Sean Carroll put out a paper explaining why Boltzmann brains are bad
https://arxiv.org/pdf/1702.00850.pdf

The gist is: "the theories that predict them are “cognitively unstable: they cannot simultaneously be true and justifiably believed.

Therefore only theories that predict low probabilities of them can be justifyably believed. The OP makes it sound like the universe must produce these more probably than a standard brain given enough time, which is false. Only under certain theories is this true, and it is a real problem if the theory that is the right one happens to be one of them.

How can we defeat the Boltzmann brain paradox? — Down The Rabbit Hole

I suppose by choosing a theory that doesn't predict a significant probability of them.

In an infinite duration, aren't all possible outcomes equally likely to occur? — Down The Rabbit Hole

No, that doesn't follow at all. I cannot think of a theory that has equal ratio of regular humans to BB's.

PS: I didn't watch the video.

https://www.youtube.com/watch?v=OpohbXB_JZU

How can we defeat the Boltzmann brain paradox?

In an infinite duration, aren't all possible outcomes equally likely to occur? — Down The Rabbit Hole

The clip doesn't say that last bit. That said, it is more confusing than anything else. I only got what it was hinting and gesturing at because I've already read more about this topic. If you are interested, I would advise you to do the same.

Countable infinities are equal, so the infinite set of worlds where we're Boltzmann brains is equal to the infinite set of worlds where we're not. It's a 50/50 chance, epistemically speaking. Given an infinitely large multiverse, of course.

Countable infinities are equal, so the infinite set of worlds where we're Boltzmann brains is equal to the infinite set of worlds where we're not. It's a 50/50 chance, epistemically speaking. Given an infinitely large multiverse, of course. — RogueAI

That's what I was thinking! Thoughts @noAxioms?

Yes, the part about all outcomes being equally likely within infinity, is my challenge to the paradox.

It would be good to have your thoughts. I have been impressed with many of the regulars knowledge on infinities.

Countable infinities are equal — RogueAI

Tosh

If that were true, if I pick a random whole number of at least 10 digits, odds are even that it would be prime because there are countably infinite numbers that large that are prime, and countably infinite numbers that are not.

Did the you-tube link make a claim of that nature? If so, it would validate my policy to not get my facts from you tube.

Thoughts noAxioms? — Down The Rabbit Hole

Post what you think the video is claiming. If your thoughts are aligned to the bit above, you're on your own.

What exactly are we counting here anyway? The point is not how many universes in the multiverse (which is not countable no matter what kind of multiverse you're talking about), but rather the probability of the physics of this universe being such that BB's are more probable than regular brains. There is no equal probability in any of that.
It seems that neither normal nor BB's are countable in any reasonable manner, especially since empirical measurement is questionable.

I'm not a math major by any means. I'm going by stuff like this:

https://math.stackexchange.com/questions/760553/are-all-uncountable-infinities-greater-than-all-countable-infinities-are-some-u#:~:text=(b)%20No%2C%20all%20countable,numbers%2C%20than%20%CE%B1%3E%CE%B2.

I think we can defeat the Boltzmann Brain problem by adopting idealism. The idea that consciousness and mind can come from non-conscious mindless stuff leads to all sorts of problems.

I'm going by stuff like this: — RogueAI

The answer there says that the cardinalities of two countable infinities are equal.
That's very different than the statement that two countable infinities are equal, which sort of suggests that there are numbers representing its sizes and those numbers are the same, which is just silly since there can be no such number.

Again I repeat, why is this relevant? Who is comparing two countable infinities? The conclusion of 'equally likely probability' is invalid from a comparison of the cardinalities, as the prime-number example illustrates.

The video says:
"But if the universe exists over an infinitely long time, extremely unlikely events will happen."
I'm sure some will. But there are an infinite number of unlikely events. No reason to think all of them will happen. There are an infinite number of things those infinite monkeys on infinite typewriters could type. There are an infinite number of things they could type that do not contain the letter E.

"But if the universe exists over an infinitely long time, extremely unlikely events will happen." — Patterner

Since the universe is infinite in size, it doesn't even take a significant amount of time for extremely unlikely events to occur. I think a comparison of how likely it is to occur within say a given volume of space would help express things better.

