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In this video, Miguel Alcubierre introduces his course on exploring the evolution of space, time, the universe's structure, origin, and history. In the first section, he looks at astronomy, geometry, and mathematics, particularly those of ancient Greeks, explaining their beliefs of the universe, including Earth being flat and the movement of planets. The video details famous philosophers like Pythagoras, Plato, and Aristotle and their contributions to mathematical theories, finding proof through logic, the Pythagorean theorem, and concentric spheres in explaining the movement of planets. They also discuss the measurement of distances, shapes of the planet, and mapping the stars, which is impressive for their time. This section sets the stage for delving into advancements in scientific discoveries, providing more insight into our universe's size, form, and age.

**00:00:00**In this section of the video, Miguel Alcubierre introduces the theme of his course, which is to explore the evolution of our current concepts of space, time, the structure, the origin, and the history of the universe. He plans to divide the course into three sections, starting with the first one today about astronomy, geometry, and mathematics, particularly those of the ancient Greeks. Alcubierre aims to provide insights into how we have learned more about our place in the universe by answering questions like the universe's size, age, structure, and form. Despite being a common inquiry among all cultures from the early days, recent scientific discoveries have shed new light on these questions, while some answers are still incomplete.**00:05:00**In this section, physicist and mathematician Miguel Alcubierre discusses the concept of the Earth as a flat planet and how it was widely believed by different cultures around the world. He also mentions that many of these cultures established the idea of seven planets, including the sun and the moon, rather than the current five that are visible to the naked eye. Alcubierre highlights that the planets do not move in a simple line across the sky and that their movements are much more complex than what was initially thought. Additionally, he briefly discusses the Mayan civilization's view on the structure of the world and their ability to precisely measure astronomical observations such as the movements of the sun, moon, and planets.**00:10:00**In this section, the speaker discusses the evolution of human understanding of the shape of Earth. The Maya civilization, while advanced in some areas of mathematics, believed the Earth was flat and divided into the sky, Earth, and underworld. The Greeks challenged this idea, believing that because of changes in star visibility during travel, Earth could not be flat. They also noted that ships seem to disappear over the horizon due to Earth's curvature. Evidences like this, as well as lunar eclipses, led to the theory that Earth may be a sphere, which was later supported by philosophers such as Pitágoras.**00:15:00**In this section, the speaker discusses the Pythagorean sect, a religious group in ancient Greece that was known for their mathematical discoveries and beliefs. The group, which included the famous philosopher Pythagoras, believed that numbers were the key to understanding the universe and that everything could be explained in terms of whole numbers or rational numbers. They also discovered the relationships between musical notes and the lengths of strings on instruments. One of their important beliefs was the concept of mathematical proof, which was important to Pythagoras himself and was already in use in ancient Greece, and they believed that an argument based on the laws of logic could irrefutably prove a mathematical proposition. The speaker gives an example of the famous Pythagorean theorem, which relates the areas of a triangle and two squares, and is a geometric description of the relationship between the lengths of the sides of a right triangle.**00:20:00**In this section, the video discusses the discovery of the Pythagorean theorem by Pythagoras and his followers, and the crisis it caused within their school of thought when they discovered the existence of irrational numbers. The video also touches on the ancient Greeks' beliefs about the universe, including the assumption that the Earth was at the center of the solar system and that the movement of planets was perfectly uniform. Platón's idea of a world of ideas is briefly mentioned, and the video notes that although this concept is not applicable to the physical world, it remains relevant in mathematics.**00:25:00**In this section, the speaker discusses the concept of mathematics being distinct from human knowledge or discovery. Mathematical concepts and structures exist independently of human knowledge and are valid regardless of whether they have been proven or not. The ancient Greek mathematician Eudoxus of Cnidus is also mentioned for his invention of the method of exhaustion, an antecedent of calculus, which allowed for the calculation of areas of complex geometries. The speaker then moves on to discuss the astronomical models proposed by Plato's disciple, Eudoxus, who imagined planets attached to spheres and explained their movements with overlapping spheres. Aristotle, a Greek philosopher, also sought to understand the universe and developed the study of physics to explain the natural world, including his belief that everything was made up of the elements of earth, water, air, fire, and ether.