Кузнецов Дмитрий Юрьевич: другие произведения.

Place of Science in the human knowledge

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  • Аннотация:
    The simple model for the classification of knowledge is suggested. The four types of knowledge are considered: customs, arts, religions and sciences. The strict definition of science is suggested to distinguish it from other kinds of knowledge and from pseudo-science.

http://samlib.ru/k/kuznecow_d_j/2010mestor.shtml Место науки (и физики) в человеческом знании, Russian version of this article
http://samlib.ru/k/kuznecow_d_j/2010mestoe.shtml Place of Science in the human knowledge, English version (this text)
http://mizugadro.mydns.jp/t/index.php/Place_of_science_in_the_human_knowledge This article at TORI, updated version


This research is motivated by the huge amount of pseudo-scientific results, that are sometimes declared as "scientific" in the publications. Especially grave the situation is in Russia. The publications make an impression, that in Russia, there exist the special pseudo-scientific academy, called "Russian Academy of Natural Sciences", raen (the abbreviation of the transliteration "Rossijskaya Akademiya Estestvennykh Nauk", Российская Академия Естественных наук), and the "academicians" of raen make mainly pseudo-science and use huge governmental foundation for this. The special bulletin [1] collects warnings about the danger tendencies in the development of the Russian science in the century 21, and indicates many cases of the abuse. In order not to criticize that raen, here the purification of the scientific knowledge is suggested instead.

The Russian version of this article [2] provides the definition of science, that allows to qualify some results as non-scientific by the formal criteria, at very beginning of the consideration. That definition is based on the simple exercise [3], which, in its turn, is based on the ideas of refutability of scientific concepts, these ideas had been developed by Karl Popper [4, 5, 6] in the past century. However, the similar phenomena of pseudo-science take place not only in Russia; this motivates me to make this English version.

An additional motivation of this research is to answer questions "how did you guess?" by my colleagues with respect to quantum stability of the optical soliton, or with respect to the divergence of the series of the perturbation theory, or with respect to interpretation of the ridged mirror in term of the Zeno effect, or with respect to behavior of the holomorphic tetrational in the direction of the imaginary axis. The section "Importance for physics" offers more examples and the references on the specific cases of such "guessing". In this article, I open my cards and explain, how did it happen, that I "guessed". I used the classification of hypothesis since century 20, but only now I formulate this as a self-consistent (and I believe, universal) methodology.

Roughly, the recipe can be expressed in the following way: "avoid pseudo-scinece, and the Science will advance". Of course, such a principle does not make the researcher's job instead of the researcher. But it helps in my case. I hope, it will help to my colleagues too. A lot of various pseudo-sciences may exist. So, the better is to classify not each kind of pseudo-science, but the Science, indicating its place in the Human knowledge. This is topic of this article.


The qualification of concepts and results in terms "science" or "pseudo-science" is very important. Over-vice, the science sinks in the sea of some new "results" that involve the perpetual motion machines, inertial propulsion, astrology and other similar staff; usually, such a pseudo-science pretends to be a new, very modern and revolutionary theory and/or effect.

Often, it is supposed, that the scientific research is true, correct, and the pseudo-scientific research is false, wrong, non-correct; so, for the qualification of any concept, it is sufficient to check it, to verify it, and, if it is wrong, to reject is. Such a common sense looks reasonable, but the abilities of pseudo-sciencists to write the wrong papers and get foundation for pseudo-science greatly exceeds the abilities of scientists to criticize them, to reveal the errors and to indicate, that some research is just wrong.

In this paper, the different approach is suggested. The idea is not to criticize each "wrong" concept, but to suggest the narrow definition of term "Science" in such a way, that the concept can be qualified as "scientific" or "non-sciencific", whenever this concept is correct or wrong. This cannot substitute the common sense, mentioned above, but some formal criteria allow to reduce the amount of results that deserve serious consideration.

Many Russian colleagues had to learn concepts that are difficult to relate with natural sciences, for ex.:
1. The observable Universe is infinite in space and time.
2. The gradual evolution of a species with genotype of 48 chromosomes leaded to the new specie with genotype of 46 chromosomes.
3. During the life of the past generation, the principles of the funding of science and all other activities should change completely. (The Communism was declared to occur in the past century, during the life of the generation that already past away.)
Such concepts seems to be wrong. It is important to understand how to avoid similar concepts in future. As the tool for the rejection of such concepts, the approproate classification is necessary.

