I suppose by choosing a theory that doesn't predict a significant probability of them.How can we defeat the Boltzmann brain paradox? — 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.In an infinite duration, aren't all possible outcomes equally likely to occur? — Down The Rabbit Hole
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
ToshCountable infinities are equal — RogueAI
Post what you think the video is claiming. If your thoughts are aligned to the bit above, you're on your own.Thoughts noAxioms? — Down The Rabbit Hole
The answer there says that the cardinalities of two countable infinities are equal.I'm going by stuff like this: — RogueAI
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."But if the universe exists over an infinitely long time, extremely unlikely events will happen." — Patterner
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.I'm sure some will. But there are an infinite number of unlikely events. No reason to think all of them will happen.
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.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.
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. — RogueAI
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.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
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
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.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
Something like that. The Carroll paper I liked states the problem far more clearly than does wiki.Physicists use the Boltzmann brain thought experiment as a reductio ad absurdum argument for evaluating competing scientific theories.
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.My question become a rather simple one. If Boltzmann brains exist, then why have we never found one? — universeness
You say you're not a math major, ask a question, then ignore the answer (given by several posters).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
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.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
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
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.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
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.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
Or a functioning entity that thinks it's a human brain.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.
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.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?
Finite sides. It represents about 5 million random keystrokes, enough to write the complete works of Shakespeare.The die has an infinite number of sides. — Patterner
The two sets are not equal. — noAxioms
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
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
Infinity just means essentially 'without bound', or more literally, not finite. "An infinite number" is a contradiction. There is no number that is infinite.I don't assign much value to notions such as infinity or 'an infinite number of possibilities,' etc. — universeness
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 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.
No. There is no 'distance' to infinity since it isn't a number.A googolpex is as far from infinity as the number 1.
Not so, and there are probably more than that many BBs in our universe, and hopefully more regular brains than that.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.'
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.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.
There's an awful lot of literature about such sets, and their relation to sets of higher cardinality.The term 'countable infinity,' has little value imo.
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.It's not possible to count all possible members of the list of integers
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.as there is NO such duration as an infinite duration
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.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. — noAxioms
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
Thank you for your unrequested, unrequired and impudent condolences.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
Seth Lloyd has stated, "They fail the Monty Python test: Stop that! That's too silly!" — universeness
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
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
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