If time travel is possible, then predicting the future is easy, and I just have to look at the future to know what will happen later. Unfortunately, however, we don't yet know how to travel through time, and the ways in which people claim to be able to predict the future, such as crystal balls or divination astrology, cannot be fully proven to be credible. However, if you really want to know what will happen tomorrow, next year or the next millennium, your best bet is to study mathematics!
Mathematics can predict whether Earth will be hit by an asteroid and how long the Sun will continue to burn. We have equations that explain various natural social phenomena, for example, weather, population growth, the trajectory of the movement after a football is kicked into the air. Although there are still some things that are difficult to predict, their roots lie in the fact that there are equations that we don't know how to solve, not that mathematics can't predict.
The ability of mathematics to predict the future gives great power to those who know the language of mathematics. From ancient astronomers who could predict the movement of planets in the night sky, to hedge fund managers who can predict the movement of stock market prices today, people use mathematics to glimpse the future. The power of mathematics was recognized by Bishop Hippo, Saint Augustine the Teacher, who warned: "Beware of mathematicians, and all those who make empty prophecies." Danger has been present, and mathematicians have made a pact with the devil to darken the soul and keep man in the chains of hell. ”
It is true that some modern mathematics is extremely difficult, but its practitioners do not keep us out of the sky, but are constantly looking for new ideas to reveal future events.
< h1 class="pgc-h-arrow-right" > math saved Tintin</h1>
In Hergé's comic strip The Adventures of Tintin: Prisoner of the Sun, the young Belgian journalist Tintin is captured by an Inca tribe after getting lost in the Temple of the Sun God. The Incas tied Tintin and his friend Captain Adok, as well as a professor of mathematics, to the stake and prepared to burn them to death. They were ready to light a fire with a magnifying glass and allow Tintin to choose the time of their death.
Prisoner of the Sun in The Adventures of Tintin
Tintin calculated that there would be a solar eclipse in the area in a few days, so he chose the time of their death to coincide with the eclipse. In fact, it was a calculation made by someone else, and he saw this prophecy in the newspaper clippings. As the eclipse was approaching, Tintin shouted, "The sun god will not hear your prayers!" Oh, magnificent sun, if you want us to live, now give us a sign! And the ending is that, as the math predicted, the sun disappears and the frightened tribesmen release Tintin and his friends.
<h1 class= "pgc-h-arrow-right" > Columbus's wisdom</h1>
The story in Prisoner of the Sun is based on a famous event in history in which explorer Christopher Columbus used a lunar eclipse (instead of a solar eclipse) to save a crew trapped in Jamaica in 1503. The local residents were friendly at first, but eventually became hostile and refused to offer support to Columbus and his crew.
Columbus came up with a cunning plan. He consulted his almanac, a book of tides, lunar cycles, and the positions of the stars used by sailors to navigate, and found that a lunar eclipse would occur on February 29, 1504. Columbus gathered the local residents three days before the incident and threatened them that if they did not provide for them, he would make the moon disappear.
However, the locals did not believe that Columbus had the ability to make the moon disappear. On the night of February 29, when the moon rose to the horizon, they saw that the moon had bitten off a piece. According to Columbus's son Ferdinand, when the moon disappeared from the night sky, the locals became frightened, "accompanied by great howls and weepings, running from all directions to ships laden with grain, praying to the admirals, interceding to God for their benefit." ”
After precise calculations, The time columbus pardoned the locals coincided with the gradual appearance of the moon. The story may have been fabricated, or it could have been made up by the Spaniards in order to contrast the clever European conquistadors with the ignorant natives. But at its core, it shows the power of mathematics.
<h1 class="pgc-h-arrow-right" > lunar and solar calendars</h1>
Mathematics is a science of discovering patterns, and that's how mathematics gives us the ability to look to the future. Early astronomers stared into the night sky and soon realized that the movements of the moon, sun, and planets were repetitive. Many cultures use these celestial bodies as a way to record the passage of time, which is the calendar.
The basic unit of time common to calendars compiled using the sun is 24 hours. This is not the time it takes for the Earth to rotate once, it is a little less than that: 23 hours, 56 minutes and 4 seconds. If we use this slightly shorter period as the length of a day, our clock and the rotating Earth will become more and more out of sync, because all these extra 3 minutes and 56 seconds will accumulate and eventually cause the noon on the clock to appear at midnight.