In this work, the simple model of the classification of the human knowledge is suggested. This model includes only four cathegories: customs, arts, religions and sciences. The definition of science had appeared first in the short version about non-tradiotional concepts [3]. Here, knowledge is ability to generalize the experience in a compact form and to transfer it to other individuals. Religions are important kind of knowledge [7], and they should be distinguished from sciences. So, this article deals with both sciences and religions. In order to keep this article similar to the Russian original [2], many examples are related to marxism, widely known among the Russian colleagues graduated in the past century. (In the USSR, marxism was taught in all schools, institutes and universities). In order to indicate the difference between the scientific and the religious knowledge, both scientific and non-scientific publications are cited.


Past century, Karl Popper had formulated the criteria that allows to identify the special, extremely efficient kind of human knowledge [4, 5, 6]. He called it science, although the term science was used before in a different meaning; that meaning included the claim of objectivity: I frame no hypothesis, Isaac Newton wrote [9]. Roughly speaking, the science was considered to be a true, that does not need any falsification or refutation. Popper, contrary, suggests the criterion of falsifiability as the key property of science, modifying the meaning of this term.

For Popper, the thing that makes a concept scientific is not its objectivity, but the possibility to verify it, to falsify it, to criticise it arguably and to refute it [4]:
1. It is easy to obtain confirmations, or verifications, for nearly every theory - if we look for confirmations.
2. Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory an event which would have refuted the theory.
3. Every "good" scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is.
4. A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice.
5. Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are degrees of testability: some theories are more testable, more exposed to refutation, than others; they take, as it were, greater risks.
6. Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory. (I now speak in such cases of "corroborating evidence".)
7. Some genuinely testable theories, when found to be false, are still upheld by their admirers for example by introducing ad hoc some auxiliary assumption, or by reinterpreting the theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status.
The requirement of refutability opposes the believe in the ability to get some objective knowledge [10]:
Objective truth is that part of our knowledge which correctly reflects reality and does not depend upon the subject, i.e. on human consciousness and will. Objective method, therefore, means the method that leads to knowledge of objective truth. For materialism the recognition of objective truth is fundamental; consequently all materialist science must be objective in method.
There were doubts about the humanitarian science, but the objectivity of the natural sciences was believed to be well established and irrefutable. Many authors pretend that their concepts are true, so true, they do not need to allow any refutation (sometimes, the term falisification is used in the similar meaning). This creates conditions for the growth of various pseudosciences, which may be extremely efficient in getting foundation but useless in any other application. The identification of pseudoscience versus science is sometimes difficult. It is especially grave in Russia: in the USSR, in its time, even the theory of relativity, quantum mechanics, cybernetics were suppressed as pseudosciences [15]; the genetics and psychiatry were exterminated [16, 17, 18, 19, 20]. Even defenders of the objectivity mention the danger of pseudoscience, [22]. Both pseudoscience and the struggle against it are dangerous for science [23], while the development of science should allow the scientific revolutions [24]. The distinguishing between science and pseudoscience is necessary. The criteria to identify science should be adjusted; this is one of goals of this article.

The conflict between the interpretation of science by K.Popper and that by the objectivism is terminological: what kind of knowledge do we call "science". Below, the terminology is adjusted; in this article, the term "science" in used in the Popper's interpretation; however, even more requirements on the scientific hypothesis are formulated.

The classification suggested below does not refer to the correctness or wrongness of a concept. Even the concept about the existence of the "Mizugadro's number" [25] (which seems to be completely wrong) should be considered as scientific, if the ways of the verification and the negation are indicated. Then, the classification easy accepts the less radical "scientific revolutions" such as, negation of concepts of the universal time for all observers, or that of trajectory as universal description of movement, or that of conservation of number of atoms of each kind in any isolated system.


