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The Nature of Light: Wave or Particle? An Analysis from Classical and Quantum Physics Wave–Particle Duality as a Profound Epistemological Break Wave–particle duality should not be understood as a simple coexistence of two descriptive models applied interchangeably, but rather as a radical epistemological rupture in the way modern science conceives the relationship between theory, reality, and observation. Prior to the twentieth century, physics relied on a relatively stable ontology: objects were assumed to possess well-defined properties independently of observation, and scientific theories aspired to describe those properties as they “really were.” Within the framework of classical physics, light had to be something: either a substance composed of particles or a continuous disturbance propagating through space. The impossibility of coherently reducing light to one of these categories not only destabilized optics, but also challenged the very ideal of scientific objectivity inheri...

  Naturaleza de la luz: ¿Onda o partícula?  Un análisis desde la física clásica y cuántica

  What Are Conventions and What Are They For? Social, Cultural, and Institutional Functions of Human Agreements Introduction: Why Talking About Conventions Matters Human societies are not sustained solely by written laws or by the direct coercion of political power. A large part of everyday social life—from how we greet one another to how we interpret a legal document or participate in a public ceremony—is organized through conventions : shared agreements, often implicit, that establish common expectations about behaviors, meanings, and procedures. Understanding what conventions are and what they are for means engaging with a fundamental dimension of social order that often goes unnoticed precisely because it functions effectively: when conventions work, they remain invisible; when they fail, conflict emerges. This article approaches conventions from a social sciences perspective, integrating sociological, historical, legal, and cultural frameworks. It does not limit itself to o...

  ¿Qué son las convenciones y para qué sirven? Función social, cultural e institucional de los acuerdos humanos Introducción: por qué hablar de convenciones importa Las sociedades humanas no se sostienen únicamente sobre leyes escritas ni sobre la coerción directa del poder político. Gran parte de la vida social cotidiana —desde la forma en que saludamos hasta la manera en que interpretamos un documento jurídico o participamos en una ceremonia pública— se organiza a través de convenciones : acuerdos compartidos, a menudo implícitos, que establecen expectativas comunes sobre comportamientos, significados y procedimientos. Comprender qué son las convenciones y para qué sirven implica adentrarse en una dimensión fundamental del orden social que suele pasar desapercibida precisamente porque funciona con eficacia: cuando las convenciones operan, no se notan; cuando fallan, el conflicto emerge. Este artículo aborda las convenciones desde una perspectiva de ciencias sociales, integrando e...

  How to Teach Mathematics: Pedagogical Foundations, Educational Challenges, and Didactic Strategies Reading Guide This article can be read continuously or by sections. The following reading guide is provided to help orient readers according to their interests: Mathematics teaching as a historical and cultural issue What it really means to teach mathematics Learning difficulties beyond individual deficit Pedagogical strategies and educational meaning Assessment, power, and inequality in mathematics education Teacher education and professional practice Teaching mathematics in unequal contexts Final reflections and conclusions

Differences Between Virtual Classes and Homeschooling: A Critical Educational Analysis Part I — Conceptual Foundations and Historical Background An in-depth academic analysis of the differences between virtual classes and homeschooling, exploring history, power, inequality, and educational models. Introduction In recent years, the terms virtual classes and homeschooling have been increasingly used as if they referred to the same educational phenomenon. Public debates, media narratives, and even institutional discourses frequently blur the distinction between these two modalities, presenting them as interchangeable responses to contemporary educational challenges. However, this apparent similarity conceals profound differences in their conceptual foundations, institutional logics, and social implications . This article argues that virtual classes and homeschooling are not merely alternative pedagogical formats, but distinct ways of organizing education in relation to the State, th...