I'm sure some will. But there are an infinite number of unlikely events. No reason to think all of them will happen.

Questionable. Some occurrences get less probable over time. They happen because of the infinite size, but if the probability of something drops in half with each passing century, it probably will never happen in a given volume even given infinite time. It all has to do with the area under the probability curve. Is it finite or not? Some infinite series approach infinity and some do not.

There are an infinite number of things those infinite monkeys on infinite typewriters could type. There are an infinite number of things they could type that do not contain the letter E.

But you didn't mention something that they cannot type (pi to full precision is a nice example), and how about anything larger than one monkey can type in its lifetime? The monkeys are not immortal, so the probability of something getting typed drops off sharply after the life expectancy of one. Sure, one monkey lives long enough to hammer out all of Shakespeare. That's why we have a lot of monkeys, which represents infinite space. Immortal monkeys represents infinite time. A single immortal monkey who never stops outputting random characters is all that is needed to eventually put out any finite work of literature, buried of course with gibberish on either side.

Who is comparing two countable infinities? — noAxioms

If the universe is infinite, then there are infinitely many Boltzmann brains and infinitely many non-Boltzmann brains. Since the two sets are equal, the subjective probability that one is a member of either set is 50/50. What else could it be? What do you think the probability that you're not a Boltzmann brain is? And how do you arrive at that value?

If the universe is infinite, then there are infinitely many Boltzmann brains and infinitely many non-Boltzmann brains. Since the two sets are equal, the subjective probability that one is a member of either set is 50/50. — RogueAI

• If the universe is infinite, then there are infinitely many @RogueAI brains and infinitely many non-@RogueAI brains. So for any given brain, there is a 50% probability that it is a @RogueAI brain.
• If the universe is infinite, then there are infinitely many @Down The Rabbit Hole brains and infinitely many non-@Down The Rabbit Hole brains. So for any given brain, there is a 50% probability that it is a @Down The Rabbit Hole brain.
• If the universe is infinite, then any given brain is either a @RogueAI or a @Down The Rabbit Hole brain.

See the problem here? Probabilities don't work like that.

In any case, this is not relevant to the OP video, which was comparing the probabilities of a "Boltzmann Brain" fluctuation and a "Boltzmann Big Bang" fluctuation. You don't need an infinite domain with its measure problems to do that.

From wiki:
The Boltzmann brain thought experiment suggests that it might be more likely for a single brain to spontaneously form in a void (complete with a memory of having existed in our universe) rather than for the entire universe to come about in the manner cosmologists think it actually did. Physicists use the Boltzmann brain thought experiment as a reductio ad absurdum argument for evaluating competing scientific theories.

My question becomes a rather simple one. If Boltzmann brains exist, then why have we never found one?
They seem as hidden as gods.

A single immortal monkey who never stops outputting random characters is all that is needed to eventually put out any finite work of literature, buried of course with gibberish on either side. — noAxioms

Anything's possible. But with an infinite number of possibilities that are not works of literature, including an infinite amount of gibberish; an incomprehensibly large number of combinations of the same number of letters, punctuation, and spaces as Shakespeare's works that are not Shakespeare's works; and a rather large number of works of literature that are not Shakespeare's works... I'd bet against it.

I'm not sure you're right, so let me ask you the same question I asked Axiom:
What do you think the probability that you're not a Boltzmann brain is? And how do you arrive at that value?

f the universe is infinite, then there are infinitely many Down The Rabbit Hole brains and infinitely many non-@Down The Rabbit Hole brains. So for any given brain, there is a 50% probability that it is a @Down The Rabbit Hole brain. — SophistiCat

We were talking about subjective probabilities, not actual probabilities, and it's already known by me that I don't have "Down the Rabbit Hole"'s brain, so this "If the universe is infinite, then any given brain is either a @RogueAI or a @Down The Rabbit Hole brain." is false. I already know that my own given brain cannot be Rabbit Hole's brain.

