Is the Boltzmann brain paradox a genuine one?

For some time, I have been wondering whether the Boltzmann brain paradox is a genuine one. Here’s how Wikipedia describes the paradox (emphases are mine):


In physics thought experiments, a Boltzmann brain is a self-aware entity that arises due to extremely rare random fluctuations out of a state of thermodynamic equilibrium. For example, in a homogeneous Newtonian soup, theoretically by sheer chance all the atoms could bounce off and stick to one another in such a way as to assemble a functioning human brain (though this would, on average, take vastly longer than the current lifetime of the universe).


The idea is indirectly named after the Austrian physicist Ludwig Boltzmann (1844–1906), who in 1896 published a theory that the Universe is observed to be in a highly improbable non-equilibrium state because only when such states randomly occur can brains exist to be aware of the Universe. One criticism of Boltzmann’s “Boltzmann universe” hypothesis is that the most common thermal fluctuations are as close to equilibrium overall as possible; thus, by any reasonable criterion, human brains in a Boltzmann universe with myriad neighboring stars would be vastly outnumbered by “Boltzmann brains” existing alone in an empty universe.


Boltzmann brains gained new relevance around 2002, when some cosmologists started to become concerned that, in many existing theories about the Universe, human brains in the current Universe appear to be vastly outnumbered by Boltzmann brains in the future Universe who, by chance, have exactly the same perceptions that we do; this leads to the absurd conclusion that statistically we ourselves are likely to be Boltzmann brains. Such a reductio ad absurdum argument is sometimes used to argue against certain theories of the Universe.


The two assumptions I’d like to question in this post are: (i) the assumption that a Boltzmann brain could self-assemble in the first place, given enough time; and (ii) the assumption that the spontaneous self-assembly of such a brain is more likely than the spontaneous formation of human observers.

Concerning (i), I would like to point out that the brain is a multi-layered organ containing 86 billion neurons, each of which is supported by glial cells and astrocytes. Within each neuron is a nucleus, surrounded by a cell body which receives signals via dendrites and sends signals along an axon, which in turn is insulated with a myelin sheath. The idea that individual atoms could arrange themselves into a brain containing tens of billions of these multi-layered structures is simply absurd, because such a “brain” would fall apart long before it formed. Without stable intermediate stages, a brain cannot spontaneously self-assemble out of atoms, even when given an infinite amount of time.

As for (ii): it seems to me that the main argument in its favor is that thermodynamically speaking, it’s easier for an infinite box of gas in equilibrium to assemble into X than it is for the gas to assemble into X + Y. Hence the spontaneous formation of a brain alone is far more likely than the self-assembly of a brain attached to a human body, which in turn is more likely to form spontaneously than an entire planet full of organisms (including humans), which is more likely to form spontaneously than a universe full of stars and planets (including our Earth). But this kind of reasoning ignores the possibility of “springboards,” or transitional stages which generate multiple paths, some of which lead to the desired target.

Thus the likelihood of a brain forming from a box of gas is far greater if the gas is first allowed to assemble into a primordial cell, as such a cell is capable of evolving into various kinds of organisms (including humans with brains). But evolution can only proceed in a physical environment; hence we need a planet for the cell and its descendants to live on. But a planet needs a source of energy to power the chemical reactions leading to life, which in turn requires energy to power its own internal processes; hence we need a star as well. And the formation of stars is rendered more likely by the postulation of an initial Big Bang, starting from a hot, dense state. In short: while the spontaneous formation of a universe, holus bolus, is many orders of magnitude less likely than the spontaneous formation of a brain, the formation of a human being possessing a brain within the framework of a Big Bang universe which is capable of generating stars and planets, some of which are capable of generating life, which subsequently evolves into the dazzling array of creatures we see on Earth, is far more likely than the spontaneous self-assembly of a Boltzmann brain – an event whose probability I have already argued is zero.

I’d like to finish with a closing thought. Is there something wrong with the way we define entropy? Currently, physicists define it in terms of the number of possible micro-states of a system which are consistent with its macro-description (e.g. “a human brain”). This, in essence, is what Boltzmann’s entropy formula expresses. However, such a definition ignores a system’s history, and makes no attempt to calculate the number of pathways by which the atoms in the system can reach their macro-level target. Boltzmann’s definition of entropy also leads many well-meaning but misinformed laypeople to mount fallacious arguments against biological evolution. Isn’t it about time we came up with a better definition, which doesn’t generate silly paradoxes? What do readers think?

