Is mathematics a tool for human beings to discover and understand the world? No, mathematics is the creator of the universe.
The secret society of Pythagoras
Pythagoras was a famous mathematician and philosopher in ancient Greece, who organized a secret society called the Brotherhood, which is a very mysterious organization, and every new brother must swear that he is not allowed to divulge any secrets of the organization, and only join this school for life. However, such a mysterious organization is neither a religious or political group nor a gangster group, but a school of mathematics. The core of their faith and the object of their devotion is numbers, which they regard as the most fundamental source of the universe, and everything in the world is composed of numbers, and nothing can exist without a form of mathematical expression. Through the study of mathematics, human beings can explore the mysteries of nature and gain insight into all things in the past and the future. The Brotherhood motto is: "Numbers are the ladder forward, not the chips of gold coins." ”
Under the leadership of Pythagoras, this mysterious group proved for the first time that human subjective experience has a purely mathematical basis, such as the harmonies we hear when playing the eighth, fifth, and fourth chords are made of digital proportions, and the matter that makes up the strings is irrelevant. When the chord length ratio is 2:1, it always produces an octave tone, a fifth-degree tone at 3:2, and a fourth-degree tone at 4:3.
The community also found that nature is full of golden ratios, such as in the human body, the navel, throat, knees and elbow joints are basically the golden section points. And the patterns on many shells are also in line with the golden ratio, the markings of trees, leaves, animals... The golden section is almost everywhere.
In this world, numbers dominate everything and give the universe structure and order, and matter is not important in itself as long as it can be divided according to these divine proportions.
Pythagoras discovered the mystery of numbers, which do not occupy space, have no shape, have no position, but never change, which is the basis of the order of the universe. This philosophical idea of his was absorbed and inherited by his student Plato, who said that reality is a projection of the perfect world, which is built by mathematics.
Plato founded his own academy, the earliest university in the West, and he attached great importance to the study of mathematics, and it is said that the door of his academy reads: "Those who do not understand mathematics are not allowed to enter." ”
Nature speaks mathematical words
Pythagoras's discovery of mathematics was just the beginning, and in the two thousand years since then, there has been a growing body of astonishing evidence that "we live in a universe governed by precise mathematical laws, and mathematics is the word that writes the universe." (Galileo)
Why do plant seeds take root, germinate, or grow into big trees, or grow into small grass? Why does a fertilized egg develop into an embryo and grow into an animal that is essentially the same as the mother's? They use the same land resources, the same light sources, the same air, why can they make the world so colorful? Modern science has found that this is due to the internal structural arrangement of genes in living organisms, which follow strict mathematical equations.
Humans have long seen mathematical features in plants: the petals are symmetrically arranged at the edges of the flower tray; the whole flower takes on a radiative symmetrical shape almost flawlessly; the leaves are stacked on top of each other along the stem of the plant; some plants have seeds that are round, some are prickly, some are lightly umbrella-shaped... All of this shows us many beautiful mathematical patterns. The most famous of these is the Fibonacci sequence – the number of petals, sepals, and fruits of the plant all fits perfectly well with a peculiar sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89... Where, starting from 3, each of the following numbers is the sum of the first two. This is the Fibonacci sequence.
If it is genetically determined by the number of petals of the flower and the number of scales of the pine cone, why is there such a coincidence with the Fibonacci number? In fact, during the growth process of plants, only by choosing this mathematical model, the distribution of seeds on the flower tray is the most effective, the flower disc becomes the strongest and strongest, and the probability of producing offspring is also the highest. In other words, plants are inseparable from fibonacci sequences, just as crystals of salt necessarily have the shape of a cube. Since the numbers in this sequence are larger and larger, the quotient of two adjacent numbers will get closer and closer to the value of 0.618034. For example, 34/55 = 0.6182 is close to it, and the exact limit of this ratio is the "gold number".
In mathematics, there is also a value called the golden horn that is 137.5°, which is the opening angle of the golden section of the circle, according to this angle, the circle can be divided evenly and gradually [the golden horn is calculated as 360 ° × (1-0.618)]. Like the number of gold, the golden horn is also favored by plants. Plantain is a common small, with an angle of exactly 137.5° between the leaves of the grass. The leaves arranged according to this angle can be well mosaicked without overlapping each other, which is the arrangement of the largest lighting area of plants, and each leaf can maximize the access to sunlight, thereby effectively improving the efficiency of plant photosynthesis. The architects designed a novel spiral high-rise building based on the mathematical model of the arrangement of plantain blades, and the best lighting effect made each room of the tall building bright.
