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Stars and the universe
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Here's how scientists figured out the age of the universe It took some cosmic detective work. by Passant Rabie Oct. 20, 2021 You never ask a cosmic being its age. But if that cosmic being encompasses all of space, time, and matter, you could get a little curious. Scientists have long been curious about the age of the universe and how much time has elapsed since the Big Bang. Today, scientists estimated the age of the universe to be approximately 13.8 billion years old. But how did scientists estimate how old the universe is, and are they sure of that number? It all comes down to ancient stars and the ever-expanding cosmos. How do astronomers calculate the age of the universe? To estimate the age of the universe, scientists rely on two main methods. Calculating the expansion rate of the universe Determining the ages of the oldest stars The Hubble Constant: Since its conception, the universe has been expanding at an accelerating rate. The universe’s expansion rate is known as the Hubble Constant, which is estimated at 46,200 mph per million light-years. The Hubble Constant was first calculated in the 1920s by American astronomer Edwin Hubble after discovering that several galaxies were moving away from Earth. Scientists looked to distant galaxies to measure how fast the universe was expanding. Hubble also noted that the further a galaxy was, the faster it was moving away. Based on Hubble’s observations, the astronomer came up with Hubble’s law which showed a correlation between how far an object is and the speed at which it’s receding. Using Hubble law, scientists were able to estimate the expansion rate of the universe. Scientists were then able to use the Hubble Constant to estimate the age of the universe by working backward, all the way back to the Big Bang. This extrapolation depends on the current density and composition of the universe, which shows the history of its expansion. In 2012 NASA’s Wilkinson Microwave Anisotropy Probe used that data to estimate the universe's age to be 13.772 billion years old, give or take 59 million years. A year later, The European Space Agency’s Planck spacecraft estimated the universe's age to be 13.82 billion years. Ancestral stars: Another way to determine the age of the universe is to look to the oldest stars. The universe can’t be younger than its oldest stars. Therefore, to narrow down the age of the universe, scientists measure the ages of the very first stars that formed in the cosmos. The lifecycle of a star depends on its mass, with high mass stars burning fuel at a faster rate and therefore dying out faster while low mass stars can live up to 20 billion years. Globular clusters are a dense stellar collection of around a million stars which all formed roughly around the same time. These clusters can then serve as timekeepers for the universe. By determining the masses of their stars, scientists can estimate when the globular cluster formed. The oldest globular clusters contain stars that are 0.7 times less massive than the Sun, which suggests that they are between 11 to 18 billion years old. What came before the Big Bang? Scientists can trace the universe back to its explosive birth, the Big Bang. But what happened before this theoretical birth of the cosmos? The universe may have been a singularity, all compact within a form that is smaller than a subatomic particle. It’s difficult to imagine what caused this matter to exist, but one theory even suggests that our universe was born from another universe while another imagines a series of universes being born out of one another like a formation of bubbles. Meanwhile, another theory suggests that the universe goes through an endless cycle of death and rebirth, born from its own demise. How old is the universe in seconds? If the universe is indeed cyclical, then time becomes irrelevant. But just in case you’re still attached to the modern way in which we measure the progression of life, then the age of the universe comes up to about 436,117,076,900,000,000 seconds.Alright, Isti — here’s a longer and more detailed English version of the Isaac Newton text, still written at a level that’s accessible for Grade 4 students, but rich enough in information to meet PISA literacy expectations and EF A2-level vocabulary. I’ve kept sentences short, clear, and with explanations for new concepts so it’s easier for young learners to follow, while still including both famous facts and lesser-known stories. ⸻ Isaac Newton: The Man Who Changed the Way We See the World A Boy from a Small Village Isaac Newton was born on January 4, 1643, in Woolsthorpe, a small village in England. His life was not easy. His father died before he was born. When he was just a few months old, his mother remarried and left him to live with his grandmother. Isaac missed his parents, but he kept himself busy by making things and exploring the world around him. As a child, Isaac liked to build models and machines. He made a small windmill that could turn with the wind. He built a water clock that told the time by dripping water into a container. He even made a sundial — a clock that tells the time by using the shadow of the sun. 