The Simulation Argument [Archive]

Discobird

October 29th, 2005, 03:28 PM

Except he pulls the "fraction" out of his ass.
Explain? It looks sound to me.
http://www.simulation-argument.com/simulation_files/image008.gif
f_sim is the fraction of all observers with human experiences (abbrev. "observers" from now on) who actually live in a simulation. This is equal to the number of observers who live in a simulation divided by the total number of observers, agree so far?

f_p is the fraction of human civilizations that reach posthuman state, N is the average number of simulations run by such humans, and H is the average number of individuals who have lived in a civilization before it reaches posthuman status.

Then the number of simulated observers is f_p * N * H, as given in the numerator. The number of total observers is the number of simulated observers plus the number of real observers, or f_p * N * H + H, which is given in the denominator. Doesn't look arbitrary to me, nor is there anything missing.*

Bostrom then goes on to factor H out of the fraction and substitute N = f_i * N_i, where f_i is the fraction of civilizations interested in running simulations and N_i is the average number of simulations they actually run. No problem with this substitution; it's like saying the total amount of music performed in the world is the fraction of people who play music times the average amount of music such people play (but see footnote).

Simple algebra leads to the following equation:
http://www.simulation-argument.com/simulation_files/image016.gif
Bostrom argues that N_i is very high given the massive computing resources available to posthuman technologies. If you agree this far, then you must agree with his disjunction. At least one of the following statements must be true:

(1) f_p -> 0
(2) f_i -> 0
(3) f_sim -> 1

Remember that f_p * f_i * N_i is the number of simulated observers. Since N_i is very large, this term dominates the constant 1 in the denominator, and the whole fraction must approach 1, unless f_p or f_i are very small, making the number of simulated observers correspondingly small.

I called this "pseudomath" because the math involved is trivial and serves as more of a diagram, presenting a compact expression of his argument, than as an argument itself. In otherwords, a purely qualititative argument would be logically as persuasive (just longer to type). However, the equation looks reasonable and not at all arbitrary to me. Which part of it do you object to?

*Actually, I lied. If you're observant you've noticed that Bostrom left out one more variable: the total number of human civilizations. However, this variable would be factored out since it multiplies both the numerator and denominator of the fraction, so Bostrom refrains from including it.

Lord Kelvin

October 29th, 2005, 03:38 PM

So something like the Matrix, except that the Machines aren't harvesting our energy, eh? Interesting.

There's still one law though: nothing can be perfect, ever. That compounds itself as the thing gets more and more complicated. Sure, as technology advances there'll likely be less and less errors and what not, but in the end, there will always be errors, even in simulations. Sure, if this were an alien species making human simulations, then it might be possible to minimize errors down to the point where we don't notice them, but somehow I don't think you can simulate something like this without fucking up something really big somewhere.

puke o'hara

October 29th, 2005, 03:41 PM

How can we notice that something in reality is "wrong", that is, doesn't correspond with what should be reality?Except he pulls the "fraction" out of his ass. If he wants to take a mathematical approach he should have a proof for his equation. It is not sufficient to just deem it so.An equation is just a way of expressing a proposition that can be described by the means of formal logic, and thus not explicitly "mathematical". In regards to proof - well, besides interesting, the paper seemed rather convincing too.His argument sounds like the "enough monkeys on enough typewriters" idea, except his conclusion doesn't make very much sense. You cannot conclude that it is likely that we are living in a simulation based on the prior premises.Don't tell us what - tell us why. It's what this guy is doing as well.This whole thing smacks of reification.Hell, your "existence" might be a reification as well ;)

Modest Genius

October 29th, 2005, 04:04 PM

he seems to be missing one factor - time. its entirely possible that these sort of things WILL happen, but have not yet happened

Lord Kelvin

October 29th, 2005, 04:13 PM

I'm tempted to say something about lag, but since this is the Firebox, I'm just going to ask you to elaborate on that a bit.

Discobird

October 29th, 2005, 04:30 PM

he seems to be missing one factor - time. its entirely possible that these sort of things WILL happen, but have not yet happened
This is accounted for in c3. If these things will happen, then it's very likely we're in a simulation already by the arguments expressed in the paper. Note that c3 is phrased probabilistically, so the extra possibility "c4: we are not presently in a simulation" is not exclusive of c3. c3 admits a vanishingly small chance of this being true.

There's still one law though: nothing can be perfect, ever. That compounds itself as the thing gets more and more complicated. Sure, as technology advances there'll likely be less and less errors and what not, but in the end, there will always be errors, even in simulations. Sure, if this were an alien species making human simulations, then it might be possible to minimize errors down to the point where we don't notice them, but somehow I don't think you can simulate something like this without fucking up something really big somewhere.
This is a good objection. As puuko points out, the only thing that matters is whether we can tell we're in a simulation or not. If I understand your argument correctly, you're saying:

1) simulations are very complex and difficult to do correctly
2) if we were in a simulation, we would expect to see gross, obvious errors in our world
3) we do not observe such errors
Therefore, 4) we are probably not in a simulation.

This argument attacks p3 of the original post. One counterargument is that the simulators would have autocorrecting facilities, e.g. everytime someone observes a glitch ("Whoa! Deja vu"), the simulator rewrites his memory so he doesn't remember it. Of course it's possible that the simulator is buggy and doesn't do this reliably, etc., but we're getting into a vague engineering problem that is hard to argue about when we know very little about future technology (except that simulators will probably be possible). Suffice it to say that the designers would make every effort to preserve the illusion.

Alternatively I can interpret your argument as attacking p2, i.e. it is so hard to make a good simulator that it will never be done. This is a pretty pessimistic view IMO that is hard to defend in light of how many technological advances today were once deemed impossible.

---------------------------------
Bostrom's paper raises some interesting questions. For example:

would it be unethical to mistreat a simulated person?
Bostrom concludes that every posthuman civilization should assume it is in a simulator (since c1 and c2 are false for them); is there any reason that "real" reality should hold a privileged position versus virtual reality?
How does this affect religion?

Modest Genius

October 29th, 2005, 04:35 PM

Discobird

October 29th, 2005, 04:38 PM

counterargument: maybe we ARE seeing big flaws, but dont think of them as such

eg. theres a bug which causes entities to have several different persona. we see this as schizophrenia, and dont think of it as a bug but a real disease (note im not suggesting schizophrenics are in any way errors, just using it as an example)
Sure, this is possible (I won't go into the "Ghosts and werewolves are misbehaving programs!" idea from Matrix 2). As long as we can't tell the difference between our world and a simulated world, though, the argument remains intact.

