On the rigidity and flexibility of thinking (Scientific superstition-3)

Scientific superstition (3)

 

5. Science is limited.

At the end of the 18th century and the beginning of the 19th century, the Fog shrouded in nature gradually dispersed under the storm of science, and the absolute dominance of theology was not stable. For the sake of this scientific view, Laplace (Pierre-Simon Laplace) takes a closer look: "the status quo of the universe is the fruits of the past and the cause of the future. If a wise man (who later generations call it the "Laplace demon") knows the position of all forces that cause natural motion at a certain time point and constitute all natural objects, then he uses a formula to describe the motion of all objects, regardless of the size of the object. For him, everything is fixed, and the future is as vivid as in the past. "When Napoleon asked why he did not mention God in his scientific works, this politically compliant character shows a strong philosophical strength and speaks out the following rhetoric: "Your Majesty, I don't need that assumption"

Laplace spoke to the vast majority of scientists in that era and expressed his belief and pride in replacing the law of God with the law of science as the dominator of the universe. The fly in the ointment is that even though he rejects God's assumptions, Newton cannot explain that he owes him to God's first impetus. His estimation of the power of science is too optimistic even if he does not leave this point alone. You may say: This only describes the limitations of the times, not the limitations of science. With the development of the times, does modern physics make up for the shortcomings of classical physics? Even if modern science is still not perfect, it will continue to develop in the future, and there is still an infinite possibility of science. This statement is quite reasonable, but what we want to question here is not the theory of the Laplace ERA itself-the theory that modern people took to blame for two centuries ago is not unfair-it is the scientific view behind the theory, including the causal law (causality) determinism, reductionism, mechanic, realism, and materialism. As we can see below, these ideas are challenged by modern science to varying degrees, and on the other hand, they depend on modern science to a considerable extent, it is precisely this rigid requirement and inherent contradiction that reflects the inherent limitations of science.

1. Causal laws and determination

The causal law describes the relationship between two successive events. The former is the cause, the latter is the effect, and the other is the effect. Deterministic usually refers to the cause-and-effect (Causal determinism). It not only advocates the reverse push of "if there is a cause and a reason", but also advocates the positive push of "if there is a cause and a result, therefore, what is happening now can determine what will happen in the future. Hard determinist even extends this idea to the realm of consciousness, denying the existence of free will.

Establishing a strict and complete causal chain for the objective world is not only the basic principle of science, but also the eternal belief and ultimate goal of science. With positive and negative causal chains, science can present its great charm and power. It can not only perfectly explain the past, but also accurately predict the future, this greatly improves the human ability to understand and transform the world. In fact, this is what Laplace advocates. Of course, his expression is more extreme-all the causal laws can even be attributed to a single differential equation about time. More and more evidence shows that this ambitious and attractive ideal is probably just a wishful thinking of mankind. According to the general theory of relativity, there are some spacetime singularity, such as at the beginning of the Big Bang or the center of the black hole, which will be ruthlessly damaged and the existing scientific theories will all fail. In addition to such extreme cases, the radioactive decay phenomenon is also embarrassing to the cause-and-effect decision-makers. It is discovered that the decay rate of radioisotope is not affected by external factors, and its decay process cannot be accurately predicted. It is completely random (this feature is even used to implement random number generators on computers ). At the time of the wave of quantum mechanics, causal certainty was under an unprecedented violent impact. Among them, the two most important forces are from Copenhagen interpretation)[1]InBoundun(Born rule) and Uncertainty Principle[2]. By interpreting the probability of the wave function that describes the state of micro particles, the former declares war on the beginning of the theory: Even if people can accurately measure all the initial states of electrons, it still cannot accurately predict its future position. The latter simply cut off the possibility of absolute accurate measurement in theory, so that the ideal of Laplace is completely lost. The great success of quantum mechanics has forced many decision-makers to leave behind and choose not to stick to the causal deterministic theory in the strict sense, but to support the causal deterministic theory in the probability sense. Another attempt was made to stick to the deterministic position in the macro field on the grounds that quantum mechanics only described the laws in the micro field. However, schrödör's cat, which Erwin schrödödödör, released to deal with the Copenhagen faction)[3]-- Although it is only an ideological experiment -- in the endless moaning, the uncertain ghost is moved from the micro-View world to the macro world.

