Origin2000
Such dichotomy was introduced probably because the physical foundation of Molecular Dynamics was poorly understood by chemists, as often chemistry students do not have to attend a course in Statistical Mechanics.
This part is confusing. I want the author to provide the following evidence: 1. The percentage of chemists who poorly understand the physical foundation of Molecular Dynamics and the percentage in theoretical and computational chemists. 2. The percentage of chemistry (graduate) students who have attended a course in Statistical Mechanics in all chemistry (graduate) students and the percentage of those in all theory and computational (graduate) students. Without these data, the author's argument is weak. (Samples from randomly selected universities/institutes are also acceptable.)
A force field is always a vector field representing forces. Its physical definition is consistent, mathematically rigorous and unambiguous. In the context of molecular modeling, a force field refers wrongly (and confusingly) to both an interatomic potential functional form and its relative parameters.
1. This claim is the same as http://en.wikipedia.org/wiki/Force_field_%28physics%29 However, http://en.wikipedia.org/wiki/Force_field_%28chemistry%29 is talking about a different concept.
2. Following description in http://en.wikipedia.org/wiki/Scalar_field, it is at least under debate that potential energy can be classified as a scalar field. First, potential energy follows the mathematical definition of scalar field, i.e. "Mathematically, a scalar field on a region U is a real or complex-valued function or distribution on U.". Second, in http://en.wikipedia.org/wiki/Scalar_field, people have mentioned that "In physics, scalar fields often describe the potential energy associated with a particular force. The force is a vector field, which can be obtained as the gradient of the potential energy scalar field.". The author argues that "Everything reported below concerns the potential energy functions...". Therefore, this "force filed" concept can be classified as scalar field. However, there is "citation needed" in the following example. It clearly shows disagreement.
3. Actually, there are many scientific concepts that seem misleading. For example, "High-temperature superconductivity"(http://en.wikipedia.org/wiki/High-temperature_superconductivity) is misleading unless people know that superconductivity happens at very low temperature. A second example is "spectral theory" (http://en.wikipedia.org/wiki/Spectral_theory) introduced by Hilbert. However, "spectral" comes from word "spectrum" (shows in google) and "spectrum" was first used in optics in 17th century (http://en.wikipedia.org/wiki/Spectrum). Another example is "support vector machine" (http://en.wikipedia.org/wiki/Support_vector_machine) is not a machine but an algorithm.
Therefore, if the author insist the above claim, one the following evidences should be provided: 1. The author should provide evidence that http://en.wikipedia.org/wiki/Force_field_%28physics%29 and http://en.wikipedia.org/wiki/Force_field_%28chemistry%29 should be combined. 2. The author should provide evidence that the definitions in http://en.wikipedia.org/wiki/Scalar_field are wrong. Since the physical definition of scalar field is still under debate, the author should at least list definitions from 3 different text books and these text books should be popular, i.e. the author should also provide information that some lectures are actually use these text books. 3. The author should provide evidence that the concept "force filed" in chemistry was invited due to poor understanding of physical foundation of Molecular Dynamics. For example, the author can provide literature of comments on the name "force field" and the response to those comments, if there is any. The author can also provide evidence that this name was not proposed due to "convenience", "easy to remember", or other reasons. Either is acceptable.
Answers: 1a - I have no statistics, but conceptual evidence that such term is misused. Please continue reading for further details.
2a - Force is a vector by definition. Not a scalar. Interatomic potential is a scalar. The definition of vector field and scalar fields DO NOT apply to the general construction of a statistical mechanical model comprising a finite number of independent particles, which is commonly used in Molecular Dynamics simulation.
Vector and scalar fields are by definition continuous. This means that to have a scalar or vector field, then you must take in account the dense set of points in an arbitrary subset of space (in 3D). A system of distinct particles confined in a box, that is the statistical mechanical model you need to use for a molecular dynamics simulation, is not continuous in this respect.