Super-Piglett

October 29th, 2005, 04:39 PM

There's still one law though: nothing can be perfect, ever. That compounds itself as the thing gets more and more complicated. Sure, as technology advances there'll likely be less and less errors and what not, but in the end, there will always be errors, even in simulations. Sure, if this were an alien species making human simulations, then it might be possible to minimize errors down to the point where we don't notice them, but somehow I don't think you can simulate something like this without fucking up something really big somewhere.

Well, how about something like the black plague, you could consider that an error. And as they have been getting better at simulating, the number of those kinds of errors has gone down.

Lord Kelvin

October 29th, 2005, 06:09 PM

My argument wasn't an attack on the simulation theory, it was just an observation. I believe that a simulation is quite possible, but that anomalies that we see could be interpreted as glitches and such. For example, miracles, illusions of whatever, and all sorts of paranormal shit that we hear about.

Well, how about something like the black plague, you could consider that an error. And as they have been getting better at simulating, the number of those kinds of errors has gone down.

But remember what he said:

Bostrom estimates that one planet-sized computer could simulate the entire mental history of humankind in less than a millionth of a second.

So unless the ones (post-human or aliens) who created the computer that's simulating everything are that fast, then it's highly unlikely that they would be able to fix a problem in that short of a time. After all, there are limits to how quickly an organic brain can process thought, and how quickly you can get your body to respond to those commands.

Walnut

October 29th, 2005, 06:17 PM

conclusion) At least one of the following propositions must be true:
c1) The human species is very likely to go extinct before achieving the level of technology in p2 (what Bostrom refers to as a "posthuman" stage).
c2) Humans will reach this level of technology but will only run a negligibly small number of simulations.
c3) We are almost certainly living in a simulation.

WTF? There are so many more possible conclusions, and the third one seems exceedingly random.

puke o'hara

October 29th, 2005, 06:59 PM

Walnut

October 29th, 2005, 07:08 PM

Do tell.

That we will run a lot of simulations, but aren't living in one.
That we will attain the technology, but have no desire to run simulations.
That it isn't possible to accurately simulate, despite it being theoretically possible.

etc.

Did you actually read the paper?

Nope. Regardless:

p3) It is not possible to determine whether we are presently in a simulation or not.

And then the third possible conclusion is that we are almost certainly living in a simulation?

And what would be the point of creating a simulation?

Lord Kelvin

October 29th, 2005, 07:14 PM

Why would these be _anomalies_ in the first place?
Assuming that they are simulating all the laws of physics, biology, chemistry, mathematics, etc. correctly, there are still shitloads of things we can't explain away, like magicians (real ones, not optical illusions), miracle healing, crying statues of Mary, and so on. Those are the anomalies I am referring to. Yes, they could be putting them into the simulation on purpose, but what would the point of that be?

And what would be the point of creating a simulation?
There's no real point in doing experiments either, except to learn from them or to prove that they work. Those might be the same principles under which the simulation is operating.

Discobird

October 29th, 2005, 08:53 PM

That we will run a lot of simulations, but aren't living in one.

See my reply to MG's first post (same answer applies).

That we will attain the technology, but have no desire to run simulations.
Yes, this is c2.

That it isn't possible to accurately simulate, despite it being theoretically possible.
This constitutes an attack on p2. Bostrom provides some evidence for p2, which you're welcome to challenge, but logically he is not missing any conclusions.

And then the third possible conclusion is that we are almost certainly living in a simulation?
Read my two replies to Faktor's posts in which I explain Bostrom's line of reasoning.

And what would be the point of creating a simulation?
This is actually the first thing I thought of when I read the argument, too. But think about it: how many historians, scientists, tourists, artists etc. would love to get their hands on a complete mental simulator? The applications may not be terribly appealing to you, but keep in mind that we don't need that many simulations before c3 looks more and more likely. If there were only one complete simulation performed through the 21st century, we'd have a 50% chance of being in it. If there were 9, we'd have a 90% chance of being in a simulation. And so on.

Enders

October 29th, 2005, 09:38 PM

I'd like to quote Douglas Adams when he said "Humans are like a newly formed puddle in a pothole, thinking 'wow, this hole is perfectly fitted to me"

Bone_Vulture

October 30th, 2005, 08:46 AM

I was just discussing this thread with Mikko on Messenger last night, and like Walnut, I question why anyone would bother creating a simulation like this.

Ultimately, I think this whole "simulation theory" is just another variation of a god myth, of a belief to an omnipotent being beyond our perception that controls our fates.

FaKToR

October 30th, 2005, 10:20 AM

I don't care for calculus or math in general but I'll give this a shot.

f_sim is the fraction of all observers with human experiences (abbrev. "observers" from now on) who actually live in a simulation. This is equal to the number of observers who live in a simulation divided by the total number of observers, agree so far?
So what? How is significance attached to this fraction? By that I mean how can you conclude that a 1 or a 0 means anything more than just 1 or 0? This is meant to indicate something, which it fails at doing as there are no numbers to use. It can't be taken as a probability because the chances of the event happening aren't equally likely. It can't be a statistic because it's not taken from a sample, in fact it deals with no numbers. Also no context is given for this equation. Does it only apply to those within the simulation, or does it apply to all people?

How exactly does f_sim = 1, or rather when does it it equal one? Does he take the limit of http://www.simulation-argument.com/simulation_files/image016.gif? That is how he calculated that value correct, he took the limit as N approaches infinity (which is rather unusual)? That's really worthless because that's what it approaches.

N is the average number of simulations run by such humans, and H is the average number of individuals who have lived in a civilization before it reaches posthuman status.
What on earth does the "average number of simulations" represent? Is it an arithmetic mean? In which case the sum of the simulations divided by what? The same goes for the "average number of individuals who have lived in a civilization before it reaches posthuman status". Does the H simply mean the number of real observers? If so why is it there. The number of simulated observers is not a function of the number of real observers, in fact the number of real observers has no baring on the number of simulated observers.

I called this "pseudomath" because the math involved is trivial and serves as more of a diagram, presenting a compact expression of his argument, than as an argument itself. In otherwords, a purely qualititative argument would be logically as persuasive (just longer to type). However, the equation looks reasonable and not at all arbitrary to me.
It looks like crap to me. This has no baring on reality. Regardless what values this equation produces, it poses no power to compel reality to conform to it's meaning. Which is why it's reification.

An equation is just a way of expressing a proposition that can be described by the means of formal logic, and thus not explicitly "mathematical".
Except he doesn't give reasons for how he constructs his formula, he just does it. There are also necessary axioms which he doesn't provide nor give reason for. I can accept the Pythagorean theorem, "In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides" because a proof can be constructed. If you simply gave me the equation C^2 = A^2 + B^2 and said that you could use it to calculate the area of the hypotenuse of a right triangle I'd be a little curious how you came up with that.