**00:30:00**In this section, the speaker discusses the physics of the ancient Greeks and their belief that the different elements had a natural place in the universe based on their weight. Earth was considered heavy and therefore tended to move towards the center of the universe, followed by water, air, and fire. They even believed in a fifth element, ether or quintessence, which made up the stars, planets, and moons and orbited around the center of the universe. Aristotle believed in a model of concentric spheres made of solid crystal, each one moving the next, and he used this to explain the movement of the planets. However, his argument against the movement of the Earth, based on the lack of inertia, held back the advancement of astronomy for centuries.**00:35:00**In this section, the speaker talks about Euclid, a person who systematized mathematics and understood all the mathematical knowledge of his time. He wrote a fantastic book called "The Elements" that explained all the mathematics and geometry from a series of simple axioms. The speaker also goes through the five postulates, or axioms, that Euclid used, such as two points determining a straight line, an infinite space, the ability to draw a circle using a point and line segment, that all right angles are equal to each other, and that two parallel lines never meet. The fifth postulate would become known as the "parallel postulate," which Euclid could not prove from the other four axioms. This would cause mathematicians and philosophers to work on the problem for over 2,000 years. The speaker also notes that 100 years before Euclid, the philosopher and astronomer, Philolaus, first proposed the idea that the Earth moved, with the sun not being at the center of the universe.**00:40:00**In this section, the speaker discusses the early Greek beliefs about the Earth and the universe. He explains that they believed the primary fire was located beneath the Earth, which resulted in the idea of a counter-Earth to balance the asymmetry. This began the idea that the Earth was moving, which was later improved by Aristarchus to a heliocentric model, putting the Sun in the center of the universe. The speaker details Aristarchus' reasoning for this view, which involved observing the Moon and the relationship between the Sun, Earth, and Moon. Aristarchus' work survived, and he was able to calculate the relative distance between the Sun and the Moon, creating a model of the solar system with the Sun at its center.**00:45:00**In this section, the speaker discusses the measurements made by the Greek scientist Aristarchus, who was able to deduce that the sun was 19 times further from Earth than the moon, and that the sun was much larger than the Earth. Aristarchus also attempted to determine the distance of the moon from Earth, using an eclipse of the moon. He determined that the moon was 40 Earth radii away, and that it was around 3 times smaller in diameter than the Earth, while the sun was around 6 times larger in diameter than the Earth. While Aristarchus' measurements were not entirely accurate, they were impressive for the time and allowed for the estimation of the relative sizes and distances of celestial bodies.**00:50:00**In this section, Miguel Alcubierre explains how Aristarchus calculated the size of the sun and the distance between the sun and the moon. Aristarchus had a good idea of how far the moon was from the Earth, but he had underestimated the distance between the Earth and the sun. However, he knew that the sun was much larger than the Earth, although he thought it was only seven times larger, while in reality, it was over 100 times larger. Aristarchus couldn't determine the size of the Earth until Eratosthenes, a Greek philosopher who directed the Library of Alexandria, used the angle of the sun's shadow to calculate the size of the Earth.**00:55:00**In this section, the speaker discusses how the ancient Greeks and Egyptians measured distances using the length of stadiums, which varied depending on the stadium used. Eratosthenes, a Greek astronomer, measured the distance between Alexandria and a city called Syene using the angle of the Sun's rays, and calculated that the circumference of the Earth was around 39,000 kilometers or 46,000 kilometers using a different stadium measurement. This measurement, made over 2,300 years ago, was an impressive feat considering the limited technology available at the time. The Greeks had already measured the size of the Moon, which allowed them to determine the diameter of the Earth with impressive accuracy. This led to the start of the understanding of the scale of the Solar System, and the importance of studying the properties of physical space, which is what geometry aims to do.

