disproof of boltzman brain?

For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.

Moderators: gmalivuk, Moderators General, Prelates

User avatar
Eebster the Great
Posts: 3211
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: disproof of boltzman brain?

Postby Eebster the Great » Thu Dec 06, 2018 2:05 pm UTC

The universe in this model is infinite, not a single point. But due to inflation, a region that was once extremely small (though not literally a single point) is now larger than the entire observable universe. This inflationary event may be the low entropy event we are discussing. In any case, the idea is that the universe is usually at or near equilibrium and only rarely fluctuates away from equilibrium. Entropy never decreases in classical mechanics. You will, in your whole life, never observe a case in which total entropy decreases. It is effectively impossible and is a violation of the second law of thermodynamics. However, it is not literally impossible, and in an infinite universe, it happens infinitely many times. But there is no reason entropy dropping gradually is more probable than it dropping quickly. At every step, it is overwhelmingly more likely that entropy will increase. You cannot set things up so entropy just coasts downhill; it always rises.

Pfhorrest, large universes would be more likely to naturally evolve brains than small universes would be, sure. But they would also be more likely to evolve Boltzmann brains, and more of them. The fact that these brains occur more frequently than natural ones doesn't change in a large event.

User avatar
Pfhorrest
Posts: 5108
Joined: Fri Oct 30, 2009 6:11 am UTC
Contact:

Re: disproof of boltzman brain?

Postby Pfhorrest » Thu Dec 06, 2018 5:57 pm UTC

Eebster the Great wrote:Pfhorrest, large universes would be more likely to naturally evolve brains than small universes would be, sure. But they would also be more likely to evolve Boltzmann brains, and more of them.

This phrasing doesn't make sense to me. In the sense of "universe" I was using, the classical image of a Boltzmann brain that just pops into being from nothing without any surrounding context is a "universe", and in the looser sense of a Boltzmann brain you seemed to be using in the post I was replying to, "naturally evolved" brains are still a kind of Boltzmann brain.

Like, one possible event is that out of the thermal equilibrium of the infinite true universe, energy just happens to arrange itself into a brain for a moment. That's the classical image of a Boltzmann brain.

Another possible event is that out of the thermal equilibrium of the infinite true universe, energy just happens to arrange itself into some other low-entropy state, which then evolves over the course of its return to equilibrium, and over the course of that evolution, a brain comes into being. You seemed to be talking about this, and saying that this also counts as a Boltzmann brain.

Yet another possible event is that out of the thermal equilibrium of the infinite true universe, a whole lot of energy arranged itself into a massively low-entropy state, which then evolved over the course of tens of billions of years as it slowly returned to equilibrium, generating everything we know, stars and planets and life with brains, along the way.

If the brains that occur in that second case still counts as Boltzmann brains, then the "naturally evolved" brains of our universe are just an edge case of Boltzmann brains too, and you really have this spectrum of spontaneous low-entropy events from ones the size of brains to ones bigger than our observable universe. The smaller ones are going to be more likely to happen, of course. But if brains are more likely to occur in the bigger ones than in the smaller ones, which seems plausible, then that seems like it negates that, as far as where you're likely to find a brain. If there are many more small random things spontaneously popping into existence across infinity all the time, but many many fewer of them ever become (or come to contain) brains than the big ones, and the big ones tend to contain many many many brains each, then the unlikelihood of a brain occurring in a small fluctuation could outweigh the greater likelihood of those small fluctuations occurring, leaving most brains most likely occurring within big fluctuations, like the universe that we know.
Forrest Cameranesi, Geek of All Trades
"I am Sam. Sam I am. I do not like trolls, flames, or spam."
The Codex Quaerendae (my philosophy) - The Chronicles of Quelouva (my fiction)

User avatar
Eebster the Great
Posts: 3211
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: disproof of boltzman brain?

Postby Eebster the Great » Thu Dec 06, 2018 8:42 pm UTC

I mean that a large universe which develops into a vacuum with a surprise brain in the middle is still more likely than a large universe with such low entropy that not only do you get a brain, but also planets and stars and stuff. Because the former is far higher entropy.

