There is a new article written more specific than the mathematical analysis in my article.
http://bbs.hoopchina.com/1009/1525287.html
I think some things are interlinked, and the
reader may understand it more like a
recommendation to everyone.
Maybe Nolan did not learn math, reading the book.
the MIT and a courseware.
http://ocw.mit.edu/high-school/courses/godel-escher-bach/
people are high school course
hey !
text has many deficiencies, led to a heated discussion.
feel sharp or extreme language, some readers may have been psychological injury
to dissent Shenru weak resistance.
Since the cause of much controversy,
and therefore update the view Post it in the supplementary part of the article.
Directly modify the original text to be unfair to critics.
New Zhike magazine sent an e-mail question,
I made some amendments and answers,
and then edited it and adopted it by the magazine.
Those who are interested can go to Xinzhike. Miscellaneous or the main page of the website
http://blog.sina.com.cn/s/blog_4b1fa9690100l373.html
caption:
Maybe we shouldn’t just be students of inception,
but also players of
inception . When inception gave us this In a big space,
facing infinity and unknown,
Let yourself with endless ideas have a good time of dreaming and planting dreams.
)
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The mathematics principles and logic
in Inception have some self-proclaimed mathematics undergraduate students said that Inception let People think of derivative operations in mathematics. Dreaming and waking are actually derivative and inverse operations.
I feel a bit far-fetched.
It is true that Inception actually uses a lot of mathematical knowledge,
but many of them are beyond the scope of ordinary people's mathematical knowledge, and even so-called mathematics majors.
This is probably the reason why many people do not understand it.
Many assumptions and phenomena in Inception are actually derived from geometric research in modern mathematics.
The main thing is the manifold.
After watching it, some viewers
think that Inception is very mysterious,
and many places are illogical.
But in my opinion, there are few scripts with a more rigorous structure than Inception.
The structure of Inception is like a thesis, and it is also proof.
It is divided into three paragraphs.
The first paragraph is from the beginning until Leo meets Loli.
This paragraph describes the problem.
The second paragraph is Leo teaching Lori.
This paragraph is to put forward the basic principles and basis.
The third paragraph is to dive into the dream.
This paragraph is actually the argumentation part and the conclusion is derived.
The climax of the whole story is the third part,
but the second part is the core of the story logic.
Many viewers in this part said they felt dull, like they were in class.
indeed so,
Because the core of the story is actually based on dialogue, and it is more like a demonstration.
Why is it so?
Because if you tell you something
you don’t understand in the easiest way to understand it in class, you won’t be able to understand the film.
Let's take a look at a few issues in this paragraph.
The first question:
Why do you want to dive into the dream?
Leo said that
diving into a dream can change a person's mind.
A person is an idea.
The idea has changed, it is not it.
(Some people don't know this universal truth) The
second question:
How to deceive people?
Leo said: When a
person is awake, there
is actually a period of time when it is impossible to tell whether the dream is true
or the present is true.
It actually judges whether it is in reality through some standards.
This is actually the key to the whole movie.
It is also the title and basic hypothesis of the entire thesis.
So how did Leo do it?
Leo said he relied on tops.
If it doesn’t stop, it’s in a dream.
If it can stop, it’s not in a dream.
Many viewers see this is easy to understand.
In fact, I want to ask, what does this show, and what are the characteristics of dreams.
Then when Leo taught Lori to dream, he
folded the whole world up and down to form a strong box structure.
The audience was stunned by the sight before them.
What does this mean?
If the world becomes like this, the person in the dream can tell it is wrong at a glance.
Why does Leo show this kind of world?
When another handsome boy taught Little Lolita, he
walked up one flight of stairs and four flights, until he felt upward, but actually walked a dead circle.
What does the director want to explain?
Speaking of this, don’t you understand?
Then there is more.
At the beginning, Leo tried little Lolita's IQ and asked Lolita to draw a maze.
Little Lori drew two mazes first, and Leo walked out at once, but the third Leo didn't come out.
What are the characteristics?
In the first two mazes, there are edges and corners, and the third maze is drawing circles.
What are you talking about?
