Certain people can't ever get it right

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Re: Certain people can't ever get it right

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Would an infinite number of books existing in close proximity become a black hole?
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Re: Certain people can't ever get it right

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Eventually, yes.

Throwing books into a black hole is a common thought experiment to illustrate the black hole information paradox.
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Re: Certain people can't ever get it right

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SeerOfProvo wrote:but he doesn’t have to yield anything by simply pointing out that there is a difference between a mathematical object which is entirely conceptual in nature and a book with physical dimensions and dispositional properties. I mean a mathematical object and a physical book are far more different in nature than an apple and unicorn could ever be, is it really digging himself a hole to ask why we think one is going to behave just like the other?
Physics Guy wrote:I still don't see anything interesting in Craig's red-and-blue-books argument. Mentioning real and mathematical worlds is just a red herring because the only features of the books that his argument uses are that they are of two distinct kinds and that they can be counted. Both are mathematical properties which do not depend on anything physical.
I'm pretty sure Physics Guy is right.
Craig wrote:What I shall argue is that while the actual infinite may be a fruitful and consistent concept in the mathematical realm, it cannot be translated from the mathematical world into the real world, for this would involve counter-intuitive absurdities.
^^^This statement right here is the smoking gun^^^ that Craig simply doesn't know what he's talking about. Infinity isn't a consistent concept in the mathematical realm either, which his own examples show, even if his examples are unoriginal to convey the paradoxes of infinity that have existed since ancient Greece and were intended to show something about the physical world.

Substitute "even and odd" for "red and blue", and now we're talking about properties of numbers rather than something in the real world. We could greatly simplify the objection that actual infinity is nonsense by imagining a library of infinite books, take one book out of the library, and there are still an infinite number of books. But we could forget about the library, and go back to High School algebra and say that infinity + 1 = infinity is nonsense because no other quantity plus one remains as it is.

A child may find it helpful to learn math by physically adding and taking away marbles. But I'm having an extremely difficult time visualizing Brouwer and Hilbert arguing about infinity, and Brouwer saying, "Oh yeah? Come David, imagine an infinite quantity of marbles, and that we take one away, are you really going to say the same number of marbles are left behind as originally there? If we're talking about real marbles?"

It seems like the examples are constructed as thought experiments geared to a lay audience; and not as actual thought experiments that would add credibility to intuitionism or advance anything at all in modern mathematical logic.

In fact, according to wiki's introduction to intuitionist objections to actual infinity:
The mathematical meaning of the term "actual" in actual infinity is synonymous with definite, completed, extended or existential,[11] but not to be mistaken for physically existing. The question of whether natural or real numbers form definite sets is therefore independent of the question of whether infinite things exist physically in nature.
The intuitionist objection share's the assumptions of "actual and potential" restricted to hypothetical consideration, and so I do not see how Craig can be said to be arguing from that perspective.

Mathematical logic is the ultimate realm of fail for pseudoscience and mysticism. Craig wouldn't be the first to trip over himself in that world. Scientists with far better credentials than he have gotten out of their depths really fast in that world, when trying to wax mysterious.
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Re: Certain people can't ever get it right

Post by dastardly stem »

Gadianton wrote:
Sat Jan 02, 2021 8:06 pm
SeerOfProvo wrote:but he doesn’t have to yield anything by simply pointing out that there is a difference between a mathematical object which is entirely conceptual in nature and a book with physical dimensions and dispositional properties. I mean a mathematical object and a physical book are far more different in nature than an apple and unicorn could ever be, is it really digging himself a hole to ask why we think one is going to behave just like the other?
Physics Guy wrote:I still don't see anything interesting in Craig's red-and-blue-books argument. Mentioning real and mathematical worlds is just a red herring because the only features of the books that his argument uses are that they are of two distinct kinds and that they can be counted. Both are mathematical properties which do not depend on anything physical.
I'm pretty sure Physics Guy is right.
Craig wrote:What I shall argue is that while the actual infinite may be a fruitful and consistent concept in the mathematical realm, it cannot be translated from the mathematical world into the real world, for this would involve counter-intuitive absurdities.
^^^This statement right here is the smoking gun^^^ that Craig simply doesn't know what he's talking about. Infinity isn't a consistent concept in the mathematical realm either, which his own examples show, even if his examples are unoriginal to convey the paradoxes of infinity that have existed since ancient Greece and were intended to show something about the physical world.