Therefore, for the purpose of timing, we define a day (or, to use the correct terminology, a solar day) as the time it takes for the Sun to return to the same position in the sky from the same point on the Earth's surface. While completing a full rotation, the Earth also orbits the Sun, which makes us have to wait about 3 minutes and 56 seconds for the Sun to return to the same point in the sky. So the 24-hour option is very suitable.
It takes 365.2422 solar days for the Earth to orbit the Sun. Most countries use calendars very close to this cycle. 0.2422 is about a quarter, so every four years we need to add a day to the calendar to keep the Gregorian calendar in sync with the Earth's orbit around the Sun. However, 0.2422 is not equal to 0.25, and we also need to correct it: every 100 years, we will skip a leap year, but every 400 years, we will cancel this skip.
In addition to the solar calendar, there are many regions that use the lunar calendar of the moon, such as the Islamic calendar, which uses the cycle of the moon. Their basic unit is a lunar month, which is the cycle of the moon around the earth. The beginning of a lunar month is determined by the emergence of a new moon in Mecca. The period of change in a moon is about 29.53 days, which makes a lunar year 11 days less than a solar year. Dividing 365 by 11 is approximately equal to 33, so Ramadan cycles through the solar calendar every 33 years.
The Jewish and Chinese calendars mix and match the solar and lunar calendars, adding a leap month approximately every three years, and the key to the calculation is a magical number of 19. The 19 solar years (=19×365.2422 days) coincide almost perfectly with 235 lunar months (= 235×29.53 days). There are 7 leap years every 19 years in the Chinese lunar calendar to keep the lunar and solar calendars in sync.
<h1 class="pgc-h-arrow-right" > when is the next lunar eclipse?</h1>
Well, after understanding these calendar rules, we can discuss prediction. If you know the time of one month's eclipse, then you can use mathematical equations to calculate the time of another month's eclipse. And these calculations rely on two important numbers.
The first is the average time it takes for the Moon to circle the Earth and return to the same position relative to the Sun, which is about 29.5306 days, which is also the average time between the two new moons. The other is related to the intersection month.
Since the Moon's orbit around the Earth is slightly inclined relative to the Earth's orbit around the Sun, the two orbits have two intersections, and the intersection moon refers to the average time it takes for the Moon to depart from one intersection point and return to the starting point through another, which is about 27.2122 days.
We remember S=29.5306 and D=27.2122. If you can find a pair of integers A and B that make AxS very close to BxD, then this number is the number of days between lunar eclipses that occur again since the last lunar eclipse occurred. This number can be used forever, but because it is an approximate equation, lunar eclipses will eventually become less and less until the sun, moon, and earth are no longer aligned, and the digital cycle is over.
For example: A=223 B=242, the period is 223× 29.5306≈242× 27.2122≈6,585 days, that is, about 11 days and 8 hours in about 18 years. The difference of 8 hours is that the next two such lunar eclipses will be observed at different locations on the Earth's surface. However, 3x8= 24, so the third lunar eclipse will occur in the same place.
< h1 class= "pgc-h-arrow-right" > Galileo's experiment</h1>
Mathematics' ability to predict the movement of celestial bodies depends on the recurrence of these phenomena, which can be said to be a reproduction of the old to some extent. But how can we predict new things? We can take a simple example of using mathematical equations to predict the motion of a simple object, such as a soccer ball.
David Scott threw a geological hammer and falcon feathers on the moon
As the Italian scientist Galileo Galilei proved at the Leaning Tower of Pisa, the weight of an object has nothing to do with the speed at which it falls, what really works is air resistance. In 1971, David Scott, commander of the Apollo 15 lunar mission, recreated Galileo's experiment on the extremely thin-air moon by dropping a geological hammer and falcon feathers. Since the Moon's gravitational pull is small and the air resistance is negligible, they slowly land on the ground at the same time, as Galileo predicted.
After discovering that the weight of a falling object had nothing to do with its speed, Galileo wanted to see if he could predict when the object would hit the ground. Objects fell from the top of the sloping tower too fast to be precisely timed, so Galileo decided to roll the ball down the slope to see how the speed changed. He found that if a ball rolled 1 unit of distance after 1 second, then after 2 seconds it would go 4 units of distance and after 3 seconds it would go 9 units. He could then predict that after 4 seconds, the ball should have traveled a total of 16 units of distance.