Up to this point, Leo has fully demonstrated his wit, and the way to put people in a dream is to let people run in circles.
According to mathematical language, Leo believes that the real world should be European space, while the dream world should be non-European space.
Nolan is a fan of architecture, and inevitably he is also a fan of geometry. In fact, he is a geometry class that teaches viewers an example.
Our space is three-dimensional. If you count time into it, it is four-dimensional. If you draw a circle in the dimension of time, the spinning top will not stop.
The other examples are actually examples of low-dimensional non-Euclidean space.
In one dimension, Euclidean space is a straight line, and non-Euclidean space can be a circle.
In two dimensions, European-style space is flat, and there can be many types of non-European-style spaces.
One is the staircase. If you remember correctly, it is the Ubis torus. This is weird because the two sides are connected and cannot be distinguished. Come on both sides.
The other is the spherical surface, that is, the world is folded up and down.
In fact, there are many kinds, such as torus, torus, cylinder, and Klein bottle.
As for the three-dimensional, the situation is more, but it is only visible in the four-dimensional space. If you can figure it out, you can engage in the theory of relativity.
What a great geometry lesson.
The next question is why you want to play non-European space.
This principle is very simple. The dream maker can think of limited things. If you want to trap people, you have to give it an infinite illusion.
If you think of the deceived person as a little bug, you can only run around in a two-dimensional world.
If it is a European-style space, it is a plane, and the design dream is limited. You can only design a large circle.
Then this little bug will run this round one day.
But if it's a sphere, it's different. No matter how the bug runs, it can't get out of the surface of the ball.
Extend a question to test your understanding, Xiaoshuai uses dice, how can Xiaoshuai check if it is in a dream?
Answer: If in a dream, Xiaoshuai's dice count will repeat periodically.
These geometric structures are actually called manifolds, and the difference between manifolds and Euclidean space is that they are locally similar and different globally.
Taking one-dimensional as an example, the one-dimensional European is a straight line, and the non-Euclidean is a circle.
If you take out a part of a straight line and then take out a part of the circle, you get line segments and arcs.
If the line segment is relatively short, or the radius of the circle is relatively large, the difference between the two will be very small, and you will not be able to separate your career.
So, if you only look at the top, or if you only walk up a flight of stairs, or live only part of the half-folded world, you will not be able to see the difference.
But in the overall situation, there is an essential difference.
The straight line extends to the two ends infinitely, while the circle can only repeat itself.
In the film, the former is the real world, and the latter is the dream.
In fact
, people who play mathematics have known about this matter for two to three hundred years. The person who first thought about this problem was actually Gauss (someone who is so unspeakable, if you don’t know that you went to school?)
Gauss first I worked on surveying and mapping for a period of time (so I came up with the Gaussian distribution and the small squares method. Didn’t you know that you went to college?),
So I found that the straight line seen on the ground is not straight on the tower (I have seen this kind of thing, but I didn’t dare to think
about it so much?) So I asked what is a bend and what is straight (both people are neurotic, Much more serious than me) After
thinking about it, I found that this problem will affect many problems. Geometry needs to be rewritten (Yes, if there is no straight line, is there any geometry? Gauss is indeed the pioneer of non-European mountains)
Gauss thought of this problem , He did not give an answer, but he gave an analytical definition of the geometric concept (that is, no ruler is used to calculate it with a vector formula), so he created differential geometry (hey, things used every day, it won’t work).
Therefore, we know that an important characteristic in non-Euclidean space is that the sum of the interior angles of triangles is not 180 degrees. (This is true, on the sphere, the straight line is the shortest geodesic, and the angle is the dot product of the geodesic differential vector).
And the method can also get high dimensions (as long as there is a standard system, there is a vector).
It’s not over yet. Soon Riemann, a student of Gauss, asked a better question (Genius taught by geniuses can only be taught by geniuses, but unfortunately died early, I didn’t see inception being released).
Gauss just got the graphics When bent, the marking system is still straight.
Riemann asked, can the standard system be curved? (You are sick, if the average teacher must say so).
If the marking system is curved, does the length angle have any meaning? (At that time, many people thought that Riemann was not asking about mathematics, but philosophy).