Substitute "even and odd" for "red and blue", and now we're talking about properties of numbers rather than something in the real world. We could greatly simplify the objection that actual infinity is nonsense by imagining a library of infinite books, take one book out of the library, and there are still an infinite number of books. But we could forget about the library, and go back to High School algebra and say that infinity + 1 = infinity is nonsense because no other quantity plus one remains as it is.

A child may find it helpful to learn math by physically adding and taking away marbles. But I'm having an extremely difficult time visualizing Brouwer and Hilbert arguing about infinity, and Brouwer saying, "Oh yeah? Come David, imagine an infinite quantity of marbles, and that we take one away, are you really going to say the same number of marbles are left behind as originally there? If we're talking about real marbles?"

It seems like the examples are constructed as thought experiments geared to a lay audience; and not as actual thought experiments that would add credibility to intuitionism or advance anything at all in modern mathematical logic.

In fact, according to wiki's introduction to intuitionist objections to actual infinity:
The mathematical meaning of the term "actual" in actual infinity is synonymous with definite, completed, extended or existential,[11] but not to be mistaken for physically existing. The question of whether natural or real numbers form definite sets is therefore independent of the question of whether infinite things exist physically in nature.
The intuitionist objection share's the assumptions of "actual and potential" restricted to hypothetical consideration, and so I do not see how Craig can be said to be arguing from that perspective.

Mathematical logic is the ultimate realm of fail for pseudoscience and mysticism. Craig wouldn't be the first to trip over himself in that world. Scientists with far better credentials than he have gotten out of their depths really fast in that world, when trying to wax mysterious.
It certainly appears to me he's pointing at the paradox of infinity and saying, "And there is God".
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Re: Certain people can't ever get it right

Post by Physics Guy »

As a little technical correction to myself I point out that the rational numbers are countable. Cantor's big contribution was to show that the irrational numbers are not. I have edited my earlier post in this thread to correct my mistake about this, which was enormous on the topic of infinities, though of no real consequence for this thread, since it remains true that both countable and uncountable infinities exist and that Georg Cantor is famous for proving that.
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Re: Certain people can't ever get it right

Post by dastardly stem »

Physics Guy wrote:
Mon Dec 28, 2020 10:12 pm
Everything that begins to exist must have a cause.
The universe began to exist.
Therefore, the universe must have a cause.
Indeed this fails as a proof that there must have been a creator, because the major premise is not beyond all dispute. Conceivably something could maybe begin without a cause.

Even if it fails as a proof, though, I think it’s a decent argument that puts some weight on the scales in favor of a creator of some sort, at least from a scientific point of view. As much as science is about testing, it’s at least as much about assuming that Why? is always going to have an answer. Settling for “That’s just how it is!” might be logically acceptable but it’s never going to be scientifically acceptable. An uncaused beginning is just as untestable as a creator, it seems to me, so it doesn’t redeem itself scientifically that way. It gets zero points as a scientific hypothesis, while a creator gets at least one point for holding out some hope of further information.

Of course, the kind of “creator” that is supported by this argument doesn’t have to be much of a God; any kind of cause would do. And the minor premise, that the universe had a beginning, is just the current indication from cosmology if you extrapolate simply. Alternative speculations are currently unsupported but nobody can say that all alternatives have been ruled out.

I still think it’s a better argument than some atheists are willing to admit. It’s not a proof but it has a point.
I think that its fair to say it has a point, and I agree it ends on arguing for a cause. On this, if one uses this to argue for God's existence, the conclusion seems to then define god as cause, and perhaps more specifically cause of the universe. If so, then he's likely not much else. Everything that has cause can potentially be explained by prior causes in the universe. Are they too God?

If everything that exists has a cause, and not one of those existences are caused by God, then why assume the universe must be also caused by God?