If and only if a potential field would be taken in account in the hamiltonian form of the chosen statistical mechanical model, then the force field acting on the particles must be accounted in the force calculation as an additional term when deriving the potential terms. However, this is NOT a general case. Unless some energy contribution indipendent from particles acts on the each and very point of the simulated system, including the particles and the voids, there can NOT be a potential field (scalar field). Without a potential field, there can not be a force field either. The term "force field" is wrong in many aspects because not only it is wrongly used to describe scalar values instead of vectors, but also because it is wrongly used to describe a finite, non continuous set of values which do not represent a field, according to the definitions of scalar and vector fields in geometry and algebra. It is clear that the usage of the term "force field" as what was described in the voice "Force field (chemistry) prior to my contribution is NOT supported by any rigurous unambiguous definition nor in physics or in mathematics. Since molecular dynamics is a physical method, any other unfounded usage of the term force field in such context is wrong, no matter who uses it.
To put it in simple terms, following the logic of the remarks above, why don't we call everything "thing"? Simple: it's confusing.
3a - The Wikipedia voice "Force field (physics)" has almost nothing to do with the concepts expressed in the voice "Force field (chemistry)". The voice "Force field (chemistry)" should be rather appended or combined with the voice "Interatomic potential", because the two voices describe from different points of view exactly the same physical and mathematical concepts. In this respect, what is reported in the voice "Force field (chemistry)" is in fact an amplification of the concepts already expressed in the voice "Interatomic potential" concerning the usage of interatomic potentials for computational chemistry applications.
The answers I reported at the point 2a are easy to be verified as the concepts expressed are fundamental, so they can be found in any scholar textbooks of physics and calculus for high school and Bachelor of Science level scholar literature.
Comments of above answers Comments on 2a: 1. In general, the boundary condition you mentioned is not included as part of the "force field" and, usually, "force field" is defined EVERYWHERE on a dense set in 3D space. Please check the potential energy form of the "force field" listed in the main article. These "force fields" can be used in Molecular Dynamics simulations with ANY boundary condition.(e.g. cluster simulation: there is no boundary, soft wall boundary, reflective boundary; condensed phase simulation:periodic boundary). The "force field" function, together with suitable boundary condition, will determine the hamiltonian form. 2. Following definition of scalar field in http://en.wikipedia.org/wiki/Scalar_field, in mathematics, a scalar field can be defined on "a subset of manifold". If there is a scalar field defined almost everywhere, it is very easy to extend the definition within a subset by defining the restricted form and the measurablity is still well defined if this subset is measurable. From probability point of view, there is no necessary to restrict a scalar field in a set with some special mathematical structure like linearity(you mentioned space, especially 3D space). Also, I will be grateful if you can provide an text book example in which a scalar field is not allowed to be defined only on one subset in 3D space. 3. Sometimes it may not appropriate to separate a concept and try to understand it term by term. I agree that "force" is a concept w.r.t vector and I believe most chemistry students do know that. However, "force field" should show up as a phrase rather than two words. there are SO MANY similar concepts. For example, does "cotangent" in "cotangent space" really means the "cotangent function"? Does "error" in "error function" really means "it is error"? "Ideal" in ring theory looks quite different from its usual meaning. Do you know "method of steepest descent" is a method to calculate complex contour integral rather than a numerical optimization algorithm? "central limit theorem" has nothing to do with "central". "Characteristic" in "Characteristic function" is unrelated with "Characteristic" in ring theory and is also unrelated with "method of characteristics" when you solve first order PDE. "Elliptic function" seems unrelated with "elliptic" by definition. "Quotient" in "Quotient space" or "Quotient topology" is far away from "results of division". If "force field" need to be changed, then so do these concepts, as we have to keep "rigorous" from mathematical point of view and all above examples are from mathematics. Therefore, name of the concepts, once determined, are often used not because it is rigorous but because people are familiar with them. A good example is "potential theory" in harmonic analysis. People invited this name since they wanted to study physical potentials at that time. However, it mainly deal with harmonic function nowadays. If you think this name is not good enough, it's fine. You can post it on wiki but you should, at least, keep the opinions of both sides, rather than simply claim that it is "wrong". This is your own opinion and you haven't ask for the majority people in this field agree with you. Moreover, you claim that "Such dichotomy was introduced probably because the physical foundation of Molecular Dynamics was poorly understood by chemists, as often chemistry students do not have to attend a course in Statistical Mechanics.", from my point of view, actually challenge all chemistry students/faculties in this world. I just want to remind you that EVERYONE, include your advisor/boss, colleagues, and other chemistry students, senior and junior research scientists, journal editors, proposal reviewers, can read this article and, finally, you are NOT anonymous here.