Quantum mechanics theoretically denies the causal deterministic theory, while chaos further denies the causal deterministic theory in practice. Although the former is more profound in philosophy, it is not the ultimate theory after all. Many people are still lucky to expect a more complete theory, such as the Hidden variable theory ), this is enough to free all uncertainty from the scientific realm. Einstein, who was one of the founders of quantum mechanics, was one of them. He expressed his unwavering belief in deterministic theory by saying "God is not throwing a dice. From a practical point of view, chaos is more destructive because it has obtained unquestionable mathematical support. A notable characteristic of a chaotic system is that the system is sensitive to initial conditions. A popular analogy is that a butterfly fan its wings in Brazil and may trigger a hurricane in North America. There is no exaggeration in the art. A more realistic statement related to this is that long-term weather forecasts are impossible. The most surprising thing about chaos is that uncertainty can come from a deterministic system, which is quite different from the uncertainty inherent in the quantum world. Taking three-body problem as an example: Suppose the universe is only composed of three objects: The sun, the earth, and the moon. They follow Newton's law of motion and law of universal gravitation. When the mass, initial position, and velocity of the three bodies are known, their motion rules are solved. Obviously, this is a simple version of Laplace's deterministic system. But such a seemingly simple system not only does not provide explicit resolution, but also has a complex moving track, neither periodic nor stable.[4]. Any accidental external interference, small measurement errors, or loss of computing accuracy may have a significant impact on the results. It is really a "difference of thousands of miles ". What's more, how can the real universe become "Chaotic" when the sky is full of sand? It can be seen that, even if the chaotic system follows the causal law in theory, it can cause the actual distortion or breaking of the causal chain, and ultimately weaken the prediction power that science is proud.

2. Restoration and Mechanics

If the causal law is the basic belief in scientific research, the theory of reduction (or simplification) is the basic method of scientific research.[5]. In order to study a complex phenomenon or system, the method of reduction theory is to divide it into multiple components, and gain a general understanding of the original through the study of these components. If this method is applied to the whole universe in terms of breadth and depth, all phenomena in the world can be attributed to the motion of basic particles. Even an advanced life movement is a combination of low-level mechanical movements. This is the premise of Laplace, which directly leads to a mechanical theory, that is, the world is nothing more than a machine, or a precise and accurate clock. If God still has the value of existence, it is to build a good clock in advance. In turn, the mechanical theory also gives the restoration theory a logical foundation-the mystery exists in the details, as long as you tirelessly parse every phenomenon, all mysteries will be invisible.

Restoration and mechanical theory have always been the dominant idea in scientific development. The former provides methods for science, and the latter provides goals for science. It can be said that every progress of science is inseparable from Restoration Theory-observation, experiment, analysis, and abstraction all penetrate into the essence of restoration thoughts; every progress in science has strengthened the mechanical theory-the mysterious phenomena that once revealed the skeleton of machines under the anatomy of science.

Just as the combination of resumable and mechanical theories pushed science to its peak, there were signs of inaccessibility. Test the simple fact that there are more than 1021 molecules in a drop of water[6]. Even if all phenomena in the world can actually be restored to the mechanical motion of basic particles, who would expect to obtain the law of the universe by calculating the behavior of each particle? With this in mind, Ludwig Mann introduced probability statistics representing uncertainty into physics for the first time in Studying Gas Molecular movements. Although the macroscopic thermodynamic was successfully restored to the microscopic statistical mechanics, it paid a price of certainty, making the mechanical theory unattainable. Here, there is also a substantial difficulty in the Restoration Theory, namely reversibility paradox: the macroscopic thermodynamic process is irreversible (irreversible) (For example, the process of heat transfer from a high-temperature object to a low-temperature object), while the microscopic particle motion is reversible (reversible ).