Whatever that exists has an ungodly cause
The universe began to exist
Therefore the universe has an ungodly cause.
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Re: Certain people can't ever get it right

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I'm not sure what "ungodly cause" means. That's kind of the problem, here. If we're talking about the origin of the universe we're not talking about any ordinary Jimmy-hit-Johnny kind of causality because we're talking about the beginning of time itself.

Science has taught us well so far that we should expect new circumstances to expand our concepts. Within a few miles of home, the world is effectively flat, but over larger distances you have to extend your concepts of geometry to include curvature. It includes and validates our short-distance expectations in many ways but it can also contradict our flat-space conclusions, for example by allowing parallel lines to meet or internal angles of triangles to sum to more than 180°. On a sphere straight lines are great circles, and all of them have to cross not once but twice. You can make a nice triangle with corners at the North Pole and on the equator ninety degrees of longitude apart, having three internal right angles.

We've been through that ringer a few times now. What once seemed like a generally necessary truth turns out not to be wrong, exactly, but to be only a special case.

So it doesn't really make sense to say that God is the cause of the universe in the same way that a kick is the cause of a soccer ball's motion. We're surely talking about cause in some generalised and expanded sense—and we don't know exactly how the sense has been expanded and generalised. It also doesn't make sense to then ask, "Well, what caused God?" That would be asking for the next expansion of the concept of causality, if there even is one, beyond the one that is beyond anything that we have yet understood.

Trying to think about that is no more worthwhile than it would have been for a disciple of Aristotle to try to imagine quantum mechanics before Isaac Newton. Humans just can't do things like that. Struggling with just the next step beyond what we now understand, in contrast, is not crazy for humans to try. It's a clumsy pursuit but we've been able to make it succeed, now and then. So I think it's just silly to even ask, "What caused God?" but it isn't so silly to think about God at all.

This is all a qualification to my statement above, that science assumes there will always be an answer to, "Why?" I think that's true, but science has learned to expect that sometimes the answer involves an expansion of our expectations of what constitutes an answer.

In one sense it's an expansion: the kinds of answer we've found have several times been things that we previously wouldn't have listed as possible answers. It's not as though the progress of science has been a steady relaxation of rules until everything is possible, though. On the contrary, so far every new theory has been stricter and narrower, ruling out scenarios that used to seem possible. It's just been stricter and narrower in unexpected ways that previously didn't make sense. This is why people think of scientific progress being a steady increase of knowledge with things getting pinned down more and more narrowly. That's true. It's still also true that our frame of possibilities has been expanding, not shrinking.

There's still a lot more room for that to keep happening. Currently the actual universe seems arbitrary in many ways, and there is a lot of room for us to discover No, it had to be this way and no other for reasons we never imagined. It's not a matter of Anything Goes. It's that only quite specific things go—but we don't know what we're talking about. We've never commanded the morning.
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Re: Certain people can't ever get it right

Post by dastardly stem »

Physics Guy wrote:
Sat Jan 09, 2021 6:41 pm
I'm not sure what "ungodly cause" means. That's kind of the problem, here. If we're talking about the origin of the universe we're not talking about any ordinary Jimmy-hit-Johnny kind of causality because we're talking about the beginning of time itself.

Science has taught us well so far that we should expect new circumstances to expand our concepts. Within a few miles of home, the world is effectively flat, but over larger distances you have to extend your concepts of geometry to include curvature. It includes and validates our short-distance expectations in many ways but it can also contradict our flat-space conclusions, for example by allowing parallel lines to meet or internal angles of triangles to sum to more than 180°. On a sphere straight lines are great circles, and all of them have to cross not once but twice. You can make a nice triangle with corners at the North Pole and on the equator ninety degrees of longitude apart, having three internal right angles.

We've been through that ringer a few times now. What once seemed like a generally necessary truth turns out not to be wrong, exactly, but to be only a special case.

