Harry Potter’s Morning Light

   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 them with "0". The so-called "vacuum" is not nothing, and there are substances that many people's eyes cannot observe.

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

  If water freezes into ice cubes, and water and sand are mixed into cement blocks, then one ice plus another ice is two ices, and one cement plus another cement is two cement blocks, there are certain rules behind this. Just like a jigsaw puzzle, it has a clear boundary, and two adjacent pieces of the puzzle must not only have matching edges, but also matching patterns. Only when the grooves of the puzzles conform to the rules of articulation, and the patterns match, can two puzzles be combined.

  When the puzzle is completed, people will see an intuitive picture, such as the Mona Lisa that is finally spelled out. 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". However, looking for a puzzle only with images, without looking for the rules in it, is like taking a chance. After completing the puzzle, there is no experience and knowledge. Why don’t you start from the edge when you make a puzzle? What kind of puzzle is the edge of the groove located at? What about the corners?

  Intelligence is like collecting and arranging the puzzles in one place according to certain rules, some people will follow the grooves on the edge, some people will follow the colors on the puzzle pieces, and then match them one by one.

1+1=2 is a qualitative leap in the process of cognition. When a primitive person first realizes that adding two numbers can get a definite number, that primitive person discovers the additivity, 1 pear plus 1 Apple can't be described as "2". The order is not important. For example, if you take 5 pieces of candy, you can take 2 pieces first, then 3 pieces, or 3 pieces first, then 2 pieces.

  In the field of mathematics, 1+1=2 does not need to be proved, but in the category theory, it is necessary to reason, and the category is a philosophical concept, both Aristotle and Kant mentioned. Under what conditions does 1+1 equal 2? This is the discussion of a priori knowledge. Numbers and the four arithmetic operations of numbers are accumulated from the accumulation of experience, and they are arranged 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 pure formal intuitions of time and space, respectively, and they represent the edges and patterns of a puzzle, respectively.

  The volume of two drops of water into one drop is larger than that of one drop, and the same is true for two piles of sand, and the length, width, and height of the chair remain the same. This kind of empirical verification is contingent rather than universal, and it does not need to be like a black swan. Human cognition must be changed by obeying the object to be known.

   But this situation is not absolute, because the change in categorization comes from the bottom, and the bottom requires each of us to return to the moment of mathematical enlightenment.

  Like Copernicus's heliocentric theory, it not only re-derives and reshapes the human worldview, but also changes the way of human thinking.

Before humans overcame gravity and reached outer space, Newton's classical mechanics was like a "white swan". In the 16th century, Galileo used two iron **** on the Leaning Tower of Pisa to prove that the falling speed of an object has nothing to do with its weight. The second law can also be obtained experimentally.

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

This is what Kant said, that all our knowledge begins with experience, the faculty of knowledge is stimulated to act, and if it were not for the object that excites our senses, our intellect operates, compares these representations, puts They unite or separate, and what is that?

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 it cannot be used 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 struggles under the devil's hands. Sad and slender, Black Swan is the daughter of the Demon King. She is proud, gorgeous, and charming, with an aura that overwhelms the audience.

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

This is very challenging for dancers. Generally speaking, ballet dancers who are good at delicate are not good at light and flexible dance postures. Most ballet companies will use two "swans". Can't dance a black swan.

  No matter what kind of swans, they will float on the water. When they bend their slender necks and look down into the water, what do they see? They are watching the swimming fish in the water and plan to dive into the bottom to hunt at any time? Or the reflection of the reflection on the water, do they realize that the shadow is themselves?

  Georgianna emerged from the icy lake, shrouded in early morning mist.

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

   She found that morning swimming was 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 journey, she changed her swimming position to lying on her back on the water, her toes kicked gently, and her eyes looked at the sky.

  The color makes people feel suffocated, obviously it was a good weather yesterday.

   So she turned around again and headed for the shore, and when she stepped on the rocks at the bottom of the lake, she stood up and walked slowly towards Figel.

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

   Their horses suddenly panicked and tried to break free from the reins tied to the tree.

  The Mamluk who hid in the forest exclaimed.

   "Go and see what happened?" said Georgiana.

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

  Georgianna took the bath 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.

   Just as she raised her head, a mass of orange fire suddenly burst, and small fireballs fell like rain.

   She drew her wand from her bracelet.

   "Ventus."

   There was a sudden ripple on the windless lake, but the ripples became bigger and bigger with the wind, and finally turned into a waterspout, which absorbed the fire and rain.

   "nebulus."

  The lake surface, which was already covered with mist, became thicker after the spell was cast.

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

   "I know you won't give up so easily, Maria," said Georgiana, then looked at the towel again, she wished it was an invisibility cloak, but she ran into the forest with it anyway.

   (end of this chapter)