Quantum mechanics still plays the role of the submitter. Randomness in statistical mechanics and chaos can still be attributed to subjective factors (for example, the investigator's insufficient computing power), while randomness in quantum mechanics is completely objective, which is a more fatal blow to mechanical theory. In addition, the integrity or non-discrimination in the quantum process and the measurement process is also incompatible with the local segmentation idea of the reduction theory.

The Restoration Theory includes two basic steps: Decomposition and integration. First, let's look at the decomposition process. It depends on a recessive hypothesis: after a transaction is decomposed to a certain level, the problem will become simple enough. If not, isn't the decomposition endless? But when people restore the complex macro world to the micro-View world, they are surprised to find that the randomness and complexity do not seem to decrease or decrease. The self-similarity (self-similarity) ry in fractal is even more powerful. No matter how many parts it is divided into, the local complexity is exactly the same as the overall complexity! It can be seen that the depth of decomposition layers does not guarantee the reduction of complexity. In addition, the decomposition process also requires that each part of the decomposition do not interfere with each other as much as possible, so that each part can be cracked.Divide and conquer(Divide and conquer ). However, due to the universal connection of things, this requirement cannot be fully met (for example, a tripe problem cannot be simply restored to a binary problem ). In order to implement the restoration method, some associations between components will inevitably be ignored, in some cases, the deviation caused by such ignorance cannot be ignored (for example, in a chaotic system ).

The integration process is also not easy. One scenario is that too much decomposition leads to difficulty in integration, such as the thermodynamic problem just mentioned. Another scenario is that part of the components or link information is lost in the decomposition process, resulting in a lack of integrity and failing to faithfully reflect the original overall characteristics. In a back-to-end scenario, the restoration may not be effective even if it is undamaged after decomposition. The core idea of the Restoration Theory is "the whole is equal to the sum of parts", which is undoubtedly correct when the whole is a simple linear superposition of parts. However, in a non-linear system, the whole may be greater than the sum of parts. For example, a very simple non-linear iteration function may also generate overall chaos. Another example is the complex system in systems theory)[7]It is characterized by self-organization in the dynamic interaction between the system and the external environment) can generate the individual does not have, the new overall characteristics, that is, the emergence of the term referred to as the emergence (emergence ). An interesting example is from ant colony. The study found that although the queen ant did not send a uniform command, every ant behavior was spontaneous, and communication between them was partial, the overall ant colony showed amazing macro intelligence, for example, finding the shortest path for food delivery and the best location for disposal of corpses. Other common complex systems include neural systems, ecosystems, social systems, and stock markets. It is worth mentioning that, although complicated systems such as spacecraft and supercomputer Are not complex systems, they can only be calledCompound(Complicated) system. Because they can obtain the complete description of the system from their individual, in other words, they can be restored.

At the academic level, the theory of reduction holds that political science is reduced to sociology, sociology to psychology, psychology to biology, biology to chemistry, and chemistry to physics. But in fact, each discipline has its own unique characteristics, concepts, rules, and methods at its own level, restoring it to a lower-level discipline is often futile-in addition to fostering the superiority of reducers, mechanical commentators, and physicists.

People finally realized that the crux of the Restoration Theory failure: It is cleverly waving a knife, often inadvertently cut off the overall contact meridian, thus Castrated the overall Original Organic traits. Ding ding's hand is clever and the knife is profitable, and it is impossible to fight the broken bull back to the original. As a result, holism, relative to the Restoration Theory, began to pay attention to it, and a number of system theories with the overall theory as the main ideology emerged, for example, the old Three Theories (general system theory, control theory, and information theory) and the new three theories (dissipation structure theory, consensus theory, and sudden changes theory. Even so, the nature of scientific tracing and the inherent quantitative and precise demands determine that the restoration theory will always be dominant. No matter how reluctant people are to equate flesh and blood with cold and heartless machines, or how mechanical theories repeatedly hit the wall in interpreting life phenomena, science will not give up its efforts to turn inspiration, impulse, free will, and even social phenomena back into basic particle collisions.

