A mathematical truth would be the same in any hypothetical universe. And facts about computers are mathematical truths if you accept the “Church-Turing thesis”:
Firstly of course this is all based on those propositions and we can deliver quite different conclusions, and recommendations for behaviour, based on another set of propositions.
But secondly I’m not sure your conclusion even follows from your propositions.
Because, just off the top of my head, you’re also implicitly assuming that:
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“Strong AI” is true
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The simulation being stopped would be a bad thing; that any consciousnesses in the simulation would cease to be, forever.
Yet, bear in mind premise (1) is strong AI, so why would we assume that? -
The simulators desire to make a “Goldilocks” level of realism: not an entirely realistic scenario (as that would be impossible to simulate), yet go to the trouble of simulating real consciousness in the minds of background characters.
For example, let’s say you go to the toilet. Is that part of the simulation? Why? Why would they go to the bother of simulating that, when they’re happy to put in false data for so many other things, from particles to galaxies? And if your toilet visit is not simulated (it’s just a false memory), then we have cause to doubt our experiences and we’re into “Last Thursdayism”.
Sure. What follows is dependent on the propositions. If you don’t buy into them, there is no reason to buy into anything that follows.
That would be likely, but I don’t think it’s a proven necessity. What we are thinking and doing could be just as programmed as an NPC ina video game. We couldn’t know for sure that it isn’t. But I agree that it is likely strong AI exists, under the simulation hypothesis i’ve Brought up.
Because this is the only existence we know and we have no reasonable expectation of another one. That is the same reason we fear death. Maybe dying isn’t a bad thing and we all go to heaven. But we don’t wish to die and find out.
For the same reason developers strive for realism in video games today. You could go to the bathroom and take a piss in Duke Nuke’em way back in the 90s. If you are trying to make a simulate, than you simulate. Going to the bathroom has been a part of life. Why would the developers of a simulation striving for realism leave that out?
Sort of. Math is based on axioms. Those axioms are very self-evident and to us nearly impossible to even conceive of them not being self-evident, but that doesn’t mean that they carry over to every other conceivable universe. (Of course there are arguments about whether it truly is axiomatic - mathematicians like to believe that it is somehow ‘pure,’ I personally don’t buy that and we’re talking hypothetically, so even if math isn’t axiomatic, we can conceive of a universe in which it hypothetically is.) When we say 2+2=4, we’re really just providing definitions to observed phenomenon and in our particular universe, those definitions seem really, really solid. (There actually are mathematical proofs for 2+2=4, but they themselves rely on axioms.) It seems very incomprehensible that we take two of something, take another two of something and don’t end up with 4 of those things. But we don’t really KNOW that it couldn’t happen in some other universe where you take a (glarb) number of things, take another (glarb) number of things and end up with some random number of things. This might be a strange universe indeed, but I don’t know that we can say it’s an impossible universe.
If I send a math book into another universe, it is just as true (or false if their are mistakes). You can go to a math library in this universe and find books proving theorems from axioms even weirder than you glarb example.
By definition, if we are Boltzmann Brain simulations, we could not determine that fact.
Interesting thought experiment, but not practical. In a universe that statistically creates functioning brains, statistically less likely items would be more common. Stuff like Mercedes Benz 540 K roadsters. Most of it’s molecules are similar (at least more so than those in a brain) so that should be a statistical snap. Also, the clumping of molecules would follow a bell curve with crude assemblages on one end and magnificent models on the other. The majority would be half car and half other stuff. The same would be true of Boltzmann Brains.
Homogenous items would burst into being with much greater frequency - nails, crowbars, rails, aluminum siding and glassware. Which brings up a far more likely random event than a Boltzmann Brain - a Boltzmann Computer. A computer is just a few molecules of aluminum over the oxide that forms when glass is exposed to oxygen. The only environment it requires to run is an energy source. Plenty of that around.
So. perhaps we are a simulation of a Boltzmann Computer. Would it make any difference if we knew? Maybe that’s Boltzmann’s point.
Sorry, re#46:
“statistically less likely items” should be - statistically less obscure items -
Right. But earlier you were saying that this is “much better” than saying we don’t know.
How so, if it’s just arbitrary assumptions?
Well we can know we’re conscious. Subjective experience is one thing you cannot be fooled about (feeling “as if” you are having a subjective experience is itself a subjective experience).
Right, but then this is contradictory. If I only believe in what we have empirical data for, then I reject the simulation hypothesis (until such a time as we find supporting data).
But if I accept the simulation hypothesis (or at least speculate on that basis), it’s reasonable to speculate about how many times a given consciousness might exist. Perhaps the simulation we’re living in right now will be repeated a billion times?
I think you’re missing my point. A supercomputer smaller than the Earth cannot simulate planet Earth to perfect fidelity. You have to take shortcuts, and the simulation hypothesis includes that understanding. Maybe when we look down a microscope what we see is, in a sense, “pre-rendered”?
Given that, do you think the simulators would find it essential to simulate all humans going to the bathroom every time? You mention Duke Nuke’em but in that game does it simulate every NPC regularly excreting waste, or just allow the protagonist to do that as a bit of fun?
Is it though? We can’t say with certainty that for instance 2+2 does equal 4 in every hypothetical universe. Math relies on us having a shared set of definitions describing phenomenon upon which we all agree. These are subjective to some degree. It is possible that in Universe X, these conditions simply don’t exist. Integers as an example rely on a concept of discrete phenomenon. What if you have a universe in which there are no discrete phenomenon, nor is it possible to have them. Some sort of random analog morass. Where for some fictional being(if we can call some sort of non-discrete entity a being or even an entity) it is impossible to conceive of a discrete object. Is math still ‘true’ in such a universe? If numbers can’t even be defined, how can they have a truth value? Again, I’m not saying that such a universe can or does exist, but I think that it’s folly to presuppose that math is somehow the pure entity that transcends all hypothetical universes. I don’t think that’s true. Math is axiomatic just like everything else and it’s more than possible that there are universes where the axioms that we observe just don’t hold.