Now let me try some math:

f_sim is the fraction of all observers with human experiences who actually live in a simulation

So f_sim is the number of simulated human observers, which I'll call X, divided by the total number of observers (real or simulated) which I'll call Z.

The number of total observers is the number of simulated observers plus the number of real observers, or f_p * N * H + H, which is given in the denominator.

Knowing that the number of observers is the sum of real observers, which I'll call Y (you call it H here), and simulated observers we can conclude Z = X + Y.

Therefore his equation is X/Z or the number of simulated observers divided by the total number of observers.

We can also measure the fraction of real observers, f_real, which can be expressed as Y/Z or the number of real observers divided by the total number of observers.

We can also conclude that X/Z + Y/Z = 1 using our knowledge of fractions. What is being argued is that X/Z approaches one. Assuming this to be true, the number of "real observers" = 0 which causes problems because the function http://www.simulation-argument.com/simulation_files/image008.gif is undefined at H equals 0. You see he took the limit, which it approaches 1, but your fraction will never equal 1 because that would be undefined.

I'll also point out again that conclusion 3 is vague. It doesn't say anything. Let's say we do conduct a shitload of simulations and it reaches one (just saying it can for the sake of argument) it doesn't mean that we are living in a simulation. Why would it?

This argument also begs the question, what is the difference between a simulated observer and real observer? Is there any significant difference?

Finally, REI-FUCKING-CATION.

puke o'hara

October 30th, 2005, 11:49 AM

Except he doesn't give reasons for how he constructs his formula, he just does it.The formula follows the general conclusions made in the paper. There are also necessary axioms which he doesn't provide nor give reason for.Like?
We can also conclude that X/Z + Y/Z = 1 using our knowledge of fractions. What is being argued is that X/Z approaches one. Assuming this to be true, the number of "real observers" = 0 which causes problems because the function http://www.simulation-argument.com/simulation_files/image008.gif is undefined at H equals 0. You see he took the limit, which it approaches 1, but your fraction will never equal 1 because that would be undefined.And the point here is? Furthermore, if X/Z approaches one, the amount of real observers will merely approach zero as well, not reach it.I'll also point out again that conclusion 3 is vague. It doesn't say anything. we are almost certainly living in a computer simulation

What part of that is vague?
Let's say we do conduct a shitload of simulations and it reaches one (just saying it can for the sake of argument) it doesn't mean that we are living in a simulation. Why would it?You can't reach one by just conducting a shitload of simulations - you need to be able to determine that you'd be living in a simulation yourself. This argument also begs the question, what is the difference between a simulated observer and real observer? Is there any significant difference?That's a wholly different, metaphysical problem.Finally, REI-FUCKING-CATION.The very concept of reification is somewhat useless in regards to this question, as there is no way of determining that the universe we observe isn't a mere abstraction of ... something.

Discobird

October 30th, 2005, 04:05 PM

I was just discussing this thread with Mikko on Messenger last night, and like Walnut, I question why anyone would bother creating a simulation like this.
I'd imagine that at least historians and other social scientists would be interested in creating historical simulations on a large scale. Maybe even the entertainment industry (think about Renaissance fairs...). Regardless, even if you don't buy these reasons, do you really think no one would create the simulations? It doesn't take many ancestor simulations at all (< 10) before the likelihood of being in the real 21st century is swamped by the likelihood of living in a simulation.

Also, the beauty of Bostrom's argument is that it presents a disjunction of conclusions, and not just one conclusion. You're essentially rejecting c3 to argue that c2 is true, but the entirety of his argument stands (the paper itself does not argue for the truth of any specific conclusion).

Ultimately, I think this whole "simulation theory" is just another variation of a god myth, of a belief to an omnipotent being beyond our perception that controls our fates.
The simulation argument itself is not a belief in anything. If you think c3 is false, there's no problem. If you think c3 is true you still have the following important differences with a god myth:

No necessary normative aspect (no judgements, no eternal rewards or punishments). In other words c3 carries no necessary moral weight or rules for living.
Creators are finite, even with respect to the simulation. It can be mathematically proven that there are hard limits on the ability of a computer to inspect its own state, for example.
We are not significantly less in control of our fates under a simulator than we would be in reality. Recall that the goal of a simulator is to represent reality as accurately as possible. Our fates in a simulator would be as much an outcome of the laws of physics as they would be in reality, no more no less. The programmers may employ heuristics to simplify certain physical interactions, but they would be indistinguishable from the "true" laws of physics from our perspective (and, of course, our programmers should believe that they are themselves in a simulation). The key point is that no one is necessarily manipulating our fate in the way that deities intervene with mortal affairs in god myths.
Most importantly, there are empirical reasons to believe the truth of c3. The paper is intended to present some true fact about the universe. Whether or not you trivialize the idea as a god myth has no bearing on the power of Bostrom's argument, whereas god myths universally lack convincing empirical support or a reason to believe one over the other.

In sum, there's no profit in calling this argument a god myth... it doesn't aid our understanding of either object in the comparison since the similarities are meaningless. It's like calling the United States government a monarchy and saying Bush has the divine right of kings. OK, if you stretch it you can find some similarities, but really, what's the use?

Bone_Vulture

October 30th, 2005, 04:22 PM

I'd imagine that at least historians and other social scientists would be interested in creating historical simulations on a large scale. Maybe even the entertainment industry (think about Renaissance fairs...). Regardless, even if you don't buy these reasons, do you really think no one would create the simulations? It doesn't take many ancestor simulations at all (< 10) before the likelihood of being in the real 21st century is swamped by the likelihood of living in a simulation.

Let's see - if the future technology was so evolved that it could be used to simulate a completely functioning virtual world, then why not its inhabitants? I mean.. what the hell is the point of creating a world that simulates obsolete technology? What inhibits the people who are supposedly unknowingly hooked up to live in this illusionary existence from being more useful in the actual futuristic reality?

Also, the beauty of Bostrom's argument is that it presents a disjunction of conclusions, and not just one conclusion. You're essentially rejecting c3 to argue that c2 is true, but the entirety of his argument stands (the paper itself does not argue for the truth of any specific conclusion).

No, I'm crumbling Bostrom's argument and throwing it out of the window for being overly complicated without serving any actual purpose.

The simulation argument itself is not a belief in anything. If you think c3 is false, there's no problem. If you think c3 is true you still have the following important differences with a god myth:

[...]