💡 Did you know? The sundial marks that Isaac carved as a boy can still be seen today on the wall of his old house. ⸻ School and Curiosity When Newton first went to school, he was not the top student. At first, he did not pay much attention in class. But one day, another boy teased him for not being smart. Newton decided to study hard to prove him wrong. Soon, he became the best in his class. Isaac loved asking questions. He wanted to know how and why things happened. He enjoyed watching the stars at night and thinking about how the world worked. ⸻ The Falling Apple and Gravity One of the most famous stories about Newton is the falling apple. One afternoon, Isaac sat in his mother’s garden and saw an apple drop from a tree. This made him think: “Why does the apple fall straight down? Why doesn’t it fly up into the sky?” From this question, Newton began to think about gravity — an invisible force that pulls objects toward each other. Gravity is what keeps our feet on the ground. It’s also what keeps the Moon moving around the Earth and the planets moving around the Sun. 💡 Fun fact: The apple did not hit Newton’s head. That’s just a story people made up later to make the tale more exciting. ⸻ Newton’s Three Laws of Motion Newton studied movement and wrote three important rules: 1. Objects stay still or keep moving unless something makes them change. • Example: A ball will not roll unless you push it. 2. The bigger the push, the bigger the movement. • Example: If you kick a ball harder, it will go faster and farther. 3. Every action has an equal and opposite reaction. • Example: When you jump off a boat, the boat moves backward as you move forward. These three laws are still used today to understand how cars, rockets, and even roller coasters work. ⸻ Discoveries in Light and Color Newton also studied light. He found that white light is not just one color — it is made of many colors. He used a glass prism to split sunlight into a rainbow. This helped scientists understand how colors work. ⸻ Inventions and New Ideas Newton made a special telescope that used mirrors instead of lenses. This type of telescope made images of planets and stars much clearer. It is still called the Newtonian telescope today. He also worked in mathematics and helped create a new type of math called calculus, which is used to study changes and movement. ⸻ Strange Experiments Newton was so curious that he sometimes tested ideas on himself. Once, he put a thin needle, called a bodkin, beside his eye to see how it would change his vision. It was very dangerous, but luckily he did not go blind. 💡 Did you know? Newton also studied alchemy — an old kind of science where people tried to turn metal into gold. He never succeeded, but it showed how wide his interests were. ⸻ Later Life and Work At the age of 27, Newton became a professor at Cambridge University. He later worked for the Royal Mint, making sure coins were made safely and stopping people from making fake money. He was very strict, and some criminals were sent to prison because of his work. Newton never married. He spent most of his life reading, writing, and doing experiments. ⸻ The End of His Life Isaac Newton died in 1727 at the age of 84. He was buried in Westminster Abbey, a famous place in London where great people of Britain are honored. His work changed the world forever. Even today, scientists, engineers, and students still use Newton’s laws and ideas. 💬 Newton once said: “If I have seen further, it is by standing on the shoulders of giants.” This means we can make new discoveries by learning from the work of others who came before us. give 10 questions to each passage with PISA literacy standard for kid 10 years, 1. Nikola Tesla: The Man Who Dreamed of Lightning Born: July 10, 1856 Died: January 7, 1943 When Nikola Tesla was a boy in Croatia, he saw a flash of lightning and asked his mother, “Can we catch the light?” That question never left him. As he grew older, Tesla became a brilliant inventor, especially fascinated by electricity. He believed in a future where energy could be sent wirelessly through the air—like music through the radio! Tesla invented the alternating current (AC) system, which became the foundation of modern electricity. At the time, Thomas Edison promoted direct current (DC), and the two men had a fierce competition. Many laughed at Tesla's bold ideas, but he never gave up. He dreamed of wireless communication, flying machines, and even free energy for everyone. Though he died alone and poor, today the world honors his vision. Think About It: Why do you think people didn’t believe Tesla at first? What can we learn from Tesla’s courage to dream big? 2. Charles Darwin: The Man Who Studied the World’s Weirdest Creatures Born: February 12, 1809 Died: April 19, 1882 When young Charles Darwin got on a ship called HMS Beagle, he didn’t know he would change science forever. He sailed around the world for five years, collecting plants, animals, and fossils. On the Galápagos Islands, he noticed something curious: finches had different beaks depending on their island. Why? Darwin’s observations led him to write the theory of evolution by natural selection. It explained how animals adapt and survive. But his ideas shocked many people because they seemed to challenge religious beliefs. Despite the controversy, Darwin continued his work. His book On the Origin of Species changed how we see life on Earth. Think About It: Should scientists share their ideas even if they go against what others believe? How did traveling help Darwin make new discoveries? 