From wiki:
The Boltzmann brain thought experiment suggests that it might be more likely for a single brain to spontaneously form in a void (complete with a memory of having existed in our universe) rather than for the entire universe to come about in the manner cosmologists think it actually did. — universeness

That's a horrible wording of the problem. What is 'the void' here? Is it that from which the universe sprang, or is it our universe, mostly nearing infinite time and space? Our universe contains an infinite number of real brains, so comparing that to the more probable BB's in 'the void' is still not comparing real to BBs. One improbable roll times infinity is questionably more than the more probable roll.

Physicists use the Boltzmann brain thought experiment as a reductio ad absurdum argument for evaluating competing scientific theories.

Something like that. The Carroll paper I liked states the problem far more clearly than does wiki.

My question become a rather simple one. If Boltzmann brains exist, then why have we never found one? — universeness

The odds of one existing exactly on our past light code is zero to an incredible number of digits. If one by super freak chance happens to exist exactly on our past light cone, the odds that we'd notice it there is zero to a whole bunch more digits. We can't even see a rock that size if its further away than the moon, let alone on the far side of the visible universe.
Other answer: Maybe you are one, in which case you've technically found one.

A BB need not be a 3 dimensional thing, or in any way resembling a human brain. It just needs to be something functioning as one in enough ways.

If the universe is infinite, then there are infinitely many Boltzmann brains and infinitely many non-Boltzmann brains. Since the two sets are equal, the subjective probability that one is a member of either set is 50/50. What else could it be? — RogueAI

You say you're not a math major, ask a question, then ignore the answer (given by several posters).
The two sets are not equal. To say they are equal is to say that every Boltzmann brain is also a normal non-Boltzmann brain. The two sets would be the same set. This is a contradiction.

"Subjective probability" is a meaningless term. Probability refers to the odds of one thing relative to another, or the odds of something being true or not.

But with an infinite number of possibilities that are not works of literature, including an infinite amount of gibberish; an incomprehensibly large number of combinations of the same number of letters, punctuation, and spaces as Shakespeare's works that are not Shakespeare's works; and a rather large number of works of literature that are not Shakespeare's works... I'd bet against it. — Patterner

So given a die with 10^10000000 sides, one of those sides corresponds to the complete works of Shakespeare, and the rest other things, mostly gibberish. You're betting that if this die is rolled an unlimited number of times, most of those other sides will come up an infinite number of times, but the one side in question will not come up even once.
You're not a math major either I take it. Neither am I, but I can do simple arithmetic at least.

The odds of one existing exactly on our past light code is zero to an incredible number of digits. If one by super freak chance happens to exist exactly on our past light cone, the odds that we'd notice it there is zero to a whole bunch more digits. We can't even see a rock that size if its further away than the moon, let alone on the far side of the visible universe.
Other answer: Maybe you are one, in which case you've technically found one. — noAxioms

If the Universe can manifest Boltzman brains, then surely they would at least be a numerous as planets or neutrinos. What would restrict their number?

The wiki article goes no to say:
Over a sufficiently long time, random fluctuations could cause particles to spontaneously form literally any structure of any degree of complexity, including a functioning human brain. The scenario initially involved only a single brain with false memories, but physicist Sean Carroll pointed out that, in a fluctuating universe, the scenario works just as well with entire bodies, even entire galaxies.

and

Sean Carroll states "We're not arguing that Boltzmann Brains exist—we're trying to avoid them." Carroll has stated that the hypothesis of being a Boltzmann brain results in "cognitive instability". Because, he argues, it would take longer than the current age of the universe for a brain to form, and yet it thinks that it observes that it exists in a younger universe, this shows that memories and reasoning processes would be untrustworthy if it were indeed a Boltzmann brain. Seth Lloyd has stated, "They fail the Monty Python test: Stop that! That's too silly!" A New Scientist journalist summarizes that "The starting point for our understanding of the universe and its behavior is that humans, not disembodied brains, are typical observers.

I underlined some of the words from the new scientist journalist, as I always perceived Boltzmann brains, as posited by Boltzmann, to be 'disembodied' notions of a thinking agent, so how could I have or be one?
Perhaps I missed something about the various descriptions I have read about Boltzmann's work.
Definitely a genius scientist but he had a very bad time by all accounts.

