expressão latina, geralmente usada para informar que determinado acontecimento tem caráter temporário e que se destina para aquele fim específico.
Um exame ad hoc, um método ad hoc ou uma função ad hoc são exemplos que definem a criação de algo provisório, que vai atender apenas determinado propósito.

Tarefas designadas a este grupo

Materializar o Fundo do Idoso de Vargem Grande do Sul sancionando a lei que esta descrita na Minuta
Verificar se da tempo para sensibilizar as empresas do Município a fazerem suas declarações do Imposto de Renda pensando em contribuir para este Fundo. Se não der tempo, deixar provisão. Acionar os Escritórios de Contabilidade ou os Departamentos encarregados das Declarações do Imposto de Renda nas empresas para esta possibilidade.
Conferir com S. João da Boa Vista como eles estão agindo
Fazer um levantamento estatístico do tamanho do grupo de pessoas que eventualmente poderiam ser contempladas pelas providências a serem tomadas
Verificar se Em S. João da Boa Vista e eventualmente outros municípios num raio de x klms existem estatísticas similares e como estão lidando com o Fundo Municipal do Idoso, quando existir e com o Conselho Municipal do Idoso, também quando existir.
A Prefeitura de Dracena e Região tem um projeto em andamento com estas características de levantamento para identificar a população atendida que pode ser vista pressionando o nome dela acima.
Observo que foi patrocinado e está sendo pago como projeto selecionado pelo Conselho Estadual do Idoso de São Paulo (CEI/SP) e da Secretaria Estadual de Desenvolvimento Social de São Paulo (SEDS). Pressionando-se em na sequência, temos uma lista dos projetos que foram aprovados que servem de referência com tipicamente o assunto é tratado pelas Prefeituras
Talvez seja um pouco cedo, mas poderia ser lançada a idéia de tornar a Vargem e Região num Polo de Atração para a Vivencia de Idosos, com oferta de espaços e incentivos fiscais, que geraria muitos empregos, consumo do comércio e industria da cidade e renda tanto para os envolvidos como os impostos. Duas hipóteses me ocorrem de imediato: Casas para Idosos e Comunidades de aposentadoria contínuas . No Brasil existem geralmente Casas de Idosos, e tem gente já interessada tentando trazer ao Brasil o modelo americano, como por exemplo A Dom Senior Living e a Garden Ville.
Um exemplo americano em que um amigo vive e testemunha favoravelmente.
No caso de ser examinado a hipótese de criar um Polo de Atração para a Vivência de Idosos as soluções indicadas foram para exemplificar e a escolha de uma que atendesse o que pretendemos teria que ser selecionada através de um estudo de caso especialmente feito para isso.
O que está inglês pode ser traduzido automaticamente bastando clicar o lado esquerdo do mouse ou tocar a tela e escolher. Pode ser criado em Português uma explicação como este projeto funciona.

Isto aqui foi um esboço para uma discussão inicial e gostaria de lembrar que nossos pais, Ana e Weimar, passaram os últimos anos da vida deles ai na Vargem. Tinham uma casa só para eles, com quatro cuidadoras, sendo 3 em turnos de 8 horas e uma para as folgas. Tinham um atendimento médico impecável ai no Hospital da Cidade. Tiveram um fim de vida invejável e claro que seu atendimento, dependeu muito da Maria Rosa e foi importantíssimo, mas sem a existência de um ambiente como o da Vargem, não seria possível a oportunidade de ouro que eles tiveram para terminar a vida de forma decente.

Para encerrar, devo mencionar que com o dinheiro que isto custou, aqui em Campinas, nossa cidade de origem, ou em S. Paulo, eles seria jogados em algum quarto dentro de alguma casa, e submetidos a um tratamento que prefiro não discutir, mas conheço bem pelas experiências de meus pares com seus pais.

Roque Ehrhardt de Campos (irmão de Maria Rosa de Campos Andrade)

Aging

Aging is the effect of the passing of time on everything that exists, especially on living beings.

The example of the wolves

The first 3 are the oldest or sickest and set the rhythm of the group. If it were the other way around, they would be left behind and lose contact with the pack. In the event of an ambush, they sacrifice their lives for the youngest.
They are followed by the 5 strongest who will defend them in a surprise attack.
In the center follow the other members of the pack, and at the end of the group follow the other 5 strongest who will protect the group.
Last, alone, follows the “alpha” wolf, the leader of the pack. In this position he can control everything around, decide the safest direction the group should follow and anticipate predator attacks.
In short, the pack follows the rhythm of the elders and under the command of the leader who imposes the group spirit, leaving no one behind.
“The true meaning of life is not to arrive first, but to arrive together at the same destination.”

Elderly birds – press and watch the video

Elderly birds cannot fly and there are no retirement homes for birds. Therefore, the younger birds feed them. This is an EXPRESS message so that human beings, if not able to be human, at least exercise the same type of care, as do other so-called “inferior” living beings, who carry in their cells Love, Compassion, Respect, Fraternity, Union and Love worthy of a Christian and which forms the axis of an appropriate attitude.

How and what to do following nature’s example

Elderly people

In our country, legally, the elderly are those who reach 60 years of age and although our concern in what will be discussed here are people over 80 years of age, it is interesting to keep in mind the Statute of the Elderly Person, sanctioned through LAW No. 14,423, DE JULY 22, 2022, which can be seen in detail in this official document.
From this Statute, the following items will serve as a basis for establishing how we can address this problem within our community, especially at the Municipal level.
As defined in the content of the Statute, the following issues will eventually be resolved if we achieve an adequate solution for what we propose.

From here on, I will not translate (you can automatically do it with Google) because it is a brazilian thing only interesting to us brazilians

Cadastramento da população idosa em base territorial

II – atendimento geriátrico e gerontológico em ambulatórios;
III – unidades geriátricas de referência, com pessoal especializado nas áreas de geriatria e gerontologia social;

Conselho Municipal da Pessoa Idosa