In two consecutive episodes of "Zero Distance Science", Jim. Professor Al Khaliri takes the audience to look at life, the universe and everything from the perspective of physical science. As the saying goes: "Seeing is believing", but since humans observe the world with scientific "eyes", we find that what we see is often not necessarily true, and reality often violates our common sense and intuition. In this episode of the documentary, James explains several of the major breakthroughs in physics in the twentieth century. These discoveries shatter our existing understanding of the world. In this article, I will mainly introduce the discussion about "space". When it comes to space, we often think of it as a canvas on which various events and motions take place. People who have received basic mathematics training will naturally set up a coordinate system on the canvas to accurately describe what is happening on the canvas.
This understanding of space is quite in line with our intuition, but it also implies some incidental ideas about space, such as "space is composed of three dimensions", "space as a background, independent of what happens in it of matter and events”, etc. These predecessors have a long history. Our intuitive space is basically a two-dimensional and three-dimensional space in the "Euclidean space" (Euclidean space). Euclid was an ancient Greek mathematician, known as the "father of geometry". His "Elements of Geometry" deduces a rich and profound geometric theory number list with a few axioms, and is a classic among the classics. The space that Euclid envisioned when he established his geometric theory was flat, like drawing figures on a drawing paper. Even when dealing with solid geometry, he just adds dimensions to the plane concept, and the resulting space is like a square box. After more than a thousand years, great thinkers such as Newton and Descartes still use Euclid's imagination of space - Newton drew the trajectory and laws of motion on this flat canvas, and Descartes for it. With a coordinate system.
These understandings also gradually become our common sense. Jim_1_9 Euclid's Elements is a mathematical classic. It has long been an essential textbook for learning geometry. By the nineteenth century, thanks to multiple mathematicians, we began to discover that Euclid's geometry was not the complete picture. The fifth postulate of Euclidean geometry is called the parallel postulate. The parallel postulate can be replaced by Playfair's axiom. Playfair's axiom states that if there is a line and a point on a plane, we can only draw a line that passes through the point and is parallel to the line. The parallel postulate is more complicated than the first four postulates. For a long time, many people have suspected that it is not self-evident, or that it can actually be proved by the first four postulates. Nineteenth-century mathematicians such as Gauss and Riemann developed a new geometric system by denying the parallel postulate. They found that if we draw a line and a point on a non-plane.