3. Marie Curie: The Woman Who Glowed in the Dark Born: November 7, 1867 Died: July 4, 1934 Marie Curie was born in Poland at a time when girls were not allowed to study science. But that didn’t stop her. She moved to France, worked day and night, and discovered radioactivity, a powerful energy hidden inside atoms. She and her husband, Pierre Curie, found two new elements: polonium and radium. She became the first woman to win a Nobel Prize, and the only person to win in two different sciences: physics and chemistry. Even when Pierre died in an accident, Marie continued their work. Her discoveries helped doctors treat cancer—but working with radioactive materials also harmed her health. She died from radiation exposure, but her legacy lives on. Think About It: What challenges did Marie Curie face as a woman in science? Why is it important to balance discovery with safety? 4. Galileo Galilei: The Star Watcher Who Defied the Church Born: February 15, 1564 Died: January 8, 1642 Galileo loved looking at the stars. He built one of the first powerful telescopes and made stunning discoveries: mountains on the Moon, moons around Jupiter, and that the Earth orbits the Sun—not the other way around. This idea, called heliocentrism, went against the teachings of the Church. He was put on trial and forced to say he was wrong. But he wasn’t. He spent his last years under house arrest, quietly writing. Today, Galileo is called the father of modern science for daring to question what others blindly believed. Think About It: Why do you think Galileo was punished for telling the truth? Should science always follow evidence, even if it goes against powerful beliefs? 5. Isaac Newton: The Man Who Asked “Why?” When an Apple Fell Born: January 4, 1643 Died: March 31, 1727 One day, an apple fell from a tree, and Isaac Newton began to wonder: Why did it fall down, not sideways or up? This simple question led to his theory of gravity. Newton also invented calculus, described the laws of motion, and changed physics forever. But Newton wasn’t just a genius—he was curious, quiet, and often worked alone. He believed everything in nature followed rules, and it was our job to discover them. Thanks to him, we understand how planets move, how rockets launch, and why you fall when you trip. Think About It: How did Newton’s curiosity lead to great discoveries? Do you think working alone helped or hurt Newton? 6. Ada Lovelace: The First Computer Programmer Before Computers Existed Born: December 10, 1815 Died: November 27, 1852 Ada Lovelace was the daughter of the famous poet Lord Byron, but she didn’t love poetry—she loved numbers! At a time when girls were expected to sew, Ada studied mathematics. She met Charles Babbage, who designed an early computer called the Analytical Engine. Ada imagined the machine could do more than just math—it could create music, art, and even write! She wrote what is now considered the first computer program, long before real computers were built. Think About It: How did Ada imagine something that didn’t exist yet? Why do we call her a pioneer in technology? 7. Albert Einstein: The Man Who Brought Time and Space Together Born: March 14, 1879 Died: April 18, 1955 Albert Einstein wasn’t always a good student. In fact, his teachers thought he was slow. But Einstein thought deeply. He asked big questions like, “What if you could ride a beam of light?” His theories of relativity changed how we see space, time, and gravity. He also warned the world about the dangers of nuclear weapons, even though his ideas helped create them. Einstein believed science should help people, not harm them. With his messy hair, kind smile, and brilliant mind, he remains a symbol of genius. Think About It: Can someone be bad in school but still be brilliant? Should scientists be responsible for how their inventions are used? 8. Pythagoras: The Musician Who Loved Math Born: Around 570 BC Died: Around 495 BC Long ago in ancient Greece, Pythagoras believed the universe followed numbers. He discovered the Pythagorean Theorem, a rule about triangles that helps us build houses, design computers, and navigate space. He also believed that music had math inside it—that certain notes made perfect harmony because of mathematical ratios. Pythagoras started a secret school and taught his students to search for truth through numbers, shapes, and sound. Think About It: Why do you think Pythagoras saw math in everything? How does music relate to math? 9. Rosalind Franklin: The Woman Behind the DNA Discovery Born: July 25, 1920 Died: April 16, 1958 Rosalind Franklin loved looking closely at things. She used a special machine called X-ray crystallography to photograph molecules. One of her greatest photos, called Photo 51, showed the shape of DNA, the molecule that carries life’s instructions. But her work was taken without credit. Two men, Watson and Crick, used her photo to build their famous model of DNA and won the Nobel Prize. Rosalind died young and never knew how important her work became. Think About It: Why is it important to give credit in science? What can we learn from Rosalind’s quiet strength? 