3. Realism and materialism

Modern science is almost synonymous with empirical science. The importance of empirical science is self-evident. Evidence is based on a premise that scientific research objects do not rely on observation or measurement. From a philosophical point of view, this is an embodiment of the truth, that is, we believe that the objective world is completely independent from the subjective and independent existence. It is not so much a scientific belief as a convenient assumption. Imagine if the original nature of the experiment object changes due to observation, or even does not have the so-called original nature at all, can the science based on the experiment actually reflect the objective law? This is not a matter of mediocrity. The uncertainty principle indicates that the observed behavior does have an impact on the observed object. Furthermore, when using the complementary principle Principle to explain the wave-particle duality, the Niels Bohr points out that whether the electron is a wave or a particle depends entirely on the observation method. At that time, the classical dream was broken, and the world that science was persistently pursuing suddenly lost its meaning. Not only is the separation of subject and object in the traditional theories broken, but also George Berkeley) the Bishop's famous saying "existence is perceived", which has been ridiculed by countless materialism, has concealed the radiance of truth. Therefore, the materialism in ontology is burned, why does this make the mechanical restoration comments feel inferior? They advocate restoring all phenomena including spirit to material form. If you think about it again, then the schörödnex and the friend of weignner's friend from it)[8]The boundaries between subjective and objective, material and consciousness, and between reality and nothingness are even more vague.

Although the theory of quantum mechanics is beautiful and has been tested for a long time, its challenge to the law of cause, reduction, and realism that science trusts and relies on exceeded the intuition and bottom line of ordinary people. Out of doubts about the completeness of quantum theory, Einstein and others proposed the EPR paradox)[9]. Unfortunately, Alain aspect and others designed an experiment against Bell's inequality, which finally resolved the blame of EPR. As a result, the local realism is denied, and the fixed domain and the real fish and the bear's paw cannot have both. If we need to stick to the truth, we will not be able to prevent the emergence of a spirit-like superdistance, and this will not threaten the existing scientific framework.

Vi. Rationality is limited

The limitations of science, on the one hand, are attributed to the complexity and changing nature of the objective world, and on the other hand, to the inherent weakness of human rationality. Note: The whole solar system is just a drop in the ocean in the universe. What kind of ignorance and arrogance a person needs to shout "man wins the sky"[10]Slogans. As Jack Pascal said: "The last step of reason is to acknowledge that there are infinite things beyond the scope of his understanding." Kant systematically reveals the limitations of reason in his pure rational criticism, in particular, the four antinomy in the book reflects the dilemmas of human cognition in the field of time and space, restoration, and causal laws, which cannot be simply solved by dialectics.

What best embodies the limitations of reason is mathematics and logic. Although the two are under the category of formal science in name, they are not scientific if they are measured by the testability. Even so, given that mathematics and logic are the cornerstone of all empirical science, their limitations must be the ultimate limitation of science. More importantly, as a product of pure mind, all mathematical conclusions and logical reasoning are prior and irrelevant to empirical facts (but may be inspired by empirical facts ), no possibility of being overturned by future experiments[11]Therefore, their limitations will be the ultimate limitations insurmountable by reason.

Historically, mathematicians made the same mistake as physicists at almost the same time. In his New Year speech by the Royal Society of England on 1900, Lord Galvin (this name is William Thomson) declared that the construction of physical subjects had been completed, leaving only the work of repairing and completing the physical objects.[12]. Although he observed that there were two inharmonious clouds in the clear physical world, he did not think that they had brought the subject into a storm. Coincidentally, in the same year, at the International Conference on mathematics, Pang galai declared that the absolute closeness of mathematics had been achieved, and once again turned the declaration of the building into the predictions of the generals. Soon, Russell's Paradox)[13]It has shaken the foundation of mathematics-set theory, triggering the third crisis in the history of mathematics. People are frustrated to find that the accuracy and certainty of reason are not only lost in physics, but not even in mathematics. What makes scientists even more embarrassed is that their arguments finally inevitably go beyond the scope of science or mathematics and enter the field of philosophy. The philosophical differences in physics have already been involved. The following briefly describes the three major mathematical Philosophical Schools in the early 20th century: logicism, intuitionism, and formalism ).