In this YouTube video, Miguel Alcubierre discusses the contributions of various cultures to science and mathematics, including the Greeks' use of multiple nested spheres for understanding planetary movements and Indians' development of positional notation and the numeral zero. He also highlights key figures in scientific history such as Archimedes, Hipparchus, and Ptolemy, and their contributions to different fields like physics, astronomy, and mathematics. Alcubierre also addresses questions from the audience about colonial science, the definition of a planet, and whether mathematics is created or discovered. Overall, the video offers a broad understanding of the evolution of science and mathematics throughout history.

**01:00:00**In this section, Miguel Alcubierre discusses the ancient Greek philosophers and mathematicians, highlighting the achievements of Aristarchus, who proposed that the sun was at the center of the universe, a concept that was largely ignored for over 1,500 years in favor of Aristotle's idea that the Earth was stationary at the center. He also discusses Archimedes, who was known for being more experimental in his approach to science, making him similar to modern-day scientists. Archimedes worked on both physical and mathematical problems and was close to discovering calculus, but due to his use of Roman numerals, he was limited in his mathematical abilities. Alcubierre also shares anecdotes about Archimedes, including the story of how he discovered a method to determine if a crown was made of gold while taking a bath.**01:05:00**In this section, the video discusses the physics of levers and pulleys, which are simple machines that allow us to multiply our physical strength. Archimedes' discoveries in this field are also highlighted, as he developed the principles of levers and pulleys and famously said, "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world." Additionally, the video delves into Archimedes' role in the war between Rome and Syracuse, where he invented war machines and was regarded as a hero for defending Syracuse against the Romans until it finally fell. The video also touches on Archimedes' astronomical studies and his creation of mechanical models of the solar system, which he made out of metal and were the predecessors to modern planetariums. The discovery of the Antikythera mechanism, a complex machine that represents the movements of the planets, is also mentioned in the video. Finally, the contributions of Archimedes and his successor Hipparchus are discussed, with the latter being regarded as the most important astronomer of ancient times and credited with developing trigonometry and creating the first trigonometric tables.**01:10:00**In this section, Miguel Alcubierre explains the discovery of the precession of the equinoxes, which refers to the slow rotation of the Earth's axis in addition to its fast rotation, taking 23,000 years to complete. This discovery was made by Hipparchus, who measured small changes in the spring and fall equinoxes over several centuries by compiling astronomical measurements from the Babylonians. Hipparchus' measurements were used to improve Aristarchus' calculations of the distance to the moon and to develop a method to predict solar eclipses with relative precision, even though he believed that the Earth was at the center of the universe. Additionally, he cataloged the positions of about 850 stars in the sky, invented the coordinate system of latitude and longitude, and classified the brightness of stars using a system of six magnitudes that is still used by astronomers today.**01:15:00**In this section, Miguel Alcubierre explains the development of the ancient Greek models for understanding the movements of the planets, which often included multiple nested spheres for each planet. He also discusses the work of Ptolemy and Apolonio, who made accurate measurements of celestial movements and compiled their knowledge into an influential book called the Almagesto. He then delves into the Ptolemaic model, which included a series of circles and epicycles to account for the backwards movements of planets, as well as eccentric and equant points. Though the model was quite complicated, it accurately predicted planetary positions and eclipses for over 1500 years, until the time of Copernicus. Alcubierre notes that during this time, astronomers were more focused on creating practical models that could predict planetary positions rather than understanding the true nature of the universe, which became known as "saving the appearances."**01:20:00**In this section, the speaker discusses the stagnation of astronomy and physics after Ptolemy's time until Copernicus' groundbreaking theories 1500 years later. He mentions the importance of Ptolemy's maps and how they were used even though their distances were inaccurate, causing Christopher Columbus to make a crucial error in his belief that the Earth was much smaller. In addition, the speaker briefly mentions the last great philosopher of the neoplatonic school in Alexandria, Hypatia, who made revisions to Ptolemy's work and faced tragic death due to the conflict between Greco-Roman and Christian worlds in Alexandria. Her death marked the end of the scientific and philosophical tradition of the Classical Greek era.