So it doesn't really make sense to say that God is the cause of the universe in the same way that a kick is the cause of a soccer ball's motion. We're surely talking about cause in some generalised and expanded sense—and we don't know exactly how the sense has been expanded and generalised. It also doesn't make sense to then ask, "Well, what caused God?" That would be asking for the next expansion of the concept of causality, if there even is one, beyond the one that is beyond anything that we have yet understood.

Trying to think about that is no more worthwhile than it would have been for a disciple of Aristotle to try to imagine quantum mechanics before Isaac Newton. Humans just can't do things like that. Struggling with just the next step beyond what we now understand, in contrast, is not crazy for humans to try. It's a clumsy pursuit but we've been able to make it succeed, now and then. So I think it's just silly to even ask, "What caused God?" but it isn't so silly to think about God at all.

This is all a qualification to my statement above, that science assumes there will always be an answer to, "Why?" I think that's true, but science has learned to expect that sometimes the answer involves an expansion of our expectations of what constitutes an answer.

In one sense it's an expansion: the kinds of answer we've found have several times been things that we previously wouldn't have listed as possible answers. It's not as though the progress of science has been a steady relaxation of rules until everything is possible, though. On the contrary, so far every new theory has been stricter and narrower, ruling out scenarios that used to seem possible. It's just been stricter and narrower in unexpected ways that previously didn't make sense. This is why people think of scientific progress being a steady increase of knowledge with things getting pinned down more and more narrowly. That's true. It's still also true that our frame of possibilities has been expanding, not shrinking.

There's still a lot more room for that to keep happening. Currently the actual universe seems arbitrary in many ways, and there is a lot of room for us to discover No, it had to be this way and no other for reasons we never imagined. It's not a matter of Anything Goes. It's that only quite specific things go—but we don't know what we're talking about. We've never commanded the morning.
Excellent thoughts. I too would agree defining an ungodly cause is the problematic issue of my previous post. I suppose my point was along the lines of suggesting since causes are not supernatural in our world, as we observe, the argument that the cause of the universe is supernatural all for the sake of arguing for the existence of a god amounts to something near begging the question. Otherwise a cause is the end of the point and we've arrived nowhere closer to God. As it were causes need not be transcending reality, nor need they be something hidden and when the cause occurs it's not as if it's an unseen religiously defined character whose sticking his finger into reality and making something happen. I think I just opened this up to an argument about the Brother of Jared knowing something about modern physics. I guess we'll see.
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Re: Certain people can't ever get it right

Post by Physics Guy »

The big problem for me is the initial conditions. Suppose we accept strict deterministic causality, so that once the universe is rolling under the laws of nature not even God gets to intervene in the course of events to diddle anything. An omniscient God could in principle still work an awful lot of what we would call miracles, just by controlling the initial conditions of the universe whenever it started.

Want to raise a dead person to life, for example? Unless you want to argue that a few tiny effects in particle physics somehow have decisive effects in biology—which would be a wild discussion—then the relevant laws of nature all have time-reversal symmetry, such that anything that happens forwards in time could in principle also happen backwards. So there's nothing strictly impossible about a dead person coming back to life: just run dying backwards.

That would require an awfully flukey conspiracy in the motions of zillions of particles and light waves and everything, but you could in principle track that conspiracy back through billions of years, following the deterministic laws of nature, to a conspiracy in the initial conditions of the universe. Given those quite special initial conditions, that one unusual event of resurrection billions of years later would be not just possible but inevitable, with all the iron certainty of perfect determinism.

Moreover nothing else in that hypothetical universe, apart from that one resurrection event, would have to look unusual at all. Right up to just a few instants before that resurrection, and forever after it, and everywhere else in the universe always, everything could look completely normal. Given absolute control over the initial conditions of the universe, one could arrange for brief "flash mob" statistical miracles to pop up anywhere in space and time without previous warning and without later trace.

So the distinction between deism and theism is pretty moot as far as I can see. A God who could foresee all the later consequences of any initial conditions, and set the initial conditions according to whim, would be hard to distinguish from an activist God who was constantly overriding the laws of nature to finagle things. The deist God might not be able to do quite everything; the total amounts of energy, momentum, electric charge and so in the universe might not be able to change, for example. I don't think those constraints would be much of an obstacle, though, to any goals that a deist God might want to achieve via miracle.

