Chapter 2365 Glacius (middle)

For the ancients, they did not understand the existence of "0".

Ancient China had the understanding of "emptiness" and "nothingness", but did not combine it with "0". The so-called "vacuum" is not empty, and there are many substances that cannot be observed by human eyes.

But you can feel that there is nothing in your pocket, a house with no furniture, it looks empty. When you put a chair in an empty room, the empty room is not so empty. A chair is not like a drop of water or a grain of sand, a chair plus a chair are two chairs.

If water is frozen into ice cubes, and water and sand are mixed into cement cubes, then one piece of ice plus another is two pieces of ice, and one piece of cement plus another is two pieces of cement. There are certain rules behind this. Just like a jigsaw puzzle, it has a clear boundary, and two adjacent jigsaw pieces must not only have matching edges, but also have matching patterns. Two puzzle pieces can only be combined if the grooves of the puzzle pieces comply with the rules of cohesion and the patterns match.

When the puzzle is completed, people will see an intuitive picture, such as the Mona Lisa in the end. If you only follow the rules of groove connection and ignore the rules of images, the final spelling may be a bunch of "garbled characters". But only looking for the puzzle with the image, not looking for the rules, is like trying your luck. After completing the puzzle, there is no experience and knowledge. Why don’t you start from the edge when you make the puzzle? What about the corners?

Intellectuality is like collecting and arranging the jigsaw puzzles in a place according to certain rules. Some people will follow the grooves on the edges, and some will follow the colors on the jigsaw puzzles, and then match them one by one.

1+1=2 is a qualitative leap in the process of cognition. When a primitive person first realized that the addition of two numbers can get a definite number, that primitive person discovered additivity, 1 pear plus 1 pear Apple cannot use "2" to describe it. The order is not important. For example, if you take 5 pieces of candy, you can take 2 pieces first and then 3 pieces, or you can take 3 pieces first and then take 2 pieces.

In the field of mathematics, 1+1=2 does not need to be proved, but it does require reasoning in category science, and category is a philosophical concept, which was mentioned by Aristotle and Kant. Under what conditions is 1+1 equal to 2? This is what the prior knowledge discusses. Numbers and the four arithmetic operations of numbers are accumulated from accumulated experience and sorted out to form the oldest arithmetic. Based on this, there are arithmetic and mathematics. No one would say that a figure with six sides is a rectangle. Arithmetic and geometry represent the purely formal intuitions of time and space, respectively, the edges and patterns of the puzzle.

The volume obtained by turning two drops of water into one drop is larger than that of one drop of water, as is the addition of two piles of sand, but the length, width, and height of the chair remain unchanged. This kind of experience has been verified, and it is accidental rather than universal. It does not need to be like a black swan. Human cognition must obey the known object and change it.

But this situation is not absolute, because the revolution of category science comes from the bottom, and the bottom needs each of us to return to the moment of mathematical enlightenment.

Just like Copernicus' heliocentric theory, it not only re-deduces and reshapes human worldview, but also changes the way human beings think.

Before humans overcome gravity and reach outer space, Newton's classical mechanics is like a "white swan". In the 16th century, Galileo used two iron balls on the Leaning Tower of Pisa to prove that there is no relationship between the falling speed and weight of an object. Newton The second law can also be obtained experimentally.

But the universal gravitation does not originate from the earth, it is derived based on Kepler's third law, and Kepler's third law is based on the observation data and star catalogs of the Danish astronomer Tycho et al. of.

This is what Kant said, all our knowledge begins with experience, and the cognitive faculties are aroused to act, if it is not because the objects excite our senses, so that our intellectual actions operate, compare these representations, and compare them. They unite or separate, so what?

Classical mechanics is applicable to the macroscopic world. People can use it to calculate ballistics, and can also be used to study low-speed moving machinery, but they cannot use it to study the microscopic world and high-speed moving objects. The microscopic world has quantum mechanics, and high-speed moving objects have special relativity. , of course none of this was known to people in the early 19th century.

Both quantum mechanics and special relativity are black swans in the physical world. In Tchaikovsky's ballet "Swan Lake", the white swan is a poor princess who is struggling under the hands of the devil. She dances gracefully, Sad and delicate, while the black swan is the daughter of the devil. She is proud, gorgeous, and charming, and has an aura that overwhelms the audience.

But they both look exactly the same, like a dual personality.

This is a test for dancers. Generally speaking, ballet dancers who are good at delicateness are not good at light and flexible dancing postures. Most ballet companies use two "swans". Can't jump black swan well.

No matter what kind of swan it is, it will swim on the water. When they bend their slender necks and look down into the water, what do they see? They are looking at the fish swimming in the water, planning to drill into the bottom of the water to hunt at any time? Or a reflection reflected in the water, do they recognize that shadow as their own?

Georgiana emerged from the icy water of the lake, shrouded in morning mist.

She looked around and saw Figel waiting on the bank, so she swam in that direction.

She found that morning swimming is a good habit, but she wondered if she could find such a beautiful place with such clean water after returning to Paris.

In the middle of the swim, she changed her swimming posture and changed to lying on her back on the water, kicking the water with her toes, and looking at the sky with her eyes.

That color makes people feel suffocating, obviously yesterday was a good weather.

So she turned around again and swam towards the shore. After she stepped on the stone at the bottom of the lake, she stood up and walked slowly towards Figel.

Figel took a large towel from the saddle and was waiting to put it on Georgiana.

Suddenly their horses panicked and tried to break free from the bridle that was tied to the tree.

Mamluks hiding in the forest exclaimed.

"Go see what's going on?" Georgiana said.

Figel threw the towel to Georgiana and walked into the forest.

Georgiana took the towel and saw the water surface out of the corner of her eye. At first she thought it was an insect, but later she realized that the black shadow on the water surface came from the sky.

The moment she raised her head, a ball of orange fire suddenly exploded, and small fireballs fell like rain one by one.

She drew her wand from her bracelet.

"Ventus."

Suddenly, there was a ripple on the windless lake, but the ripple became bigger and bigger with the wind, and finally turned into a waterspout, absorbing the fire rain.

"nebulus."

The surface of the lake, which was already shrouded in mist, became thicker after the spell was released.

She dried her clothes with a spell, walked to the shore, and then she put a red signal.

"I know you won't let it go so easily, Maria," Georgiana said, then looked at the towel again, wishing it was an invisibility cloak, but she ran off into the forest with it.