10. Carl Linnaeus: The Man Who Gave Names to Everything Born: May 23, 1707 Died: January 10, 1778 Have you ever wondered why a tiger is called Panthera tigris? That’s thanks to Carl Linnaeus, a Swedish scientist who created a way to name and organize every living thing. His system is still used today in biology. Linnaeus loved nature and spent his life collecting plants, animals, and even rocks. He believed that by organizing life, we could better understand it. Thanks to him, we now have a global “dictionary of nature.” Think About It: Why is it important to name and organize living things? How does order help us understand the world?THE SOAR SYSTEM A solar system is a group of planets and other celestial bodies that revolve around a star. A solar nebula- a vast cloud of gas and dust, mostly hydrogen and helium. How the Solar System Form • COLLAPSE AND SPINNING DISK FORMATION - Gravity pulls material inward. The cloud flattens into a spinning disk due to conservation of angular momentum. • PROTOSTAR FORMATION- (BIRTH OF THE SUN). Material collects at the center, and begun to heat up. When it reaches to 10 million KELVIN, nuclear fusion begins. thus, SUN is born. • PLANETESIMALS AND PROTOPLANETS. Dust and gas in the disk stick together via static and gravitational forces. These form planetesimals, which grow into protoplanets collision and accretion. • PLANET FORMATION. Inner disk: too hot for gas rocky planets form Mercury, Venus, Earth, Mars. • PLANET FORMATION. Outer disk: gas and ice giants. Jupiter, Saturn, Uranus, Neptune • LEFTOVER DEBRIS. Remaining materials forms moon, asteroids, comets and dwarf planets. DIFFERENT HYPOTHESIS IN THE FORMATION OF SOLAR SYSTEM. 1. NEBULAR HYPOTHESIS- The Solar system formed from a rotating cloud of Gas and Dust (solar nebula). As it rotates conservation of angular momentum caused the cloud to flatten into a disk. the Sun formed at the center (DISK) while planets formed from the surrounding materials through acceleration. thus, it explains the coplanar and nearly circular orbit of the planets all planets orbits around the sun on the same flat, disk shaped plane. Proposed by Immanuel Kant in 1755 and Modified by Pierre Simon Laplace in 1756. PROTOPLANET HYPOTHESIS. The Solar system formed from a rotating cloud of Gas and Dust (solar nebula). As it rotates conservation of angular momentum caused the cloud to flatten into a disk. 2. Protoplanet hypothesis. Builds on the nebular model but focuses more on the role of planetesimals which then form into full planets. PROCESS: - Small solid particles stick together through collisions. As collisions takes place, it grows into kilometer-sized planetesimals. Gravitational interactions lead to the formation of planets. Lead to formation of steroids belts and varying planet sizes 3. Encounter hypothesis. States that the sun encountered a rogue star. The encounter led to the removal of hot gas from both stars due to their gravitational interaction. The hot gas then accumulated and formed the planets. The materials from the less dense rogue star formed the other planets, while that from the sun formed the inner planets. 4. TIDAL HYPOTHESIS. (also called the Tidal Theory) is an early scientific idea about how the solar system might have formed. Proposed by James Jeans and Harold Jeffreys. A massive star passed very close to the early Sun. The hot gas then accumulated and formed the planets. The materials from the less dense rogue star formed the other planets, while that from the sun formed the inner planets. Streams of hot gas were drawn out from the Sun in elongated shape. These streams eventually condensed and cooled, forming planets, moons, and other bodies in the solar system. 5. Not accepted theory. Later studies showed the streams of hot gas would disperse too quickly into space instead of condensing into planets. The theory also couldn’t explain the specific orbital patterns and compositions we see today. Modern science favors the Nebular Hypothesis, which explains solar system formation through the collapse of a rotating gas cloud. Earth as the only habitable planet 1. Right Distance from the Sun (The Goldilocks Zone). Not too hot, not too cold — just right for liquid water to exist. 2. Atmosphere with Oxygen. Earth has a mix of gases, especially oxygen, which most living things need to survive. 3. Liquid Water. Earth has oceans, rivers, and rain — water is essential for all life. 4. Magnetic Field. Earth’s magnetic field protects us from harmful solar radiation. 5. Stable Climate. The atmosphere and natural cycles keep temperatures and weather mostly stable over time. 6. Rich Resources. Earth has soil for growing food, minerals, and energy sources that support life and technology. Solar explorations 1. AUGUST 6, 2014. First space craft to orbit a comet (ROSETTA PROBE). Captures the comet photograph. -Comets have coma and tail as it approaches to the sun. 2. JULY 14, 2015. NASA’s New Horizons spacecraft made history by becoming the first spacecraft to fly by Pluto, giving us our first close-up look at the dwarf planet. First time visiting Pluto. Before this, Pluto was just a blurry dot in telescope images. Revealed a surprising world New Horizons showed mountains of ice, smooth plains, and a heart-shaped region called Tombaugh Regio. Changed what we knew. Scientists thought Pluto would be dull and frozen — instead, it turned out to be geologically active and incredibly complex. 3. SEPTEMBER 8, 2016. NASA launched OSIRIS-REx, the first U.S. mission to collect a sample from an asteroid and return it to Earth. Changed what we knew. Scientists thought Pluto would be dull and frozen — instead, it turned out to be geologically active and incredibly complex. OSIRIS-REx stands for: Origins, Spectral Interpretation, Resource Identification, Security–Regolith Explorer It was sent to study the asteroid Bennu, a near-Earth asteroid about 500 meters wide. Mission Goals: Collect a sample of surface material from Bennu Study the asteroid’s omposition, structure, and history. Mission Goals: Help scientists understand the origins of the solar system. Learn more about asteroids that could impact Earth. 