In the dream, how do you know the truth? This is a philosophical question in Inception.
In a curve marking, how do you draw a straight line is to transform a philosophical problem into an equivalent mathematical problem.
So Riemann created a set of things on the curve marking, which is today's Riemannian manifold and Riemannian measurement.
For more than 100 years, no one understood Riemann's contribution.
Then it affected film production (Inception), and then the theory of relativity in physics (don’t you know you’re still an earthling?)
Now you know how smart Leo's corner is (not smart, but more importantly, knowledge. Do you think that a genius in the architecture department is a high test score?)
You also understand that Nolan is not only imaginative, but also very rigorous. (The main reason is that the audience generally has a low level of knowledge, thinking that Nolan is playing through love).
But this is more than that in Nolan's world.
When Leo asked the old professor for a genius helper, the
old professor said to find you a little loli who was more genius than you.
In fact, one of the biggest questions taught in the whole film, I will analyze in detail later, is what the genius Lori did.
In the third paragraph, there is nothing at all.
In the second paragraph, if you can see clearly, you will find that Little Lori is an order of magnitude stronger than Leo.
The first little Lori learns very quickly.
The second little loli sneaked into Leo's heart.
The third little Lolita broke Leo when she played Dreamland for the first time.
The fourth point is how little Lolita verifies her dream: to push down a chess.
Note: His method is completely different from others.
Therefore, the geometric structure of Lolita's dream world is completely different from other people.
you guess!
you guess!
You go on to guess!
I know, but honestly, I didn't expect it either.
Nolan, you can't figure it out.
It’s a fractal!
Let’s think about it. In the
second paragraph,
someone taught Little Lori at the beginning.
When Xiao Mengli showed the world how he would bring down the old handsome man Leo,
Little Lori did this
Yes : He took Leo to a place, closed the door, and made two mirrors, so there were endless figures in the two mirrors.
Nolando is clever, what a beautiful metaphor.
If people are real, the image in the mirror is the image in the dream, and dreams can be endless.
What's more, if you are a little bit in the mirror, if you enlarge it, you will get a complete person.
This nesting is unlimited.
And zoom in at every point, and you will get another endless world.
It's like a point in a dream. As soon as you extend the time, you will get another dream world.
And the scale of this zoom is a certain amount. In the dream, the zoom is an amount of time.
In the mirror, the zoom is the size of the portrait.
In dreams, it depends on the inherent properties of the human brain,
while in reality, it depends on the distance between the two mirrors.
Improper looks good
on the scene, but logically it is absolutely absolutely.
It's absolutely unbelievable,
absolutely unbelievable.
How do you say it?
Of course, the director is just a good metaphor, and the real idea is still playing mathematics.
If you say fractal, you can't help but say chaos.
The first person to think of this is Poincaré (too cow to be so famous).
Poincaré's role is more than that in Nolan's logic.
One question is why dreaming is about building buildings. Is dreaming about building buildings?
Actually, it's not that simple.
Poincaré proposed the concept of phase and phase space.
Therefore, you can represent everything in the world with a geometric structure in phase space.
Therefore, in physics after Pang, there are basically geometric methods, such as superstrings and relativity, and there is no more analytical method.
The reason is that of course Poincaré came up with a conclusion when he played the three-body problem. The analysis method is impossible to be accurate and will produce huge misunderstandings. If you want to figure it out, you can only use geometry.
This is almost the source of the concept of stability in mathematics, and it also announced the death of analytical mechanics.
In the geometric method, Pang did not use differential geometry. He used the topological point of view, called qualitative analysis.
This is why Pang has a huge reputation in dynamics and the problems left behind are all related to geometric topology. (Poincaré conjecture)
Pang has actually known the existence of the chaos manifold structure for a long time.
Nolan may not play mathematics, but Nolan must have a geometric view of the world and universe, which is not surprising in Britain, where "A Brief History of Time" can become a bestseller.
If the universe is geometric, of course humans are also geometric, and human thoughts cannot escape the geometric structure.
So for philosophical issues, you can use a geometrical analogy to illustrate.
The question I most want to ask in Nolan's film is actually to question the true meaning.