In 1906, Boltzmann's deteriorating mental condition, forced him to resign his position, and his symptoms indicate he experienced what would today be diagnosed as bipolar disorder. Four months later he died by suicide on 5 September 1906, by hanging himself while on vacation with his wife and daughter in Duino, near Trieste (then Austria).

But with an infinite number of possibilities that are not works of literature, including an infinite amount of gibberish; an incomprehensibly large number of combinations of the same number of letters, punctuation, and spaces as Shakespeare's works that are not Shakespeare's works; and a rather large number of works of literature that are not Shakespeare's works... I'd bet against it.
— Patterner
So given a die with 1010000000 sides, one of those sides corresponds to the complete works of Shakespeare, and the rest other things, mostly gibberish. You're betting that if this die is rolled an unlimited number of times, most of those other sides will come up an infinite number of times, but the one side in question will not come up even once.
You're not a math major either I take it. Neither am I, but I can do simple arithmetic at least. — noAxioms

The die has an infinite number of sides. Not the finite number that the one you postulate has. It's not simple arithmetic. You could roll this die an infinite number of times, and you would never see every side. There are an infinite number of sides you would never see.

If the Universe can manifest Boltzman brains, then surely they would at least be a numerous as planets or neutrinos. What would restrict their number? — universeness

I don't know what you mean by 'their number'. Things which occur an unlimited number of times don't have a number to restrict, and thus has no bearing on the likelihood of finding one. See the example about the primes in my post above.

The wiki article goes no to say:
Over a sufficiently long time, random fluctuations could cause particles to spontaneously form literally any structure of any degree of complexity, including a functioning human brain.

Or a functioning entity that thinks it's a human brain.

I underlined some of the words from Seth Lloyd as I always perceived Boltzmann brains as posited by Boltzmann to be 'disembodied' notions, so how could I have or be one?

They're subjectively indistinguishable from a regular one, at least for a moment. BBs don't last but for a moment usually, unless a life-support system also springs into existence along with it.

The die has an infinite number of sides. — Patterner

Finite sides. It represents about 5 million random keystrokes, enough to write the complete works of Shakespeare.
You suggest the number is not finite. How can you justify that? Is there a finite probability of the letter 'T' being typed first? If so, is it infinitely unllkely that a 'h' would follow? Exactly at what character (out of the 5 million) does the next correct keystroke suddenly become infinitely improbable? There are about 65 characters from which to choose. Perhaps you are suggesting that the product of 5 million of of these nonzero numbers is zero, and not just a really small number with only about 10 million leading zeros.

The two sets are not equal. — noAxioms

Your claim is then that the two countable infinite sets (Boltzmann brains and non-Boltzmann brains) are not equal? Any math people want to comment on that? It's my understanding all infinite countable sets are equal.

With these definitions, here are the answers (without proofs):

(a) Yes, every uncountable infinity is greater than every countable infinity.

(b) No, all countable infinities are the same: if A and B are both countable and infinite, then α=β
.
https://www.google.com/search?q=%22countable+infinities+are+equal%22&rlz=1C1CHBH_enUS956US956&oq=%22countable+infinities+are+equal%22&aqs=chrome..69i57j33i160l2.10534j0j4&sourceid=chrome&ie=UTF-8

I wonder how many Boltzmann brains think they are Martians. And how many think they are from sentient stars. And how many think they are in a universe with entirely different laws of physics than those in the universe I think I am from. And how many think they are God. And how many think they are…. Well, anything else we can imagine, as well as any number of things we don’t get around to imagining.

Is there any reason any of these things couldn’t happen?