User avatar
ucim
Posts: 6680
Joined: Fri Sep 28, 2012 3:23 pm UTC
Location: The One True Thread

Re: disproof of boltzman brain?

Postby ucim » Fri Dec 07, 2018 2:40 am UTC

Eebster the Great wrote:I mean that a large universe which develops into a vacuum with a surprise brain in the middle is still more likely than a large universe with such low entropy that not only do you get a brain, but also planets and stars and stuff. Because the former is far higher entropy.
Is it?

In the latter case, all you need is a random (particle distribution in the) universe, whose (small finite number of) laws generate life, which generates Brians, or perhaps brains. How many (from the set of possible) laws will lead to the generation of brains? Probably (IMHO) more than random fluctuations of the Void will spontaneously generate a brain. (Or a Brian)

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Please help addams if you can. She needs all of us.

User avatar
tomandlu
Posts: 1095
Joined: Fri Sep 21, 2007 10:22 am UTC
Location: London, UK
Contact:

Re: disproof of boltzman brain?

Postby tomandlu » Fri Dec 07, 2018 3:07 pm UTC

ucim wrote:
Eebster the Great wrote:I mean that a large universe which develops into a vacuum with a surprise brain in the middle is still more likely than a large universe with such low entropy that not only do you get a brain, but also planets and stars and stuff. Because the former is far higher entropy.
Is it?

In the latter case, all you need is a random (particle distribution in the) universe, whose (small finite number of) laws generate life, which generates Brians, or perhaps brains. How many (from the set of possible) laws will lead to the generation of brains? Probably (IMHO) more than random fluctuations of the Void will spontaneously generate a brain. (Or a Brian)

Jose


I don't think anyone's claiming that the evolution of the universe, including life, is anti-entropy - just the initial change from total entropy to low entropy (which then allows everything else to happen). That said, I too am struggling with the notion of a large-scale anti-entropy event, but which is essentially unorganised (creation), vs a small-scale anti-entropy event that is highly organised (a BB), but I think that's my puny brain, rather than something wrong with the BB principle.
How can I think my way out of the problem when the problem is the way I think?

User avatar
doogly
Dr. The Juggernaut of Touching Himself
Posts: 5495
Joined: Mon Oct 23, 2006 2:31 am UTC
Location: Lexington, MA
Contact:

Re: disproof of boltzman brain?

Postby doogly » Fri Dec 07, 2018 3:14 pm UTC

What do you mean by "Organized" here?
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?

User avatar
Xanthir
My HERO!!!
Posts: 5366
Joined: Tue Feb 20, 2007 12:49 am UTC
Location: The Googleplex
Contact:

Re: disproof of boltzman brain?

Postby Xanthir » Fri Dec 07, 2018 3:46 pm UTC

ucim wrote:
Eebster the Great wrote:I mean that a large universe which develops into a vacuum with a surprise brain in the middle is still more likely than a large universe with such low entropy that not only do you get a brain, but also planets and stars and stuff. Because the former is far higher entropy.
Is it?

It is, by virtue of the simple fact that it's a *much* smaller amount of energy that had to locally-entropy-reverse into that tiny inflationary point, versus *all* the energy that had to do the same to form our full universe. Every quantum of energy you add to the event decreases its likelihood of occurring in the first place (exponentially, iirc); a vacuum+brain is *vastly* smaller than the mass-energy of our physical universe!

Once you set up a physical universe like ours, it may be inevitable that brains develop that are capable of thinking about themselves and having memories and such, versus the clearly ad hoc/random nature of a brain arising in a void with built-in memories of a life, but the starting probabilities of such a physical universe versus the brain universe are so mind-bogglingly tilted toward the brain-void universe that, as far as many of our attempts at cosmology can tell, the brain-void is going to happen *way* more often than brains in a physical universe capable of developing them normally.

In conclusion, Last Thursday-ism appears to be the most statistically-correct religious stance of all.
(defun fibs (n &optional (a 1) (b 1)) (take n (unfold '+ a b)))

User avatar
ucim
Posts: 6680
Joined: Fri Sep 28, 2012 3:23 pm UTC
Location: The One True Thread

Re: disproof of boltzman brain?