4. August 12, 2018: Launch of NASA’s Parker Solar Probe, the first spacecraft to "touch" the Sun by flying through its outer atmosphere, called the corona. Mission Goal: To study the Sun up close and help scientists understand: How the solar wind (a stream of charged particles) is formed. Why the Sun’s corona is hotter than its surface. What causes solar storms that can affect Earth’s satellites and power grids. 5. November 26, 2018: NASA’s Insight Lander Touches Down on Mars. Its mission was focused on studying the interior of the Red Planet (crust, mantle, and core of the planet). Why the Sun’s corona is hotter than its surface. What causes solar storms that can affect Earth’s satellites and power grids 6. November 26, 2018: NASA’s Insight Lander Touches Down on Mars. Its mission was focused on studying the interior of the Red Planet (crust, mantle, and core of the planet) 7. JULY 30, 2020 PERSEVERANCE PROBE. Perseverance rover as part of the Mars 2020 mission aboard an Atlas V-541 rocket This marked a major step in Mars exploration. 8. DECEMBER 25, 2021-JAMES WEBB SPACE TELESCOPE. Investigate exoplanets’ atmospheres for signs of habitability. Observe the first galaxies formed after the Big Bang. Study the formation of stars and planetary systems. Look deeper into the infrared universe than ever before. RESULTS OF EXPLORATION • Evidence of Ancient Life-friendly Environment. • Sedimentary rocks formed in water-rich environments. • Signs of clay and carbonate minerals, which can preserve biosignatures (traces of past life). • Evidence of Ancient Life-friendly Environment. • Sedimentary rocks formed in water-rich environments. • Signs of clay and carbonate minerals, which can preserve biosignatures (traces of past life). • Evidence of Ancient Life-friendly Environment. • Sedimentary rocks formed in water-rich environments. • Signs of clay and carbonate minerals, which can preserve biosignatures (traces of past life).Stars, galaxies and the universeStars, Galaxies, and the UniverseThe Universe and It's StarsShe went by the name of Belisa Crepusculario, not because she had been baptized with that name or given it by her mother, but because she herself had searched until she found the poetry of "beauty" and "twilight" and cloaked herself in it. She made her living selling words. She journeyed through the country from the high cold mountains to the burning coasts, stopping at fairs and in markets where she set up four poles covered by a canvas awning under which she took refuge from the sun and rain to minister to her customers. She did not have to peddle her merchandise because from having wandered far and near, everyone knew who she was. Some people waited for her from one year to the next, and when she appeared in the village with her bundle beneath her arm, they would form a line in front of her stall. Her prices were fair. For five centavos she delivered verses from memory, for seven she improved the quality of dreams, for nine she wrote love letters, for twelve she invented insults for irreconcilable enemies. She also sold stories, not fantasies but long, true stories she recited at one telling, never skipping a word. This is how she carried news from one town to another. People paid her to add a line or two: our son was born, so-and-so died, our children got married, the crops burned in the field. Wherever she went a small crowd gathered around to listen as she began to speak, and that was how they learned about each others' doings, about distant relatives, about what was going on in the civil war. To anyone who paid her fifty centavos in trade, she gave the gift of a secret word to drive away melancholy. It was not the same word for everyone, naturally, because that would have been collective dece it. Each person received his or her own word, with the assurance that no one else would use it that way in this universe or the Beyond. Belisa Crepusculario had been born into a family so poor they did not even have names to give their children. She came into the world and grew up in an inhospitable land where some years the rains became avalanches of water that bore everything away before them and others when not a drop fell from the sky and the sun swelled to fill the horizon and the world became a desert. Until she was twelve, Belisa had no occupation or virtue other than having withstood hunger and the exhaustion of centuries. During one interminable drought, it fell to her to bury four younger brothers and sisters, when she realized that her turn was next, she decided to set out across the 2 plains in the direction of the sea, in hopes that she might trick death along the way. The land was eroded, split with deep cracks, strewn with rocks, fossils of trees and thorny bushes, and skeletons of animals bleached by the sun. From time to time she ran into families who, like her, were heading south, following the mirage of water. Some had begun the march carrying their belongings on their back or in small carts, but they could barely move their own bones, and after a while they had to abandon their possessions. They dragged themselves along painfully, their skin turned to lizard hide and their eyes burned by the reverberating glare. Belisa greeted them with a wave as she passed, but she did not stop, because she had no strength to waste in acts of compassion. Many people fell by the wayside, but she was so stubborn that she survived to cross through that hell and at long last reach the first trickles of water, fine, almost invisible threads that fed spindly vegetation and farther down widened into small streams and marshes. Belisa Crepusculario saved her life and in the process accidentally discovered writing. In a village