As his mother recounted her conclusions, Mitsuki Umihara had the idea of interrupting several times. It's not that there is anything in his mother's words that he wants to deny, but that the topic that his mother started later entered a different field.

This field is called quantum information transfer. If the estimate is correct, it should be the basis for the ability of my sister's best friend Harugami Jinyi, who has never tried to explain. He has always kept his promise to Harugami and avoided the topic of his sister and Harugami as much as possible. It's just that I didn't expect my mother to guess Yanbi's ability, starting from assuming a proposition that seems to be unrelated, and following the flawless logical deduction, it will be exactly related to Harumami's ability in the end.

If it were someone else, I'm afraid it would be okay to hear about it. But a girl like Dome is probably not likely to think of anything.

Mitsuki Haihara looked at his sister beside him, and sure enough, he found that his sister's beautiful face showed a hint of surprise. I immediately realized that it was too late to interrupt the conversation. Since this is already the case, he simply does not know what to do.

He really didn't do anything anyway, it was all just a coincidence. Although this coincidence seemed incredible—he instinctively felt a little uneasy about it when he thought of it. It's like simply asserting that a formula is unprovable, only to be shocked to find that the formula is exactly the one that represents the proposition.

This incredible coincidence does not seem to bode well.

"Surprised?"

Mother didn't seem to pay much attention to Mitsuki Umihara's thoughts, but instead noticed the slight change in Dono's expression

Dome nodded. She had something she wanted to ask, but when she spoke, she realized that she didn't know how to ask.

Topics related to Harukami's clothes, not to mention mothers, not even fathers. And what my mother said before was all related to my brother's senior sister, so it doesn't seem good to interject here.

Mrs. Kaihara smiled indifferently, and she snapped the soft clasp on the refill of the quill pen to close the passage through which the ink flowed. Then wipe the ink off the quill with a damp paper towel from the dining room, and gently insert the pen back into Doni's hair.

"Nothing to be surprised at. Let's go and pay the money first, this store only accepts cash. ”

There is a strange and strange thing that sounds commonplace, and it is a habit that exists in the Kaihara family. It's also strange to say that whenever they go out together, the male camp of the Umihara family never carries money banknotes. This bad habit has existed even since the previous generation, and now it is no surprise that it has been retained in Mitsuki Haihara. So in this kind of situation where only cash can be used, the only way to do it is to let the dome pay the bill. Even the chaotic students who worked at Haiyuan's house knew about this, and of course the Kaihara brothers and sisters themselves didn't care about it.

However, when Qiong Nai got up and took the slip to pay, Mrs. Kaihara suddenly said to Mitsuki Haihara.

"Guanggui, there are some things I think it's better to just say to you."

Mitsuki Umihara looked up a little strangely. The mother's tone of voice has always been calm and gentle, and there is almost never the slightest change. So it's usually difficult to know her true meaning.

I don't know if it's funny by his doubts, Mrs. Kaihara smiled slightly.

"In my opinion, there should be a crucial problem that needs to be solved first. Again, it starts with Alice's theory. Alice's theories may not seem surprising today, because we live in an era of highly developed information and communication. But you know, even just a hundred years ago, such a transmission of information was a fantasy that only existed in the age of mythology. In the human mind, the importance of communication was formed long before humans really began to understand the world. In the eyes of the ancients, it was even considered to be the authority of God. The ancient Greeks attributed the authority of communication to Hephaestus, the god of fire, for a reason that it was so clear – because the message on the battlefield was transmitted through the beacon relay. However, there is a limit to the amount of information that fire can convey – in fact, only one bit – and the desire for unlimited information communication has led almost all humans in the world to conceive of something called an 'angel'. As the name suggests, it is an imaginary messenger of God's message—you see, I said that 'angels' are not sacred in themselves, and this is also a testament.

"If you look at the language of the ancients, you will find a peculiarity, and that is that the ancients seemed to be quite keen on introducing redundancy into the language. For example, both Homer and Hesiod use a very interesting description in their verses. For example, Zeus is rarely referred to by his first name, but is used as 'Zeus the Great Wise', 'Zeus the Gathering Clouds', 'Son of Cronus'. Athena is rarely referred to by her first name, and they even prefer to use cumbersome and seemingly meaningless language such as "the daughter of Zeus who lifted the shield". Unique to non-action, the sacred scriptures use the same phrase as 'I am the alpha, I am the omega.' I am now, I was, everywhere'. The same is true of the Buddhist Tantric texts. It goes without saying that such a narrative is very inefficient, but the ancients seem to have enjoyed it. Why is that?