I don't know what you mean by 'their number'. Things which occur an unlimited number of times don't have a number to restrict, and thus has no bearing on the likelihood of finding one. See the example about the primes in my post above. — noAxioms

I don't assign much value to notions such as infinity or 'an infinite number of possibilities,' etc.
A notional number like a googolplex, cannot be written out as 1 followed by the number of zero's required, as there is not enough space in the universe to do so. A googolpex is as far from infinity as the number 1. If there were a googolplex of boltzmann brains in the universe then every coordinate in the universe would contain one and we would know what the universe was 'made of.'
If I wandered freely in the universe, the chances of me encountering a galaxy, a star and a planet are quite good, given an adequate amount of time. So, based on Boltzmann's description of a Boltzmann Brain, I think we would have encountered them by now, if they existed, regardless of any probability arguments you have offered regarding primes.

if I pick a random whole number of at least 10 digits, odds are even that it would be prime because there are countably infinite numbers that large that are prime, and countably infinite numbers that are not. — noAxioms

The term 'countable infinity,' has little value imo. I don't know what a maths expert such as @jgill would comment, on the 'usefulness' of terms such as 'countable and uncountable infinities,' perhaps he will offer us his view.

The maths stack exchange has:
A countable infinite set is a set where you can list the elements one-by-one, but your list is infinitely long. Some examples are the natural numbers, integers, and rationals.

It's not possible to count all possible members of the list of integers, sure, you can start to count them, and I suppose that's why such a list is called 'countable,' but, the concept is 'over burdened,' as it is self-defeating to suggest that a list of items is 'countable' and then demonstrate that you can start the count, but the heat death of the universe will complete before the counting process completes, so 'countable infinity' is about as useful a notion as a permanently hidden deist god.

The points I have been making SUPPORT your (and Sean Carroll's ) proposal that we need not consider that in 'an infinite duration we are more likely to be a disembodied brain,' as there is NO such duration, as an infinite duration, so there is NO possibility that we are in REALITY, some disembodied brain.

I appreciate that I am a maths child, in comparison with someone who merits the title maths prof.
I cannot see any particular usefulness for the notion of 'different types of infinity' based on notions such as cardinality and bijective/injective functions, but perhaps someone like @jgill could explain why such notions are essential and support the notion of Boltzmann brains.

I don't assign much value to notions such as infinity or 'an infinite number of possibilities,' etc. — universeness

Infinity just means essentially 'without bound', or more literally, not finite. "An infinite number" is a contradiction. There is no number that is infinite.

Y'all are missing the point. It hasn't anything to do with infinity. It all has to do with one's theory of choice and not with the actual universe. Any theory that produces BB at a higher probability cannot be justified by empirical means or any other means. That's the point.

A notional number like a googolplex, cannot be written out as 1 followed by the number of zero's required, as there is not enough space in the universe to do so.

Lack of ability to write a number down doesn't make it a not-number. People have expressed numbers an awful lot higher than a googleplex.

A googolpex is as far from infinity as the number 1.

No. There is no 'distance' to infinity since it isn't a number.

If there were a googolplex of boltzmann brains in the universe then every coordinate in the universe would contain one and we would know what the universe was 'made of.'

Not so, and there are probably more than that many BBs in our universe, and hopefully more regular brains than that.

If I wandered freely in the universe, the chances of me encountering a galaxy, a star and a planet are quite good, given an adequate amount of time. So, based on Boltzmann's description of a Boltzmann Brain, I think we would have encountered them by now, if they existed, regardless of any probability arguments you have offered regarding primes.

Non-sequitur. Stars and planets are pretty persistent; BB's are not. Stars and planets are readily visible,. BBs are not. The sun has wandered freely for about a third the age of the universe and hasn't encountered a star yet, so I suppose I can deny the first assertion as well. A random walk through the universe will probably not hit an object as large as a planet before those objects have long since gone cold and dead. You will on the other hand encounter small things like dust once in a while, but not often enough to say doom a spacecraft like Voyager before it stops talking to us.

Nobody is claiming that BB's are popping up constantly around every corner. They're incredibly unlikely things, but then you multiply that super-low probability by unlimited 'time', if 'time' is a meaningful concept outside of our own posited spacetime.

The term 'countable infinity,' has little value imo.

There's an awful lot of literature about such sets, and their relation to sets of higher cardinality.

I don't know what a maths expert such as jgill would comment, on the 'usefulness' of terms such as 'countable and uncountable infinities,' perhaps he will offer us his view.