Best — Preceding unsigned comment added by 216.165.95.69 (talk) 18:31, 8 January 2015 (UTC)
Thanks for your answer. Finally some constructive comments. I would like to remark few points in advance:
a - My interest is to provoke a clarification where needed in order to improve the overall quality of the article "force field (Chemistry)".
b - Thanks for reminding me not to be anonymous. Nowadays nobody really can say to be. However, I rely on the judgement of the reader to understand what to do with my contributions in Wikipedia. Ignorance is nothing I am ashamed of, and if somebody demonstrates that also my mental capacity is not enough for being a scientist, the world won't fall and I will be too stupid to care. Whatever I do in science is for the love of it and nothing else. I don't need it to earn my bread and my roof.
c - If somebody is right and proves me wrong, then I can totally admit my fault and apologize if needed or fix what is wrong. Of course that provocatory statement which brought us here now is just for the sake of provocation and apparently is working quite as expected. Nothing personal.
d - We're getting to the root of the issue and I will indeed delete the provocatory sentence. I just wanted some decent, competent reply faster than otherwise and that's why I thank you.
Said so, I will answer point by point your comments as before:
1 - The force field is a vector field, so it is defined for each and every point of a dense set of space. That is correct and nothing to object there. If in the wikipedia voice for the term "force field (chemistry)", the term "force field" would be mentioned in this way, I would not see any problem, except that they should not talk about force fields at all. Here is why I think so: let's talk equations a little.
To define the domain of existence of my statements, I take the following statistical mechanical model, comprising N particles having momentum and position so that its Hamiltonian form is:
where is the kinetic energy term (scalar) and is the total potential energy term (scalar) for each particle.
This Hamiltonian form describes a system where forces are conservative.
Because forces are conservative, the force acting on each particle of the system is related to the potential term according to the following equation:
The potential energy term can be described by a many body expansion
Because of the given Hamiltonian form, we know that the term . Such mathematical construction is the starting point to define a statistical mechanical model suitable for classical molecular dynamics simulations (if any errors, please correct it). Because of that, referring under any circumstances to as "force field" is conceptually wrong. I hope we can agree on this point and move on.
Let's take the definition of the total force acting ""on each particle"" of the system . This force describes only the force acting on each particle, but ""not"" on each point of a dense set of the space. According to this formulation, I do not see either why should be defined as a force field.
2 - You correctly mention that a scalar field can be defined on a ""subset of a manifold". And it is also right that in principle there is no necessity to restrict a scalar field in a set with some special mathematical structure like linearity. If you refer to the description of the system in the phase space, then we can indeed consider and agree that the total force and energy contributions for each point of the phase space can define a scalar, potential field and its relative force field. If we refer to the 3D space in which I define the position of the particles then we have a restriction, because particles have well defined positions, separated by void, so the subset of 3D space where the particles are cannot form, according to the mutually agreed definition, a scalar field. If there would be continuity in the potential or its relative force, then the potential would be defined per system indipendently of the particle positions, rather than in function of them. If particles would be a dense subset in 3D space or constitute a manifold for a certain n-dimensional space, then I believe that we would also have additional issues because of the definition of number density, which is fundamental in respect to the ultimate reasons for which you would build such statistical mechanical model.
In some cases you can surely introduce an additional potential field in function of the dense subset of 3D space, but that cannot be regarded as a general case for classical molecular dynamics simulation.
The wikipedia voice "force field (Chemistry)" does not even mention such point. Maybe it should be mentioned.
3 - To answer this more philosophical remark, I need to develop a little bit more the mathematical formulation of the previously mentioned and defined .
Usually in computational chemistry and computational biology the statistical model which is defined to run a classical molecular dynamics simulation is exactly the same as the one I reported at point 1. To this simple model it is often added a chemical order to the particles. Usually two main kinds of energetic interactions are defined: bonded and non-bonded.
None of those interactions is defined in every dense set of a 3D space where the atomic coordinates are defined. Voids between particles (atoms) still exist.