In sum, there's no profit in calling this argument a god myth... it doesn't aid our understanding of either object in the comparison, and the similarities are too weak to be worth noting. It's like calling the United States government a monarchy and saying Bush has the divine right of kings. OK, if you stretch it you can find some similarities, but really, what's the use?

Was there some use to begin with?

Discobird

October 30th, 2005, 04:48 PM

Let's see - if the future technology was so evolved that it could be used to simulate a completely functioning virtual world, then why not its inhabitants?
Huh? That's exactly the point-- simulating the inhabitants.

I mean.. what the hell is the point of creating a world that simulates obsolete technology?
I gave some reasons earlier. Maybe some historian wants to find out what would happen if Hitler hadn't been assassinated in 1942. Maybe some rich tourist wants to experience life before the great meteor strike of 2067. These may sound like fringe applications to you, but knowing what you know of human curiosity and ingenuity, can you really say that the number of simulations will be zero?

What inhibits the people who are supposedly unknowingly hooked up to live in this illusionary existence from being more useful in the actual futuristic reality?
OK, I think I see the misunderstanding. By c3 of the simulation argument, we are not people living in the future hooked up to VR machines. We are AI inhabitants of a virtual world. You and I are software agents believing that we're flesh and blood humans.

No, I'm crumbling Bostrom's argument and throwing it out of the window for being overly complicated without serving any actual purpose.
Like I said in my first post: if you define "serving a purpose" as "having a material effect on my life," then no, this argument does not serve a purpose. But that doesn't make it wrong, nor it does it justify throwing the argument out. If you really believe there's no use in arguing about it, then just ignore this thread.

Was there some use to begin with?
My point is that the marginal utility of treating c3 as a god myth is practically zero. The question of whether c3 has utility in the first place is entirely separate. By analogy: you might believe tricycles are slow, but that doesn't mean you are justified in calling them pogo sticks.

puke o'hara

October 30th, 2005, 04:56 PM

No, I'm crumbling Bostrom's argument and throwing it out of the window for being overly complicated without serving any actual purpose.Isn't the purpose of an argument to prove that the description of reality it supposes as reality corresponds with the actual reality, nothing more?

Of course, the arguments discussed here are of little practical use in applied sciences at least, but that doesn't diminish their value. Furthermore, being very complicated and serving no apparent purpose as such doesn't disprove an argument.

Bone_Vulture

October 30th, 2005, 05:23 PM

Huh? That's exactly the point-- simulating the inhabitants.

Sorry, I missed that part - thought this was a Matrix'sque theory.

I gave some reasons earlier. Maybe some historian wants to find out what would happen if Hitler hadn't been assassinated in 1942. Maybe some rich tourist wants to experience life before the great meteor strike of 2067. These may sound like fringe applications to you, but knowing what you know of human curiosity and ingenuity, can you really say that the number of simulations will be zero?

And you said that this theory doesn't sound like another version of a god myth? If the case is as described above, then that's just what this is: that our whole existence has been designed by a supreme being. Sort of like a computer geek variation of "intelligent design".

OK, I think I see the misunderstanding. By c3 of the simulation argument, we are not people living in the future hooked up to VR machines. We are AI inhabitants of a virtual world. You and I are software agents believing that we're flesh and blood humans.

And if we fulfill our mission succesfully we may return to Heaven.. er, or to the Source? ;)

Like I said in my first post: if you define "serving a purpose" as "having a material effect on my life," then no, this argument does not serve a purpose. But that doesn't make it wrong, nor it does it justify throwing the argument out. If you really believe there's no use in arguing about it, then just ignore this thread.

I recall Mikko commented in our discussion that since there is no scientific way of proving this theory one way or the other, it's wholly a matter of philosophical debate.

My point is that the marginal utility of treating c3 as a god myth is practically zero. The question of whether c3 has utility in the first place is entirely separate. By analogy: you might believe tricycles are slow, but that doesn't mean you are justified in calling them pogo sticks.

Your analody makes me go :confused:.

Lord Kelvin

October 30th, 2005, 05:28 PM

Your analody makes me go :confused:.
I think he meant that pogo sticks are also slow, and since tricycles are slow, you are equating the two of them.

Bone_Vulture

October 30th, 2005, 05:28 PM

Isn't the purpose of an argument to prove that the description of reality it supposes as reality corresponds with the actual reality, nothing more?

Entirely philosophical, yes.

Of course, the arguments discussed here are of little practical use in applied sciences at least, but that doesn't diminish their value. Furthermore, being very complicated and serving no apparent purpose as such doesn't disprove an argument.

I admit that I'm a grumpy skeptic.

Bone_Vulture

October 30th, 2005, 05:29 PM

I think he meant that pogo sticks are also slow, and since tricycles are slow, you are equating the two of them.

Could be.

puke o'hara

October 30th, 2005, 07:11 PM

Bone_Vulture

October 30th, 2005, 08:08 PM

Intelligent design is a matter more of a religious than a philosophical debate.

O RLY?

Of course it's a matter of philosopical debate, since the whole thing isn't based on empirical observations! As a sidenote, did you notice the little text "Department of Philosophy, Oxford University" under the author's name? Speaking of philosophy - it's a field of science as well, and not science as in, for example, christian "science", since it's based on logical reasoning instead of the word of an omnipotent entity. You're being overly empiristic here.

You know, I've never bothered looking in the dictionary for "empirical". My loss.

puke o'hara

October 30th, 2005, 08:49 PM

Alas, alas.

FaKToR

October 30th, 2005, 09:41 PM

The formula follows the general conclusions made in the paper.
That's not an explanation. A lot of my questions were not answered, for example why is the number of simulations run a function of real observers? God I hate this shit. I'm reminded of the time Bertrand Russell proved he was the pope.

Bertrand Russell, in a lecture on logic, mentioned that in the sense of material implication, a false proposition implies any proposition. A student raised his hand and said "In that case, given that 1 = 0, prove that you are the Pope". Russell immediately replied, "Add 1 to both sides of the equation: then we have 2 = 1. The set containing just me and the Pope has 2 members. But 2 = 1, so it has only 1 member; therefore, I am the Pope."

Like?
Well in math their are rules about how numbers work that are assumed, which are necessary in order to construct proofs. You seem to be missing my point THIS EQUATION IS WORTHLESS. At least on its own because there is not a justification for how it necessarily maps onto our world.

And the point here is? Furthermore, if X/Z approaches one, the amount of real observers will merely approach zero as well, not reach it.
You're missing the point, it can't reach one. That means there can be no certainty with this approach and it gives us nothing more than we started with. It gives us no finite probability for determining whether we are in a simulation or not and it doesn't further our knowledge with regard to that question. It's not even valuable as a philosophical pursuit.

