Read Gotham, Eisele and Bach.

# "Gotham, Eisele, Bach" EGB· Douglas hofstadter

The introduction of this book in Kai Zhi Dian is:

As a town group book, as the first of a hundred books, friends say it is difficult and dare not dabble. Library encounter (really! ), picked it up and flipped through it at will. I saw an interesting translation of the title (the collection of different treasures, the collection of different treasures, the origin of the subtitle "an eternal golden belt"), and suddenly felt that this work was so cute. Even though I know little about math, music and painting, even though this book is as thick as an Oxford dictionary, I still recite it.

The meeting was wonderful. After reading 35 pages, I found that I only read an introduction = = There is a short story dialogue of the protagonist of Greek mythology in front of each chapter, which seems to be nonsense, but in fact it is full of metaphors. Amazingly, four algorithms were born from several simple theorems and the strict derivation of "if, then". Then gradually, through the comparison and circulation of paintings, the circulation of Bach's music chapters extends to mathematics, revealing the mystery of artificial intelligence in a simple way that you never expected (you often secretly say "wow" in your heart, meaning what you have learned before). I wonder if math would attack me if I met it earlier?

The "strange circle" phenomenon is that when we go up (or down) through some levels in a certain level system, we accidentally find that we are back to the starting point. (tangled level)

Eisele's Paintings: Rise and Fall, Waterfalls and Painters.

Isn't cycle a way to express endless process in a limited way?

Epiman Nittis paradox (liar paradox)-Epiman Nittis is a Crete, and he said an immortal word; "All Cretes are liars." (= "I'm lying" or "This sentence is false." )

Most of the collections are "ordinary". However, some autophagic sets do include themselves as elements of the set. (I don't understand = =)

Those who want to eliminate universal paradoxes must have some similar "layering methods" to ban loops in language. Every sentence clearly belongs to a certain level in the hierarchy.

Our way to remedy this paradox is to get rid of all forms of self-reference.

Where is the boundary between non-intelligent behavior and intelligent behavior? The basic ability of intelligence: flexible response to situations; Make full use of opportunities; Understand vague or contradictory information; Recognize what is important and what is secondary in a certain situation; Similarities can be found between different scenarios; Look for differences from those things linked by similarity; Synthesize new concepts with old concepts and combine them in new ways; Put forward new ideas.

One of the main purposes of this book is to encourage every reader to face this seemingly contradictory thing, taste it, fiddle with it, open it and immerse himself in it, so that readers can finally realize the seemingly insurmountable gap between formal and informal, living and inanimate, flexible and inflexible things. (This is all that artificial intelligence should study. )

The flexibility of intelligence comes from a large number of different scales and rules.

"After reading 35 pages, I found that I only read the introduction of one author."

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"The wind does not move, and the heart listens automatically."

Greek philosopher in the city of Arria (which lies between point A and point B)

"Exercise is essentially impossible." = "Dichotomy Paradox"

"Nothing is moving" —— Zhi Nuo Theorem

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Ok, let's talk about pq system. (Coordinates: Chapter II Meaning and Form in Mathematics)

This is a formal system with three symbols: the letter P, the letter Q and the short bar-.

Pq system has infinite axioms, so it is axiomatic to define x-qxp- as long as X only consists of a series of short rods.

For example: -q-p-, -q-p-? ,

It is found that pq theorem is very similar to addition in form, so it is determined whether the short bar in front of Q is equal to the addition of the latter two. (The author deliberately chooses q = equal, p = plus)

Pq system and addition are isomorphic. So pq system has a new meaning.

If Q is a horse, P is happiness, and-is an apple, then -Q-P- has a new explanation, "Apple, horse, apple, apple, happiness, apple", which is meaningless.

In chapter 3, an axiom is added to the axiom of pq system: if X is a short bar string, xqxp- is an axiom.

Then-q-p-p-is also a theorem in the new system. The original interpretation is "2=2+ 1", which is inconsistent with the outside world. (illogical)

There are also problems in the internal world of the new system, such as -q-p- (old axiom) and -Q-P- (new axiom), which cannot be explained.