Not only plants, but also animals are natural "mathematical experts". Cats and spiders are "geometry experts", and in the cold winter, cats always sleep in a spherical shape, because the spherical shape makes the body the smallest surface area exposed in cold air, and thus emits the least amount of heat. The "gossip" web of spider knots is both complex and very beautiful, and when this beautiful structure is analyzed mathematically, the various figures that appear in the spider web so strikingly coincide with mathematical concepts—strings, parallel segments, triangles, full equal corresponding angles, logarithmic spirals, catenary lines, and transcendental lines.
There are too many "geometrists" among animals. Geese often fly in a "human" glyph or "one" glyph, which is the most labor-saving when flying. When geckos prey on small insects such as mosquitoes, flies, and moths, they always crawl along a spiral curve, which is mathematically called a "spiral line". When the snake crawls, the spine is like a train, which is connected section by section, and there is a large room for movement between the knots. If you fix the plane coordinates of each section and use the starting point as the coordinate origin, you will find that the snake moves regularly according to the sine function curves of 30 degrees, 60 degrees and 90 degrees.
Ants are "computational experts." The British scientist Henston did an interesting experiment, he cut a dead grasshopper into three pieces, the second piece was twice as large as the first piece, the third piece was twice as large as the second piece, when the ants found this food 40 minutes later, there were 28 ants gathered next to the smallest grasshopper, the second piece 44, the third piece 89, the latter group almost twice as many as the previous group. It's amazing that the ants' calculation skills are so precise!
Polyps are "algebraic geniuses". It wrote down a "calendar" on itself, and every year it "carved" 365 rings on the body wall, "painting" one a day. Biologists have found that 350 million-year-old polyps "draw" 400 rings a year, and astronomers tell us that the Earth at that time was only 21.9 hours a day and night, not 365 days a year, but 400 days.
It can be said that from plants to animals, from the earth to the entire universe, mathematics is everywhere. Whether it is the waves of the sea, or the cliffs of the mountains, whether it is the crystal snowflakes or the roaring tornadoes, there is no mathematical figure. In the universe, the motion of the planets is strictly according to mathematical equations; in the tiniest quantum world, particles whose paths can never be determined can also be described by specific mathematical functions.
The laws of physics are actually mathematical laws
We know that 1, 2, 3... These numbers are invented by human beings, addition, subtraction, multiplication, division these calculation methods are also invented by human beings, mathematics is the product of human labor, is the crystallization of human intelligence, but since mathematics is the invention of human beings, then why long before human invention of mathematics, all matter in the universe, all motion strictly follow the laws of mathematics?
Thus, since Plato, many scientists have believed that mathematics is fundamentally not a human invention, but an innate existence, Newton's law of universal gravitation, Einstein's theory of relativity, Maxwell's theory of electromagnetism, and modern quantum theory, all of which reveal the laws of the universe, in the final analysis, are expressed in terms of specific mathematical equations — the whole universe speaks in mathematics.
Sometimes mathematicians develop a whole set of research without thinking of any practical application. But after decades or even centuries, physicists discovered that the study of this branch of mathematics was very consistent with actual observations. The list goes on and on, and in 1854, Riemann described the non-Euclidean geometry now known as Riemannian geometry, a peculiar space where parallel lines could intersect or drift farther and farther away. More than half a century later, Einstein used this geometry to establish general relativity. Furthermore, the French mathematician Galois developed group theory in the early 19th century, with the sole purpose of judging the solvability of polynomials. As a result, in the 20th century, this very abstract mathematics became the most important tool for depicting elementary particles.
The development of modern mathematics is getting farther and farther away from the real world, and it seems to have become a pure theory of mathematicians' self-appreciation. However, the universe is mathematical, and some of the mathematics developed by pure theory will be useful in the future, such as vector analysis, non-Euclidean geometry, functional analysis, probability theory, statistical methods, group theory, vector cluster theory, and so on. For physics, mathematics is like clothes in a window, ready to be chosen.
All this means that mathematics is the root of this universe, and that man and the universe seem to have a natural intimate relationship, and that the human soul has some kind of hidden commonality with the soul of the universe. Therefore, before any observations are made, people can discover the mathematical mysteries of the universe, and then these mysteries are confirmed by observational experiments.