259 thoughts on “Is the Boltzmann brain paradox a genuine one?

  1. BruceS: Knowing is Justified True Belief.I don’t even believe that I know God exists.Hence not everyone knows God exists since I in particular do not even believe it.

    Unless you think I believe it, but just do not know I believe it.

    Which I guess you probably do.

    I should have known better.

    This stuff has been explained to FMM maybe 5,000 times on this site since I’ve been here. He has no interest whatever in learning anything. What he wants is for his God to love him and save him from death. And, apparently to pester people who don’t need that kind of baby food, because, since he does, maybe everybody else should too.

    That’s it.

  2. BruceS:
    Not that I mean to take the thread off topic, but does anyone know what happened to vjtorley?I would have supposed that he would participate in his thread.

    Maybe that is even a presupposition for doing an OP.

    Or maybe he has concluded he is in fact a BB and hence participating would be incoherent.

    FWIW, he does that all the time. It’s one reason why I don’t spend a lot of time commenting on his OPs.

  3. BruceS: Knowing is Justified True Belief.I don’t even believe that I know God exists.Hence not everyone knows God exists since I in particular do not even believe it.

    Answer:incorrect you do subconsciously per revelation.

    I should have known better.

    You did know better subconsciously.

  4. newton: Answer:incorrect you do subconsciously per revelation.

    You did know better subconsciously.

    Re “subconscious”–a careful study of “The Future of an Illusion” and “Moses and Monotheism” would likely be more beneficial here than any musings about Reid or Boltzmann. It’s a psych issue hindering growth, IMHO–not a matter of “reasoning.”

  5. walto: Re “subconscious”–a careful study of “The Future of an Illusion” and “Moses and Monotheism” would likely be more beneficial here than any musings about Reid or Boltzmann. It’s a psych issue hindering growth, IMHO–not a matter of “reasoning.”

    Freud. Ugh. Perhaps one area where Popper was on to something.

    I prefer cognitive science, eg as in
    https://www.amazon.com/Natural-History-Theology-Cognitive-Philosophy/dp/0262028549/
    Admittedly, however, that one is focused on natural theological arguments (like design) rather than the general psychology of religious belief.

    But even if religious belief has a psychological explanation, how does that affect its potential to be true? One could make a sort of anthropic argument that such a psychological property is exactly what we would expect God to install in humanity.

    As for discussing BBs, there is case for doing it given the OP.

  6. OMagain: It seems like fmm is unaware that the “Christian Bible” has only existed for a small part of recorded human history. So presumably it was absurdity all around until that book got “written”.

    No the axiom is not the Christian Bible it’s the Christian God of scripture.

    God existed before he revealed himself in scripture. In fact according to the passage I quoted God has been making himself known since ever since the creation of the world.

    Even today God exists and makes himself known in places that have never seen a bible and to people who never read it.

    peace

  7. Kantian Naturalist: What can be asserted without evidence (or argument) can be dismissed without evidence (or argument),

    You asserted that with out evidence or argument so I guess we should just dismiss it . Correct??

    Kantian Naturalist: I don’t feel any rational obligation to show you why your “presupposition” is absurd.

    I don’t expect you to.

    What I expect you to do is be able to show that your presuppositions don’t lead to absurdity before you ask us to treat them like they are the default position.

    peace

  8. BruceS: Unless you think I believe it, but just do not know I believe it.

    Ever hear of cognitive dissonance or self deception

    I hope you know these are real things.

    peace

  9. BruceS: But I could be arguing just for the entertainment value.

    I know that is a good part of why I do it. I enjoy the give and take and to learn about the worldviews of other people.

    Here I was just talking about the interesting topic of BBs and made the suggestion that folks should ponder them and what they mean to epistemology.

    It’s like I touched a raw nerve or maybe brought something to the surface that had long been pushed to the subconscious.

    Just like clockwork we were back to discussing and cussing presupostionalism again.

    I do never cease to be amazed at how hot under the collar folks get about this stuff or how they constantly keep bringing it up in every thread I participate in.

    It seems to me that a more rational response would have been to say something like.

