Science, Time, and Spirit

Entropy and Jigsaw Puzzle Solving: A Framework for Understanding Problem-Solving Strategies  Entropy and Jigsaw Puzzle Solving: A Framework for Understanding Problem-Solving Strategies Abstract This paper examines the relationship between entropy, information theory, and jigsaw puzzle solving strategies, proposing that puzzle assembly represents a microcosm of general problem-solving methodologies. Through analysis of various puzzle-solving techniques—from edge-first approaches to color clustering and shape matching—we demonstrate how entropy reduction serves as a fundamental organizing principle in both specific puzzle contexts and broader cognitive problem-solving frameworks. The paper argues that jigsaw puzzles provide an accessible model for understanding how humans navigate complex problem spaces through systematic entropy reduction, offering insights applicable to diverse domains including artificial intelligence, project management, and scientific methodology. ...

Sixty Years Later: The Untold Story Behind Vatican II's Suppression of the St. Michael Prayer How a single line in a 1964 liturgical instruction eliminated a worldwide Catholic devotion—and why it's making a comeback VATICAN CITY — On September 26, 1964, with just eight words buried in a technical liturgical document, one of the Catholic Church's most beloved prayers effectively disappeared from Sunday worship around the world. "The last gospel is omitted; the Leonine Prayers are suppressed," read the terse directive in Inter Oecumenici , an instruction implementing the liturgical reforms of the Second Vatican Council. With that simple statement, the Prayer to St. Michael the Archangel—composed by Pope Leo XIII in 1886 and recited by millions of Catholics after Mass for nearly eight decades—was quietly removed from the universal liturgy. A Prayer Born from Papal Vision The prayer's origins trace back to what Pope Leo XIII described as a terrifyin...