Postby ucim » Fri Dec 07, 2018 4:43 pm UTC

tomandlu wrote:just the initial change from total entropy to low entropy (which then allows everything else to happen)
What is "total entropy" and how does it even apply to a universe that doesn't exist yet?

Xanthir wrote:
ucim wrote: Is it?
It is, by virtue of the simple fact that it's a *much* smaller amount of energy that had to locally-entropy-reverse into that tiny inflationary point, versus *all* the energy that had to do the same to form our full universe
But also the bigger the universe that is created, the more likely it is that, within that universe, there will be pockets that develop into brains. It would happen due to the (small number of) natural laws, rather than the (huge number of) boundary conditions that are needed to support a BB.

Xanthir wrote:In conclusion, Last Thursday-ism appears to be the most statistically-correct religious stance of all.
Heretic! It's last Wednesday-ism!

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Please help addams if you can. She needs all of us.

User avatar
Xanthir
My HERO!!!
Posts: 5366
Joined: Tue Feb 20, 2007 12:49 am UTC
Location: The Googleplex
Contact:

Re: disproof of boltzman brain?

Postby Xanthir » Fri Dec 07, 2018 5:44 pm UTC

ucim wrote:
Xanthir wrote:
ucim wrote: Is it?
It is, by virtue of the simple fact that it's a *much* smaller amount of energy that had to locally-entropy-reverse into that tiny inflationary point, versus *all* the energy that had to do the same to form our full universe
But also the bigger the universe that is created, the more likely it is that, within that universe, there will be pockets that develop into brains. It would happen due to the (small number of) natural laws, rather than the (huge number of) boundary conditions that are needed to support a BB.

Sure, but again, Every. Single. Quantum of Energy. you add to the entropy fluctuation that becomes a universe exponentially decreases the likelihood of it occurring. A bigger universe is *fundamentally* more unlikely than a smaller one, before you even start doing the math for figuring out the chances of brain-o-genesis!

Basically you're not doing the math hard enough if you think that pockets of brains in gigantic energy-full universes end up being more likely than a small brain in a void. (Or at least, many respected cosmologists who *have* done the math seem to currently agree that, based on our current understanding of things, it's way more likely we're a BB than a big universe.)

Also, I'm not quite sure if you got this point or not from your wording, but the BB hypothesis doesn't need to support a brain, like long-term or anything. It's sufficient to have a universe that conjures a brain into existence for a bare moment, just long enough to meaningfully exist and process the most recent part of the thought you are currently thinking. Prior existence is irrelevant; conjuring the brain with pre-built memories of prior existence is *far* more likely than conjuring the brain with sufficient life-support and hallucinatory inputs to make it actually *have* a prior existence. (Giving the brain particular memories is basically just rearranging some of the energy making it up; it doesn't increase the cost of the universe. Giving the brain a long-lived existence *does* increase the cost of the universe.)

Most brains will *not* have coherent pre-built memories, and will pop into being insane and inchoate before their entropy fluctuation dissipates and they dissolve back into the high-entropy soup of background particles. And of course, most fluctuations won't produce a brain at all; a Rubik's cube in a void is probably more likely than a brain, being smaller and less massive and thus requiring a smaller entropy fluctuation to produce.

The BB hypothesis is just saying, basically, that if you list *all possible entropy fluctuations* in order of how likely they are to occur in an infinite universe with infinite time, then "a brain in a void with pre-built memories of an existence in a meaningful universe exists for a moment before dissolving" is way, way, way closer to the front of the list than "a large universe enjoys a stable existence for billions of years, eventually producing a brain (plus the body, biosphere, planet, star, etc surrounding it) that experiences a meaningful existence".
(defun fibs (n &optional (a 1) (b 1)) (take n (unfold '+ a b)))

User avatar
Eebster the Great
Posts: 3211
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: disproof of boltzman brain?

Postby Eebster the Great » Fri Dec 07, 2018 9:10 pm UTC

It is not the case that a larger universe is more likely to develop a brain, because the issue is not just size, but entropy. A very large universe that is at thermal equilibrium will not produce brains in any way except by spontaneous fluctuations, because it's in equilibrium already, so nothing else can happen. The question is not volume or mass but entropy.