    “Yes you are right BBs are a big deal if they exist.We should explore the possible implications”

    peace

  10. BruceS: One could make a sort of anthropic argument that such a psychological property is exactly what we would expect God to install in humanity.

    I am not a big fan of arguments for or against the existence of God.

    It makes us humans out to be the judge of something that is way beyond our pay-grade.

    It’s also pretty insulting I think, Just imagine us sitting around and arguing about whether or not you exist.

    peace

  11. BruceS: Freud.Ugh.Perhaps one area where Popper was on to something.

    I actually like Freud. I think he’s gotten a bad rap. And not only from Popper. (Adolf Grunbaum REALLY went after him, e.g.)

    But even if religious belief has a psychological explanation, how does that affect its potential to be true? One could make a sort of anthropic argument that such a psychological property is exactly what we would expect God to install in humanity.

    I don’t know about it’s relevance to the question of whether God exists. But it’s entirely relevant to questions about whether various people are in a position to rationally consider the question of whether God exists.

    As for discussing BBs, there is case for doingit given the OP.

    Oh, it’s extremely interesting, for sure. But I don’t like VT’s MO when it comes to OPs

  12. fifthmonarchyman: I am not a big fan of arguments for or against the existence of God.

    It makes us humans out to be the judge of something that is way beyond our pay-grade.

    It’s also pretty insulting I think, Just imagine us sitting around and arguing about whether or not you exist.

    peace

    Oh, this God of yours is sooooooo sensitivo!

  13. walto: Oh, this God of yours is sooooooo sensitivo!

    It’s not about his sensitivity it’s about what is proper behavior for us.

    It may be that your African American coworker does not get offended by racist jokes but that does not mean that you should tell them.

    peace

  14. How about a reset.

    Do you think that the case has been made that (sans God) it is highly likely that you are a BB because BBs are much more likely thermodynamicly speaking than our supposed world yet have exactly the same explanatory power for the sensory experiences you have?

    If not why not?

    Peace

  15. fifthmonarchyman: It may be that your African American coworker does not get offended by racist jokes but that does not mean that you should tell them.

    Suppose no person ever were offended by them–indeed couldn’t care less– would it still be bad? Even if a case could be made that it would be bad even if nobody were ever offended (and couldn’t be), I think it’s quite likely to be the case that it is actually YOU who is offended by remarks about Jesus on this site. However, if you ever should come to realize that nothing worthy of worship could possibly give a shit, you might get over it yourself. After all, God, unlike my thick-skinned African-American co-worker can’t really complain about his treatment (since Calvary, anyhow).

  16. walto: Suppose no person ever were offended by them–indeed couldn’t care less– would it still be bad?

    I think so. Racist jokes are bad because they foster a false sense of superiority in the people who tell them regardless of whether anyone is ever offended.

    walto: I think it’s quite likely to be the case that it is actually YOU who is offended by remarks about Jesus on this site

    I’m quite sure that is the case along with any other Christians here.. When it comes to mockery and juvenile besmirchment at least.

    I’m not sure they would share my opinion about arguments for and against God’s existence however.

    I just don’t think it is ever conducive to fruitful discussion to offend anyone needlessly. Don’t you agree?

    walto: However, if you ever should come to realize that nothing worthy of worship could possibly give a shit, you might get over it yourself.

    In the end it’s really not about me or God it’s about you. When you scoff you show that you hate knowledge.

    Quote:
    “How long, O simple ones, will you love being simple? How long will scoffers delight in their scoffing and fools hate knowledge?
    (Pro 1:22)
    end quote;

    I just don’t think You will like will ultimate result.

    quote:
    I also will laugh at your calamity; I will mock when terror strikes you, when terror strikes you like a storm and your calamity comes like a whirlwind, when distress and anguish come upon you. Then they will call upon me, but I will not answer; they will seek me diligently but will not find me. Because they hated knowledge and did not choose the fear of the LORD, would have none of my counsel and despised all my reproof, therefore they shall eat the fruit of their way, and have their fill of their own devices. For the simple are killed by their turning away, and the complacency of fools destroys them;
    (Pro 1:26-32)

    end quote:

    peace

  17. walto,

    If one were to take even the most cursory look at your posting record here, they would see that NO ONE is more obsessed and bitter about someone else’s religious beliefs than you are about FMM. One can feel the bile driven hatred boiling inside you, because, oh no, someone has faith that you don’t!