It's not possible to count all possible members of the list of integers

Of course not. Each integer (and each rational number for that matter) can be assigned a unique position in the list. That's the mathematical definition if it being countable. So for instance, the integer 75 is probably 150th on the list of integers by the simplest method of counting. Since there is no integer that cannot be assigned such a position, the list is deemed countable. You're definition seems to be "can be counted". If it could be counted, it would be by definition finite.

as there is NO such duration as an infinite duration

That's like saying that the spatial extent of the universe must be finite. There is nothing precluding unbounded time, and my condolences if you cannot handle it.

Your claim is then that the two countable infinite sets (Boltzmann brains and non-Boltzmann brains) are not equal? — RogueAI

You just endlessly repeat the same claim, without backing and without addressing any of the counter arguments. The links you supplied do not support your case.

For two numbers to be equal, they would need to be the same number. Similarly, for two sets to be equal, they'd need to be the same set. Maybe you're working from a different definition of what it means for two things to be equal, but you've not provided that.
There's been plenty of counterexamples to your assertion and you've not found fault with any of them.

As for your claim of my claim above, that too is false since it is possible for both sets to be empty, and therefore equal.

You just endlessly repeat the same claim, without backing and without addressing any of the counter arguments. The links you supplied do not support your case. — noAxioms

Sure they do. If A and B are both countably infinite, A=B. Do you dispute this? Is the link I proved wrong? You also haven't provided any links to back up your point. Can you do so? Do you want to say they're the same size instead of being equal? That's fine with me.

ETA:
In the late 19th century, the German mathematician Georg Cantor captured the spirit of this matching strategy in the formal language of mathematics. He proved that two sets have the same size, or “cardinality,” when they can be put into one-to-one correspondence with each other — when there is exactly one driver for every car. Perhaps more surprisingly, he showed that this approach works for infinitely large sets as well.
https://www.quantamagazine.org/mathematicians-measure-infinities-find-theyre-equal-20170912/

If there were a googolplex of boltzmann brains in the universe then every coordinate in the universe would contain one and we would know what the universe was 'made of.'
Not so, and there are probably more than that many BBs in our universe, and hopefully more regular brains than that. — noAxioms

I think your statement above is nonsense, based in the definition of a googolplex.

That's like saying that the spatial extent of the universe must be finite. There is nothing precluding unbounded time, and my condolences if you cannot handle it. — noAxioms

Thank you for your unrequested, unrequired and impudent condolences.

The geometry of the universe is currently considered flat, and unbounded, not infinite. It could seem flat to us based on its actual size. It could be an expanding sphere shape, but not expanding into anything as it IS everything. I think this train of thought is why Carl Sagan liked the idea that this universe may be like an atom, and every atom in this universe, being a universe. An unlikely but more plausible idea, than the existence of boltzmann brains imo.
I agree with Seth.

Seth Lloyd has stated, "They fail the Monty Python test: Stop that! That's too silly!" — universeness

Can you address my reply to you about subjective probabilties?

Have you replied to the wrong poster here? You did not reply to me asking about subjective probabilities,
you directed that towards noAxioms and sophistiCat. For what it's worth, you posted this reply to SophistiCat

We were talking about subjective probabilities, not actual probabilities, and it's already known by me that I don't have "Down the Rabbit Hole"'s brain, so this "If the universe is infinite, then any given brain is either a RogueAI or a @Down The Rabbit Hole brain." is false. I already know that my own given brain cannot be Rabbit Hole's brain. — RogueAI

My response would be:
I think 'subjective probability,' defined as:
Subjective probability is a probability that reflects an individual's personal judgment or own experience about the likelihood of an event. It is not based on formal calculations, data, or theory. It may vary among different people and situations. It is sometimes used when more objective methods are not available or feasible.

Is at best, a limited way to offer credible evidence of a proposal, and as your subjective probability is further based on a complete unknown, such as 'is the universe infinite?' then this does not add to my confidence level that Boltzmann brains are possible.

Is at best, a limited way to offer credible evidence of a proposal, and as your subjective probability is further based on a complete unknown, such as 'is the universe infinite?' then this does not add to my confidence level that Boltzmann brains are possible. — universeness

Yes, I confused you with another poster, sorry about that.

Assuming that the universe is infinite, what do you think the probability is that you're a Boltzmann brain?