What part of that is vague?
Who or what is "we"? What does that encompass exactly? Would any society be running simulations essentially be forced to reason that they're probably living in a simulation?

You can't reach one by just conducting a shitload of simulations - you need to be able to determine that you'd be living in a simulation yourself.
The argument is based on N being sufficiently large, essentially referring to limits. It does nothing for determining that we are living in simulation, not a damn thing. No quantitative or qualitative information is provided.

That's a wholly different, metaphysical problem.
No it's not. It's an essential part of his solution, because we need to discern the two. If being a simulation is no different than being "real" (whatever that means) than we've gotten no where. "What's in a name? That which we call a rose By any other word would smell as sweet."

The very concept of reification is somewhat useless in regards to this question, as there is no way of determining that the universe we observe isn't a mere abstraction of ... something.
There is an inherent disconnect (unless otherwise stated, *cough* axioms *cough*) from our mind and what defines reality e.g. one might not claim their dreams as being "real". In that same sense you would not assert that your words or ability to manipulate numbers has any effect on dictating how reality must be.

puke o'hara

October 30th, 2005, 10:16 PM

The whole approach in regards to the equation appears to be not getting us anywhere, since I'm feeling that nobody can even understand each other's argument.

Also, the paper doesn't speak of certainties, merely of likelihoods, due to the very limitations of it's own arguments.
No it's not. It's an essential part of his solution, because we need to discern the two. If being a simulation is no different than being "real" (whatever that means) than we've gotten no where.Hardly. If the simulation was competently run, there would be no way of determining it a simulation - whether we live in a simulation or not is irrelevant in regards to the arguments of the paper.There is an inherent disconnect (unless otherwise stated, *cough* axioms *cough*) from our mind and what defines reality e.g. one might not claim their dreams as being "real". In that same sense you would not assert that your words or ability to manipulate numbers has any effect on dictating how reality must be.Indeed, words don't have any effect on reality - they merely describe it. The fact that reasoning might appear in a logical picture of the world different from yours doesn't mean that the reasoning is changing anything.

FaKToR

October 30th, 2005, 10:25 PM

Also, the paper doesn't speak of certainties, merely of likelihoods, due to the very limitations of it's own arguments.
Than it is totally worthless. I'm saying that unless it can offer something more concrete, more than what we had to start with it's of no use.

Hardly. If the simulation was competently run, there would be no way of determining it a simulation - whether we live in a simulation or not is irrelevant in regards to the arguments of the paper.
No it is totally relevant, because if he is just renaming the "real world" a "simulation" than he's done nothing.

Indeed, words don't have any effect on reality - they merely describe it. The fact that reasoning might appear in a logical picture of the world different from yours doesn't mean that the reasoning is changing anything.
Except he's using his words to say how the world must function a priori.

puke o'hara

October 30th, 2005, 11:10 PM

Than it is totally worthless. I'm saying that unless it can offer something more concrete, more than what we had to start with it's of no use.It offers us a different way of interpreting reality - food for thought, to put it differently - if nothing else. In terms of it's effect to concrete real-world happenings, the paper is pretty much pointless. In terms of philosophy, it's interesting.No it is totally relevant, because if he is just renaming the "real world" a "simulation" than he's done nothing.He's not renaming the "real world" a "simulation", merely stating that if simulations of the "real world" can be run, we're very likely to be in one instead of being in the "real world".Except he's using his words to say how the world must function a priori.One can surely observe how the world must function, since otherwise all science would be meaningless.

Discobird

October 30th, 2005, 11:19 PM

Faktor, you're misunderstanding Bostrom's math on two levels. First is his reason for using math and its relation to reality. Second are the details of the equation.

First things first: Bostrom's equation is for finding the frequency of human observers who are actually simulated. Perhaps an analogy will help:

Suppose you want to know the frequency of Elvis impersonators among Las Vegas residents. To find out, you write:

f_king = {# of Elvis impersonators} / {# of Las Vegas residents}

Stop and look at this equation for a second: what have we done? We've written down an equation such that, if we filled in the variables on the right, we would obtain exactly the frequency of Elvis impersonators among Las Vegas residents. I hope I don't need to explain where this equation "comes from" because it's literally the definition of frequency. I cannot explain it any further. Note that the variables on the right are empirically discoverable, that is, we could go and fill them in if we had the proper methods or knowledge.

Now, back to the paper. f_sim is a real quantity that measures something in our universe. It is like the distance from the Earth to the Sun, or the mass of the donut you ate this morning. Like with my previous example, each of the variables in Bostrom's equation is discoverable (perhaps not practically in this time with our available means, but each variable represents some quantity that exists in the universe).

The key point is that f_sim is a real number, just like the frequency of Elvis impersonators in Las Vegas. If f_sim = 0, then no simulated human observers exist. If f_sim = 0.5, then half of all human observers are simulated. If f_sim = 0.9, then 90% of all human observers are simulated. And so on.

Bostrom's math and reasoning show that we should believe f_sim is close to 1, unless humanity dies out before achieving simulator technology or humanity chooses not to use it.

How do we proceed from a value of f_sim to a belief in whether we are simulated? This is the subject of Part V of Bostrom's paper. In brief: suppose that f_sim = x. We have no information that helps us determine whether we are in a simulator or not. Therefore, the rational thing to believe is that P(we are simulated) = x. One intuitive way to argue this is to imagine that all the observers in the universe (both simulated and real) were to place bets on whether they were simulated or not. If f_sim is near 1, and everyone bets that he is simulated, then most of the observers will win their bets. Thus it is rational to believe that one is simulated.

Here's another thought experiment: suppose you have an urn containing 99 white tokens and 1 black token. You reach in and pull out a token, but do not look at its color. I then ask you, "What color is your token?" The rational response from you is, "Probably white," since you are overwhelmingly more likely to draw a white token than a black one. Does this make sense now? We can define an f_white that is the frequency of white tokens, and if we say that f_white is close to 1, then it is rational to believe that the token we pulled is white. In exactly the same way, if f_sim is close to 1, we should believe that we are simulated observers.

Now, on to details:

How exactly does f_sim = 1, or rather when does it it equal one? Does he take the limit of http://www.simulation-argument.com/simulation_files/image016.gif? That is how he calculated that value correct, he took the limit as N approaches infinity (which is rather unusual)? That's really worthless because that's what it approaches.
f_sim does not equal 1. It is not possible for f_sim to equal one because the denominator is 1 larger than the numerator. Bostrom does not take the limit as N approaches infinity. Instead, he reasons that N is very large (but finite) and asks "What happens to f_sim?" (N's large size is established by the previous arguments in his paper). Bostrom is not taking the limit.