"In fact, this is the inevitable feature of 'oral tradition'. Introducing redundancy, while cumbersome, minimizes ambiguity. At a time when information and communication were not developed enough to be verified, it was an indispensable bit that was introduced specifically for error correction. In the early years of ancient Greek literature, great works such as Hesiod's Theogony and Homer's Iliad were almost certainly written and passed down in the absence of writing from their redundancy alone.

"The people who have been immersed in this point for the longest time may be the ancient alchemists. In their theory, 'as is above, so is below.' If you are below, you are also above', and to be able to describe the world means that it is possible to reproduce the world being described. But in fact, this system of thinking, which is inherited from Pythagoras-Plato, has its limitations. First of all, in order to describe the world in its entirety, it has to introduce a lot of redundancy to disambiguate, and the result is that it is inevitably unbearably long. Secondly, it itself rejects literalization, because literalization cannot truly describe the truth. It is true, as Plato said, that the description of words can only be a real likeness, not the reality itself. However, as a result of the rejection of literalization, this purely colloquial system of thinking has a fatal flaw, that is, the absence of logical thinking links, also defined by Aristotle. Plato defined the defect of literal thinking versus oral thinking as being unable to describe the truth, while his disciple Aristotle defined that the defect of oral thinking versus literal thinking is the inability to reason logically.

If you don't understand, let's take this example: Dome is a Tokiwadai student, and Tokiwadai is a girls' school. People who live in a literal thinking environment will take it for granted that she is a girl. However, people who live in an environment of oral thinking can only answer 'I don't know', because they cannot make any logical inferences from two pieces of information, and oral thinking can only remember what is known.

"Do you think that human thinking determines the language and writing that humans use? This seems like a no-brainer, because everyone knows how to think, but not everyone knows how to use words, doesn't it? But that's not the case. Archaeology has proved that human thinking comes from the symbols of reasoning, that is, logical reasoning. Logical reasoning, on the other hand, must be based on the evaluation of the content. Assessment takes time, and it is a task that cannot be accomplished by listening to spoken words that can only be memorized by listening to them. In other words, for the colloquial thinking system, the present can only be described by accumulation, and the past and future cannot be deduced logically. After all, the Golden Great Technique could not reproduce what he did not know, and that was because the imagination of the oral thinking system could not make logical deductions. It can only describe what is, not what is not. We know that logical reasoning is the way to prove. The lack of logical reasoning means that its own correctness cannot be proved, and the process of 'asking a question and solving a problem' as expounded by Aristotle in epistemology cannot be realized. In mathematical terms, it will naturally lack the 'axiomatic deductive' thinking. In the oral thinking system, there is no such thing as 'proof'. This absence will make it unable to face the questioning of itself, and it will also make the thinking untenable. Because the step of logical deduction is called 'thinking' in Aristotle's mouth.

Ironically, the ancient alchemists were obsessed with describing the world, but the more accurately they described the world, the farther away from knowing the world. The world is 'thinking'. Even the universe may not just be a 'being', but a 'mind'. The real way to know the world is to deduce logically, not descriptively, because in order to understand the world, you have to deduce the unknown of the world.

"If capacity is also calculated as information, it is impossible to ignore the existence of redundancy. Guanggui, it seems that the salt classmate you are talking about can be turned into anything. It seems to me that according to Alice's theory, this 'anything' represents a step backwards, because it can be equated to a redundant colloquial language that can only reproduce what is known. As I said before, redundancy is to avoid the accumulation of ambiguity, and it is necessary to supplement it because of the lack of logical relevance. So more redundancy means less can be converted to causal logic. Without getting rid of this redundancy, the ability of the salt classmates can only stay on a fairly low-level basis.

"It is a fact that, as the foundation of modern science, the existing logical reasoning of human beings is based on words, not the other way around. In order to go further in the construction of knowledge, it is necessary to enter into logical reasoning thinking, and transform 'narrative' into 'concept'.

"It's a pity that Alice's argument on this has not been preserved in Lyceum City, but there is a backup in the UK. It has survived to this day, alongside Salisbury's John (note 1) treatise on logic. So I can't show you the details of her argument, only the general content.