In fact, this was not the first question Nolan asked. It has been asked in philosophy for hundreds of years, and there should be new ideas in modern times.
Nolan’s greatest contribution is to tell us the meaning of this question:
"A person is an idea. If an idea is replaced by a person, it is the same as killing the person."
In fact, Leo in the film is the person who understands this point best. .
He not only knows the power of this kind of thought, but also the lethality of this kind of thought.
Because of this, he killed his own wife, even though he did not intend it.
He just wanted to know if he could put ideas into other people's minds, and make them think it was their own ideas.
And the idea he wanted to implant was to "make a person treat reality as a dream and dream as reality", of course he succeeded.
Then he was tragic, and his wife jumped off the building.
In fact, what Leo struggles with is not just his feelings for his wife, but also his fear of the idea itself.
Because the power of this idea has grown so much,
he can't get out of it himself.
In fact, others can kill it with dreams, and he can do nothing.
Moreover, he himself could not conclude that his thoughts were true, that he was not implanted, and he was not dead.
This is the question of how to draw straight lines in the curve marking system.
In fact, there is no answer.
In the third part of the film, there are too many doubts.
The key problem is that you don't know whether it is the real situation in the dream or the assumption made by others to deceive people.
First of all, before sneaking in, it is said that the enemy’s dream will have five layers, or even more. In fact, the enemy only broke through the third layer,
so you don’t know if the enemy was actually defeated on the third layer or was there. The third floor was circled in.
Because the third dream was not made by Leo, but the enemy's dream.
You don't know.
Second, according to Leo's design, the mission failed on the third floor. In fact, Lori came up with a way to save it.
Was it really rescued or did Loli fall into the trap?
Third, you will find that on the fourth floor, Leo did not replace the enemy's thoughts, but actually said all his thoughts.
After that, Leo was in danger.
Fourth, according to my understanding, the more a master,
the deeper he should be able to dive in the dream. In fact, Leo is actually transparent on the fourth floor, and we have not seen the first master Lori dreaming.
Little Lolita made it once in the film and broke Leo. Leo said not to use real things to create dreams.
why? Because Leo is only a master of the fourth-level dream, and little Lolita is a master of the fifth-level dream.
The dream made by the master of the fifth-level dream can only doubt, but can't tell the truth from the false.
Therefore, after the fourth floor, Leo has no confidence in the truth. In fact, from Leo's point of view, we don't know what is true or not.
Fifth:
We know all the people in the film what they think, but we don't know what Loli thinks.
And I didn't see Lori experience her dream.
So in the end there is actually no end.
Someone guessed several endings,
saying that it could be a dream from the beginning.
I can think of dozens more.
It is entirely possible that the old man made a little loli trap Leo so that he would stop doing bad things (how justice I am).
This is entirely possible, think about it, Lori has never met Leo's wife, but why did she create a beautiful woman in her first dream? (The old man told him).
Second, you said that Leo saw the child's face, which means it is not a dream, it is real. (I’m not right, others can’t make it, but if the old man told the little loli, it’s entirely possible. The old man has seen a child).
And the talented little Lori fell in love with the clever old handsome man, (my favorite ending)
trapped him in her own dream YY (although it’s a bit too much, but it’s possible)
Otherwise, why does Xiao Luo always always What do you care about Leo's ideals?
Why did Leo's wife ask Little Lori to be Lover?
If I was a little Lolita, I could do it at all. I would trap Leo in a dream first, then go back to the old man to look at the child's picture, and then fill in the dream. (The power and wit of love are infinite).
In fact, as long as you dare to think about it, the final outcome can be anyone’s dream in the film.
If you dare to think again, the ending can be anyone’s dream dream. , Maybe all people are not real, they all came up with it.
So Nolan doesn't want to give you the ending, the ending is like this forming a fractal structure.
He tells you that in such a structure, you will never know the truth.
Nolan successfully proved a sad conclusion with the construction method:
"Although the idea is important to a person, the idea of changing a person is like killing a person, but the idea of a person is his own, or He may never know if it is implanted by others." At
this point, you see, isn't Nolan's film a rigorous essay.
