travelogues & articles

"Back-of-the-envelope calculations" is an idiomatic expression that refers to rough or informal calculations, typically done quickly and without extensive analysis, using readily available information and minimal assumptions. The term originates from the idea of performing calculations on the back of an envelope or a scrap piece of paper, rather than using more formal or detailed methods. Here are the key characteristics and meanings associated with "back-of-the-envelope calculations": Informal and Approximate: These calculations are not meant to be precise or highly accurate. They are rough estimates that provide a quick and general sense of the magnitude or feasibility of a certain idea, project, or problem. Simplicity: The emphasis is on simplicity and speed. The goal is to obtain a rough answer without delving into complex or time-consuming mathematical or analytical processes. Readily Available Information: Back-of-the-envelope calculations rely on easily ...

"Un bel dì vedremo" is a renowned aria from Giacomo Puccini's opera "Madama Butterfly," also known simply as "Madame Butterfly." The opera is an Italian tragedy in three acts with a libretto by Luigi Illica and Giuseppe Giacosa. It was first performed in 1904 and is one of Puccini's most celebrated works. Plot Summary: "Madama Butterfly" is set in Nagasaki, Japan, in the early 20th century. The opera tells the story of Cio-Cio-San, a young Japanese woman, and B.F. Pinkerton, an American naval officer. Pinkerton marries Cio-Cio-San, known as Butterfly, in a ceremony that he treats lightly, as he plans to return to the United States. Butterfly, however, takes the marriage seriously and believes that Pinkerton will come back to her. Aria Context: "Un bel dì vedremo" is sung by Cio-Cio-San in Act 2 of the opera. At this point, Pinkerton has left Japan and Butterfly is awaiting his return. She has been waiting for three years, dur...

"Pace, mio dio!" is an aria from Giuseppe Verdi's opera "La forza del destino" (The Force of Destiny). The opera is known for its dramatic and complex storyline. Here is the story in detail behind "Pace, mio dio!" and its context within the opera: Setting: "La forza del destino" is set in Spain and Italy in the 18th century. The opera's plot revolves around the fateful events that befall the two main characters, Leonora and Don Alvaro. Characters: Leonora: The opera's heroine, in love with Don Alvaro. Don Alvaro: A nobleman from South America, Leonora's lover. Don Carlo di Vargas: Leonora's brother, who seeks to avenge his family's honor. Padre Guardiano: The friar who plays a pivotal role in the characters' destinies. Plot: The aria "Pace, mio dio!" is sung by Leonora in Act IV of the opera. By this point in the story, the characters' lives have been tragically intertwined, and the consequences of t...