The bonded interactions are highly variable, but non of them is function of each point of a dense set of 3D space, hence they do not constitute, according to my understanding, a scalar field in 3D. The non-bonded interactions are of two kinds: electrostatic and Van der Waals. Electrostatic interactions are calculated by applying the Coulomb's law, in function of the interparticle/interatomic distance. The Van der Waals can present different equation forms, depending on the convenience. However, the most popular Van der Waals potentials are pair-wise. The pair-wise potential is obtained truncating to the second term, so that:
One of the most popular mathematical formulations for such non-bonded, Van der Waals potential is the Lennard-Jones (LJ). The LJ potential is parametric and often its parameters are reported for each, so called, atom type. It is use for SOME scientific communities to refer to entire sets of such parameters as "force field" too. I don't know about you, but for me this is pretty much ambiguous and confusing.
I understand that "force field" is not the only concept that has been distorted by different scientific communities. However, I think that such lack of communication between different groups it is a very hot topic nowadays. Different scientific communities do not talk to each other exactly because of such misunderstandings. Science is ultimately one. My efforts are focused on promoting such interdisciplinary communication, for which your suggested approach to terminology needs to be revised. The case of "force field" is a case close to my expertise, being a computational physicist specialized in Molecular Dynamics simulation.
I think that the examples you reported do not describe yet a comparable example with the level of distortion introduced by whoever started using the term "force field" with the acceptions I have described here.
I already removed the catalyzing sentence where I challenge the chemists, because I think that with this reply I ultimately defined and explained thoroughly the reasons why I have modified the voice "Force field (chemistry)" and the reason why I think that such voice should be integrated as a section in the wikipedia voice Interatomic potential.
I hope that everything has been now clarified.
P.S.: How's life in New York University? I love New York! :-)
So Here is the point we have disagreement. Your define a "field" in 3D space while I define it, especially for the "force field" concept, in 3N dimensional space where N is the number of particles. It is actually a subspace of the complete 6N dimensional phase space including the position and momentum of all particles. I agree that potential energy function of many-particles is not even a function of coordinates in 3D space. Now the question becomes: is it possible to generate the concept of "field" that is "usually" defined on 3D space to spaces with other dimensions. To me, from mathematical point of view, it is a straightforward generalization since analysis in R^3 is the same as analysis in R^n for any finite n. So you can keep your opinion if you believe a "field" must be defined on 3D space but, if you really want to claim your point, you probably need to clarify that your definition of "field" is in 3D space.
P.S. The life in New York is great. — Preceding unsigned comment added by 207.237.48.15 (talk) 04:22, 11 March 2015 (UTC)
Welcome
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Your editing of force field
editI am sorry, but after looking at this your edit, it is abundantly clear that you do not have a slightest idea about this subject. Not only what you are telling here is wrong, but it is completely unsourced (of course). Whst's wrong? For example, you included (diff above) this nonsense: An interatomic potential is defined in physics as a scalar, discrete quantity that can be estimated by a function for each particle of the system. For this reason, the usage of term force field to define an interatomic potential is indeed wrong. What this suppose to mean? "the usage of term force field to define an interatomic potential is indeed wrong" Can you explain it please? "Interatomic potental is a ... discrete quantity". Why? Interatomic potentials are mathematical functions, not "quantities", and they are usually continuous. My very best wishes (talk) 01:33, 11 March 2015 (UTC)
--- Very simple:
If the Hamiltonian of the system is then the potential is defined per particle and it does not constitute a scalar field in the 3D Euclidean space where the particle configuration is described. If there is no scalar field, its derivative cannot be a vector field representing forces (force field). This is true for whatever form you give to , which is usually approximated with a many-body expansion lacking the first term.
The model will work for whatever form you would like to use for the term . For this reason such term can be defined as arbitrary, including case limits like hard spheres.
If your system presents chemical order and you want to explicitate with a parametric function comparable with experiment, your simulation model is defined as realistic. This is opposed to toy models which are commonly used to describe systems without chemical order.
The force field as intended in chemistry is one of the infinitely possible explicitations of the term of the Hamiltonian. Hence it is not a force field.
If you would like to introduce a force field (real one), you must add a third term representing a spatially varying external energy field (scalar) to the Hamiltonian reported above:
Once you derive the third term, then you will get your force field.
This last Hamiltonian does not represent the standard case.
The usage of force field to indicate a quantity that is scalar (instead of vector) and is a discrete quantity (instead of a field) is fundamentally wrong.
Force field is used as jergon in the context of molecular modeling.