Newton and the scientists of his time were devout Christians who discovered the dominance of mathematics in the universe and were convinced that God was a super mathematician and that the efforts of scientists were merely to understand God's intentions and plans for creating the universe.
The power of mathematics in the modern world
Since God created the universe with mathematics, when mankind has seen through the mystery of God, it can turn God's tool into the tool of mankind itself.
Today, due to the development and perfection of mathematics, mathematics is gradually applied to various sciences or produces new sciences, becoming the door and key to almost all branches of science. Not only physics, chemistry and other disciplines are still widely enjoying the fruits of mathematics, but even biology, linguistics, history, etc., which rarely used mathematics in the past, have also combined with mathematics to form marginal disciplines such as biomathematics, mathematical economics, mathematical psychology, mathematical linguistics, and mathematical history.
The first was mechanics, then astronomy, and finally the whole of physics was created and perfected by mathematics. The two pillars of modern physics, relativity and quantum theory, were created through mathematical models, and Halley Comet, Neptune, electromagnetic waves, black holes, positrons, etc. were also discovered on the tip of the pen with mathematical thinking, and then confirmed by experiments or facts. For example, in 1928, the British physicist Dirac developed a set of equations for electron waves, and the solution of this equation is very special, including both positive and negative energy states. Dirac thus made a prediction of the existence of positrons, arguing that positrons are a mirror image of electrons that have strictly the same mass, but with opposite charge signs. In 1932, when the American physicist Anderson was studying the traces of high-energy electrons in cosmic rays, he discovered the positron predicted by Dirac - the positron seems to jump out of the equation.
In biology, mathematics can help people describe the laws of biological population growth, and can help people calculate the relationship between population growth rate and population density. Since the research of modern biology has penetrated deep into the inside of the cell and analyzed at the molecular level, mathematical methods have become the main research methods of modern biology, and the study of organ function, the deciphering of experimental genetic codes, and the study of gene sequences are typical examples. The complex structure of DNA is closely related to the esoteric kink theory of mathematical topology.
Modern medicine uses many different scanners – CT scans, PET scans, ultrasounds. What they all have in common is that by analyzing signals detected by specialized equipment, they mathematically calculate the shape of the scanned object, which was the result of the study of the Austrian mathematician Johann Ladon more than a century ago— as a pure mathematician, he did not know that after his death, his research was appropriately adjusted and saved many lives.
Mathematical models can model climate change and help people predict future climate change; mathematical calculations can identify the location of different rock layers, help geologists study geological evolution, and help oil companies find oil buried in the ground. The field of economics is more attached to mathematics. For example, market forecasting, economic information analysis, financial credit, price system, enterprise management, etc. are all related to basic mathematics. If you do not understand mathematics, it is impossible to become a real economist, for example, Nobel Laureates in economics have a strong mathematical foundation, more than half of them have a background in direct mathematical research, such as One of the 1994 Nobel Prize winners in economics Nash, in addition to making great contributions to game theory, but also in the study of core mathematics has a lot of contributions.
Difficult scientific research requires mathematics, and our daily favorite electronic gadgets, such as mobile phones, DVD players, digital cameras, the Internet, satellite positioning, etc., also rely on a lot of mathematical knowledge. We also used mathematical formulas to ensure the night flight of the aircraft, the extreme speed of the F1 car and the design of the structure of the building. Even a new style of soccer launched by FIFA applies complex systems of equations to calculate how air flows through the ball, involving not only the style of the individual blocks of the sphere, but also the details of the seams.
Mathematics is a universal way of thinking that works for everyone. In everything you do, consider whether your actions are in accordance with justice. For example, geometry is to do things with an axiom, and all subsequent results must be an extension of this axiom and cannot contradict each other, which is the basic principle of geometry. This is "rational trading". The U.S. Constitution adopts the euclidean approach of geometry, starting with a fundamental law or fundamental axiom, such as, "All men are created equal." Under such a basic law, it is easy to conclude that "the president is guilty of the same crime as the people." For another example, things are equal, so the principle of equal exchange must be followed, so in business, they have established the commercial standard of equal exchange.
We can say that mathematics is the driving force behind the whole world, and if you want to understand how the world works, you have to thank mathematics for its existence. Without mathematics, we would never be able to unravel the mysteries of the world or develop modern technology.