AbnormallyHonest Posted April 7, 2017 Posted April 7, 2017 (edited) Although this may be met with some skeptic dismissal or active rejection... isn't it possible all of the "dark" we perceive in the Universe be a result of life? Say, harnessing something like zero point energy and bringing huge amounts of excess energy into this Universe and using that to manipulate forces artificially? I would say, that's a more reasonable explanation than nothing at all. If you think about it, this could also explain the expansion of space. If by harnessing zero point energy somehow accelerates the entropy of the space, it would also explain inflation. At the inception of the Universe, all that energy would've been pulled into space and then returned leaving only the fraction of what originally existed as the energy and baryon matter we see today. Inflation would've only been temporary, and the matter and energy that receded back into the structure of space would explain zero point energy and uncertainty, (which are basically the same thing but I'm simply separating the energy and matter by specifically using uncertainty as the creation and deletion of matter). I apologize, I guess there's a couple different topics there, and none of them are discretely supported by empirical data, but it is a nice way to describe what we see. Edited April 7, 2017 by AbnormallyHonest
Lord Antares Posted April 7, 2017 Posted April 7, 2017 Although this may be met with some skeptic dismissal or active rejection... It's because none of this makes any sense. It is philosophy at best. Since you are posting this in physics (and it was best put in speculations), you need to have some evidence or mathematical model of what you are talking about. Otherwise, it's just word salad. Science does not accept vague, unsupported definitions and therefore, any reasonable scientist must dismiss this skeptically. I apologize, I guess there's a couple different topics there, and none of them are discretely supported by empirical data, but it is a nice way to describe what we see. Because there is no empirical data, it is not a nice way to describe things by default. Do you have any predictions or evidence that this would be useful?
swansont Posted April 7, 2017 Posted April 7, 2017 How is that a simpler/more reasonable explanation than "a (relative) lack of photons"?
AbnormallyHonest Posted April 7, 2017 Author Posted April 7, 2017 (edited) It's because none of this makes any sense. It is philosophy at best. Since you are posting this in physics (and it was best put in speculations), you need to have some evidence or mathematical model of what you are talking about. Otherwise, it's just word salad. Science does not accept vague, unsupported definitions and therefore, any reasonable scientist must dismiss this skeptically. Because there is no empirical data, it is not a nice way to describe things by default. Do you have any predictions or evidence that this would be useful? I have our view of the Universe, which is shared by anyone who is willing to look. As I understand, this forum is for people who want to discuss topics related to science, and an interest in it. It is a public forum and designed to accumulate ideas and spark discussions, or is my interpretation fundamentally flawed? Is a science forum not a good place to introduce a new idea to those who have an interest, and perhaps and ability to take an idea and pursue the truth, or at the very least make a point out of it rather than a point of it. If you would like a deeper, more specific mathematical understanding, I do not believe this forum to be the venue to present those ideas, and at that level. Although, here is one: The observable universe contains 100,000,000,000 galaxies, each one on average contains about 80-100,000,000,000 stars, and about 80-90% (probably more) of those stars have not just a planet, but planetary systems. In truth, the Universe is probably infinite, it's just that an expanding view of space inevitably outruns light at far enough distances, no matter how slow the expansion is. We just can't see past where the speed of light is able to move toward us. So, assuming that we're the only living intelligence in the Universe, is 1 in a very large number and actually probably 1 in Infinity. I don't know how you would mathematically describe impossible, but 1 in Infinity takes a pretty good stab at it. I'd say those odds are pretty solid compared to invisible light... or missing photons. I'd say one idea creates a lot more disparity with Universal laws of physics than the other, and it's not the one that needs to create some new form of physics or an imbalance of conservation in order to explain it. The second paragraph is just the union of entropy and uncertainty, which are basically explained in very similar ways. The first thought inspired the second. I apologize if you find that offensive. Is it not possible, that people on a "science" forum, know what "science" is or at least have a pretty good idea of it. So you can think you sound intelligent by pointing out that you know what science is too, or you could present some yourself. Just a thought. Is it not better to bash using the very thing you mean to defend? Edited April 7, 2017 by AbnormallyHonest
