A room full of monkeys, hitting keys randomly on a typewriter, will eventually bang out a perfect copy of Hamlet. Assuming, of course, that their typing is perfectly random, and that it keeps up for a long time. An extremely long time indeed, much longer than the current age of the universe. So this is an amusing thought experiment, not a viable proposal for creating new works of literature (or old ones).
There’s an interesting feature of what these thought-experiment monkeys end up producing. Let’s say you find a monkey who has just typed Act I of Hamlet with perfect fidelity. You might think “aha, here’s when it happens,” and expect Act II to come next. But by the conditions of the experiment, the next thing the monkey types should be perfectly random (by which we mean, chosen from a uniform distribution among all allowed typographical characters), and therefore independent of what has come before. The chances that you will actually get Act II next, just because you got Act I, are extraordinarily tiny. For every one time that your monkeys type Hamlet correctly, they will type it incorrectly an enormous number of times — small errors, large errors, all of the words but in random order, the entire text backwards, some scenes but not others, all of the lines but with different characters assigned to them, and so forth. Given that any one passage matches the original text, it is still overwhelmingly likely that the passages before and after are random nonsense.
That’s the Boltzmann Brain problem in a nutshell. Replace your typing monkeys with a box of atoms at some temperature, and let the atoms randomly bump into each other for an indefinite period of time. Almost all the time they will be in a disordered, high-entropy, equilibrium state. Eventually, just by chance, they will take the form of a smiley face, or Michelangelo’s David, or absolutely any configuration that is compatible with what’s inside the box. If you wait long enough, and your box is sufficiently large, you will get a person, a planet, a galaxy, the whole universe as we now know it. But given that some of the atoms fall into a familiar-looking arrangement, we still expect the rest of the atoms to be completely random. Just because you find a copy of the Mona Lisa, in other words, doesn’t mean that it was actually painted by Leonardo or anyone else; with overwhelming probability it simply coalesced gradually out of random motions. Just because you see what looks like a photograph, there’s no reason to believe it was preceded by an actual event that the photo purports to represent. If the random motions of the atoms create a person with firm memories of the past, all of those memories are overwhelmingly likely to be false.
This thought experiment was originally relevant because Boltzmann himself (and before him Lucretius, Hume, etc.) suggested that our world might be exactly this: a big box of gas, evolving for all eternity, out of which our current low-entropy state emerged as a random fluctuation. As was pointed out by Eddington, Feynman, and others, this idea doesn’t work, for the reasons just stated; given any one bit of universe that you might want to make (a person, a solar system, a galaxy, and exact duplicate of your current self), the rest of the world should still be in a maximum-entropy state, and it clearly is not. This is called the “Boltzmann Brain problem,” because one way of thinking about it is that the vast majority of intelligent observers in the universe should be disembodied brains that have randomly fluctuated out of the surrounding chaos, rather than evolving conventionally from a low-entropy past. That’s not really the point, though; the real problem is that such a fluctuation scenario is cognitively unstable — you can’t simultaneously believe it’s true, and have good reason for believing its true, because it predicts that all the “reasons” you think are so good have just randomly fluctuated into your head!
So, before reading the last sentence quoted I had no issue with the idea that I turned up as a random fluctuation, but that last sentence gives me pause—and my brain refuses to cross it and give useful thoughts.
The expansion of the universe blows up the Boltzmann Brain problem. The universe is not of uniform density over time, and far into the future things get thinner and thinner on average with more and more concentrated local knots of matter of changing atomic/etc composition.
It pushes the question to why we see the universe as it is rather than something smaller in space rather than in time, which becomes a question about the properties of the event we call the big bang, which nobody really understands—was it a singular event or one of many such events and what was its/their scale?
My issue is much ‘earlier’ in terms of logic. When I started reading that post, the Boltzmann brain problem seemed like a non-problem; an inevitable conclusion that people were unwilling to accept for reasons of personal bias—analogous to how most LWers would view someone who insists on metaphysical free will.