The category of customs should include not only the commonly accepted behavior of humans, but also the habitual semantics of commonly used human languages. For example, the usual meaning of the Bible is custom, widely accepted in the Christian community. The sentence You shall love your neighbor as yourself allows various interpretations, including the homosexual orientation of Jesus Christ [27, 28], dependently on the meaning of the word love and its Hebrew and Aramaic equivalents. Similarly, the interpretations by Tim Rice [29] and Michael Bulgakov [30] should be qualified not as a custom but as an art.

Aiming the description of knowledge, the definition above drops out some meanings of the word "custom". For example, the consumption of tobacco and alcohol in some countries also may be considered as a custom, but there may be doubts in the including of such a custom into the category of "knowledge".

The semantic of the human languages and their understanding, the meaning of words is the most important part of the human knowledge. Namely this kind of knowledge gives sense to other kinds of knowledge considered below. In this sense, customs are the most important kind of knowledge.


Art is knowledge that is free from internal rules and is realized in a reproducible form that allow its systematic investigation [8]. Such a definition corresponds to a goal formulated in the introduction, although it slightly reduces the set of things which could be called art.

Usually a product of art has the following properties:
A1. Beauty: Here, the beauty is the extensive ability of any unexpected use. The prehistoric hunter, painting and observing an image of an animal on a rock, may guess how to catch this animal; the reader, laughing on a comedy, may ask himself: Either I am free from all the evils shown? - although the primary goal could be just laugh.
A2. Structureless. Intents to bring into the arts rules are not efficient. The arts use all other knowledges; the same product may have both artistic and scientific value.
A3. Wisdom. Artists with their works say more, than they planned to say, and more, than they understand by themselves. In this sense, the product of art may be wiser than the author.
A4. Entirety. Intents to correct, to improve a product of art destroy it.
A5. Amoralism. Creatures that have goal to bring some moral to the society, have low artistic value if at all; the creature may violate any taboo.

Aiming the specific application of the classification, the topics of customs and arts are presented here only declaratively.


Religion is kind of the human activity and knowledge based on some (specific for each religion) set of irrefutable concepts, believes, texts, symbols and performances. [7]

Usually, any religion is characterized in the most of following:
R1. The existence of at least one God is presumed.
R2. There exist canonical sacred text, that allow the humans to guess the will of God(s) and follow it.
R3. God likes some actions of human, these actions are called Good.
R4. God dislikes some actions of human, these actions are called Evil.
R5. The suggested set of concepts pretends to play an organizing role in the society: The following to namely this religion provides abilities for the kindness, prudence and wisdom significantly wider, than any other religions.

It this article, God is generic term denoting any intelligent subject that in some way (that is not available for humans) has abilities that greatly exceed those of a human. Actions related to these abilities are called miracles.
God may look like a human (Jesus Christ, Buddha, Lenin), but also can be "non-material" (God - Holy Spirit, World Revolution, Marxism). God may be omnipotent (almighty), invincible, immortal and predicts future:
The Marxist doctrine is omnipotent because it is true.[31]
Long live invincible marxism-leninism-mao tsetung tonight.[32]
Lenin lived, Lenin lives, and Lenin will live.[33]
The generation of those who are now fifteen will see a communist society, and will itself build this society.[34]
The immortal beacon of Comrade Stalin will forever illuminate the path on which the Chinese people march forward.[35]
And he said unto Abram, Know of a surety that thy seed shall be a stranger in a land that is not theirs, and shall serve them; and they shall afflict them four hundred years. [36]

World religions, each in their own way, offer a unique set of moral values and rules to guide human beings in their relationship with the environment [37]. This set may justify the performances, that result the death of some of participants (see the figure at right). Often, such rules are presumed to be truth without limits and alternatives:
The law of the LORD is perfect, restoring the soul; The testimony of the LORD is sure, making wise the simple.[38]
... he who chooses a religion other than islam, it will not be accepted from him, and in the everlasting life he will be among the losers.[39]

Some religions do not identify themselves as religions, pretending to be sciences. [40, 41]. The adepts consider their own belief as the only true concept, deny the dogmatic character of their believes [42] and treat any deviant behavior as crime, heresy and mental illness; the wrong-believers are punished or undergo the forced medical treatment [17-21]. Some religions justify lies, sacrifices, betrays, massacre, murdering and wars, if they serve God: You cannot make revolution in white gloves.