AbnormallyHonest Posted April 7, 2017 Author Posted April 7, 2017 (edited) It's because none of this makes any sense. It is philosophy at best. Since you are posting this in physics (and it was best put in speculations), you need to have some evidence or mathematical model of what you are talking about. Otherwise, it's just word salad. Science does not accept vague, unsupported definitions and therefore, any reasonable scientist must dismiss this skeptically. Because there is no empirical data, it is not a nice way to describe things by default. Do you have any predictions or evidence that this would be useful? The lack of "empirical" data was meant to be a paradox... "to describe what we see." Anyway, wouldn't it save a lot of time and energy spent on dead end's if it's true? Is that not the goal of all theories? Edited April 7, 2017 by AbnormallyHonest
koti Posted April 7, 2017 Posted April 7, 2017 (edited) The lack of "empirical" data was meant to be a paradox... "to describe what we see." Anyway, wouldn't it save a lot of time and energy spent on dead end's if it's true? Is that not the goal of all theories? "Dark" is a subjective term as different animals are capable of seeing different wavelenghts. A healthy human eye sees roughly between 400nm-700nm wavelenght region. Lack of radiation in that particular wavelenght region is "darkness" for us humans(all primates see roughly in those wavelenghts) Frankly, I couldn't think of a simpler case of explaining what something is - look up swansont's explanation above. Edited April 7, 2017 by koti 1
Argent Posted April 7, 2017 Posted April 7, 2017 Although this may be met with some skeptic dismissal or active rejection... isn't it possible all of the "dark" we perceive in the Universe be a result of life? Say, harnessing something like zero point energy and bringing huge amounts of excess energy into this Universe and using that to manipulate forces artificially? I would say, that's a more reasonable explanation than nothing at all. However, the conventional explanation does not involve nothing at all, and therefore your proposed alternative does not appear to be reasonable. In what way do you propose that manipulating forces artificially would generate "dark". I don't see any mechanism that would achieve that. Could you explain the details please. If you think about it, this could also explain the expansion of space. If by harnessing zero point energy somehow accelerates the entropy of the space, it would also explain inflation. I don't understand how you accelerate entropy, or how such an acceleration would explain inflation. Again, could you expand on this with specifics. Is a science forum not a good place to introduce a new idea to those who have an interest, and perhaps and ability to take an idea and pursue the truth, or at the very least make a point out of it rather than a point of it. You seem to be suggesting that others might be interested in developing your idea beyond where you have yet taken it? Do I have that correct. If so, I think you are mistaken. You have offered a very vague supposition, lacking in detail, evidence or justification. It lacks substance. It lacks conviction. It lacks a foundation. Why would anyone else be willing to spend any time developing it. If you can flesh it out a little and provide some supporting evidence or logical argument then there may be some willing to ask pertinent questions that would help you develop it further. At present, though, you are not offering anything of interest. Is it not possible, that people on a "science" forum, know what "science" is or at least have a pretty good idea of it. So you can think you sound intelligent by pointing out that you know what science is too, or you could present some yourself. Just a thought. Until you provide some science rather than an agglomeration of terminology, strung together haphazardly, there is little point or need of other posters responding with currently accepted science.
swansont Posted April 7, 2017 Posted April 7, 2017 I have our view of the Universe, which is shared by anyone who is willing to look. As I understand, this forum is for people who want to discuss topics related to science, and an interest in it. It is a public forum and designed to accumulate ideas and spark discussions, or is my interpretation fundamentally flawed? Is a science forum not a good place to introduce a new idea to those who have an interest, and perhaps and ability to take an idea and pursue the truth, or at the very least make a point out of it rather than a point of it. If you would like a deeper, more specific mathematical understanding, I do not believe this forum to be the venue to present those ideas, and at that level. This is indeed a science site, so we expect science rather than a personal view. The proper place to float new ideas in speculations (where this will be moved), but we still require some minimal amount of rigor in your presentation of the idea.