In order to produce a universe that, even if largely composed of diffuse plasma (which, to be fair, is still very far from equilibrium), also has lots of structure, up to galaxy superclusters, you need to start with something that has very, very low entropy. In order to produce a universe of the same size (or bigger, or smaller, or whatever) that can only produce mostly diffuse plasma plus a brain or two, you only need to start with something that has kind of low entropy. That's really all there is to it. A lot of structure is necessary to evolve a brain, and that beginning will always be more structured than the brain itself, because that's how thermodynamics works.

User avatar
Quizatzhaderac
Posts: 1657
Joined: Sun Oct 19, 2008 5:28 pm UTC
Location: Space Florida

Re: disproof of boltzman brain?

Postby Quizatzhaderac » Thu Dec 13, 2018 10:39 pm UTC

@OP:
  1. We're not because we assume a priori we're not. If we live in a real universe, we benefit from acting like we live in a real universe. If we're Boltzmann brains we can't benefit from believing that fact. Therefore believing the universe is real is strictly better than not believing it. There's also the fact that we're hard wired to believe in the external universe, and (thought experiments aside) really believing anything contrary isn't possible.
  2. Somebody already mentioned thins, but the Boltzmann brains hypothetical is a proof by contradiction. We learn the laws of thermodynamics by observation. The laws of thermodynamics plus some assumptions indicate that out observations are meaningless. This contradiction can be resolved two ways. Either observation doesn't work (in which case we have no specific reason to believe that, since we can't trust the laws of thermodynamics). The other option is that one of our assumptions was bad.

Regarding the assumptions:
The second law of thermodynamics only holds when the first law holds (conservation of energy).

Conservation of energy (In Boltzmann's, pre-relativity time) only makes sense when space is static.

In general relativity we can "balance the books" for local events to keep conservation of energy, but when we get to cosmology (i.e., the edges of the observable universe, and creation of the universe, et cetra) the books can't be balanced and we don't have anything like the first law of thermodynamics for the whole universe.

ucim wrote:What is "total entropy" and how does it even apply to a universe that doesn't exist yet?
Two conflicting uses of "universe" are being thrown around here. I will use "Universe" to refer to a closed set of things that might interact with each other. I will use "partialverse" for a subset that displays negentropy.

The question of BBs are set in an infinite universe with exactly the laws of physics (as known at Boltzmann's time) that is at maximum entropy. Each sub section (taken separately) has a chance of having less than maximal entropy. Of the partialverses, we consider only the ones where a mind asks "Am I a Boltzmann brain?" We then further narrow our considerations to two types of partial verses: one that consists of a nothing but the brain asking that question, and one that looks like the scientifically standard observable universe (which I will call the standard partialverse). And we compare the for the frequency of each partialverse and the likelihood that a mind is in each type of partialverse.
Xanthir wrote:Basically you're not doing the math hard enough if you think that pockets of brains in gigantic energy-full universes end up being more likely than a small brain in a void.
Agreed. The chance is super exponential to the number of particles needed. A brain with 10^25 particles is a one in k^(10^25) chance. A partialverse with 10^80 particles is a one in k^(10^80). If we assume 10^40 brains in the standard partialverse, and that it is already at 99.9% of maximal entropy, the relative chance of the BB versus the standard partialverse is k^((10^80)/1000- (10^25 * 10^40))
=k^(10^77)
Last edited by Quizatzhaderac on Mon Dec 17, 2018 4:09 pm UTC, edited 1 time in total.
The thing about recursion problems is that they tend to contain other recursion problems.

User avatar
Eebster the Great
Posts: 3211
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: disproof of boltzman brain?

Postby Eebster the Great » Fri Dec 14, 2018 7:19 am UTC

Quizatzhaderac wrote:Each sub section (taken desperately) has a chance of having less than maximal entropy.

What about the stoic subsections that know no desperation?

User avatar
Quizatzhaderac
Posts: 1657
Joined: Sun Oct 19, 2008 5:28 pm UTC
Location: Space Florida

Re: disproof of boltzman brain?