near the coast, the wind blew a page of newspaper at her feet. She picked up the brittle yellow paper and stood a long while looking at it, unable to determine its purpose, until curiosity overcame her shyness. She walked over to a man who was washing his horse in the muddy pool where she had quenched her thirst. "What is this?" she asked. "The sports page of the newspaper," the man replied, concealing his surprise at her ignorance. The answer astounded the girl, but she did not want to seem rude, so she merely inquired about the significance of the fly tracks scattered across the page. "Those are words, child. Here it says that Fulgencio Barba knocked out El Negro Tiznao in the third round." That was the day Belisa Crepusculario found out that words make their way in the world without a master, and that anyone with a little cleverness can appropriate them and do business with them. She made a quick assessment of her situation and concluded that aside from becoming a prostitute or working as a servant in the kitchens of the rich there were few occupations she was qualified for. It seemed to her that selling words would be an honorable alternative. From that moment on, she worked at that profession, and was never tempted by any other. At the beginning, she offered her merchandise unaware that words could be written outside of newspapers. When she learned otherwise, she calculated the infinite possibilities of her trade and with her savings paid a priest twenty pesos to teach her to read and write, with her three 3 remaining coins she bought a dictionary. She poured over it from A to Z and then threw it into the sea, because it was not her intention to defraud her customers with packaged words. One August morning several years later, Belisa Crepusculario was sitting in her tent in the middle of a plaza, surrounded by the uproar of market day, selling legal arguments to an old man who had been trying for sixteen years to get his pension. Suddenly she heard yelling and thudding hoofbeats. She looked up from her writing and saw, first, a cloud of dust, and then a band of horsemen come galloping into the plaza. They were the Colonel's men, sent under orders of El Mulato, a giant known throughout the land for the speed of his knife and his loyalty to his chief. Both the Colonel and El Mulato had spent their lives fighting in the civil war, and their names were ineradicably linked to devastation and calamity. The rebels swept into town like a stampeding herd, wrapped in noise, bathed in sweat, and leaving a hurricane of fear in their trail. Chickens took wing, dogs ran for their lives, women and children scurried out of sight, until the only living soul left in the market was Belisa Crepusculario. She had never seen El Mulato and was surprised to see him walking toward her. "I'm looking for you," he shouted, pointing his coiled whip at her, even before the words were out, two men rushed her -- knocking over her canopy and shattering her inkwell -- bound her hand and foot, and threw her like a sea bag across the rump of El Mulato's mount. Then they thundered off toward the hills. Hours later, just as Belisa Crepusculario was near death, her heart ground to sand by the pounding of the horse, they stopped, and four strong hands set her down. She tried to stand on her feet and hold her head high, but her strength failed her and she slumped to the ground, sinking into a confused dream. She awakened several hours later to the murmur of night in the camp, but before she had time to sort out the sounds, she opened her eyes and found herself staring into the impatient glare of El Mulato, kneeling beside her. "Well, woman, at last you've come to," he said. To speed her to her senses, he tipped his canteen and offered her a sip of liquor laced with gunpowder. She demanded to know the reason for such rough treatment, and El Mulato explained that the Colonel needed her services. He allowed her to splash water on her face, and then led her to the far end of the camp where the most feared man in all the land was lazing in a hammock strung between two trees. She could not see his face, because he lay in the deceptive shadow of the leaves and the indelible shadow of all his years as a bandit, but she imagined from the way his 4 gigantic aide addressed him with such humility that he must have a very menacing expression. She was surprised by the Colonel's voice, as soft and well-modulated as a professor's. "Are you the woman who sells words?" he asked. "At your service," she stammered, peering into the dark and trying to see him better. The Colonel stood up, and turned straight toward her. She saw dark skin and the eyes of a ferocious puma, and she knew immediately that she was standing before the loneliest man in the world. "I want to be President," he announced. The Colonel was weary of riding across that godforsaken land, waging useless wars and suffering defeats that no subterfuge could transform into victories. For years he had been sleeping in the open air, bitten by mosquitoes, eating iguanas and snake soup, but those minor inconveniences were not why he wanted to change his destiny. What truly troubled him was the terror he saw in people's eyes. He longed to ride into a town beneath a triumphal arch with bright flags and flowers everywhere, he wanted to be cheered, and be given newly laid eggs and freshly baked bread. Men fled at the sight of him, children trembled, and women miscarried from fright, he had had enough, and so he had decided to become President. El Mulato had suggested that they ride to the