Write a summary below:
Nolan raised a question about whether one’s thoughts are personal or implanted by others
. Inspired by fractal geometry, Nolan used a simple hypothesis to construct a fractal structure.
In this hypothesis, Nolan derives endless conclusions from a starting point, thus clarifying that "this problem is actually impossible to solve".
Nolan's hypothesis is reasonable, the argument is rigorous, and the explanation is convincing.
It is a good essay rarely seen in film majors in the past 30 years.
I hope everyone will circulate and study hard.
Extended discussion:
1 For a nation that has no knowledge, no ideas, and does not understand the importance of independent thinking, such as China, can such a movie be made?
2 For an audience who has no knowledge, no ideas, no thinking ability, and whose ideas have been stifled since childhood, such as a Chinese audience, can they really understand the movie except for five stars?
If you don't say it, it's all tears.
In the future, movie tickets can be saved a lot.
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(
Supplementary note:
Everyone has their own opinions, and I accept different opinions.
The original text was written in one breath, and many places were not considered too much, and the words were not clear, leading to unnecessary quarrels.
Some explanations:
1 The explanation of the mathematics part is
mainly to try to find the connection between the scene design and the theme of the story.
Extension To say a little about the history of mathematics is intended to give non-technical friends a little intuitive understanding.
I think many things were not made by Nolan out of thin air. Some people thought about it first, and he was inspired. The
circular argument and the infinite recursive logical structure will It leads to the logical unknowability.
Different people can think of this conclusion in different ways.
But it may be more concise to explain with mathematics.
It will be more intuitive to explain with geometry.
2 The extended part is a kind of cultural criticism.
My extended part criticizes not that the audience does not understand mathematics.
Because our education and culture tend to kill ideas and discourage people from having unique ideas.
We do
n’t know how to cherish unique ideas, and we do n’t know how far-reaching the harm is to strangling ideas.
We have no defensive intentions and resistance to implanting ideas.
I think the unknowable situation on the one hand reveals the possibility that a person is implanted in thoughts without being aware of it. On the other hand, being agnostic also provides space for multiple ideas to coexist.
Many people pay too much attention to specific details without paying attention to themes and meanings.
3 Some extreme remarks are not verbal abuse, but criticism.
Cultural criticism does not mean spending compatriots’ money and killing compatriots.
Criticism shows responsibility, feelings, and expectations.
Different experiences will make people choose different ways to express their feelings.
Don't make personal attacks.
)
Then add
{
one about errors in plot analysis.
This article is written based on the viewing experience of the second day of the premiere on July 17th (the original sound has no subtitles). The author also has many views on the second day of the premiere. Question, many thoughts completed this film review in the first time, because there are spoiler content, so it was a week to post it. I admit that there are some errors in the plot analysis.
As totem's answer, Mal is the projection of leo, the third part of the layering, generally accepted is four layers plus limbo. I am grateful for the criticism that pointed out my mistakes. In the plot analysis, some of the original texts were not revised mainly because of two points:
1. This would be unfair to critics
2. Some important conclusions can be remedied.
For example, from the perspective of non-European space (where Ubis is a mistake),
mirrors and stairs are the analogy of geometric structure to the logical structure of the story, the logical structure of an
infinite variety of endings,
as well as the grasp of the theme, and
even the second aspect of the ending of the story. Kind of conjecture (the old man and the little loli story).
These views have not been reasonably overthrown.
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2. Significance of an in-depth mathematical analysis attempt.
I think there are two levels of understanding a thing: The
first is that you think it’s okay.
The second is that you can construct the same thing.
For inception, the
first level is that you get some inspiration and insights from watching movies.
The second level is that you can write a script comparable to inception.
Just because you have the same perception does not mean that you can write the same script.
Each of us has a lot of insights in our lives,
but who can write ten years of insights in a story and express it in a 48-minute movie.
The story of inception triggered various discussions. Many people said that it was because the ending was open. I don't think it is that simple.
Many movies cut the last ten minutes, the audience can guess an eighth, and there is no room for interest in thinking. My view is that many places are well-designed, and the final opening is just to detonate everything in ambush.