So whatever chooses the initial conditions of the universe would have pretty much all the power over what happens in the present that we would attribute to an omnipotent God. It would have determined exactly how everything is, and was, and will be, and its choices at the beginning of time could imply all kinds of apparent statistical miracles happening any time, anywhere, without warning.

It might be completely wrong to attribute emotions or intentions to whatever it is that set the initial conditions, let alone a white beard. But whatever chooses the initial conditions of the universe does seem to be tantamount to God. If you held a job interview for God and the only candidate that showed up was the thing that set the initial conditions of the universe, it might turn out not be the kind of candidate that you'd had in mind, but you'd have to give it the job.

What can science tell us about how the initial conditions of the universe were determined? So far, nothing whatever at all. And this is not just another one of those scientific gaps behind which theists like to place God. It's a gap like that, sure, but it's not just another one of the gaps: it's the one big gap. Ever since Newton the basic laws of nature have been differential equations, and it is the basic feature of differential equations that they don't tell you the initial conditions. They take arbitrary initial conditions as input, and output what happens next. So it's not even just that there are no natural laws about initial conditions: it's in the Constitution of Physics that Congress shall make no law about initial conditions.

I know of two hypothetical ways to get rid of initial conditions. One is to say that there was really only ever one possible set of initial conditions. For whatever strange, mathematical reasons, the history of this universe as it has been has been logically necessary down to the smallest detail. Nothing could have been different. So there were no choices to make. I find that option sort of logically conceivable, I suppose, but impossible to swallow. Too many things seem as though they could just as easily have been different. And the whole structure of natural law, as differential equations with arbitrary initial conditions, would seem to be an unnecessary two-stage complication if the initial conditions were also inevitable. So I cannot buy this one.

The other escape from initial conditions that I know is to say that all possible initial conditions have been realised, in a ridiculously uncountable infinity of alternative worlds that are all just as real as our own. The world that we're in is just the world in which we happen to be. So no choices were made, because all of them were. This hypothesis gets a few points for breathtaking consistency, and for thinking outside the box, but it's impossible to overstate how absurdly unparsimonious it is as an assumption. It's also untestable, and indeed has no consequences or implications at all that I can see. It raises no follow-up questions; it's such a final answer all by itself that I think it's actually indistinguishable from simply shrugging and saying, "That's how it is." So the so-called Many Worlds answer to the problem of initial conditions seems to me to be a lot less scientifically acceptable than the hypothesis of a guy in a long white beard reaching down with a compass.

Failing either of those two escape hypotheses, we seem to be stuck with physics permanently pointing to something beyond itself, to set the initial conditions of the universe. It's not obvious from science that that something has to be much like anything that any religion has called God. But it seems to me that many atheists fail to appreciate how tremendous that something does have to be. It somehow made an awful lot of very specific detailed choices. How? Why? These aren't scientific questions in the sense that they are likely to yield to scientific methods, but they are very much the same kinds of basic questions that motivate science, and so in this sense they're not unscientific. They're just appallingly hard.
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Re: Certain people can't ever get it right

Post by mentalgymnast »

Physics Guy wrote:
Tue Jan 12, 2021 12:50 pm
The big problem for me is the initial conditions. Suppose we accept strict deterministic causality, so that once the universe is rolling under the laws of nature not even God gets to intervene in the course of events to diddle anything. An omniscient God could in principle still work an awful lot of what we would call miracles, just by controlling the initial conditions of the universe whenever it started.

Want to raise a dead person to life, for example? Unless you want to argue that a few tiny effects in particle physics somehow have decisive effects in biology—which would be a wild discussion—then the relevant laws of nature all have time-reversal symmetry, such that anything that happens forwards in time could in principle also happen backwards. So there's nothing strictly impossible about a dead person coming back to life: just run dying backwards.

That would require an awfully flukey conspiracy in the motions of zillions of particles and light waves and everything, but you could in principle track that conspiracy back through billions of years, following the deterministic laws of nature, to a conspiracy in the initial conditions of the universe. Given those quite special initial conditions, that one unusual event of resurrection billions of years later would be not just possible but inevitable, with all the iron certainty of perfect determinism.