What on earth does the "average number of simulations" represent? Is it an arithmetic mean? In which case the sum of the simulations divided by what? The same goes for the "average number of individuals who have lived in a civilization before it reaches posthuman status".
See my footnote to my previous reply. Both top and bottom are multiplied by an implicit variable C = total number of human civilizations. Thus, multiplying C and N gives us the total number of simulations (you can rearrange these variables to produce the familiar equation for arithmetic mean: N = {total number of simulations} / C). Likewise for H.

Does the H simply mean the number of real observers? If so why is it there. The number of simulated observers is not a function of the number of real observers, in fact the number of real observers has no baring on the number of simulated observers.
No. H is the average number of individuals who have lived in a civilization before it reaches posthuman status. There are therefore an average of H real observers per civilization, and H simulated observers per simulation. The number of simulated observers is dependent on the number of real observers because that's what is being simulated!

For example, suppose H = 100 billion and the civilizations run four ancestor simulations. Then there are a total of 500 billion observers, 100 billion of which are real (and f_sim for this civilization is 0.2).

It looks like crap to me. This has no baring on reality.
I'm sorry you feel that way.

Regardless what values this equation produces, it poses no power to compel reality to conform to it's meaning.
I don't know what to say to this. If you still think this way after reading this reply, you really do not understand math.

There are also necessary axioms which he doesn't provide nor give reason for.
This paper requires no more axioms than are necessary for performing simple algebra.

Now let me try some math:

So f_sim is the number of simulated human observers, which I'll call X, divided by the total number of observers (real or simulated) which I'll call Z.

Knowing that the number of observers is the sum of real observers, which I'll call Y (you call it H here), and simulated observers we can conclude Z = X + Y.

Therefore his equation is X/Z or the number of simulated observers divided by the total number of observers.

We can also measure the fraction of real observers, f_real, which can be expressed as Y/Z or the number of real observers divided by the total number of observers.

We can also conclude that X/Z + Y/Z = 1 using our knowledge of fractions.

Good so far.

What is being argued is that X/Z approaches one.
No, Bostrom argues that X/Z is close to one. You can alternatively say that X/Z approaches 1 as N approaches infinity, which is true, but it's not what Bostrom is arguing.

Assuming this to be true, the number of "real observers" = 0 which causes problems because the function http://www.simulation-argument.com/simulation_files/image008.gif is undefined at H equals 0. You see he took the limit, which it approaches 1, but your fraction will never equal 1 because that would be undefined.
No. Y/Z is close to zero, but in this case it does not mean Y is close to zero. It means that Z is very large (remember that Z = X + Y, so when X is very large, so is Z).

Y is an independent variable. It does not change at all as X grows.

This is a good place to provide another example. Suppose you have a function f(n) = an, where a is in the interval [0, 1]. I then ask you what is f(1000000000000). You can't give me an exact answer, but you can say that f(n) is very large unless a is extremely close to 0. Bostrom's equation boils down to essentially the same thing, except there are two coefficients and not just one (so there are, correspondingly, three possible outcomes).

I'll also point out again that conclusion 3 is vague.
"We are almost certainly living in a simulation." Doesn't look vague at all to me.

Let's say we do conduct a shitload of simulations and it reaches one (just saying it can for the sake of argument) it doesn't mean that we are living in a simulation. Why would it?
First, it is not possible for f_sim = 1. This means that every single observer is simulated and there have never been any real humans, which is absurd (assuming God isn't playing tricks on us).

Second, you are misinterpreting c3. c3 does not say we are living in a simulation, it says we are almost certainly living in a simulation. Read the earlier parts of this reply for explanation of why we should believe we are simulated if f_sim is close to 1.

This argument also begs the question, what is the difference between a simulated observer and real observer? Is there any significant difference?
As Puuko correctly pointed out, this question is orthogonal to Bostrom's argument. The only important thing is that we are unable to tell whether we are simulated or real. It is an interesting question though, and I was hoping to generate more discussion about these implications than about the argument itself.

In my opinion there is no difference between real and simulated observers in any way that matters.

Finally, REI-FUCKING-CATION.
You keep using that word. I do not think it means what you think it means.

Discobird

October 30th, 2005, 11:31 PM

And you said that this theory doesn't sound like another version of a god myth? If the case is as described above, then that's just what this is: that our whole existence has been designed by a supreme being. Sort of like a computer geek variation of "intelligent design".
No, I don't believe this is another kind of god myth, for the reasons I gave above. Even if I accepted this, what does that have to do with anything? The argument is still as solid as it was before.

And if we fulfill our mission succesfully we may return to Heaven.. er, or to the Source? ;)
The Great Garbage Collector in the sky. :D

I recall Mikko commented in our discussion that since there is no scientific way of proving this theory one way or the other, it's wholly a matter of philosophical debate.
Remember that this argument does not say "We are living in a simulation." It gives three outcomes, one of which is "We are almost certainly living in a simulation". At least one outcome must be true. In this sense, there is nothing to prove; the paper itself is a proof of this disjunction, but it does not attempt to decide which conclusion is true.

Perhaps you meant that there's no way of telling which conclusion is true, to which I reply that we can certainly use reasoning and evidence to assign probabilities to each one. For example, you may think that a growing global nuclear arsenal and political instability make p1 most likely, while a more optimistic person may think that humanity will reach ethical maturity and choose not to run simulations (arguing for p2). True, we can't know for sure which conclusion is correct, but we can at least talk about it in terms we can all understand. This kind of debate is no less philosophical than a discussion on who will win the next World Cup.

Your analody makes me go :confused:.
Sorry, that was a pretty funky analogy. Lord Kelvin's interpretation is correct.

Discobird

October 30th, 2005, 11:40 PM

Who or what is "we"?
"We" is the population of humans living in what most of us think is the 21st century. "We" is the intended audience of the paper.

Would any society be running simulations essentially be forced to reason that they're probably living in a simulation?
Yes, and this is one very interesting result of the argument.

No it's not. It's an essential part of his solution, because we need to discern the two. If being a simulation is no different than being "real" (whatever that means) than we've gotten no where. "What's in a name? That which we call a rose By any other word would smell as sweet."
Simulation and reality are different in at least the physical sense. Simulations run on computers and reality runs in meatspace. A simulated mind is software while a real mind is flesh and blood.

You may think, "But so what! We can't tell the difference!" And then you will understand the argument.

By the way, the question of whether there is an ethical or other humanistic difference between simulation and reality is entirely separate from the question of whether we are in fact simulated or real.

In that same sense you would not assert that your words or ability to manipulate numbers has any effect on dictating how reality must be.
No one is asserting this.