Most of religions avoid any refutable concepts. The concept is called refutable, if (and only if) in terms if this concept, some specific observation can be described that negates the concept. For example, the statement The Party officially declares: The current generation of the soviet people will live in communism! [43] is refutable: based of such a declaration, the next generation may shame the soviet veterans as liars and impostors. Within few generations after creation of a new religion, it abandons and forgets all its refutable concepts and becomes more stable. Here are the examples of irrefutable concepts:
Communism is future of all the humanity, or
God blesses America, or
Imperialism is evil, or
God gives the immortal soul to everyone, or
The righteous will be at Heaven.

The canonic texts describe the marvels, miracles that are specific for each religion. The miracle may refer to the magic conversion of water into vine, to the drastic increase of the efficiency of the production by the inspiration of the Fuhrer, catching of the spies by children, destruction of an army of the enemy tanks by few heroic soldiers, launching grenades, etc.

The definition in the beginning of the section does not specify features R1-R5 as necessary; so, many kinds of knowledge falls into the definition of religion. In particular, it includes the shintoism [44] and the civil religions [45-48], although these religions do not pretend to be the "only true" knowledge and Gods in these religions are not omnipotent.

Religions form significant part of the human knowledge and play important role in the human history. While a religion is tolerant with respect to other kinds of knowledge (and in particular, to other religions), it may assist the prosper development of the society. No one religion can substitute other kinds of knowledge, end even other religions, as one specific science cannot substitute all other sciences. The society, where any religion dominates in an aggressive way, becomes barbarian compared to other countries within few generations; the people of such a society loss the ability to analyze the information.


As it was mentioned in the second section, the term "science" may have different meanings. Following K.Popper, in this article, this term applies only to a refutable knowledge. In order to distinguish science at the background of pseudoscience and religion, the term science should be defined as follows:

Science is kind of knowledge, activity and notations, based on concepts that have all the six properties below:
S1. Applicability: Each concept has the limited range of validity, distinguishable from the empty set.
S2. Verifiability: In the terms of the already accepted concepts, some specific experiment with some specific result, that confirms the concept, can be described.
S3. Refutability: In the terms of the concept, some specific experiment with some specific result, that negates the concept, can be described.
S4. Self-consistency: No internal contradictions of the concept are known.
S5. Principle of correspondence: It the range of validity of a new concept intersects the range of validity of another already accepted concept, then, the new concept either reproduces the results of the old concept, or indicates the way to refute it. (For example, the estimate of the range of validity of the old concept may be wrong.)
S6. Pluralism: Mutually-contradictive concepts may coexist; if two concepts satisfying S1-S5 have some common range of validity, then, in this range, the simplest of them has priority.

All the six properties are compulsory. For example, if the range of validity of a concept is the full set (id est, the concept is valid every time and everywhere), then it does not satisfy S1, and there is no need to check properties S2-S6 to qualify such a concept as non-scientific.

Scientific concepts are built on the base of observations, experiments, axioms, hypothesis, theorems and theories.
Observation means identification of some phenomena which are in some sense similar.
Definitions allow to use compact notations, making the description of scientific concept shorter and simpler.
Axioms are statements that are considered as initial at the building-up of some concept.
Concept with commonly accepted axioms is called "paradigm".
Theorems are statements that are proven on the base of axioms and definitions. Sometimes this term is used even in those cases then the proof of the statement is not yet constructed but is expected to be constructed in future. In such cases the term "hypothesis" or "Conjecture" is more suitable.
If the hypothesis is deduced from the postulates and other, already proven theorems, it becomes theorem.
If a hypothesis had predicted some non-trivial results of observations or experiments, it becomes theory.

Activity, related with development of new concepts is called research. The most important classification of sciences is based on the subject of the research, the goal and the methods, that dominate in the research: humanitarian -- natural, fundamental -- applied and theoretic -- experimenal. These three criteria roughly determine 23=8 main branches that may exist in any science.
Not all sciences are developed sufficiently to allow the use of the full scheme above. Before Hooke and Newton, the deduction was prerogative of mathematics and was not so often in physics, if at all. Before the quantum mechanics, the deduction in chemistry was not possible. Until now, many concepts in biology and the humanitarian sciences are built up on the base of guesses and the verification rather than on the base of the deduction.