Moreover nothing else in that hypothetical universe, apart from that one resurrection event, would have to look unusual at all. Right up to just a few instants before that resurrection, and forever after it, and everywhere else in the universe always, everything could look completely normal. Given absolute control over the initial conditions of the universe, one could arrange for brief "flash mob" statistical miracles to pop up anywhere in space and time without previous warning and without later trace.

So the distinction between deism and theism is pretty moot as far as I can see. A God who could foresee all the later consequences of any initial conditions, and set the initial conditions according to whim, would be hard to distinguish from an activist God who was constantly overriding the laws of nature to finagle things. The deist God might not be able to do quite everything; the total amounts of energy, momentum, electric charge and so in the universe might not be able to change, for example. I don't think those constraints would be much of an obstacle, though, to any goals that a deist God might want to achieve via miracle.

So whatever chooses the initial conditions of the universe would have pretty much all the power over what happens in the present that we would attribute to an omnipotent God. It would have determined exactly how everything is, and was, and will be, and its choices at the beginning of time could imply all kinds of apparent statistical miracles happening any time, anywhere, without warning.

It might be completely wrong to attribute emotions or intentions to whatever it is that set the initial conditions, let alone a white beard. But whatever chooses the initial conditions of the universe does seem to be tantamount to God. If you held a job interview for God and the only candidate that showed up was the thing that set the initial conditions of the universe, it might turn out not be the kind of candidate that you'd had in mind, but you'd have to give it the job.

What can science tell us about how the initial conditions of the universe were determined? So far, nothing whatever at all. And this is not just another one of those scientific gaps behind which theists like to place God. It's a gap like that, sure, but it's not just another one of the gaps: it's the one big gap. Ever since Newton the basic laws of nature have been differential equations, and it is the basic feature of differential equations that they don't tell you the initial conditions. They take arbitrary initial conditions as input, and output what happens next. So it's not even just that there are no natural laws about initial conditions: it's in the Constitution of Physics that Congress shall make no law about initial conditions.

I know of two hypothetical ways to get rid of initial conditions. One is to say that there was really only ever one possible set of initial conditions. For whatever strange, mathematical reasons, the history of this universe as it has been has been logically necessary down to the smallest detail. Nothing could have been different. So there were no choices to make. I find that option sort of logically conceivable, I suppose, but impossible to swallow. Too many things seem as though they could just as easily have been different. And the whole structure of natural law, as differential equations with arbitrary initial conditions, would seem to be an unnecessary two-stage complication if the initial conditions were also inevitable. So I cannot buy this one.

The other escape from initial conditions that I know is to say that all possible initial conditions have been realised, in a ridiculously uncountable infinity of alternative worlds that are all just as real as our own. The world that we're in is just the world in which we happen to be. So no choices were made, because all of them were. This hypothesis gets a few points for breathtaking consistency, and for thinking outside the box, but it's impossible to overstate how absurdly unparsimonious it is as an assumption. It's also untestable, and indeed has no consequences or implications at all that I can see. It raises no follow-up questions; it's such a final answer all by itself that I think it's actually indistinguishable from simply shrugging and saying, "That's how it is." So the so-called Many Worlds answer to the problem of initial conditions seems to me to be a lot less scientifically acceptable than the hypothesis of a guy in a long white beard reaching down with a compass.

Failing either of those two escape hypotheses, we seem to be stuck with physics permanently pointing to something beyond itself, to set the initial conditions of the universe. It's not obvious from science that that something has to be much like anything that any religion has called God. But it seems to me that many atheists fail to appreciate how tremendous that something does have to be. It somehow made an awful lot of very specific detailed choices. How? Why? These aren't scientific questions in the sense that they are likely to yield to scientific methods, but they are very much the same kinds of basic questions that motivate science, and so in this sense they're not unscientific. They're just appallingly hard.
Mind blowing post. I enjoy reading your stuff.

Thanks for your thoughts,
MG
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