Logically, mathematics can be restored to logic, so it is only an extension of logic. However, the logics rely on some of the principles such as the axiom of infinity, the axiom of choice, and the axiom of contractual cibility. Their logic, rationality, and truth are not self-evident, and their selection is more non-logical. In particular, the logic of mathematics is totally attributed to logic, not only polishing the boundaries between the two, but also cannot explain a fundamental problem: why can a subject purely relying on logical deduction be widely and effectively applied to natural science? In other words, after thinking completely disconnects from nature, why is the law of thinking consistent with the law of nature? In addition, the logistic theory builds integers on the logic, but before that, it actually involves the Integer Concept and is suspected of circular argument.

Intuition is the opposite of the logic. The former tries its best to rely on logic, while the latter tries its best to get rid of logic and resort to intuition. Although the intuition school does not deny the necessity of logic, it rejects the logic as the source of truth. They believe that logical derivation is not more reliable than direct perception. Rather than complying with external formal logic rules, it is better to follow the rational constraints from the heart. Intuition only acknowledges that the object of mathematics is the product of the intellectual structure.ConstructionConstructive statement and proof, thus rejecting the actual infinity, rejecting the choice principle, and opposing the use of the exclusive law in the infinite set (that is, any proposition is false or not ). But as a result, the magnificent mathematical Palace will not collapse, but it will only be broken. It's no wonder that David Hilbert protested that the use of exclusive law by mathematicians is just as limiting astronomy to the use of telescopes. Apart from the limitations of practicality, intuition also has deficiencies in theory: human intuition is difficult to clearly define, not to guarantee absolute correctness.

If you want to test where you can find a rigorous and reliable mathematics, the logic will answer: in logic, intuition will answer: in the mind, while formalism will answer: on paper. In the form of a game headed by Hilbert, the idea is to extract all practical meanings of mathematics and turn it into a symbolic operation. Formalism faces a challenge similar to the logic: Why do meaningless and out-of-reality symbols fit with the experience world? Furthermore, since everything is an empty symbol, what is the reason for choosing a specific justice system? Although the style school is not very calm, it is still trying to build a complete and compatible form system to take all the mathematics into consideration. Unfortunately, the two incomplete theorems (Gödel's incompleteness theorems) of kurt_gödel (kurt_gödel) Wake them up from their dreams like two pots of cold water. It turns out that any form system that contains elementary number theory is incompatible and does not contain any contradictions. It must be incomplete-there must be a proposition that cannot prove and cannot prove. In fact, the compatibility of the system itself cannot be proved (within the system. It is undoubtedly a pity that mathematics, which is famous for being absolutely accurate and always correct, cannot get rid of the shadows of uncertainty and human reason is under unprecedented questioning. However, the spiritual and creative mathematical thinking is not a symbolic mechanical program, and the human's rationality is respected and worthy of luck.

The gedeli theorem not only implies that humans cannot obtain all mathematical truths once and for all, but also for computer science based on formal systems.[14]Set the ceiling (mathematicians are relieved, and their dignity and rice bowl are kept at the same time ). For example, Turing's halting problem is called the godeltheorem of the Computer Science Edition. This is incredible.Not computable(Incomputable) orUnidentifiable(Unsolvable) is not just an isolated case, but far more computable or deterministic. In mathematical language, the former is uncountable, and the latter is countable ). In this sense, although the computer is an extension of the human brain, the extension scope is very limited, but it can be used as a cane but cannot be used as wings.