    Just out of perverse curiosity, one has to wonder why you are so obsessed, so angry, so persistent, and so deranged about that. There seems to be no one else here even close to such an affliction, so consumed by what someone else has chosen for their personal worldview. Omagain comes close. Dazz is just a blathering toddler slams his drool covered rattler, but for you, its your passion.

    Its one thing to question the evolution belief, because they believe the science is being manipulated wrongly, but to just go on and on about how one feels personally, that is just weird Walto.

    It seems rather likely that you are doing some kind of personal reflection avoidance.

  18. phoodoo:
    walto,

    If one were to take even the most cursory look at your posting record here, they would see that NO ONE is more obsessed and bitter about someone else’s religious beliefs than you are about FMM.One can feel the bile driven hatred boiling inside you, because, oh no, someone has faith that you don’t!

    Just out of perverse curiosity, one has to wonder why you are so obsessed, so angry, so persistent, and so deranged about that.There seems to be no one else here even close to such an affliction, so consumed by what someone else has chosen for their personal worldview.Omagain comes close.Dazz is just a blathering toddler slams his drool covered rattler, but for you, its your passion.

    Its one thing to question the evolution belief, because they believe the science is being manipulated wrongly, but to just go on and on about how one feels personally, that is just weird Walto.

    It seems rather likely that you are doing some kind of personal reflection avoidance.

    As I know well what a cool, rational person you are, phoodoo, one who looks at things with a calm and unprejudiced eye. I’ll certainly take this post under advisement and give it exactly the reflection that knowledge of its source merits.

    Heaven knows FMM has done nothing to encourage anybody’s hostility at this site. It’s not like he’s called anybody a liar or anything. He’s just Bible thumping. What the hell is wrong with that? What harm has the Bible or any of its most vocal supporters ever done to anybody?

  19. fifthmonarchyman: In the end it’s really not about me or God it’s about you. When you scoff you show that you hate knowledge.

    And who could mind this kind of deep understanding? I mean, it’s clear that anybody who scoffs at the Bible hates knowledge, isn’t it? Why shoot the messenger?

    I whack him. He turns the other cheek. It’s disgusting.

  20. dazz:
    fifthmonarchyman,

    I really feel for you. You don’t realize that religious bullshit has turned you into a horrible person. It’s probably not your fault though, that’s what indoctrination does to people.

    Yes, it isn’t his fault. We should forgive him. He knows not what he does.

  21. Second attempt at a reset

    Does anyone dispute the idea that a BB could be a simple computer instead of something like a wet human brain?

    Peace

  22. dazz: You don’t realize that religious bullshit has turned you into a horrible person

    You forget I’m a Calvinist I believe in total depravity. That means that left to our selves we are all horrible people.

    I think problems happen when we try to convince ourselves that on our own we are good.
    Peace

  23. walto: Heaven knows FMM has done nothing to encourage anybody’s hostility at this site

    If I have done anything to offend you in some way. I apologize

    It was never my intention.

    Perhaps you could take your own advise and not take things so personally

    and If you don’t want hear what the bible says don’t constantly bring the subject up. If you don’t I won’t

    Peace

  24. walto: He’s just Bible thumping.

    I’m just one guy in the internet who disagrees with you about the universality of the knowledge of God.
    It’s not like I’m a Trump voter or enjoy burning stryfoam 😉

  25. fifthmonarchyman: You forget I’m a Calvinist I believe in total depravity. That means that left to our selves we are all horrible people.

    Strange that a source of logic ,truth and goodness can and choose create such a horrible mess.

    I think problems happen when we try to convince ourselves that on our own we are good.
    Peace

    Obviously problems happen when we feel otherwise as well. Seems like thinking we are capable of good would be a step in the right direction no matter how successful we are. Free will is pointless if we can only choose to be depraved.

  26. phoodoo: Its one thing to question the evolution belief, because they believe the science is being manipulated wrongly, but to just go on and on about how one feels personally, that is just weird Walto.

    How about the subject of moderation, ok to go on and on?

  27. newton:

    How about the subject of moderation, ok to go on and on?

    Sure, given the continued moderation abuses.

    Are you going to tell us we should all shut up about Trump, because you’re tired of hearing complaints about our president?