Lord Antares Posted April 7, 2017 Posted April 7, 2017 As I understand, this forum is for people who want to discuss topics related to science, and an interest in it. It is a public forum and designed to accumulate ideas and spark discussions, or is my interpretation fundamentally flawed? Yes, your interpretation is flawed. Exactly because this is a science site, you cannot make unsupported claims. The rules of this forum state that you can ask a question you don't know the answer to. This question may or may not clash with the mainstream, but you are forgiven simply because you didn't know the answer to the question. If you are making a claim outside of mainstream science, which is what you are doing, you are required to support it with evidence and mathematics and you are required to answer the other members' questions. If you fail to meet those requirements, the thread gets closed. Although, here is one: The observable universe contains 100,000,000,000 galaxies, each one on average contains about 80-100,000,000,000 stars, and about 80-90% (probably more) of those stars have not just a planet, but planetary systems. In truth, the Universe is probably infinite, it's just that an expanding view of space inevitably outruns light at far enough distances, no matter how slow the expansion is. We just can't see past where the speed of light is able to move toward us. So, assuming that we're the only living intelligence in the Universe, is 1 in a very large number and actually probably 1 in Infinity. I don't know how you would mathematically describe impossible, but 1 in Infinity takes a pretty good stab at it. I'd say those odds are pretty solid compared to invisible light... or missing photons. I'd say one idea creates a lot more disparity with Universal laws of physics than the other, and it's not the one that needs to create some new form of physics or an imbalance of conservation in order to explain it. This seems to be largely philosophy, rather than science. These kinds of vague, philosophical statements cannot be accepted as science, you must understand that. There are professional scientists on this page. They know what level of rigor and detail is required for a theory to be accepted. I'm sure there are more liberal sites on the internet on which you can post anything you want, but this is not one of them. So, assuming that we're the only living intelligence in the Universe, is 1 in a very large number and actually probably 1 in Infinity. I don't know how you would mathematically describe impossible, but 1 in Infinity takes a pretty good stab at it. I'd say those odds are pretty solid compared to invisible light... This makes no sense, even for philosophy. Why not just say ''0% chance'', instead of ''1 in infinity''. And it has nothing to do with light and dark.
Manticore Posted April 7, 2017 Posted April 7, 2017 Since "Zero Point Energy" is, by definition, the lowest possible energy level. And since work can only be extracted from something moving from a higher to a lower energy level. To extract work from "Zero Point Energy" you would need a lower level still, which does not and cannot exist. 2
Eise Posted April 7, 2017 Posted April 7, 2017 It's because none of this makes any sense. It is philosophy at best. This seems to be largely philosophy, rather than science. No, it is not philosophy. AbnormallyHonest makes empirical claims; philosophy does not. But because he presents no logical or empirical evidence, and he contradicts science, these are just wild speculations. 1
Lord Antares Posted April 7, 2017 Posted April 7, 2017 Well, some of the claims are philosophical (i.e. they just seek to describe stuff and not make empirical claims) and some are empirical. Neither look to be of use for science either way. 1
Eise Posted April 7, 2017 Posted April 7, 2017 (edited) Well, some of the claims are philosophical (i.e. they just seek to describe stuff and not make empirical claims) and some are empirical. Neither look to be of use for science either way. Philosophy does not just describe stuff. It is an academic subject. During my study at university AbnormallyHonest's stuff never was a topic. For good reasons. Very good reasons... Philosophy is not the trash bin of science. Edited April 7, 2017 by Eise 1
Strange Posted April 7, 2017 Posted April 7, 2017 Although this may be met with some skeptic dismissal or active rejection... isn't it possible all of the "dark" we perceive in the Universe be a result of life? Say, harnessing something like zero point energy and bringing huge amounts of excess energy into this Universe and using that to manipulate forces artificially? I would say, that's a more reasonable explanation than nothing at all. It seems far simpler to say that the dark is an absence of light. Done. Why make it so complicated? And, as others have noted, impossible. 1
Mordred Posted April 7, 2017 Posted April 7, 2017 Here is the main problem with zero point energy with the above. Under QFT one learns that on a virtual particle production basis following from The Heisenburg uncertainty principle. The VP has insufficient mass and momentum to cause effective action. Particularly at [latex]\frac{1}{2}\hbar w [/latex] action (sufficient energy to cause interferance or motion) requires a minimal a quanta of energy. Zero point energy falls below this point even when you consider its vacuum expectation value