Discobird

October 30th, 2005, 11:45 PM

Than it is totally worthless. I'm saying that unless it can offer something more concrete, more than what we had to start with it's of no use.
There is no certainty when it comes to real events. Nada. None. The very best you can do is to say that an event is almost certain, which is what Bostrom does. This does not make his argument worthless in the least.

No it is totally relevant, because if he is just renaming the "real world" a "simulation" than he's done nothing.
He's not doing that. Reality and simulation are different; we just can't tell which one we're in.

Except he's using his words to say how the world must function a priori.
No, Bostrom's argument is not a prescription of future events any more than using the physics equation f=ma forces the universe to conform. Also, you're still not grasping that there are three possible outcomes.

P.S. to mods: Sorry for posting so many times back to back, but this argument has grown pretty lengthy and I don't want to make my posts too large.

FaKToR

October 31st, 2005, 03:27 AM

It offers us a different way of interpreting reality - food for thought, to put it differently - if nothing else. In terms of it's effect to concrete real-world happenings, the paper is pretty much pointless. In terms of philosophy, it's interesting.
I wouldn't consider it interesting in any philosophical sense because it's based on bad reasoning. Much as I would not consider the ontological proof of god good for philosophy because of it's bad reasoning.

He's not renaming the "real world" a "simulation", merely stating that if simulations of the "real world" can be run, we're very likely to be in one instead of being in the "real world".
I beg to differ. The way his definitions work out for conclusion 3 then everyone would be in a simulation. In which case you've simply renamed the "reality".

One can surely observe how the world must function, since otherwise all science would be meaningless.
You said yourself this isn't based on empirical observations and that it therefore was not science.

Of course it's a matter of philosopical debate, since the whole thing isn't based on empirical observations!

Suppose you want to know the frequency of Elvis impersonators among Las Vegas residents. To find out, you write:

f_king = {# of Elvis impersonators} / {# of Las Vegas residents}

Stop and look at this equation for a second: what have we done? We've written down an equation such that, if we filled in the variables on the right, we would obtain exactly the frequency of Elvis impersonators among Las Vegas residents.
Except we would have to know whether or not you are an Elvis impersantor in order to determine the number of impersonators. Assuming you're not one, then the chances of you being one is 0, regardless of the number of Elvis impersonators who live in Vegas.

Note that the variables on the right are empirically discoverable, that is, we could go and fill them in if we had the proper methods or knowledge.
The only way we could do that though is if we already knew how to distinguish a real observer from a simulated observer. Otherwise we could do nothing more than count observers.

If f_sim = 0.5, then half of all human observers are simulated. If f_sim = 0.9, then 90% of all human observers are simulated. And so on.
Even though that makes no sense. The population you're drawing from don't interact. Unless you're suggesting somehow there are simulated people living amongst us real people, which I'd be curious to know how that works.

Bostrom's math and reasoning show that we should believe f_sim is close to 1, unless humanity dies out before achieving simulator technology or humanity chooses not to use it.
Which doesn't tell us anything because the number of real people is mutually exclusive from the number of simulated people.

One intuitive way to argue this is to imagine that all the observers in the universe (both simulated and real) were to place bets on whether they were simulated or not. If f_sim is near 1, and everyone bets that he is simulated, then most of the observers will win their bets. Thus it is rational to believe that one is simulated.
But they would have to then comprise the same population, you would need real observers living with simulated ones. If we imagine a world in which we create simulated people and they all live on hive of servers there would be no doubt if you were outside those servers that all those living inside the servers were simulated. You would know that for a fact. Thus the number inside the servers wouldn't matter, even if it became infinitely large because you would know that all the simulations were not you.

Here's another thought experiment: suppose you have an urn containing 99 white tokens and 1 black token. You reach in and pull out a token, but do not look at its color. I then ask you, "What color is your token?" The rational response from you is, "Probably white," since you are overwhelmingly more likely to draw a white token than a black one. Does this make sense now?
But how are the populations mixed. How is it that the real observers are in the bag with the simulated observers?

f_sim does not equal 1. It is not possible for f_sim to equal one because the denominator is 1 larger than the numerator.
It's also not possible because the function is undefined there, there's an asymptote.

Instead, he reasons that N is very large (but finite) and asks "What happens to f_sim?" (N's large size is established by the previous arguments in his paper). Bostrom is not taking the limit.
It's the same idea though. I'm saying you cannot have a simulated world with both real people and simulated people.

Thus, multiplying C and N gives us the total number of simulations (you can rearrange these variables to produce the familiar equation for arithmetic mean: N = {total number of simulations} / C).
If we know the total number of simulations then why do we need to calculate it? The total number of simulations is X in X/Z for our frequency. So why don't you just put that in there instead?

H is the average number of individuals who have lived in a civilization before it reaches posthuman status.
Average what? There cannot be an average if there is only one civilization. Do you mean the average number of people per civilization, in other words Civ1 + Civ2 + Civ3....CivN/N? Why do that, why count the old civilizations? Who gives a shit about the old civilizations, if they dont' exist anymore (which they would have to in order to distinguish them from the others) than they are not part of this current population and have no baring on it because this current population of real observers and simulated observers isn't based on the previous ones. It can be whatever it wants to.

There are therefore an average of H real observers per civilization, and H simulated observers per simulation.
Then the N is redundant because. If the number of simulated observers is equal to the number of real observers than they must be the same value, even if you divide them by the same number C. N must therefore equal H and yet you multiply the two for no reason.

The number of simulated observers is dependent on the number of real observers because that's what is being simulated!
But they cannot be the same, and what's more the number of simulations cannot be greater than the number of real people if they are based on the number of real observers. In which case you can only have at best a 50 percent chance of being real or 50 percent chance of being simulated.

Here's how I would approach it. Assuming the simulations are based on real people, as I believe I understand that is what you are saying we can discern the following:
X = # Simulations
Y = # Real
Z = # Total
Z = X + Y
f_sim = X/Z
f_real = Y/X
X/Z + Y/Z = 1
X = Y
Y/Z + Y/Z = 1
2Y/Z = 1
Y/Z = 1/2
Y = 1
X = 1
Z = 2

For example, suppose H = 100 billion and the civilizations run four ancestor simulations. Then there are a total of 500 billion observers, 100 billion of which are real (and f_sim for this civilization is 0.2).
You've only given two variables, so how did you calculate this might I ask?

I'm sorry you feel that way.
I'm sorry you feel otherwise?

f_p = Fraction of all human-level technological civilizations that survive to reach a posthuman stage

Which is strange. Let's say we reached that level. Well then the total would be 1 and the average would be (if I understand the still poorly worded explanation of these averages) f_P= P ( wouldn't it just be C again?) / C. In our case that would simply be 1 because I'm not aware of any other post human civilizations.