Postby Quizatzhaderac » Mon Dec 17, 2018 4:16 pm UTC

Those are a lot easier to take, all you need to do is demonstrate that it's in your power to take them. And if they've taken the axiom of choice they always think anybody has the power to take them (incidentally, this is Princess Peach's problem: she's actually just as tough as Mario or Bowser, she just doesn't believe in resisting kidnapping.)
The thing about recursion problems is that they tend to contain other recursion problems.

User avatar
Yakk
Poster with most posts but no title.
Posts: 11103
Joined: Sat Jan 27, 2007 7:27 pm UTC
Location: E pur si muove

Re: disproof of boltzman brain?

Postby Yakk » Mon Jan 21, 2019 7:19 pm UTC

To be clear, Boltzman Brain's where designed as a counter to inflation being triggered by a simple unlikely entropy decrease. Basically, something akin to a whole pile of atoms all appearing at one spot, or smashing themselves together for no good reason.

Based on an infinitely large and long universe with nothing in it, such an event would happen, requiring zero new physics.

This was viewed as quite neat, because it means we don't need new physics to explain the universe. Just eternity. What more, you can extrapolate the future of our universe, and it looks like an infinitely large and long lasting universe with nothing in it.

Which then implies that out future also holds an infinite number of unlikely events that spawn yet more universes.

Big bang problem: solved. Check. All done.

But wait!

The same zero new physics implies far more Boltzman Brain's than brains brought into effect by spontaneous universe generation. Worse than that, it implies that given a universe with a fixed start condition (like ours), if it then evolves into a flat, empty, eternal universe, that Boltzman Brain's in the far cold future of *that* universe will far ounumber any intelligences that could develop in the young, warm part of its history.

So we went from a solution to the Big Bang, to a brain-in-a-jar paradox that breaks even traditional cosmology.

But wait!

New physics can solve this. Suppose there is an unlikely, but far less unlikely than Boltzman Brain, arrangement of subatomic state that causes an inflationary big bang.

Specifically, it triggers a region of space time that inflates rapidly from quantum scales up to many powers of 10s of light years, chock full of energy.

So long as its probability of occuring is lower enough that we'd almost certainly not have experienced it over the lifetime of the universe, yet it is more likely than a Boltzman Brain, we would have no experimental evidence that it cannot occur.

But such inflationary big bangs would seed new hot universes in a cold, eternal "empty" universe, be it the "theoretical" infinite pre-big bang universe, or our own future cold heat death universe. And as they are more likely than Boltzman Brains, they basically make such Brains far less likely than "real" Brains in "real" universes.

The problem with this "solution" is that it requires new physics. And it gives very little guide on how that physics works. It just gives an upper bound on how unlikely the event occurs, but that upper bound is so remote it is untestable.

Still, it implies that there "should" be new physics, and that our current understanding of physics is insufficient to "explain away" the big bang, or what happens in the heat death of our universe. (as, if we presume we are typical observers, the fact we aren't Boltzman Brains in our own universe's heat death remains unexplained).
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

User avatar
Eebster the Great
Posts: 3211
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: disproof of boltzman brain?

Postby Eebster the Great » Mon Jan 21, 2019 8:28 pm UTC

This sounds exactly like what we said earlier in the thread. To the last point, there does indeed have to be some more probable way to cause inflation than the universe spontaneously tunneling into a singularity or whatever, but there are already many proposals for such mechanisms. Regardless of anything else, all such proposals must of course rely on physics beyond the standard model (though not necessarily anything new), because the standard model does not include gravity.

User avatar
Quizatzhaderac
Posts: 1657
Joined: Sun Oct 19, 2008 5:28 pm UTC
Location: Space Florida

Re: disproof of boltzman brain?

Postby Quizatzhaderac » Tue Jan 22, 2019 6:11 pm UTC

Yakk wrote:To be clear, Boltzman Brain's where designed as a counter to inflation being triggered by a simple unlikely entropy decrease.
That's why the idea is prominent, not why it was conceived. It was conceived before we knew of cosmic inflation.
The thing about recursion problems is that they tend to contain other recursion problems.


Return to “Science”

Who is online

Users browsing this forum: No registered users and 14 guests