Some endings are open, but they are extended. You just continue to expand the story,
and inception will induce you to doubt what you see and subvert the part of the story.
My view is that many places are well-designed, and the final opening is just to detonate everything in ambush.
No matter how many ideas, they must be stuffed into the logical space of the story.
This may be the most difficult thing in creation.
We can say that Nolan has made at least three movies in the space of a movie.
A romance film, a commercial disc, an action gunfight film, and this structure is still expandable, the dream adds another layer, and there is more space to accommodate new elements.
What I praised most is the comment that inception uses
infinite mathematics to construct infinite skills from a finite structure .
This kind of statement is more relevant and accurate than my manifold and fractal, chaos said. It is a more advanced abstract generalization.
The various geometric phenomena in the first half are geometric methods from finite to infinite, and the
storyline is logically finite to infinite.
I don't know if similar ideas have been produced in the field of basic knowledge except mathematics.
To understand this,
we may understand the logical correspondence between the first half and the second half.
Many things are no longer fun, but delicate.
Maybe ordinary people have also mastered the way to make the story completely different.
This is meaningful for creation.
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re-criticism of the three cultures only
appears every day, and I think of European and American cultures.
Whenever I see the spirit of serious learning and inheritance, I think of Japanese culture.
Other phenomena make people think of Lu Xun involuntarily.
｝
｛
One is popular science or ZB?
I received countless criticisms,
saying that I made mystery and
made people faint.
When I wrote it, I didn't expect anyone to be so resistant. The
enclosing ones were meant to be a joke.
Who would think that a bunch of people were hurt without laughing.
The Department of Mathematics says that it's not wrong at all.
What I said was a basic point of view and some prominent figures in modern mathematics.
It has been one or two hundred years to this day, and the influence is everywhere.
Like non-Euclidean geometry, relativity, chaos, Poincaré conjecture (proved by the Chinese in the newspaper Tiantianbao).
These are not all words we have heard.
In the movie, I thought that the mathematics department would recognize it at a glance, and anyone who studies mathematics doesn't know the point of non-Ou.
Just write it down so that you can combine the things you usually listen to and talk about history with the movie.
I thought that the audience would understand that many scientific things are actually connected together, and there is a context.
Listening to the mysterious words is actually very simple, just to deepen the intimacy of mathematics,
and understand why mathematicians are worthy of respect,
because they think deeper than we think, think far, and future generations will benefit infinitely.
Remember a character like Gauss,
whose popularity is about the same as that of Newton.
In Germany, the head is printed on banknotes.
The story of the sum of 100 numbers at the age of three . The elimination method of the
regular heptagonal story
line number solution equation system is called Gaussian elimination, and the
iteration method is called Gaussian iteration,
least squares,
Gaussian distribution on probability, and
signal Gaussian filtering in the,
geometric Gaussian radian. I forgot about the
basic theorems of algebra
,
and there is Gaussian atomization in ps.
There is also a physical unit called Gauss in the electromagnetic field.
I always thought that those who went to school would regard knowing Gauss as common sense.
What kind of professional knowledge is used for this thing.
In the UK, this is what a general undergraduate book and a two-episode documentary.
Second, don't think that foreign writers are like literary youth.
The scientific quality of many writers in foreign countries is very good.
The writer who wrote Alice in Wonderland was playing mathematical topology.
It's not surprising that someone who studies architecture like Nolan has a basic geometric background.
Some people also said that he still read Turing and Gödel.
If that were the case, agnosticism would be easier to understand.
Turing was famous for playing chaos.
Gödel is to prove that the axiom system is unknowable.
They don't read mathematics,
but they can read scientific ideas and influence through various methods.
The penetration of Western science into culture is ubiquitous.
Don't think that things without depth should be dug.
Everyone in the dream has thought,
if you were given a chance to steal something, what would you steal?
If you are given a chance to harm others, what do you most want to destroy him?
Most people think that stealing someone’s money and ruining his official position.
That method is only useful to ordinary people.
A real hero is like a great ancestor, who has
no money to do it himself, and even responds if he is seized of power.
Has anyone ever thought of stealing people’s ideas and planting them?
This is the cruel way to get rid of geniuses and heroes.