Welcome to illuminate me with a demonstration if I'm wrong. :-)
- I am sorry, but you did not answer my questions. Unfortunately, that your response tells once again that you probably have no idea about "force fields" in molecular mechanics (the subject of the page in question). To put it simple, the force field in molecular mechanics (a part of molecular physics) is something entirely different from the vector field you are talking about. Please read very carefully WP:Five pillars and other policies, including WP:OR. All edits like that represent "original research" and will be reverted. My very best wishes (talk) 02:39, 11 March 2015 (UTC)
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I completely understand that the word is used differently, but physics is one and terminology is rigorous (or should be). The usage of jergon, like in the case of "force field" in molecular mechanics, is common in many branches of science. If you are talking about Physics or whatever branch of science based on Physics, force field has one and one only definition, which is what I reported above.
What chemists use under the name of force field are energies, not forces. Whether or not this is a good practice is more of a philosophical question, rather than scientific.
Moreover, you did not actually explain your statement at all. You cannot just tell me that I am wrong without bringing scientific evidence. The wikipedia articles you cited are probably authored by the same person who made the same mistake. Could you either cite better sources or just explain me what you mean with your own words? More specifically, from your links I still see how "force" is used instead of "energy" and how "field" is used instead of "space". What I explained to you is the fundament of molecular dynamics simulation, which is based on classical mechanics.
Anyway, please keep your wikipedia article as you like. I don't have more time to invest in this topic.
The references to what I explained above are the following:
1) J.P. Hansen, and I.R. McDonald - Theory of Simple Liquids - Academic Press
2) Mark E. Tuckerman - Statistical Mechanics: Theory and Molecular Simulation - Oxford Graduate Texts
3) J.M. Haile - Molecular Dynamics Simulation: Elementary Methods - Wiley Professional
- Do you agree with the following: (a) Molecular dynamics simulations are based on Force field (chemistry), (b) Force field (chemistry) actually belongs to the field of computational molecular physics? Yes, I can agree that Force field (chemistry) in molecular mechanics sounds misleading, however this term is significantly more common than "interatomic potential" (and therefore preferred, see WP:Common name), which does not prevent some usage of "interatomic potential", of course. My very best wishes (talk) 04:59, 11 March 2015 (UTC)
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Molecular dynamics simulation is a deterministic computational method which calculates the trajectory of a system (described mechanically by the Hamiltonian I reported above) of N particles in the phase space (6N-dimensional hyperspace), provided certain boundary conditions. Your point a) describes a specific case of molecular dynamics simulation that is popular among computational chemists. It is not the general case, hence I do not completely agree. b) is conceptually correct, although the terminology is indeed abused.
- OK. Then the following is happening. You do not like this terminology (and it does look stupid for a "classical physicist" - I agree), however this is common terminology in the field of molecular mechanics and dynamics. Therefore, you should not replace it by something that you think is better. Doing so is WP:OR. My very best wishes (talk) 13:44, 11 March 2015 (UTC)
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You are missing an important point, which is that molecular dynamics simulation is not only performed with systems containing chemical order. In other fields, like condensed matter physics, soft matter physics and materials physics it is often the case that systems without chemical order are simulated. Yet, it is classical molecular dynamics. Classical by definition indeed.
It's not about what I think, it's about what it is. As I previously stated, definitions are and should stay rigorous. Hence, in the "force field (chemistry)" voice it should be reported that the word is used as jergon within a certain category of scientists, nevertheless is conceptually wrong.
Omitting that such improper usage of scientific terminology belongs to jergon is omitting a very important point of the whole story.
So, in my opinion, in the voice "force field (chemistry)", it should be clearly stated that the terminology is inconsistent with the canonical definition of force field in Physics and that nevertheless it is popularly used as jergon (slang) among scientific communities of computational chemistry.
Such piece of information is crucially important within such context.
It is indeed conceptually wrong to suggest that force field could have different definitions in Physics.
- OK, can be fixed this way. This is not an inconsistent definition in Physics. This is a very common situation when the same combination of words may denote several completely different things. We have disambig. pages for that, and we used it in "force field" page. That is what Opabnia r. talked about on this article talk page.My very best wishes (talk) 14:31, 11 March 2015 (UTC)
The problem with force field is that self-inconsistent within its jargon acception. In this sense it is not really comparable with situation where combinations of words change depending on their context. It's not force field in economics. It's force field in a branch of Physics. Physics must be self-consistent. So, I believe that it would be acceptable to state textually the following: "Force field is used as a jargon term in molecular modeling scientific communities to define both the interatomic potential form and its relative parameters. It should not be confused with "force field" definition in Physics."
