"Let me Pangu create the world!"
crack a joke ...
A long time ago, in ancient times, some scholars really tried to do this!
Plato once associated five regular polyhedrons and four basic elements with the universe. The followers of Pythagoras school are particularly obsessed with finding this type of explanation, but we must realize that their theory is simply unreliable in most cases. Because these theories are based on pure metaphysics and have never been tested, in the end, most of them are found to be wrong.
The picture above shows Pythagoras himself: "It is good to be born early, so tell me everything first". But not all of them are so reliable ...
Galileo and astronomy, physics and mathematics
Interdisciplinary trend
Time has come to17th century. A most prolific and innovative scientist in human history wrote a book, Il Saggiatore, which is one of the most famous works in the history of human science in 1623.
There is such a passage in The Gold Tester:
"Philosophy is written in this great book called the universe, which is always open to our gaze. But if we don't master its language and interpret its recorded words, then we can't understand this great work. It is written in mathematical language, and the characters are geometric figures such as triangles and circles. Without these, mortals can't even understand a word; Without these, people will wander in the dark maze. "
This is a great speech. The greatness lies in that it shows that algebra and geometry are bound to merge and will become an irresistible trend for scientific language to explain the world.
Who the hell is this scientist? Yes, the man who invented the astronomical telescope; The periods of Saturn's rings, sunspots, Venus and Jupiter are discovered. Copernicus, the most influential advocate of Heliocentrism; Explain the relative motion of objects:
Ga! Li. A little!
Galileo (grandfather), his resume always makes people feel "trembling"
The book The Gold Tester records the scientific progress in Galileo's era, especially the increasingly close relationship between mathematics and physics. Galileo was one of the pioneers of this interdisciplinary process.
Newton and the Development of Mathematical Model in17th Century
Although mathematics has been often used to study and understand the world from the beginning of human birth to the present long historical years? As we have witnessed countless times, what happened in the17th century is still brand-new and unprecedented.
Prior to this, the mathematical model has always stayed at the level of human body structure, and has always been based on real reality, rather than some rules created by reality. When land surveyors in Mesopotamia used geometry to measure rectangular fields, these geometric shapes above the surface were drawn by surveyors. Before people drew rectangles in the period of agricultural civilization, rectangles did not exist in nature. Similarly, although geographers use triangulation to draw regional maps, the triangles they conceive and draw are pure and unnatural products.
Therefore, it is a completely different challenge to try to explain the world that existed before human beings appeared with mathematics!
Like Galileo, scholars in the17th century realized:
-Nature operates according to its inherent laws,
-Nature is controlled by precise mathematical laws,
The laws of nature can be revealed to the world through repeated experiments!
In this period, the most remarkable achievement is undoubtedly Newton's law of universal gravitation.
From the senior high school entrance examination to the college entrance examination, Newton, the most prominent student in mechanics, can never be avoided.
The British scholar first proposed in the book "Mathematical Principles of Philosophy E Naturalism" that both the free-falling motion on the earth and the circular motion of celestial bodies in the sky can be explained by a phenomenon, that is, everything has a number. Everything in the universe attracts each other. For small celestial bodies, this kind of gravity is almost imperceptible, but when this kind of gravity is generated between planets or stars, its role will become particularly significant. The earth can attract objects on the ground, which is why there is free fall. The earth is also attractive to the moon. In a sense, the moon is also "falling to the earth". But because the earth is a sphere and the moon moves very, very fast, the moon is always in a state of "falling on the edge of the earth", which is also the reason why the moon moves around the earth! The planets in the solar system revolve around the sun for the same reason.
Newton not only put forward the law of universal gravitation, but also accurately calculated the gravitation between two attractive objects. In fact, he used a number.
This formula accurately expresses this force. Any two particles are attracted to each other by the force through the connecting line, and the magnitude of this attraction is directly proportional to their mass product and inversely proportional to the square of their distance. Due to Wada's written calculation, this rule can be written in the following form:
Once the formula is established, physical problems are transformed into mathematical problems. Then we can calculate the trajectory of celestial bodies, especially their future evolution! Finding the next solar or lunar eclipse is equivalent to solving the unknown of an algebraic equation.
Newton's formula will record a lot of achievements in the next few decades. However, the most remarkable success of Newton's theory should be to calculate the regression period of Halley's comet.
An interdisciplinary subject of astronomy, physics and mathematics.
Powerful Power-Halley's Comet
Since ancient times, scholars have been observing and recording the random appearance of comets in the sky. In order to explain the appearance of comets, two opposing factions have been derived:
-Aristotle school thinks that comets are some kind of atmospheric phenomenon, so they are relatively closer to the earth;
The Pythagorean school thinks that comets are similar to some kind of planets, that is, more distant celestial bodies.
When Newton published Mathematical Principles of Natural Philosophy, the debate was still inconclusive, and scholars of two schools were still arguing about this issue.
One way to prove that "a comet is a distant celestial body, which rotates around the sun with a certain period" is that an object that moves in a circle will return to the same point periodically.
Unfortunately, at the beginning of18th century, no such rule was observed.
Then, in 1707, Emond Halley, a British astronomer and Newton's good friend, announced that he might have discovered something.
The man named "Halley's Comet" after him is the British astronomer Emond Halley.
1682, Harley observed a comet. When he first saw it, he didn't think it was anything special. But in 168 1 year, Harley went to France, visited the Paris Observatory and met Cassini-1. Cassini-1 and Harley discussed the hypothesis about the periodic cycle of comets. Later, Harley consulted a large number of astronomical archives and found that there were two other comets. One in 153 1 and one in 1607. The comets in 153 1, 1607 and 1682 are 76 years apart. Is it possible that this is the same comet?
Harley decided to speculate boldly and predicted that the comet would return again in 1758.
A conclusion that needs to wait for decades to be confirmed! The long wait is not only unbearable, but also stressful. Other scholars took the opportunity to improve Harley's prediction while waiting.
In particular, it has been suggested that two giant planets in the solar system, Jupiter and Saturn, should be considered, because the gravity of these two planets may change the orbit of Halley's comet.
1757, astronomer Jerome Lalander and mathematician Nicole Rene Leppert began to calculate a mathematical model, which was based on the Newton equation created by Alexis Claude Clairau. The calculation process is long and boring. It took three scholars several months to finally predict that the next time Halley's Comet will approach the sun will be in April of 1759, with an error of about 1 month.
Then, an incredible scene appeared. Halley's Comet arrived as scheduled, and the whole world saw its figure in the sky, witnessing the victory of Newton and Halley.
Halley's Comet came near the sun on March 1759, just within the range predicted by Claire, Lalander and Leboti.
Through Halley's comet, the mathematical theory of gravity and physics proved their incredible power to the world with dazzling facts.
Eggs! ! !
As the saying goes, science is always on the road of pursuing truth and will never become truth. No great scientist is absolutely right. It's like:
Galileo, in his book The Gold Tester, not only expressed his views on the mathematicization of the world, but also supported the view that comets are atmospheric phenomena!
No matter how authoritative you are, don't be superstitious about me
In fact, the gold tester is actually a response to Orazio Gracie, a mathematician who defended the opposite view a few years ago. Because of Galileo's reputation and his tough attitude in the book The Gold Tester, this book became one of the best sellers at that time, but neither fame nor success is an inevitable condition of truth.
Gracie should have said to Galileo, "But the earth moves around the sun (e pur si muove) ..."
The above content is taken from everything counts ~ ~
Is mathematics an invention of human beings or an independent existence? Are mathematicians creators or discoverers?
Pursuing questioners and researchers in human history, and feeling the wonder and elegance of mathematics in daily life.
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