  28. fifth:

    I am not a big fan of arguments for or against the existence of God…

    It’s also pretty insulting I think, Just imagine us sitting around and arguing about whether or not you exist.

    walto:

    Oh, this God of yours is sooooooo sensitivo!

    Another example of people creating gods in their own image.

  29. walto: I actually like Freud.

    I don’t know about it’s relevance to the question of whether God exists. But it’s entirely relevant to questions about whether various people are in a position to rationally consider the question of whether God exists.

    Oh, it’s extremely interesting, for sure. But I don’t like VT’s MO when it comes to OPs

    On Freud: My problem is that I understood his views to be based on contemplation of his own thoughts only, not a process of doing science or of engaging with it . I understand that process may not have been available to him, but that does not affect how I think we consider his ideas today. It is only the ones that have been subject to subsequent science that I would consider.

    Now perhaps one can consider Freud as literature and so telling us important things about about the human condition in the way Tolstoy does. I don’t know about that. I’m only talking about science.

    On psychology and religion: Good point. The book I linked addresses that point as well, focusing on the attempts to prove God’s existence by reason, eg design argument, and how these relate to cognitive quirks. I’ve only listed the the NBN podcast about it, BTW.

    On VJT: I had not noticed that habit of his. His posts are interesting, if long-winded IMHO.

  30. keiths: Are you going to tell us we should all shut up about Trump, because you’re tired of hearing complaints about our president?

    It’s a very effective way of achieving change, sure. 😕 More effective might be getting him voted out of office, impeached or prosecuted.

  31. BruceS,

    Vincent leads a very busy life as a peripatetic English teacher. I’m amazed he finds time to contribute what he does.

  32. keiths:

    He lives in Japan, teaching English as a foreign language.

    So are you saying his verbosity here is a compensation for living within the minimalist nature of Japanese culture?

  33. newton, to phoodoo:

    How about the subject of moderation, ok to go on and on?

    keiths:

    Sure, given the continued moderation abuses.

    Are you going to tell us we should all shut up about Trump, because you’re tired of hearing complaints about our president?

    Alan:

    It’s a very effective way of achieving change, sure. 😕 More effective might be getting him voted out of office, impeached or prosecuted.

    Those aren’t orthogonal, which is why a free press is essential.

  34. Bruce,

    So are you saying his verbosity here is a compensation for living within the minimalist nature of Japanese culture?

    Heh. No, just pointing out why he might not be a regular reader of Strunk and White, despite being an English teacher.

  35. keiths:
    newton:

    Sure, given the continued moderation abuses.

    If I cared about moderation abuses , I would deal with it in the moderation.

    Are you going to tell us we should all shut up about Trump, because you’re tired of hearing complaints about our president?

    Not me , I am all for personal choice.No one is forcing me to read anything. Whether it is Trump’s intrinsic danger to the Republic, religious views or whether an extra click is required to view a post.

    Phoodoo , on the other hand, finds it weird, not in a good way, unless it aligns with his views. Which , of course, he is free to do.Likewise to which, I am free to note the ironic nature of his view if I stay within the rules of the site.

  36. fifthmonarchyman: If I have done anything to offend you in some way. I apologize

    It was never my intention.

    Perhaps you could take your own advise and not take things so personally

    and If you don’t want hear what the bible says don’t constantly bring the subject up. If you don’t I won’t

    Peace

    Couple of things.

    First of all you have not offended me and don’t have to apologize. phoodoo’s (kind of sweet) defense of you against meanie me notwithstanding, I like you you. The only person I have viscerally disliked at this site has, thankfully, departed. I didn’t care for Gregory’s antics at one time, but maybe he’s changed for the better. He’s not in my face anyhow, so I don’t mind him at all. Everybody knows I–along with several others–have fought bitterly with keiths on occasion, but that’s (at least mostly) been about his style of argumentation (and likely mine too).

    Now, I very much disliked the political positions of the guy who departed, and I very much dislike your religious position. But while I thought he was a complete asshat, I don’t think that of you. I think you’re generally nice, and also someone who cares about this stuff and has read and thought about related issues a lot. In a way, my scoffing partly results from the fact that I think you could be a decent philosopher and pleasant person if you weren’t so robotic. What annoys me is the sad and sheepish repetition of stuff that has been rebutted over and over.