Even if certain facts about the universe didn’t solve the issue, it seems to me that Carroll would still want to find reasons that we weren’t Boltzmann brains. Now, from my own interest in entropy and heat death, I had long ago concluded that I might, right now, be part of a random fluctuation that is gone the next moment; in fact, I had concluded that every moment of my existence turns up somewhere during heat death. That’s not an issue, as far as I can see—whatever fact we see about the universe, that would just be part of this fluctuation (I don’t know about this acceleration thing—my technical understanding of the issue is not good enough, but I’m willing to take your and Carroll’s words for it). At this level, ‘we’re part of a random fluctuation’ is one of those uninteresting hypotheses like maya that could very well be true but are unverifiable.
(Continued adherence to ordered laws can’t really be considered evidence, since we may have just popped into existence a second ago with memories as we have. It truly can predict everything.)
But then, Carroll argues that believing you’re a Boltzmann brain is inconsistent, since you can’t trust your own brain which is a product of a random fluctuation. Of course, I don’t believe I’m a Boltzmann brain, I just note that no experience (modulo expanding universe) contradicts the hypothesis and therefore I should reason without giving a shit about it.
However, Carroll’s argument gives me pause, and I can’t really see whether I should consider it seriously.
It’s not necessarily an either/or situation. Maybe this universe has started a few billions of years ago in a Boltzmann-like event, but since then it evolves, uhm, just like we think it does.
The analogy of the monkeys with typewriters is misleading. The laws of physics are local: what happens next does depend on what happens now; that’s unlike the monkey with the typewriter where the following letter is completely independent on the previous part of the book. If some random process would create a brain, in a body, in a room, then even if the room is immediately destroyed at the speed of light, still, during those few microseconds until the destruction reaches the brain, the brain would operate logically.
On the other hand, random processes creating the brain in the body in the room are much less likely than random processes creating only the brain, or only parts of the brain. So this requires some more though, and I am too tired now to make it.
But my point is that if you are randomly created exactly in this moment, you don’t have a reason to trust your reason… but if you were created a while ago, and your reason had some time to work, that’s not the same situation. In the extreme situation, if the universe was created randomly billions of years ago and then we have evolved lawfully, that’s business as usual: the details of random creation of the universe long ago should not be relevant for our reasoning about our reason now.
After some thought on why your argument sounded unsatisfatory to me, I decided that I have a much more abstract, much less precise argument, to do with things like the beginning of epistemology.
In the logcial beginning, I know nothing about the territory. However, I notice that I have ‘experiences.’ However, I have nore ason for believing that these experiences are ‘real’ in any useful sense. So, I decide to base my idea of truth on the usefulness of helping me predict further experiences. ‘The sun rises every morning,’ in this view, is actually ‘it will seem to me that every time there’s this morning-thing I’ll see the sun rise.’ All hypotheses (liike maya and boltzmann brains) that say that these experiences are not ‘real,’ as long as I have no reason to doubt ‘reality,’ form part of this inscrutable probability noise in my probability assignments. Therefore, even if I was randomed into existence a second ago, it’s still rational to do everything and say “I have no issues with being a boltzmann brain—however it’s just part of my probability noise.′
I haven’t fleshed out precisely the connection between this reasoning and not worrying about Carroll’s argument—it seems as if I’m viewing myself as an implementation-independent process trying to reason about its implementation, and asking what reasoning holds up in that view.
From http://www.preposterousuniverse.com/blog/2013/08/22/the-higgs-boson-vs-boltzmann-brains/
So, before reading the last sentence quoted I had no issue with the idea that I turned up as a random fluctuation, but that last sentence gives me pause—and my brain refuses to cross it and give useful thoughts.
Anyone have any useful comments? Thanks.
The expansion of the universe blows up the Boltzmann Brain problem. The universe is not of uniform density over time, and far into the future things get thinner and thinner on average with more and more concentrated local knots of matter of changing atomic/etc composition.