capital, gallop up to the Palace, and take over the government, the way they had taken so many other things without anyone's permission. The Colonel, however, did not want to be just another tyrant, there had been enough of those before him and, besides, if he did that, he would never win people's hearts. It was his aspiration to win the popular vote in the December elections. "To do that, I have to talk like a candidate. Can you sell me the words for a speech?" the Colonel asked Belisa Crepusculario. She had accepted many assignments, but none like this. She did not dare refuse, fearing that El Mulato would shoot her between the eyes, or worse still, that the Colonel would burst into tears. There was more to it than that, however, she felt the urge to help him because she felt a throbbing warmth beneath her skin, a powerful desire to touch that man, to fondle him, to clasp him in her arms. All night and a good part of the following day, Belisa Crepusculario searched her repertory for words adequate for a presidential speech, closely watched by El Mulato, who could not take his eyes from her firm wanderer's legs and virginal breasts. She discarded harsh, cold words, words 5 that were too flowery, words worn from abuse, words that offered improbable promises, untruthful and confusing words, until all she had left were words sure to touch the minds of men and women's intuition. Calling upon the knowledge she had purchased from the priest for twenty pesos, she wrote the speech on a sheet of paper and then signaled El Mulato to untie the rope that bound her ankles to a tree. He led her once more to the Colonel, and again she felt the throbbing anxiety that had seized her when she first saw him. She handed him the paper and waited while he looked at it, holding it gingerly between thumbs and fingertips. "What the shit does this say," he asked finally. "Don't you know how to read?" "War's what I know," he replied. She read the speech aloud. She read it three times, so her client could engrave it on his memory. When she finished, she saw the emotion in the faces of the soldiers who had gathered round to listen, and saw that the Colonel's eyes glittered with enthusiasm, convinced that with those words the presidential chair would be his. "If after they've heard it three times, the boys are still standing there with their mouths hanging open, it must mean the thing's damn good, Colonel" was El Mulato's approval. "All right, woman. How much do I owe you?" the leader asked. "One peso, Colonel." "That's not much," he said, opening the pouch he wore at his belt, heavy with proceeds from the last foray. "The peso entitles you to a bonus. I'm going to give you two secret words," said Belisa Crepusculario. "What for?" She explained that for every fifty centavos a client paid, she gave him the gift of a word for his exclusive use. The Colonel shrugged. He had no interest at all in her offer, but he did not want to be impolite to someone who had served him so well. She walked slowly to the leather stool where he was sitting, and bent down to give him her gift. The man smelled the scent of a mountain cat issuing from the woman, a fiery heat radiating from her hips, he heard the terrible whisper of her hair, and a breath of sweetmint murmured into his ear the two secret words that were his alone. "They are yours, Colonel," she said as she stepped back. "You may use them as much as you 6 please." El Mulato accompanied Belisa to the roadside, his eyes as entreating as a stray dog's, but when he reached out to touch her, he was stopped by an avalanche of words he had never heard before; believing them to be an irrevocable curse, the flame of his desire was extinguished. During the months of September, October, and November the Colonel delivered his speech so many times that had it not been crafted from glowing and durable words it would have turned to ash as he spoke. He travelled up and down and across the country, riding into cities with a triumphal air, stopping in even the most forgotten villages where only the dump heap betrayed a human presence, to convince his fellow citizens to vote for him. While he spoke from a platform erected in the middle of the plaza, El Mulato and his men handed out sweets and painted his name on all the walls in gold frost. No one paid the least attention to those advertising ploys; they were dazzled by the clarity of the Colonel's proposals and the poetic lucidity of his arguments, infected by his powerful wish to right the wrongs of history, happy for the first time in their lives. When the Candidate had finished his speech, his soldiers would fire their pistols into the air and set off firecrackers, and when finally they rode off, they left behind a wake of hope that lingered for days on the air, like the splendid memory of a comet's tail. Soon the Colonel was the favorite. No one had ever witnessed such a phenomenon: a man who surfaced from the civil war, covered with scars and speaking like a professor, a man whose fame spread to every corner of the land and captured the nation's heart. The press focused their attention on him. Newspapermen came from far away to interview him and repeat his phrases, and the number of his followers and enemies continued to grow. "We're doing great, Colonel," said El Mulato, after twelve successful weeks of campaigning. But the Candidate did not hear. He was repeating his secret words, as he did more and more obsessively. He said them when he was mellow with nostalgia; he murmured them in his sleep; he carried them with him on horseback; he