Galileo's slopes
In other words, the distance an object falls is proportional to the square of the time it falls. If mathematical notation is used, d is the distance it falls, and t is the time. Factor g is called gravitational acceleration, so a free-fall formula is obtained:
Galileo's formulas were one of the first examples of using mathematical equations to describe nature, which came to be known as the laws of physics.
<h1 class="pgc-h-arrow-right" > uses a formula to predict object motion</h1>
Using mathematical formulas to describe the motion of objects has revolutionized the way we understand the world. Prior to this, people used everyday language to describe nature, which was very vague. You can say something is falling, but you can't say when it will reach the ground. In mathematical language, one can not only describe nature more precisely, but also predict how it will behave in the future.
On the football field, you can also calculate what is "going to happen". Each shot by Messi can describe the goal line by solving the equation, and Ronaldo's free kick can also calculate its angle and landing point by solving the equation.
Of course, you need to know a lot of initial values, such as the size of the football, the hardness, the strength of the person playing the ball, the angle of the ball and so on. Equations are like recipes, just enter these materials and you will get a result.
Let's take a simple model as an example: for example, we know the horizontal velocity u and vertical velocity v of the sphere, and the gravitational acceleration g of the Earth. Assuming that the horizontal running distance of the football is x and the altitude from the ground is y, then we get an equation:
Once we know y, the altitude at which the ball is flying, we can find x, which is where the ball lands. This kind of equation is a quadratic equation that we all learned in school, and solving this equation seems easy.
<h1 class= "pgc-h-arrow-right" > the ancient Babylonian solution</h1>
The first people to start solving this equation were the ancient Babylonians, whose quadratic equations were not meant to describe the trajectory of a football, but to measure the land around the Euphrates River. Because a lot of land is square, its area appears quadratic. But the Babylonians' approach to solving the equations was ingenious.
Let's take an example. If the area of a rectangular field is 55 square units, and one side is 6 units shorter than the other, how long is the long side? Generally we call the long side x, then the problem becomes an equation:
The Babylonians came up with x in a clever way. They first cut out a small rectangle of 3 × (x-6) from the end of the rectangle and then move to the bottom of the rectangle. The whole area has not changed, only the shape has changed. The new shape is almost a square, with each side length of (x-3), but in the lower right corner there is a small square of 3×3 missing.
If we add this small square, we add 9 units to the area of this shape. Thus the area of this large square is 55 + 9 = 64. The square root of 64 is the side length of the large square, and it is easy to find that this is 8. So x-3=8, which is x=11.
Although the Babylonians were only moving into pieces of land, behind this matter was a general way to solve these quadratic equations.
< h1 class="pgc-h-arrow-right" > the emergence of algebraic equations</h1>
When contemporary numbers were created in Iraq in the 9th century, mathematical formulas could be recorded. Algebra was pioneered by the scholar Abu Abdullah Mohammed ibn Musa Al-Khwarazmi of the House of Wisdom in Baghdad.
Abu Abdullah Mohammed ibn Musa Al-Harazimi
The House of Wisdom was the leading intellectual center of its time, attracting scholars from all over the world to study astronomy, medicine, chemistry, zoology, geography, alchemy, astrology, and mathematics. Muslim scholars collected and translated many ancient texts, effectively passing them on to future generations. Arguably without these jobs, we might never have learned about the ancient cultures of Greece, Egypt, Babylon, and India. However, the scholars of the House of Wisdom were not content to translate other people's mathematics. They wanted to create their own mathematics and move the discipline forward.
The advent of algebra formulated the methods of the ancient Babylonians
In the early days of the Islamic Empire, intellectual curiosity was actively encouraged. The Quran teaches that secular knowledge brings people closer to divine knowledge. In fact, Islam requires mathematical skills because devout Muslims need to calculate the time of prayer and need to know the direction of prayer to Mecca.
The algebra of the varazium rice changed mathematics. Algebra is a language that explains the patterns behind the behavior of numbers, and its syntax is the basis for the interaction of numbers. A bit like the code that runs a program, it will handle any number entered into the program. Although the ancient Babylonians had devised a clever way to solve specific quadratic equations, the algebraic formula of the faradmi ultimately gave a method that could be used to solve any quadratic equation. And this allows us to solve the problem of prediction in football.
(To be continued)