machapungo Posted April 8, 2017 Posted April 8, 2017 I'm very pleased to find a "speculations" category where my unfounded ideas can be expressed. Thank you scienceforums!! Regarding zero point energy and vacuum space being a zero point field. In other words, what that means is that it is the most diluted form of energy that can exist. Fine. Let us also accept that energy can be neither created or destroyed, it can only change forms. So, space is one of those forms. Therefore, one could assert that the expansion of our universe is nothing more than our observation of the conversion of some form of denser non space energy into space. Things that are referred to as "dark" are really "invisible" as is space and therefore why not simply assert that dark energy and space are one and the same? That assertion leaves us with the task of explaining how denser forms of energy could be transformed into space. I feel comfortable in speculating that everything in the universe is a form of energy and is the total sum of physical reality. Now, let's address the idea of whether the universe is finite or infinite. The notion that the universe is infinite requires that it is possible to have a never ending blob of energy in one form or another. If one asserts this notion then one is simultaneously asserting that there is nothing else other than energy and that volume of energy has no boundary. I find this idea difficult to swallow. The other possibility is that the universe is finite but tremendously large. If it is finite then it is natural to ask about what is beyond the bounds of the universe. Then, I think, it is logical to say that there is "nothing" beyond the universe where nothing means there is a total lack of energy. Let's call this the void. But then, if one asks what is beyond the void what could a reasonable answer be? I think the reasonable answer is nothing. In other words the void is infinite, A limitless amount of nothing strikes me as much more reasonable than a limitless amount of something. Furthermore, from a philosophical perspective it makes sense. Nothing and something define each other and definitions are a good thing from the point of view of understanding. So, here we have a universe that is currently expanding because of conversions of denser energy into space with "nothing" to impede it. We currently think that the current expansion of the universe has taken about 13.8 billion of our puny earth years, so far. It is natural for us to ask if the universe had changes before the beginning of this expansion (big bang). It is also natural for us to ask if there will be an end to this expansion. I have read speculations that eventually the black holes in the universe will consume all conventional matter and that they will eventually evaporate and leave a universe that consists of nothing but space. I find that idea to be a reasonable speculation. If we accept that notion then what, if anything, happens to the universe consisting of nothing but space? Does it make sense that the universe will then exist unchanged thereafter? If so, that means that somehow we were lucky enough to get a ticket on the one and only one way trip into the oblivion of a blob of space bounded by nothing. I find this to be a hard to swallow idea. My experience with the universe is that it has a tendency to change. Therefore, that naturally leads me to ask how can the universe get from a form where it is composed of all space to a form where it can, once again, explode with a big bang and begin a never ending cycle of expansion and contraction. This, I think, is a puzzle best left in the hands of physicists and astrophysicists. Regards
machapungo Posted April 12, 2017 Posted April 12, 2017 (edited) Further notions regarding the mechanism of an eternal cycle of expansion and contraction of the universe: A point to keep in mind while considering this speculation is that matter itself from a volume perspective is mostly space and this means that space and matter have no problem intermingling at all scales of size. Let's consider the case where during expansion all matter gets consumed by black holes and the black holes evaporate to leave only a finite amount of space surrounded by the infinite void of nothing. Here, let's assert that electromagnetic energy cannot pass the space void boundary. Let's also assert that space's density of energy also has gravity. This gravity of space would provide a cohesiveness to allow all of finite space, to exist as a bubble surrounded by the void and to remain contiguous and not become somehow mixed and infinitely diluted by the void. However, before all of the more concentrated forms of energy ultimately transform into space their gravity and the gravity of space were mutually pulling on each other. But since the gravity of space is very weak, space becomes stretched to it's limit of minimal density. This affect of stretching would be maintained as long as any matter or black hole exists. However, once they themselves become space there is no force to stretch space to its point of minimal density and when this situation is reached the gravity of space begins to cause it to collapse upon itself and that collapse causes the gravity of space to continuously increase to provide a positive reinforcing feedback to the process. This process requires the attractive force of black hole gravity pulling on space gravity to be not only insufficient to somehow overcome