The author points out that this is a deliberate argument in the Eight Classics of Zhengge, and the new pq system needs new isomorphic meanings, such as interpreting Q as "less than or equal to". So the original axiom "2"

Emma doesn't know if the explanation is clear. This theorem is probably derived from axioms. The formal system of symbols has practical significance through isomorphic interpretation, but what is important is to choose what meaning.

The third chapter talks about figure and base. The positive space and negative space in the pattern can form a smooth figure, that is, both figure and base are complete and smooth figures, which is very obvious in escher's paintings.

At the same time, it is also difficult to distinguish between graphics and matrix in music, that is, melody and accompaniment, which is also called double fluency, such as Bach's music.

Corresponding to the field of mathematics, recursion can be enumerated and become the expression of "fluency and paintability" in mathematics.

At this point, Gothic titles such as Chan, Aysil and Bach have appeared. Although Godel's theorem appeared, I still don't know what the hell it is. = = The author indicates that it will be discussed in the following chapters. ) I also vaguely feel the author's profundity. Three seemingly unrelated mathematicians, painters and musicians have the same sex under the author's explanation and construct a new way of understanding the world. Mastering the way of meaning transformation between different fields will probably gradually approach the way that computers understand and express human thinking, so artificial intelligence is on the rise.

The third chapter is selected:

Graphics and Bases —— Positive Space and Negative Space

Time Smoothing-The foreground and background are drawn smoothly. ? For example, escher's chart.

Graphics and substrates in music-melody and accompaniment. ? Bach's music, for example, is twice as smooth. )

Formal system

Recursive enumeration (R.E.)-Mathematical fluency can be drawn.

#W0 104 Gothic, Eisele and Bach styles

It started with the dialogue between tortoise and Achilles, and the argument that an excellent singer can't play all the records is as long as 10 page. The record player can't play all the records. There is always a sound vibration of a record that will cause the phonograph to vibrate and then destroy itself. Record the isomorphism between particles and air tremor; And the isomorphism between any air tremor and phonograph tremor. When the phonograph passes through the record, it means that the grain brings air vibration, produces sound, and the sound vibration reacts on the phonograph, eventually destroying the phonograph.

Finished reading it? I haven't finished yet. Let's watch it again. The first word at the beginning of each conversation is bold. Put together: the famous German composer Hou Shida inspired me ... At this time, I borrowed his counterpoint to write a dialogue and embedded his name to show my sincere admiration for his outstanding talent. You may remember that he once wrote his name at the end of a fugue.

This person is B-A-C-H. At the end of the fugue, B-A-C-H is transformed into the corresponding notes, which are perfectly integrated. The specific description is a bit long, so I'll just skim it here.

The tortoise said that no strong enough singing opportunity is complete in the following sense: it can reproduce all possible sounds on the record. Godel said that no formal system strong enough is complete, because every true statement can be reproduced as a theorem in the system.

Isomorphism leads to the emergence of meaning. Chapter 1 Pq system. Axiomatic pattern: If X is a short string, xqxp-is an axiom. Then -q-p- is also a theorem in the new system. It is interpreted as "2=2+ 1", which is inconsistent with our common sense of external systems. If q is replaced by something else, such as "less than or equal to", then "2"

This linguistic interpretation of symbols has become one of the most profound lessons in19th century, which comes from Euclid's Principles of Geometry, and the whole building of geometry is derived from five postulates.

Then discuss non-Euclidean geometry and study undefined terms. Replace symbols with various practical meanings by consistency, and explore whether it is reasonable.

Then there is the stability of visual perception. A painting with a seemingly reasonable structure (such as escher's works below) is unreasonable in reality. The formal number theory extended to mathematics is incomplete.

In a word, this book is too informative, reading and writing are very tiring, and it is impossible to be comprehensive. The details can only be deduced slowly according to the author's ideas.