It pushes the question to why we see the universe as it is rather than something smaller in space rather than in time, which becomes a question about the properties of the event we call the big bang, which nobody really understands—was it a singular event or one of many such events and what was its/their scale?
Thanks for your comment.
My issue is much ‘earlier’ in terms of logic. When I started reading that post, the Boltzmann brain problem seemed like a non-problem; an inevitable conclusion that people were unwilling to accept for reasons of personal bias—analogous to how most LWers would view someone who insists on metaphysical free will.
Even if certain facts about the universe didn’t solve the issue, it seems to me that Carroll would still want to find reasons that we weren’t Boltzmann brains. Now, from my own interest in entropy and heat death, I had long ago concluded that I might, right now, be part of a random fluctuation that is gone the next moment; in fact, I had concluded that every moment of my existence turns up somewhere during heat death. That’s not an issue, as far as I can see—whatever fact we see about the universe, that would just be part of this fluctuation (I don’t know about this acceleration thing—my technical understanding of the issue is not good enough, but I’m willing to take your and Carroll’s words for it). At this level, ‘we’re part of a random fluctuation’ is one of those uninteresting hypotheses like maya that could very well be true but are unverifiable. (Continued adherence to ordered laws can’t really be considered evidence, since we may have just popped into existence a second ago with memories as we have. It truly can predict everything.)
But then, Carroll argues that believing you’re a Boltzmann brain is inconsistent, since you can’t trust your own brain which is a product of a random fluctuation. Of course, I don’t believe I’m a Boltzmann brain, I just note that no experience (modulo expanding universe) contradicts the hypothesis and therefore I should reason without giving a shit about it. However, Carroll’s argument gives me pause, and I can’t really see whether I should consider it seriously.
It’s not necessarily an either/or situation. Maybe this universe has started a few billions of years ago in a Boltzmann-like event, but since then it evolves, uhm, just like we think it does.
The analogy of the monkeys with typewriters is misleading. The laws of physics are local: what happens next does depend on what happens now; that’s unlike the monkey with the typewriter where the following letter is completely independent on the previous part of the book. If some random process would create a brain, in a body, in a room, then even if the room is immediately destroyed at the speed of light, still, during those few microseconds until the destruction reaches the brain, the brain would operate logically.
On the other hand, random processes creating the brain in the body in the room are much less likely than random processes creating only the brain, or only parts of the brain. So this requires some more though, and I am too tired now to make it.
But my point is that if you are randomly created exactly in this moment, you don’t have a reason to trust your reason… but if you were created a while ago, and your reason had some time to work, that’s not the same situation. In the extreme situation, if the universe was created randomly billions of years ago and then we have evolved lawfully, that’s business as usual: the details of random creation of the universe long ago should not be relevant for our reasoning about our reason now.
I think this is a good argument. Thanks.
After some thought on why your argument sounded unsatisfatory to me, I decided that I have a much more abstract, much less precise argument, to do with things like the beginning of epistemology.
In the logcial beginning, I know nothing about the territory. However, I notice that I have ‘experiences.’ However, I have nore ason for believing that these experiences are ‘real’ in any useful sense. So, I decide to base my idea of truth on the usefulness of helping me predict further experiences. ‘The sun rises every morning,’ in this view, is actually ‘it will seem to me that every time there’s this morning-thing I’ll see the sun rise.’ All hypotheses (liike maya and boltzmann brains) that say that these experiences are not ‘real,’ as long as I have no reason to doubt ‘reality,’ form part of this inscrutable probability noise in my probability assignments. Therefore, even if I was randomed into existence a second ago, it’s still rational to do everything and say “I have no issues with being a boltzmann brain—however it’s just part of my probability noise.′
I haven’t fleshed out precisely the connection between this reasoning and not worrying about Carroll’s argument—it seems as if I’m viewing myself as an implementation-independent process trying to reason about its implementation, and asking what reasoning holds up in that view.