"The rule of culture is better than martial arts", not everyone understands it.
What is the eight-legged selection of scholars, the sole respect of Confucianism, the
sage of the inside and the king of the outside, and the rites of the Siyi.
What the ancestors said every day, I can't remember it then.
Being cultured in China does not mean that Chinese people are all cultured people.
Those who have played the sun never set will have this kind of insight. The
London script-writing community even Nobel took it a few times.
People have profound insights,
The culture people play is not just popular culture and popular culture.
}
{
About Goedel and Agnosticism (it's a second on the Internet, not written by me)
Modern Agnosticism
The question of philosophy and metaphysics cannot be proved or denied. But rational thinking can model meaningful assumptions. This school of agnosticism does not focus on
the seven powerful basis for the existence of God to support agnosticism.
Is the world knowable? We can decompose knowledge into two types:
theoretical knowledge: knowledge of a law, such as knowledge of the essence of the theory of relativity.
Knowledge-based knowledge: To understand the existence of an object, such as recognizing that there are nine planets in the solar system.
More than three hundred years ago, the progress of science, especially the progress of physics, seemed to imply that mankind: there are no unrecognizable things, only unrecognized things. Of course, at that time, a truly complete scientific research system was initially formed, and it was obviously too early to draw such a conclusion.
Now, many scientific facts point to the fact that the world is unknowable.
First, the uncertainty principle. This theory shows that it is impossible for us to accurately measure the position and momentum of a particle at the same time. Don't forget that the world is fully known as "knowable." Of course, I don't know whether this law is enough to completely overthrow the theory of knowability, but there is no doubt that this shakes up the theory of knowability.
It is true that this theory still has many doubts and loopholes, but it is already a recognized physical law. It has been developed for decades, has withstood the test of experiments, and has been applied in production. It is quite difficult to overthrow it. . At least not those philosophers can overthrow it casually.
Second, Gödel's theorem. This theorem states: in any formal system that includes natural numbers, there must be undecidable propositions. This should at least show that, in scientific theory, the world is unknowable, so the whole world is also unknowable. Unlike the uncertainty principle, this is a mathematical law based entirely on theoretical derivation, and it cannot be overturned at all.
The third is about the relationship between observation and existence. This point is essentially the same as the first one. Schrödinger’s quantum cat is in a dead and alive state if it is not observed. This is the description of the microcosm by quantum mechanics (the observation object of a quantum cat is uranium atoms, not cats, but microscopic ). Generalized to macroscopic objects, this effect is very small, but not zero. This is similar to the view of the ancient Chinese philosopher Wang Shouren: "When you don't see this flower, this flower is dead with you. When you look at this flower, you will understand the color of the flower for a while, and you will know that this flower is not outside your heart." The state of existence of the world is related to the state of observation of people, so it is obviously impossible for us to know a thing that does not exist objectively.
There is a well-known "delay experiment" in physics that allows photons to pass through two possible paths. The specific one can be determined after passing. It is still effective to extend photons to physical particles, but the operation is more difficult. Please pay attention to two points. 1: The specific status of this event is determined after the event; 2: The specific status of the event is determined by people, and we can decide subjectively. From this point of view, the objectivity of the existence of the world is indeed questionable.
This is a bit of an attack on materialism, because materialism itself claims that science should be combined with experimentation. If the results of the experiment do not match him, it does not rule out the possibility of slapped in the face. Of course, there are big loopholes in this view. First of all, quantum mechanics must be correct, but quantum mechanics has not been applied at the macro level. It has only been confirmed by experiments at the micro level. If the quantum effect is applied to macroscopic objects, he and he admits that the world exists objectively. The deviation of will be extremely small, and such a small space-time is certainly meaningless in practice. Secondly, the reason why quantum mechanics has reached such a result is that it uses another way of describing the world, which is the same as describing the world with conventional methods and adding a "quantum parameter" to modify it. Which one is correct? This is just to see which one is better to use. The simpler mathematical process and the more perfect physical explanation chose the former.