Mathematics makes the basis of other sciences. No one science dare to contradict mathematics. The computational mathematics and cybernetics provide a bridge between mathematics and other knowledge. The general physics and theoretical physics relates mathematics with other sciences, although some sciences (even humanitarian ones) may use, for example, the statistical methods without to refer to physics.

If some science, concept contradicts the basic paradigms of mathematics of physics, then, according to S5, there should be indicated a way to see that they are wrong. To avoid the confusions, the term science should be used only in the sense of the definition above. In all other cases, the terms pseudoscience, sovietscience, christianscience, quasiscience may be used to specify that an activity or a knowledge looks similar to science or a scientific research.

Sciences and the society

Usually the sciences, and especially the fundamental ones do not give a fast benefit. The spending of the budget funding to support the satisfaction of the personal curiosity of researchers requires justification. There were intents to submit the development of science to other goals (creation of facilities of the modernization of the industry, or increasing of the military power of a country, etc.). Some researches, especially applied ones, can be motivated in such a way; and sometimes the results have the scientific value. However, often the results of such a research are just fake. During the human history, there was not developed more efficient motivation for science, than curiosity of researchers who do it. Yet, there is no other way to make the deep science. However, the needs of industry can be mentioned as motivation for the financial support of the curiosity of researchers.

The distribution of funds assigned for the development of science is serious problem. Administrators of funds cannot drill deeply into the research they finance. The funds are distributed on the base of the formal criteria: publications, citation, participation in the conferences. The ability to write the grant applications and good relations with colleagues and the distributors of funds become important, if not dominant, factor in the success in the getting of the financial support. For the same reason, the spectacularity of the new effects is important for their promotion.

Especially non-efficiently the funds are sent in the countries with corrupted bureaucracy; and not only because the significant part of foundation is spent for bribes and the private security. The government being unable to keep the growth of the technology of the country at the international level begins to secret the scientific achievements in order to enable the monopolistic use in the military industry. Often, the results are fake: the secrecy protects them from critics and opens wide field for both wanted and unwanted errors.

In a totalitaristic country, some sciences may be declared as pseudo-science, and then not only left without foundation, but crashed by the physical repression of researchers, as it happened in the USSR with the theory of relativity, quantum mechanics, cybernetics and genetics. [14-16,23]. Previously, in Europe, in the epoch of the Holly Inquisition, the similar phenomena took place with respect to astronomy. In all these cases the sciences were destroyed by a religion that pretended to be the holy true knowledge.
The properties S1-S6 allow to separate scientific concepts from others without fighting the pseudo-sciences.

About the terminology

Often the errors are caused by a smooth, fussy definitions of terms and the concepts. The most crying examples refer to the humanitarian science.
In 2009, Dmitry Medvedev had announced the setting up of a commission to counter the falsification of history [12,13]. This makes the Russian concept of history unfalisifiable and disqualifies it as science. There is still hope, that this is just terminological confusion, and that commission does not have the aim to destroy the historic science in the Russian Federation.

The aim of this paper is not to provoke conflicts, but to mitigate them. Therefore, I suggest not to use words "falsification", "falsifiability", at least in the scientific texts. Such terms are ambiguous, they may mean either the negation of a concept for the contradiction to observations or the misinformation.
Any term that has two opposite meanings should not be used at all. With respect to historical texts (whenever they scientific or not), the terms revisionism, opportunism and refornism appear in the similar (ambiguous) meaning [51,52], but the term refutability does not seem to be used in such a way.
In this paper, the term "refutability" is used. However, if refutation of the Russian official version of history will be also prohibited, then will be no way to attribute the confusion to terminology, and that concept should be qualified as non-scientific.

Importance for physics

The author would not like to teach colleagues, what to write and how to write, but just indicate, what properties make the research scientific. This section explains, why I boil up so old question, and why it is important for physics.