The fourth chapter is selected:

Implied meaning and obvious meaning

Understanding the symbolic operation process of human language is much more complicated than the symbolic operation in typical formal systems.

The principle behind Godel's theorem is visualized: two maps are back to back, which has unexpected flying effect. The first mapping from the track mode to the sound is realized by the phonograph. The second one is common but often overlooked, from the sound to the vibration of the record player. Note that the second mapping exists independently of the first mapping, because any sound nearby-not just the sound generated by the record player itself-will cause this vibration. The uniqueness of Godel's theorem is that for any record player, there are records that it cannot play, because the latter will lead to the indirect self-destruction of the former.

In formal systems, meaning is transmitted through isomorphism.

The Mapping between Dual Tibetan Poetry and Godel Theorem

Treacherous wine glasses and records

The history of Euclid's geometric principles: using five postulates as the basis of geometric architecture.

Non-Euclidean geometry.

We can use the term "consistency" to summarize our observations so far. Our discussion begins with the construction of an inconsistent formal system-internal inconsistency and inconsistency with the outside world. But after a while, we withdrew this statement, we realized our mistake, and we chose an unfortunate explanation for this symbol. After changing the interpretation, we regained consistency!

Logical consistency, physical consistency, mathematical consistency, biological consistency and so on.

But in such a world, the laws of biology, physics, mathematics and even logic will be ignored at one level and followed at another, which makes it a very strange world. Such as escher Falls.

#W0 105 Goth, Eisele and Bach

The harmonious maze is also a dialogue story between tortoise and Achilles, full of nesting, layer after layer, such as Inception. I want to realize a meta-wish of "My wish is to have 100 wishes" (I thought so when I was a child! ! ! ) Enter escher's paintings and read the story book in the story. The protagonist is a scholar. Find the end point in the harmony maze (actually Bach's record). It seems that they are finally out of danger, but in fact, their real bodies are waiting to be slaughtered on the plane. (The author indents the dialogue intimately, prompting the reader to enter the next level of nesting. )

While reading, I wrote down some key terms. It is too much work to repeat words, but it is a meeting to use this story vocabulary. I can tell you the story again. (Attached with a schematic diagram of the story structure)

# # Harmonious maze keyword list

Playgrounds, windmills, airplanes, elves and cooking and drinking.

Push the dew, escher's painting "Bump", magic lamp, three wishes.

100 wish, no type wish, meta-wish, meta-wish.

Yuan Deng, Yuan Yao

Yuan Yuan lamp, Yuan Yuan monster

……

creator

……

Super monster, through.

Monster, approved.

Creator-Creator (recursive prefix combination) has an infinite number of monsters above him or her.

I hope my wish doesn't come true and the system crashes.

Next floor, the adventures of tortoise and Achilles roaming the world.

A harmonious maze occupied by terrible eagles

The stick rubbed against the wall and made music.

The center ate until the crispy pot popped out and fled to the next floor.

Lizard, run away along the right angle of the painting.

Recursion is nesting.

In daily life, making a phone call, busy, transferring, accessing a new phone, suspending the current phone and accessing a new phone is a recursion.

Push, pop and stack (part of the early IPL language of artificial intelligence)

Stack is used to record a pause at a certain level and connect again next time.

Then I talked about the stack in music and recursion in language. (I skipped it selectively, um = =)

Modularity, cycle and process.

Seeing that it is finally kind here, thanks to the little foundation of Python class.

Write a computer program to decompose the task into subtasks-modular concept.

Do I need to list all the operations in turn? No, write a loop and jump out when certain conditions are met.

Chess program-the best chess means the best for one side and the worst for the other.

So the best way to run the program is to take a step and call yourself from the opponent's point of view. At the same time, it takes a step and then calls itself from the opponent's point of view.

The article says that in the early days of chess, people were better at playing chess with machines. Some people speculate that computers can beat people in ten years, but now it seems that it will take another ten years. Illustrates a recursive law-Hou Shida's law: it always takes longer to do things than you say, even if you consider Hou Shida's law in anticipation.