    Now, one might say, “Well, this is a just a matter of he thinks this, and you think that. Maybe it’s YOU who are wrong.” It always possible that I am wrong. Having no Bible or revelation claims to fall back on (i.e., being a rational human being) I have to admit that. But (and in this way FMM is very much like keiths, which is why my disagreements with both of them get so snarky) FMM has his recourse to Bible Blah Blah and Revelation Rummy (where keiths has his to weird and often false “gotcha” claims that he won’t let go of) so the normal “agree to disagree” that one expects to have between–not just gentlemen or scholars–but pretty much every person with an ounce of civility, doesn’t occur much in those confabs.

    So that’s why we fight. It’s personal in that sense only.

    Second of all, I really hope you realize that it is YOU who brings up the Bible constantly. Anytime I or anybody else brings it up first, which does happen on rare occasions is just a sort of anticipatory defense. If you didn’t bring it up or quote any passage from it for, say, a year, nobody would ever mention it to you again here. But, as said above, you’re 98% robot, and will just go on doing what you think you must do to guarantee that you’ll meet your lord and savior in heaven. And that is because everything else pales in importance to that in your (in my view pretty pathetic for that reason) life.

    In sum, you haven’t offended me, I like you, you have nothing to apologize to me for, and you should buy phoodoo some flowers or something.

    [ETA: sorry for clogging up this thread with personal stuff, but I wanted to respond fully to phoodoo and Fifth.]

  37. BruceS: On Freud: My problem is that I understood his views to be based on contemplation of his own thoughts only, not a process of doing science or of engaging with it . I understand that process may not have been available to him, but that does not affect how I think we consider his ideas today. It is only the ones that have been subject to subsequent science that I would consider.

    Now perhaps one can consider Freud as literature and so telling us important things about about the human condition in the way Tolstoy does. I don’t know about that. I’m only talking about science.

    I can’t defend Freud from that sort of complaint. I suppose it wasn’t science that he was doing, in spite of his claims. But take a Dennett or any philosopher you like. (I used Dennett here because I know keiths likes him, and he’s written a lot about a lot of important stuff. But I don’t think he’s actually one of YOUR faves; so, please insert whoever you like.) You read his work and it seems not just true but importantly so. You think he’s on to important considerations that other writers before him may have missed or not put so well. His ruminations show the world in an entirely new way. I guess you could sniff and call it “literature,” but I don’t think that’s quite right either. What I get from Freud is him saying, e.g., “I have suggested to you how I think our minds are structured. Now, consider your own dreams or your own mistakes or your own neuroses; try stream of consciousness yourself. Does what I have suggested rung true? Is it a sensible theory? How else might we explain the same sort of phenomena? What do you think we can we learn about the results of your own experiences with respect to thought, attention, consciousness, etc.?” Admittedly, that’s not an accepted or acceptable “scientific” method. But I don’t think it has to be discarded for that reason, or dismissed as interesting “fiction.”

    Anyhow, a lot of Freud’s writing–especially up until about 1920–seems really brilliant to me. ( Ok, not everything; maybe “penis-envy” was dumb.)

  38. newton: Strange that a source of logic ,truth and goodness can and choose create such a horrible mess.

    Probably the reason you find that strange is because you don’t understand or value grace.

    peace

  39. newton: If he doesn’t know that he knows God exists , how can he know if he knows what cognitive dissonance is?

    I think just like Meno’s servant he’d be surprised what he knows.

    peace

  40. walto: Second of all, I really hope you realize that it is YOU who brings up the Bible constantly.

    If I remember correctly there was a time that you found my occasional quoting of scripture to be quaint.

    I do from time to time casually quote scripture because often it seems to be pertinent to a particular discussion but I don’t usually “bring up the Bible”.

    Think of it like you casually quoting Quine in a conversation about set theory or logic with out constantly bringing up his political conservatism.

    You just need to learn to compartmentalize a little bit.

    Look at the quote itself and don’t think about any peripheral issues might you have with it’s source.

    peace

  41. walto: you should buy phoodoo some flowers or something.

    I do appreciate folks like phoodoo and Mung chiming in from time to time. Just so that I know that my comments are not universally understood the way that folks from your side choose to understand them.

    His comment reminds me of a verse 😉

    Gracious words are like a honeycomb, sweetness to the soul and health to the body.
    (Pro 16:24)

    peace

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