Fourth, the problem of
resolution of why "In the process of understanding nature, we will put forward many whys, and when you try to answer a why, you did not answer him thoroughly, but just attributed this question to another one. Why, usually the latter makes people feel more credible, or more difficult to answer. And this process can continue, forming a chain of why."
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This is doomed to at least one reason why it is unexplainable.
Fifth, our physics theory is not so much an understanding as it is a guess. In addition to the propositions in mathematical logic that are both possible to prove and possibly to be disproved, there are three types of propositions: those that are possible to prove but cannot be disproved, such as "a disaster will happen here." It is impossible to prove but it can be proved that it is not as good as "No one can climb this mountain". Neither can it be proved nor can it be disproved, such as "the pi has an infinite number of zero decimal places". Unfortunately, all laws of physics are propositions that are impossible to prove but can be proved. We can never be sure that he is right, but he may be overturned by counterexamples at any time. Don't say "practice proves the theory", because it should be said "practice proves the theory of denial". For such a theory, it is not so much knowledge as it is speculation. (Idealism may avoid this problem, but it is still unavoidable.)
Sixth, we can never be sure that the information we get from the outside world is true. This point is essentially the same as the fifth point. How can we understand the world? Look? hear? think? It's just sight, hearing, and chemical reactions in the brain. These are completely possible fakes. For example, your brain is put into a bottle, and electrodes are connected to a specific place to simulate vision, hearing, smell, etc., and you think you are alive and well. Or, you were born yesterday, and the memory in your brain is only artificially input, so you mistakenly believe that you have lived for many years. You can never be sure that what you are in front of you is true, but it's just a guess from experience.
Seventh, we do not have the information foundation to fully understand the world. The process of knowing a thing (intellectual knowledge) is just storing the information of that thing in the brain, which is impossible for the entire universe. Because the total number of possible arrangements of particles in the entire universe is more than our brain, and our memory information cannot be more than our brain, so it is impossible to put the information of the entire universe into the brain, and it is impossible to understand the entire universe. .
In summary, the world is unknowable.
}
{
Some explanations about mathematics. :
There are some imprecise points in my introduction to mathematics, which I don't think can be called nonsense.
Sometimes it may be easier to understand and image, losing rigor.
I'm not writing a textbook, I just want readers to have a feeling.
Some places are not rigorous enough, professional criticism, express gratitude, and
explain some problems.
1. Regarding manifolds,
I introduce the concept of manifolds in the article mainly to explain why people are easily fooled.
The main reason is to highlight the feature of "local similarity, global difference".
The definition of manifolds in mathematics is very complicated,
and the current definition is not the same as originally thought.
Gauss studies curved surfaces in Euclidean space, and Riemann studies curved surfaces in Riemann space.
I think that the reader may be confused to say this.
The low-dimensional Riemann space may be understood as a smooth surface.
I think that the standard system is straight and the standard system is curved.
Although not accurate, I think readers can separate the two at once.
And in actual application, it feels like a standard curve.
A straight line on the surface is defined by the shortest defined length.
I remember it is called a geodesic. If it is wrong, please correct me. I will also study it.
2 Regarding the "Ubis" error
I first came into contact with "Mobius" early in middle school.
Because that thing can be used to construct many "impossible figures".
So when I saw the impossible staircase, I thought of it instinctively.
I know that it is in a space with a different structure.
Now when I actually use it, there are still more balls and torus.
And the notation used has been de-geometricalized.
More often use the quotient space as the product method.
I apologize for making a mistake in the geometry name.
3 Regarding fractals and chaos,
I think this thing is conclusive.
Fractal is a kind of chaos,
and the person who originally proposed fractal also did atmospheric physics modeling.
At that time Pang knew there was such a thing, called a strange attractor.
Later, people found it with a computer.
In fact, drawing fractals and using a computer to solve differential equations are essentially the same thing.
It turned out that I knew about fractals and chaos,
and the connection between the two was only later known.
4 Godel and Agnosticism
At first, I didn't think about the relationship between Godel.
I think the friend who left the message has a deeper understanding of mathematics and knows more than me.
As for the relationship between Goedel and agnosticism, to be
honest, I just know, but I don't know the details.
I quote the introduction on the Internet because I think it speaks very well.
}
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