  Cómo dar clases de matemáticas: fundamentos pedagógicos, desafíos educativos y estrategias didácticas  Guía de lectura Este artículo puede leerse de forma continua o por secciones. A continuación se presenta una guía para orientar la lectura según tus intereses: La enseñanza de las matemáticas como problema histórico y cultural Qué significa realmente enseñar matemáticas Dificultades en el aprendizaje matemático más allá del déficit individual Estrategias pedagógicas y sentido educativo Evaluación, poder y desigualdad en la educación matemática Formación docente y práctica profesional Enseñar matemáticas en contextos de desigualdad Reflexiones finales y conclusiones

  The Christmas Lantern  —  Version for children aged 13 to 15 years   December slowed the town of San Jacinto. Not because of the lights, but because people seemed more aware of one another. The lantern in the square had been restored that year. Anyone could place a wish inside—no names, no explanations. Luna stood in line with her grandmother, watching impatience ripple through the crowd. She felt it too. The cold, the waiting, the quiet pressure to move faster. Ahead of her, a younger child struggled to write. The pencil scratched faintly. A pause stretched longer than expected. Luna considered stepping forward. It would be easy. Instead, she stayed where she was. She handed over her pencil and held the silence. The child wrote slowly, carefully, as if time itself had softened. When the lantern lit up, the light didn’t promise anything extraordinary. It simply stayed on. Luna understood that some gestures don’t shine loudly—but they remain.  

  El farol de la noche — Para público de  13 a 15 años San Jacinto cambiaba cada diciembre. No solo por las luces, sino por el ritmo distinto de las personas, como si el tiempo aceptara caminar más lento. El farol de la plaza era una tradición recuperada. Restaurado con paciencia, invitaba a dejar deseos anónimos, sin nombres, sin expectativas. Luna observaba la escena con atención. La fila avanzaba con irregularidad. Había murmullos de prisa. Cuando estuvo cerca, notó a un niño pequeño incapaz de escribir con claridad. Algunos evitaban mirarlo. Luna sintió la incomodidad de la espera. Pensó en su propio deseo, en lo fácil que sería adelantarse. En cambio, se quedó. Le tendió su lápiz y sostuvo el silencio como un gesto. El niño escribió despacio, como si ese tiempo también fuera un regalo. Al encenderse el farol, la luz no prometía milagros. Pero iluminaba lo suficiente. Luna comprendió que el respeto no siempre se nota, pero deja huella.

  The Christmas Lantern — Version for children aged 8 to 12 years   Christmas Eve changed the rhythm of San Jacinto. Lights softened the streets, and people spoke more quietly. That year, an old lantern stood in the town square. Families could place a written wish inside before nightfall. Luna arrived with her grandmother as the sky turned orange. The line moved slowly. Luna felt impatient. She wanted to write her wish before it got dark. Then she noticed a younger child ahead of her. The child struggled to write. The pencil barely marked the paper. Someone behind sighed. Luna hesitated. She could move ahead. Instead, she stayed. She offered her pencil and waited without speaking. The child wrote carefully and smiled when finished. When the lantern finally lit up, its glow wasn’t bright, but it was steady. Luna felt calm. Waiting had mattered.

    El farol de la noche — Para niños y niñas de 8-12 años La Nochebuena siempre transformaba el pueblo de San Jacinto. Las calles se llenaban de luces, las ventanas olían a canela y las voces parecían hablar más despacio. Ese año, la plaza tenía algo especial: un farol antiguo restaurado por las personas mayores del pueblo. La idea era sencilla. Cada quien podía dejar dentro un deseo escrito, y al anochecer el farol se encendería como símbolo de encuentro. Luna llegó con su abuela poco antes del atardecer. Observó la fila de personas esperando. Algunos se impacientaban, otros conversaban en silencio. Luna sentía prisa. Quería escribir su deseo antes de que oscureciera. Cuando avanzó, notó a un niño que no lograba escribir. Su papel estaba arrugado, y sus manos temblaban un poco. Detrás, alguien suspiró con molestia. Luna dudó. Podía pasar primero. Nadie lo impediría. Pero se quedó. Le ofreció su lápiz y esperó sin decir nada. El niño levantó la mirada, sorprendido. Escribió c...

                           The Christmas Lantern   The Christmas Lantern —  Version for children aged 5 to 7 years   Christmas Eve arrived softly in the town of San Jacinto. Tiny lights blinked in the square, and the air smelled sweet and warm. Luna walked beside her grandmother, holding her hand. In the middle of the square stood a lantern. It wasn’t big, but it was special. Everyone could place a small wish inside. Luna wanted to go first. She stepped closer, but her grandmother gently slowed down. They waited. In front of them, a small child tried to write a wish. The pencil didn’t work well. The paper wrinkled. Luna looked at her own pencil. Then she held it out. The child smiled and finished writing. That night, when the lantern lit up, the light felt warm. Luna smiled too. Christmas felt brighter.