It is unclear if anything in our universe is really continuous. Yet we have the notion of it. Maybe in another universe no one would have any reason to care about integer arithmetic. But if you sent a book about it in their language to their universe, they could read it and say “yes making those definitions and axioms your theorems are true” (and perhaps “you made a mistake on page 297”, etc.). (They could then see the use in 2+2=4 in going from page 200 to 204 directly, instead of first leafing to page 202.) The axioms of plane geometry do not hold on a sphere. That doesn’t make a textbook on plane geometry wrong if you are reading it on a yoga ball.
The problem i have always had with the Boltzmann ideas is that he assumes a closed universe.
In a closed universe, not only does everything have to happen at least once, it has to happen an infinite number of times.
We do not have a closed universe, we have an expanding universe. That means that the parameters are changing.
As an analogy, take a deck of cards. If you shuffle them, there is a small chance that they come up in order. A very small chance. However, if you keep doing it, over and over, that chance approaches 1. With an infinite number of shuffles, you will have an infinite number of perfect decks.
Change this slightly. Every time you shuffle, add a blank card in. Now the chances of shuffling and getting 52 cards in a row in order goes down, and approaches 0. With an infinite number of shuffles, you still have chances of getting a perfect deck, but you will not be guaranteed even one, much less infinite.
I think, strictly speaking, even this is not true.
Let’s say we roll a die an infinite number of times. We’d expect to get an infinite number of 1s, an infinite number of 2s and so on.
However, there are also an infinite number of infinitely-long sequences that are missing one or more numbers, e.g. the following sequences:
{1, 1, 1, …}
{1, 2, 3, 1, 2, 3, …}
{4, 4, 6, 6, 4, 4, 6, 6, …}
If the universe has to “pick” an infinitely-long sequence, why not one of these? They are as likely as any other infinitely-long sequence.
Or explained here:
I think Dopers in the thread are giving entirely different meanings to the concept “The universe is a simulation.”
In one view, a human who thinks he’s “in a simulation” might do something unusually charitable or peculiar, hoping to attract the attention of one of the higher-level players who will then cause him to win a lottery or date a hot chick.
In another view, the “simulation” follows the laws of physics and would be indistinguishable from a “real” universe.
And of course the idea of higher-level player(s) interacting with the universe doesn’t require that the universe be a “simulation”! Cf. Christian faith in prayer.
And none of this has anything to do with Boltzmann brains, a concept which began as a thought-experiment trying to understand the possibly “paradoxical” nature of thermodynamics.
But that is the case if the size of the set is infinite. In this case, the size of the set is finite, but the number of iterations is not. Which is my point. If we have a closed universe, then everything happens, and happens an infinite number of times. If the universe is not closed, then you end up with situations where you have an infinite number of sets that never happen.
Hard to put together a Boltzman Brain, when the average distance between any two particles is a few billion light years.
But an infinite number of finite sets can be considered as a single infinite set; just concatenate them.
Anyway, seems we are in agreement that the logic of why Boltzmann Brains would exist (and outnumber meat brains) is on questionable ground.
The simple counterargument regarding Boltzmann brains is that a single brain is actually a lot more complex than a universe, and thus, given a uniform distribution, actually a lot less likely to spontaneously form.
This is counterintuitive, at first: we expect a collection of complex things to be more complex than any of the items of the collection. But that’s not the case.
The relevant notion of complexity here is description-length or Kolmogorov complexity: very roughly, an object is as complex as the shortest-length description of that object. This is usually formulated in terms of computers and their programs: the Kolmogorov complexity of an object (say, a bit string) is given by the shortest program (over an appropriate notion of computation, such as prefix-free Turing machines) producing that object.
The thing is, now, there is a very short program producing the set of all bit strings: you simply print out every string in an interleaved manner. Hence, this set has low complexity—you could easily imagine this program being generated randomly, i. e. by having the state of a computer randomly fluctuate.
However, any particular bit string may have very high complexity—in general, for almost all bit strings, there is no program significantly compressing them, i. e. the program generating the average bit string is of roughly the same length as the string itself. Hence, that such a bit string could be created randomly is very unlikely.
This works also with sets of numbers: the set of all natural numbers is very easily described, say by giving the Peano axioms. But that set has subsets which don’t have any finite description at all—which can only be described by naming all of their members. Consequently, there are subsets of the natural numbers that are vastly more complex than the set of all natural numbers. (Indeed, I’m reasonably confident that almost all subsets of the natural numbers are more complex than the natural numbers themselves.)
The same, now, is true for the universe and any given brains it includes. Specifying the entire universe comes down to very little information—indeed, there are conjectures stating that the information content of the universe is close to zero. Any given brain, however, is vastly more complex than that, needing a huge amount of information to specify its exact state.
Consequently, it’s vastly more likely that your apparent experience of a universe is actually due to you being embedded in a universe, than that you’re a Boltzmann brain that has randomly fluctuated into existence.
I think this sort of argument can be developed further into discounting most skeptical hypotheses—essentially giving a quantifiable version of Occam’s razor stating that the set of all possible explanations for our experience is dominated by those elements in which that experience is approximately veridical—but this would require a bit more work and care to establish rigorously.