- To do that you must provide very strong scholarly sources which tell literally this: "Force field is used as a jargon term in molecular modeling scientific communities". I doubt you can find it because this is not jargon, but an established terminology in the certain sub-field of science. In addition, you contradict yourself. First, you tell that "force field (chemistry)" actually belong to Physics (yes, I agree: it belongs to Molecular Physics). But then you suggest to write that it should not be confused with "force field" definition in Physics." Simply using a disambig. page (plus my addition above) solves everything. My very best wishes (talk) 17:12, 11 March 2015 (UTC)
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I do not contraddict myself. I specify my statement: (the jargon meaning) should not be confused with the definition of force field in Physics. With 'jargon' i mean: "special words or expressions used by a profession or group that are difficult for others to understand."[1]
Force field (chemistry) definition is specific of Molecular Mechanics to define a mathematical expression that describes the dependence of energy of a molecule on the coordinates of the atoms in the molecule (literal quote from ref. 2) [2,3], and does not constitute a general case for Molecular Dynamics [4,5]. This is clearly a case of jargon. If you simply substitute molecule with system and atoms with particles you have the general definition of interparticle potential which applies to all simulation methods based on classical, quantum or statistical mechanics where the system can be described mechanically (with the Hamiltonian reported in my first reply to you).
The difficulty consists in the realization that a specific, rigorously defined terminology, which is the canonical definition of force field in Physics, has been adopted by a specific community of scientists to mean a special case of interparticle potential, generating confusion in whoever scientist does not directly belong to computational chemistry (and even more within computational chemists too, in my professional experience).
To stress further the fact that computational chemistry community uses force field as jargon, I would like to remark that the usage of the canonical definition of force field in Physics must be used in case of a three terms Hamiltonian[6], which makes sense in the general context of physical simulation of systems of particles, including a specific type of molecular dynamics simulation.
References:
1 - Oxford Dictionary: http://www.oxforddictionaries.com/definition/english/jargon
2 - Schleyer, Paul von R. - Encyclopedia of computational chemistry. Vol. 2, E-L., p. 1015 (1998) - ISBN: 0-471-96588-X (This is the original, formal definition)
3 - Burkert, Ulrich and Allinger, Norman L. - Molecular Mechanics (1982) - ISBN: 0-8412-0584-1 (This is the oldest reference where force field has been introduced as jargon in molecular mechanics)
4 - J.M. Haile - Molecular Dynamics Simulation: Elementary Methods - Wiley Professional (1997), p. 1
5 - Mark E. Tuckerman - Statistical Mechanics: Theory and Molecular Simulation - Oxford Graduate Texts (2010) , p. 114-115
6 - J.P. Hansen, and I.R. McDonald - Theory of Simple Liquids - Academic Press (2005), p. 11
- Did any of these sources use word "jargon" with regard to force fields in molecular mechanics? No one would object definition like "a mathematical expression that describes the dependence of energy of a molecule on the coordinates of the atoms in the molecule". My very best wishes (talk) 01:24, 12 March 2015 (UTC)
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The acception of jargon is a factual evidence. However, I think that my last comment is fully exhaustive and unambiguous. Do whatever you like with it. After that point is not science anymore. My very best wishes.
- What you call "factual evidence" is "original research" by WP standards. OK, since you said above that "I don't have more time to invest in this topic", let us both do something more productive. My very best wishes (talk) 13:02, 12 March 2015 (UTC)
Alfredo Metere moved to draftspace
editAn article you recently created, Alfredo Metere, does not have enough sources and citations as written to remain published. It needs more citations from reliable, independent sources. (?) Information that can't be referenced should be removed (verifiability is of central importance on Wikipedia). I've moved your draft to draftspace (with a prefix of "Draft:
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editThe article contains several independent sources and citations already. Are there exact minimum numbers of citations and sources or is this something arbitrary? If it is arbitrary, it is quite vague. I cannot find exact numbers anywhere in the guidelines. Could you please clarify this point? Origin2000 (talk) 03:06, 20 February 2020 (UTC) talk.
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