thought them before delivering his famous speech; and he caught himself savoring them in his leisure time. And every time he thought of those two words, he thought of Belisa Crepusculario, and his senses were inflamed with the memory of her feral scent, her fiery heat, the whisper of her hair, and her sweetmint breath in his ear, until he began to go around like a sleepwalker, and his men realized that he might die before he ever sat in the presidential chair. "What's got hold of you, Colonel," El Mulato asked so often that finally one day his chief broke 7 down and told him the source of his befuddlement: those two words that were buried like two daggers in his gut. "Tell me what they are and maybe they'll lose their magic," his faithful aide suggested. "I can't tell them, they're for me alone," the Colonel replied. Saddened by watching his chief decline like a man with a death sentence on his head, El Mulato slung his rifle over his shoulder and set out to find Belisa Crepusculario. He followed her trail through all that vast country, until he found her in a village in the far south, sitting under her tent reciting her rosary of news. He planted himself, spraddle-legged, before her, weapon in hand. "You! You're coming with me," he ordered. She had been waiting. She picked up her inkwell, folded the canvas of her small stall, arranged her shawl around her shoulders, and without a word took her place behind El Mulato's saddle. They did not exchange so much as a word in all the trip; El Mulato's desire for her had turned into rage, and only his fear of her tongue prevented his cutting her to shreds with his whip. Nor was he inclined to tell her that the Colonel was in a fog, and that a spell whispered into his ear had done what years of battle had not been able to do. Three days later they arrived at the encampment, and immediately, in view of all the troops, El Mulato led his prisoner before the Candidate. "I brought this witch here so you can give her back her words, Colonel," El Mulato said, pointing the barrel of his rifle at the woman's head. "And then she can give you back your manhood." The Colonel and Belisa Crepusculario stared at each other, measuring one another from a distance. The men knew then that their leader would never undo the witchcraft of those accursed words, because the whole world could see the voracious-puma eyes soften as the woman walked to him and took his hand in hers. Copyright © 1989 by Isabel Allende From The Stories of Eva Luna, Translated by Margaret Sayers PedenOne factor vs Two factor analysis of variance. If we look at the most common types of analysis of variance, we distinguish between the one factor and the two factor analysis of variance, and on the other hand, the analysis of variance without repeated measures and with repeated measures. What is the difference between single factorial and two factorial? Let's start with the question of what a factor actually is. A factor is, for example, the gender of a person with the characteristics male and female, or the form of therapy used for a disease with therapy A, B, and C. Or it could be the field of study with, for example, medicine, business administration, psychology, and math. 0:51 In the case of analysis of variance, a factor is therefore a categorical variable. You use an analysis of variance whenever you want to test whether these categories have an influence on the so-called dependent variable. For example, you could test whether gender has an influence on salary, whether the therapy has an influence on the blood pressure or whether the field of study has an influence on the duration of study. Salary, blood pressure and study duration are then the dependent variables. In all these cases, you could use a single factor analysis of variance. You're right if you say, well, in the first case, we have a variable with only two categories. So, of course, we could use the t-test for independent samples as well. 1:56 Now, of course, you may say, but I have another categorical variable that may also have an effect on the dependent variable and I want to include that variable as well. Maybe you would also like to know if in addition to gender the highest level of education has an impact on salary. Or in addition to the form of therapy maybe you would also like to include gender. Or in the third case you would also like to know whether in addition to the field of study, the university attended also has an influence on the length of study. Now, in these cases, you would not have one factor, but two factors in each case. 2:40 And since you now have two factors, you use the two-factor analysis of variance. With the help of the two-factor analysis of variance, you can now answer three things. Once, whether the first factor has an influence on the dependent variable. Once, whether the second factor has an influence on a dependent variable. And then you can also make a statement whether there is a so-called interaction effect between the two factors. Therefore, in the case of single factor analysis of variance, we have one factor from which 3:20 we create the groups. In the case of the two-factor analysis of variance, the group results from the combination of the expression of the two factors. If we have a factor or variable with three expressions and one with two expressions, we get a total of six groups that we want to compare. If we have a factor or variable with three expressions and one with two expressions, we get a total of six groups that we want to compare. I hope you enjoyed the video and see you next time.