**01:25:00**In this section, the transcript highlights the scientific knowledge of the Ancient Greeks, who knew that the world was spherical and had a pretty accurate measurement of its size. They also had an idea about the size and distance of the moon and a vague understanding of the sun's distance and size. However, they held back scientific progress with their complicated model of the solar system that had no predictive power. After the fall of the Roman Empire and before Copernicus, scientific advancements were made in India and the Middle East. Figures like Aryabhata and Brahmagupta made significant contributions to mathematics, astronomy, and the invention of the modern number system.**01:30:00**In this section, the speaker discusses the development of the positional numeral system by the Indians and how it was crucially improved by the invention of zero as a numeral. It was mathematically significant as it made complex calculations easier, as evidenced by the Greeks who didn't have zero and hence faced difficulties in making calculations. The speaker also discusses Al-Khwarizmi, who was a Persian who invented modern-day algebra and from whose name the word algorithm was derived. Other famous people discussed in this section include Omar Khayyam, who was an astronomer and poet and also made significant contributions to calendrical reforms. The speakers also discuss Roger Bacon, one of the most important scientists of his time who contributed significantly to modern scientific thinking.**01:35:00**visión tan amplia y detallada, su pensamiento tenía un gran peso en la época. En cambio, personas como Roger Bacon y Nicolas Oresme tuvieron éxito en cambiar los programas de estudio de las primeras universidades, introduciendo materias como las matemáticas ópticas y la astronomía. Guillermo de Occam también introdujo un concepto científico muy importante, el principio de la parsimonia, que nos hace pensar en maneras muy diferentes a los antiguos. Este principio dice que no se deben multiplicar las hipótesis más allá de lo necesario, y que se deben buscar las teorías más simples posibles que expliquen los fenómenos, pero no más simples que eso.**01:40:00**In this section, Miguel Alcubierre discusses the origins of systematic study of nature and science among cultures, and how the Greeks were unique in their approach. He also talks about the concept of uncertainty in measurements, which was first introduced by Galileo. He points out that the Greeks did not emphasize accuracy in their measurements and were satisfied with the results they obtained. Alcubierre also touches upon the methods used by different cultures to calculate the trajectory of planets and discusses the importance of "saving appearances" in predicting scientific phenomena. Finally, he recommends the book "The Revolutions of Heavenly Spheres" as a good read on the Copernican revolution in science.**01:45:00**In this section, Miguel Alcubierre discusses the importance of the number zero in mathematics, as it allows for positional notation and more powerful algorithms. He also clarifies that the Earth and other planets do not actually move in loops, but rather appear that way due to the Earth's speed and the relative movement of the planets. Alcubierre explains that the reason for the prevalence of spherical shapes in the universe is due to the force of gravity, which compels large objects to form spheres. He notes that the definition of a planet includes the criterion of having sufficient gravity to achieve a spherical shape and dominate its region of the solar system.**01:50:00**In this section, a member of the audience expresses gratitude for a diagram showing contributions from cultures around the world to scientific knowledge. They mention the idea of colonial science which highlights the contributions of non-European cultures to the development of knowledge about nature, and how this is not always acknowledged. They also ask a question about whether mathematics are created or discovered. Miguel Alcubierre explains that from his point of view, it is a bit of both; while certain rules and axioms are invented, the rest is about discovering the properties of these invented rules, which can then be used to explain the natural world.**01:55:00**In this section, Miguel Alcubierre explains that when inventing something like math or science, you create certain rules and then discover the consequences that follow. The rules are not necessarily known at the outset, but are discovered through experimentation and observation. He also explains that the rules of math, such as axioms, are used to approximate properties of the physical world, like those found in geometry. Alcubierre notes that the Greeks knew about magnetic and electric forces, but these were seen more as curiosities until the 19th century when they began to be taken more seriously by scientists in Europe.

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