The author used to meet several "strange" concepts that pretended to be scientific. The examples are:
quantum annihilation of the optical soliton [53a],
reduction of the quantum noise due to the pre-amplification of the signal [53b],
single-mode approximation in quantum optics [53c],
extrapolation of the quasi-optical approximation in the atmospheric physics [55],
the "radius of convergence" of the primary series of the theory of perturbation [56],
quantization of the magnetic flux in a free space [57],
violation of the McCumber relation for the cross-sections of emission and absorption in laser media [58],
Violation of the Kramers-Kronig relation for the active laser materials [59],
non-equivalence of the van der Vaals potential to the index of refraction in paraxial atom optics, [60,61],
"proportional" increase of the power of a disk laser at the increase of size of the active element [62],
the immanent impossibility of the analytic extension of the tetrational [63],
the square root of factorial (which was declared to have no sense) [64],
the "symmetry" (x,-y) of the graphic of the tetrational to the base sqrt(2), y=tetsqrt(2)(x) [65],
and the itentioids (that violate the law of conservation of momentum) [3,66].
The author had participated in the discussions on very similar topics in various branches of physics. The common feature of these cases is that often the colleagues do not indicate a way to confirm their concepts (or do not indicate a way to refute them). In these sense, my coauthors and I had to fight against the religious concepts.

I cannot write a separate erratum or article on each of such topics. I suggest to adjust the criteria that the scientific results are supposed to satisfy. This does not mean to make the requirements harder, but to soften the struggle between the authors and reviewers, that sometimes takes the strange form: the authors try to hide the cases when the concept fails while the reviewers are supposed to reveal these cases. In particular, the criterion S1 strongly suggests that the researchers estimate, until where their concepts are valid. In the similar way, the criterion S3 invites the authors to indicate, which result of which experiment would indicate that they are wrong. Such indications and estimates greatly simplify the refutation of concepts, making them scientific.
This approach will help to deal with strange phenomena like observation of the "torsion fields" or the "cold nuclear fusion"; either to reveal the error of the concept at very early stage or to turn the research into the scientific methods, making them different from a circus trick. The definition of science suggested should allow this without to struggle against pseudoscience; such a struggle is dangerous for the science, especially in the countries where the abilities to the critical analysis were persecuted.

I do not suggest to make any scientific censorship. Even the texts of ideologists of fascism should be available, at least to allow the people to understand, what the fascism is. (Over-vise, the fascistic ideas will be discovered again and again by the new and new authors, and developed until to see the results.) Similarly, the pseudo-scientific texts should be published, at least to allow the people to understand, what is pseudo-science. (From my side, I offer the pseudo-scientific text Atlantide desert). However, the development of the pseudo-scientific ideas and the pseudo-scientific publications should not be supported from the governmental funds.

About the technologies

Technologies are older than sciences. First, Homo Habilis, and then - Homo Sapience. Technologies are close to both sciences and arts. On the one hand, technology uses the scientific achievements (and in this sense is close to science). On the second hand, any good technological solution is product of art. The margin between science and technology is determined by the the definition of Science. Technologies have no need to demonstrate the evidences of correctness of their concepts; the proof of technology is the efficiency in business. The intents to boost the technology with governmental support are not efficient; they boost the pseudo-science and the corruption. I consider the governmental foundation of technologies as fraud.

The classification of the human abilities and the analysis of the foundation of technologies fall out from the scope of this article and may be subject for the independent research.


The strict definition of science with criteria S1-S6 is suggested. These criteria are based on the idea of falisifiability developed by K.Popper [4-6]. By itself the term falisification causes confusions; in particular, it disproves the Russian concept of history [49,50]. This problem may come to other sciences, for example, into physics. The term refutability is better.
According the definition, the scientific results should include all the properties S1-S6. Recognition of these six conditions as compulsory is necessary to save physics and other sciences from profanation. I suggest that all the civil organizations and the courts consider as fraud any governmental foundation of any research that does not satisfy the criteria S1-S6. I suggest that the editorials of the scientific books and journals and the chairs of the scientific seminars accept S1-S6 as the main requirements for the scientific results. This applies not only to Russia, but to all countries.

Acknowledgment. Author is grateful to Shoko Okudaira for her help with references and to Kirill Velikanov, Alexander Kaminskii, Andy Blunden and Margarita Kallistratova for the critics and help.

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