The reason independent from experience (that is, Kant's so-called "pure rationality") is that it surpasses the physical limitations of human bodies and can analyze the principles of heaven and earth and observe the changes of everything. But there is one biggest obstacle to reason: infinity ). From Zeno of Elea's series of paradox about sports (Achilles and turtles, dual division, and flying yarn ), to Kant's back-to-back of a series of laws on time and space, combination and simplicity, causes and results, from Berkeley's infinite paradox to Georg Cantor's cardinal number) paradox, infinite is like a huge black hole, which has swallowed up the glory of reason. Mathematicians can use love and hate to describe their attitudes toward infinity. On the one hand, from the perspective of research objects and research methods, mathematics cannot be separated from infinity. On the other hand, infinity is a breeding ground for paradox and controversy, this can be seen from the three crises in the history of mathematics and the differences between the three major mathematical schools. Taking the selection principle as an example, it is generally described as: Any box containing balls can always select one ball from each box. If the number of boxes is limited, the choice is not a problem, but what if the number of boxes is unlimited? Most mathematicians acknowledge this principle and, in fact, they always use it intentionally or unintentionally. Constructivism, including intuition, believes that such a so-called choice is too abstract and cannot be constructive. Therefore, Constructivism refuses to accept it. Especially when they find that the right to choose will derive some intuitive conclusions, the opposition will be louder. For example, the point-to-ball theory based on the selection principle (*** Tarski paradox)[15]It sounds so absurd: You can split a three-dimensional solid ball into a limited block. After rotating and moving it, You can spell out two balls of the same size as the original ball![16]Obviously, on an infinite number of issues, computers with limited storage capacity and computing speed still cannot provide substantial help to the human brain.

Another common obstacle to reason is self-reference ). From the logic of the lie author paradox ("I am lying"), to the Russell paradox in mathematics, the Golder theorem, to the shutdown problem in computer science, in the philosophical sense, Kant's dual-law back-to-back (using reason to study reason itself) often puts reason into the strange circle of "dog biting the tail. People began to realize that rationality must discard overly-ambitious "Narrative Style" and treat with caution the words "all" and "everything" that were previously used. But this means that in order to open the knot of the self-directed point of reason, we must first open our own gap (rather a bit of a taste of "self-healing first ).

Note

1. SeeHttp://en.wikipedia.org/wiki/Copenhagen_interpretation.

2. The original translation method ("Uncertainty Principle") is somewhat inappropriate. It may lead to the mistake that the physical quantity itself is determined, but the measurement is inaccurate.

3. SeeHttp://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat.

4. There is another important reason why people are so concerned about the stable cycle solution of the three bodies: If a tiny disturbance will cause the sun to leave the earth, or the moon to collide with the Earth, then how insecure humans are.

5. Restoration can be either a Philosophical Viewpoint or a research method. The latter is used here.

6. Assuming that a drop of water is 0.05 ml, the number of water molecules is 0.05/18 × afowadro constant ≈ 1.67 × 1021.

7. Do not confuse complex systems with chaotic systems. Although both of them are non-linear, unpredictable, and complex, the latter is extremely sensitive to initial conditions. Although the former is active, it also has a certain degree of stability to maintain the survival of the system itself.

8. SeeHttp://en.wikipedia.org/wiki/Wigner%27s_friend.

9. SeeHttp://en.wikipedia.org/wiki/EPR_paradox.

10. The term "man wins heaven" may have different interpretations. Here we use the most common word meanings.

11. As mathematical proofs become more and more complex, a mathematical theorem may be incorrectly proved and accepted. But does this not also explain the limitations of rationality?

12. The original saying is: there is nothing new to be discovered in physics now. All that remains is more and more precise measurement.

13. One popular version of Russell's paradox is the barber's paradox: A barber claims that he only gave a face to anyone who didn't shave his own face. Should he shave his own face?

14. Computer science is also a form of science.

15. Strictly speaking, it should be called the Division theorem ". It is called "Strange Theory" or "Paradox" only because it is against common sense ".

16. A more powerful form of this theorem allows a table tennis sphere to be combined into a sphere of the earth's size.

Extended reading: 1. the colon classroom Douban link: http://book.douban.com/subject/4031906/

2. Internet link: http://www.china-pub.com/196068