However, the just-concluded "AlphaGo" has attracted much attention. The earliest version of GEB was found as 1979, which has been more than 30 years. For the first time in human history, Go AI defeated professional players in a fair competition.

#W0302？ Gottchen, Eisele and Bach.

Information carrier and information display device

Genetic types and phenotypes

People give meaning to materials, or meaning is there. The latter.

To what extent does meaning act on intelligence in a predictable way? To this extent, it is a part of the object.

Any message is divided into three layers: 1) frame message-confirming a decoding mechanism; 2) External messages-establish or know how to establish a decoding mechanism that can correctly interpret internal messages; 3) Intrinsic information-information intended to convey, phenotype in genetics.

Genetic information must be stored in an amorphous crystal structure. What is "Irving Schrodinger" life? The book itself is an aperiodic crystal structure with regular geometry.

What is the significance of returning to the question at the beginning of this chapter? In the dialogue between Tortoise and Achilles, they have different understandings of the notes in cookies-different decoding. But even if you don't eat it at first, you will still read the same information after opening the note, so we think the meaning is there, not given by people.

I found a bottle with a note on it on the beach. First, the frame information will confirm that it is an artificial information carrier. When I opened the note, I found that the font on it was written in Japanese, which was an external message. But I don't have the ability to read Japanese, and what I originally wanted to convey is still an unsolved mystery.

Man launched a metal record into space, believing that aliens would capture it. Regular geometry means that it carries information. As for whether the aliens can decode it correctly, it is only a matter of time. Because that's where the meaning is.

A new formal system--propositional calculus. Rule: If both X and Y are system theorems, then string is also a system theorem. Defines a subset of all strings-a collection of "well-constructed strings". (Recursive definition)

In particular, this system has no axioms, only rules. So the author calls him "the law of fantasy". If x is a theorem, then y will be a theorem. The real theorem is.

Infer a "clause" of a "→" string after knowing the sentence, provided that the string itself and the clause are theorems. -this is called "deductive theorem" (Modus Ponens)

After that, with the expected interpretation of symbols (including many special laws), you can substitute meaningful sentences, such as "Heart is Buddha". After symbolic argumentation, a new theorem is formed-either the heart is Buddha or the heart is not Buddha. It can also be used to explain the final ending of stories such as "the axe of the rock head" After 24 steps, Q: Both heads will be cut off.

Proof is deductive: proof is informal, or in other words, it is the product of daily thinking, written in people's language and told to people. All kinds of complex thinking characteristics are willing to be used in proof. Although "the feeling is right", I don't know if it can be guaranteed logically. This is the real purpose of formalization.

In all fields of life, contradiction is the main source of clarification and progress, and mathematics is no exception. A more relevant example is the contradiction between the way we really think and the way propositional calculus imitates us. However, propositional calculus is still very valuable, which provides effective propositional reasoning-all those that can be made. Therefore, if the incompleteness or inconsistency is exposed at any time, people can be sure that it must be the fault of the larger system, not his subsystem propositional calculus.

This chapter seems to be very difficult and has been turned over many times. The author has made many definitions to deduce and explain, which is too verbose and complicated. I try to generalize with my own understanding, and put the logical "OR and NOT" of the proposition through symbolic operation. It is difficult to defend yourself with logic and reasoning. You can't keep your reasoning mode forever. At a certain point, you can only rely on faith. The "fantasy law" (personal feeling is more like a hypothesis) is derived from a fantasy theory. The deduction is extremely rigorous and proves to be human thinking. There are contradictions between the two, but they are still of great significance. Propositional calculus is a symbolic system, an idea, a poem, a logic, and a bridge between man and computer.

Palindrome in Crab Gun-Gene Fragment-Indirect Self-Reference

If you want to see the self-reference, you must see the content and form of this conversation at the same time.

Define a formal system-number theory of printed symbols: number theory is expressed by printed symbols, abbreviated as TNT (typography number theory).

(To be continued)