the evaporation of a black hole into space BUT could actually be the cause of a black hole evaporating and becoming space. This could be viewed as a tug of war in which the limit of the minimal density of space actually sucks energy out of the black hole. A kind of cosmic jujitsu. As the process of collapse proceeds the temperature of space continues to increase. Eventually, is gets so hot that the sub atomic particles which at cooler temperatures seem to pop into and out of existence begin to fuse. I speculate that once this collapse achieves a certain critical magnitude of gravity further collapse builds to fantastic superluminal speeds and super temperatures causing all forms of matter to fuse and ever more powerful black holes to form and merge with phenomenal inward momentum and speed until a big bang occurs. Thereafter, everything once again expands and cools. Yes, this story is not backed up by evidence. It does, I think, contain a rather cohesive chain of events even though they are fetched from imagination. Regards r Edited April 13, 2017 by machapungo
AbnormallyHonest Posted April 12, 2017 Author Posted April 12, 2017 How is that a simpler/more reasonable explanation than "a (relative) lack of photons"? Darkness is lack of light. End of story. "Dark" is a subjective term as different animals are capable of seeing different wavelenghts. A healthy human eye sees roughly between 400nm-700nm wavelenght region. Lack of radiation in that particular wavelenght region is "darkness" for us humans(all primates see roughly in those wavelenghts) Frankly, I couldn't think of a simpler case of explaining what something is - look up swansont's explanation above. I find that all of these explanations use the lack of empirical evidence, (the ability to see) as a way to substantiate circumstantial evidence. I would say the fact that we exist, and are capable of manipulating energy and forces, and the sheer probability paired with an extensive amount of time that to Universe has had to realize those probabilities would be more substantial that using the problem to explain the problem (seems paradoxical to me). -1
Strange Posted April 12, 2017 Posted April 12, 2017 I find that all of these explanations use the lack of empirical evidence, (the ability to see) as a way to substantiate circumstantial evidence. We can use objective measurements (e.g. a light meter) to quantify how little light there is. I would say the fact that we exist, and are capable of manipulating energy and forces, and the sheer probability paired with an extensive amount of time that to Universe has had to realize those probabilities would be more substantial that using the problem to explain the problem (seems paradoxical to me). This is meaningless and unnecessary verbiage. Dark is, by definition, the absence of light.
AbnormallyHonest Posted April 12, 2017 Author Posted April 12, 2017 (edited) Yes, your interpretation is flawed. Exactly because this is a science site, you cannot make unsupported claims. The rules of this forum state that you can ask a question you don't know the answer to. This question may or may not clash with the mainstream, but you are forgiven simply because you didn't know the answer to the question. If you are making a claim outside of mainstream science, which is what you are doing, you are required to support it with evidence and mathematics and you are required to answer the other members' questions. If you fail to meet those requirements, the thread gets closed. This seems to be largely philosophy, rather than science. These kinds of vague, philosophical statements cannot be accepted as science, you must understand that. There are professional scientists on this page. They know what level of rigor and detail is required for a theory to be accepted. I'm sure there are more liberal sites on the internet on which you can post anything you want, but this is not one of them. This makes no sense, even for philosophy. Why not just say ''0% chance'', instead of ''1 in infinity''. And it has nothing to do with light and dark. Isn't the "lack of evidence" being used to as a theory to support itself seem like a heavily "unsupported" claim. Yes, absence of data can be used to deduce a truth, but without a control, or anything else at all, even a speculation that has more statistical potential, would make the original explanation nothing but a description of what we want to explain. e.g. It is "dark" because there is not light". If I were to discover lightening that made absolutely no sound, and explained by simply saying, "we do not hear thunder because there is no sound", how do you think that theory would be regarded? Yet I'm the speculative one? Because zero chance is not the same as 1 in Infinity. They are completely different ideas. Edited April 12, 2017 by AbnormallyHonest -1
koti Posted April 12, 2017 Posted April 12, 2017 I find that all of these explanations use the lack of empirical evidence, (the ability to see) as a way to substantiate circumstantial evidence. I would say the fact that we exist, and are capable of manipulating energy and forces, and the sheer probability paired with an extensive amount of time that to Universe has had to realize those probabilities would be more substantial that using the problem to explain the problem (seems paradoxical to me). You want empirical evidence, I got it for ya. Shut your eyes and open them. There.