"I must also tell you one more thing, as Alice pointed out in her paper: the expression of ability is like proving a huge system that only requires a series of mechanical rules. Of course, she was only pointing out the possibility of a carryover expression of ability, not really assuming that there is a person who can be used as a carryover expression of ability. However, she pointed out an important point: in order to understand the expression of competence, it is only necessary to distinguish between three questions – 'completeness', 'consistency', and 'decidability'. My guess is that this last question will probably be encountered by the salt students. ”

After saying this, Mrs. Kaihara casually picked up the teacup and took a sip of black tea. However, the biggest explosion of thinking in the world today fell with this sentence.

In Mitsuki Haihara's impression, his mother has always been known for her amazing erudition, but this part goes far beyond the ordinary concept of "erudition". It starts from history and converges towards mathematics.

Even the students of the school city,I'm afraid most of them don't know what these three propositions represent.。 However, Mitsuki Umihara is an exception.

Although Mrs. Kaihara's words seemed vague and long, he could understand why his mother had said it in such a way that they were all too familiar and unsettling. Even Mitsuki Haihara needs a certain buffer time to accept this conclusion - not to understand, but to accept, just to accept.

There is nothing in those three questions per se. These are just three questions that David Hilbert, one of the greatest mathematicians in human history, put forward at the beginning of the twentieth century. The key lies in the answers to these three questions.

The answers to each of these three questions are a blow to the realm of logic. Because the answer to the three questions is very unfortunate, and they are all no.

The first two of these three questions were answered by the mathematician Gödel, and the answer is the famous "incompleteness theorem". The third question was answered by Alan Turing, one of the greatest mathematicians in human history. It is commonly expressed as: "There is no such machine that, when provided with a standard description of any machine, can determine whether any of these machines have ever printed a given symbol".

It is only when the calculated and the calculated are entangled that the paradox is born.

Turing's answer is known today in the computer world as the "downtime problem".

The most crucial and important part of the mother's guess was finally revealed.

Mitsuki Umihara was staring at his mother's face almost deadly, his eyes full of meanings that were too complicated to express in words. Mrs. Kaihara looked at him, slowly put down the teacup, and sighed softly.

"Guanggui, I'm not trying to prove anything. However, 'it is probably preferable to think of communicating with a computer rather than a friend' (Note 2). ”

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Note 1: Secretary of the Archbishop of Canterbury in England in the 12th century, a representative of medieval European logic. This man was suspected of being a mystical philosopher.

Note 2: In the field of informatics, this is a proverb. The originator of it is no longer known. Some people think it's Gregory Zeitin, but in fact, there are at least three people who have expressed similar views before Caiting. The same meaning is implicit in Claude Shannon's definition of communication in the quotation to this volume.

PS: This chapter is actually a setting and solution chapter - that being said, it's too deep. It's really hard to express it in a way that doesn't have to be too jargonal, and I checked a lot of information. The results are more content, and the time is longer.

After this incident, we can better understand Plato's evaluation of words. That's really a troubling thing.

PS uploaded by: The core of this chapter is actually mathematics. I'm afraid few people would think that there is a correlation between the language we use in our daily lives and mathematics. But in fact, they do have a lot of correlation. At the root of this, the literal (or symbolic) language we use gives rise to "logical inference", which in turn is the foundation of mathematics and modern science. There is even an inseparable link between them.

It is said that John Wheeler once asked Gödel a question. The certainly great physicist asks a mathematician, perhaps even greater, a rather peculiar question: whether the incompleteness theorem is related to the uncertainty principle of quantum mechanics. Gödel closed his eyes and thought for a long time, but did not give a yes or no answer, but refused to answer the question.

This is a very interesting question: is there a connection between the two theories that symbolize the limits of human understanding of the world?

Astonishingly, the answer is yes. The correlation lies in randomness, in uncertainty, in Alan Turing's answer to that last question (which is very complex and I don't understand it either).

And the most important thing for this paper is that it is achieved through information theory.

The core of information theory is also mathematics, which is almost the only way to understand information theory. It's really hard to get it out of a way that doesn't get too mathematical. However, this incomprehensible theory has now become one of the basic theories of human society, and its importance is almost equal to that of quantum mechanics and higher than that of general relativity.

Even the inquiry into human beings themselves will ultimately rely on information theory – a fact that has been a definite fact since Claude Shannon wrote down on a piece of paper the amount of information he estimated about the human gene.

In fact, this idea is the origin of the idea that the author and I conceived of Ji Yanbi.

PS: By the way, it is surprising, but few people know that there may be an equally remarkable figure who discovered the hidden problem of random uncertainty earlier than the above, and applied it to a surprising field – human society itself. That man had almost the same status as Einstein was to physics in the field he pioneered. His name is John Maynard Keynes, the father of modern macroeconomics.