AbnormallyHonest Posted April 12, 2017 Author Posted April 12, 2017 However, the conventional explanation does not involve nothing at all, and therefore your proposed alternative does not appear to be reasonable. In what way do you propose that manipulating forces artificially would generate "dark". I don't see any mechanism that would achieve that. Could you explain the details please. I don't understand how you accelerate entropy, or how such an acceleration would explain inflation. Again, could you expand on this with specifics. You seem to be suggesting that others might be interested in developing your idea beyond where you have yet taken it? Do I have that correct. If so, I think you are mistaken. You have offered a very vague supposition, lacking in detail, evidence or justification. It lacks substance. It lacks conviction. It lacks a foundation. Why would anyone else be willing to spend any time developing it. If you can flesh it out a little and provide some supporting evidence or logical argument then there may be some willing to ask pertinent questions that would help you develop it further. At present, though, you are not offering anything of interest. Until you provide some science rather than an agglomeration of terminology, strung together haphazardly, there is little point or need of other posters responding with currently accepted science. Artificial forces are forces that could be created without utilizing the typical means we are aware for creating such manipulations of space. If you believe that a machine might someday be able to produce some type of gravitational or electromagnetic force that exists with the apparent absence of the massive objects that are associated with those kinds of distortion seems like a viable explanation, because it is the lack of those massive objects that sparks ALL of the speculation, for which there is no mathematical grounds for. I am simply attempting to provide a speculative explanation that at least has probability and the evidence of our existence to support an unconventional theory. For inflation, this is purely speculative as well, but not without logic. If there were some relationship between the structure of space and the energy within, it might be able to explain a few things simultaneously. For instance, if the dissolution of energy from space somehow made the space "expand" and as energy is released from this binding force, this expansion has an increase in rate. Since there was so much more energy available just after the Big Bang, it could have been the energy for the binding force of space, which would have set the expansion rate to almost infinite, until the energy was able to be reduced and forged back into the structure of space, slowing down the rate of expansion. "Dark" energy would be the release of that energy and thereby increasing the rate of expansion... e.g. entropy. Since "Zero Point Energy" is, by definition, the lowest possible energy level. And since work can only be extracted from something moving from a higher to a lower energy level. To extract work from "Zero Point Energy" you would need a lower level still, which does not and cannot exist. My understanding of zero point energy is that, if you were to take all the energy out of a quantity of space, if there is matter present in that space, it can never be completely static. Therefore the energy that is represented by the movement of the subatomic particles is abundant and unpreventable. This seems like a chaotic state of disorder, a preservation of energy, only due to the state of it being uncertain. Is the preservation of energy in anything certain? If it were, wouldn't it be true that our streets and highways would never need to be repaved? Due to entropy, we know that is not the case.
Strange Posted April 12, 2017 Posted April 12, 2017 Isn't the "lack of evidence" being used to as a theory to support itself seem like a heavily "unsupported" claim. Yes, absence of data can be used to deduce a truth, but without a control, or anything else at all, even a speculation that has more statistical potential, would make the original explanation nothing but a description of what we want to explain. e.g. It is "dark" because there is not light". Gibberish. Why do you need evidence to know that "dark" is a synonym for "absence of light". But if you insist: Definition of dark 1a : devoid or partially devoid of light https://www.merriam-webster.com/dictionary/dark If I were to discover lightening that made absolutely no sound, and explained by simply saying, "we do not hear thunder because there is no sound", how do you think that theory would be regarded? That is a poor analogy. There is a difference between trying to identify the reason for thunder making no sound and calling the absence of sound "silence". Similarly, there could be all sorts of explanations for there being no light (the electricity has failed, the candle has blown out, your eyes are closed, etc). But "dark" is not an explanation, it is just another word for "no light" in the same way that "silence" is another word for "no sound". I cannot believe you are making such a fuss about the definition of a word.
AbnormallyHonest Posted April 12, 2017 Author Posted April 12, 2017 (edited) Gibberish. Why do you need evidence to know that "dark" is a synonym for "absence of light". But if you insist: https://www.merriam-webster.com/dictionary/dark That is a poor analogy. There is a difference between trying to identify the reason for thunder making no sound and calling the absence of sound "silence". Similarly, there could be all sorts of explanations for there being no light (the electricity has failed, the candle has blown out, your eyes are closed, etc). But "dark" is not an explanation, it is just another word for "no light" in the same way that "silence" is another word for "no sound". I cannot believe you are making such a fuss about the definition of a word. I am not, I understand how light works. The same idea is true in thermodynamics, you cannot add "cold" to something, only diffuse energy. The sound analogy is only ineffective that the experience of the lightening is not circumstantial, it might be more appropriate to say that we hear the thunder, but we do not see any light. I would also dispute that it is not my "fuss" about the definition of a word, it is others' focus... on "empirical evidence". Perhaps that phrase should be defined. Edited April 12, 2017 by AbnormallyHonest -2
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