N = simulations run / C which happens to just be N again

N is dependant on the number of humans H. what I find interesting is that for some reason N != H in his reasoning, why is that? Why multiply N by the number of real observers? (this would be a lot easier if he could more clearly explain his math, especially those "averages".

The H doesn't belong there, because it's redundant.

So I would conclude f_P * N (which is actually H)/ f_P * N (again H) + H which is just 1/2 again.

I don't know what to say to this. If you still think this way after reading this reply, you really do not understand math.
Maybe you don't understand reasoning?

This paper requires no more axioms than are necessary for performing simple algebra.
It requires qualifications, qualifications that algebra doesn't share.

No, Bostrom argues that X/Z is close to one. You can alternatively say that X/Z approaches 1 as N approaches infinity, which is true, but it's not what Bostrom is arguing.
He's agruing that it is close enough to one to be worth betting on. I'm making what I feel to be the import distinction that it cannot possibly equal one.

Y is an independent variable. It does not change at all as X grows.
I'm aware of that.

Second, you are misinterpreting c3. c3 does not say we are living in a simulation, it says we are almost certainly living in a simulation. Read the earlier parts of this reply for explanation of why we should believe we are simulated if f_sim is close to 1.
Except that doesn't follow. You can say there are a lot of simulations, but there is nothing to indicate that we are in fact living in a simulation.

The only important thing is that we are unable to tell whether we are simulated or real.
There has to be a distinction. The formation of his arugment implies that it is possible for us to be both a simulation and a real observer. It's contradictory. It's like being inside a room and outside of it at the same time.

It is an interesting question though, and I was hoping to generate more discussion about these implications than about the argument itself.
You could have just posed it as a question, instead of bring out the psuedomath.

You keep using that word. I do not think it means what you think it means.
Feel free to enlighten me then. I'm saying that your use of probabilities to explain this topic is specious because it attempts to say how existence must function with respect to simulated and real observers i.e. there are only three possibilities and I don't agree that there must be three possibilities. There is nothing to dictate that there must be three possible outcomes.

FaKToR

October 31st, 2005, 03:37 AM

"We" is the population of humans living in what most of us think is the 21st century. "We" is the intended audience of the paper.
Is that "me" and "everyone else" or is it just "everyone else"? Is it timeless? Is it just me? Does it apply to those who might be running a simulation of "me" or "everyone else" or "me" and "everyone else"?

Yes, and this is one very interesting result of the argument.
I think it just shows the inadequacies of math to explain everything. Just as we cannot explain with words something that is all powerful i.e. able to do anything including preventing itself from doing everything and still being able to do anything aka the unstoppable force vs the immovable object. These problems are flaws of language, not of reality.

You may think, "But so what! We can't tell the difference!" And then you will understand the argument.
What an irrelevant approach to the obvious conclusion.

No one is asserting this.
Then we have no more reason to believe in the assertion of "his probability" than we do to not believe it.

There is no certainty when it comes to real events. Nada. None.
See above.

The very best you can do is to say that an event is almost certain, which is what Bostrom does. This does not make his argument worthless in the least.
Yes it is. You'd be better off to assume one or the other and discuss it's implications than waste your time with this.

He's not doing that. Reality and simulation are different; we just can't tell which one we're in.
For all we know they are the same, regardless of what he says.

No, Bostrom's argument is not a prescription of future events any more than using the physics equation f=ma forces the universe to conform.
Except we don't create the equation f=ma and then say that is how the world must act. We observe how the world acts and discover that f=ma is a good model for explaining the relationship between force, mass and acceleration. There is empiricle evidence, which you do not have.
Also, you're still not grasping that there are three possible outcomes.
Who says there can only be three possible outcomes?

Lord Kelvin

October 31st, 2005, 04:44 AM

Damn, you guys are probably going to start needing spoiler tags if you keep this up :D

Discobird

October 31st, 2005, 05:10 AM

I beg to differ. The way his definitions work out for conclusion 3 then everyone would be in a simulation. In which case you've simply renamed the "reality".
No, not everyone. Almost everyone. And if by chance your definition of "reality" is "where the majority of people live," well, that's not a very good definition.

Except we would have to know whether or not you are an Elvis impersantor in order to determine the number of impersonators. Assuming you're not one, then the chances of you being one is 0, regardless of the number of Elvis impersonators who live in Vegas.
The Elvis example was intended purely to demonstrate the equation for frequency. It has nothing to do with sampling or probability.

The only way we could do that though is if we already knew how to distinguish a real observer from a simulated observer. Otherwise we could do nothing more than count observers.
All this means is that we do not have the proper methods or knowledge. There exists an actual, true number of simulated observers and real observers in the universe. This is a statistic. It might be impossible for humans to ever know this statistic, but it still means something in this universe. By analogy, it might be impossible for humans to ever directly measure the temperature at the core of Alpha Centauri, but it does have some temperature. We may never know the true population of the United States at 11:45 EST on 30 October 2005, but it is some number.

Even though that makes no sense. The population you're drawing from don't interact. Unless you're suggesting somehow there are simulated people living amongst us real people, which I'd be curious to know how that works.
OK, I see a misunderstanding here. Each ancestor simulation is defined as a complete simulation of the history of the human race, up to the point at which it develops simulator technology (this is not a necessary cutoff; Bostrom just picks it because the computational cost of simulating a posthuman civilization grows exponentially if one must simulate a simulator).

Let's say f_sim = 0.5. This does not mean that 3 billion people in this world are real and 3 billion are simulated. It means that either this entire world is real or this entire world is simulated. Simulations run through the entire history of mankind. There is no mixing of real and simulated people (although, technologically, there's no reason this couldn't happen a la The Matrix).

Similarly, if f_sim = 0.9, that means that there are 9 complete simulated worlds (and 1 real one, of course).

(I've used "world" interchangeably with "human history" in the above examples to make the population figures more comprehensible. This doesn't change the argument).

But they would have to then comprise the same population, you would need real observers living with simulated ones.
They comprise the same population in the sense that they all occupy the universe. However, they do not (necessarily) co-exist in the same subjective reality.

I think I should make one thing clear. I'm assuming that there exists a "real" reality, the toplevel element that contains all the nested realities inside it. I use the word "universe" interchangeably with this toplevel reality.

Thus the number inside the servers wouldn't matter, even if it became infinitely large because you would know that all the simulations were not you.
You would know those simulations are not you, but you still don't know you're not in a simulation.

If you're speaking from the POV of an advanced civilization that has developed simulator technology, then c1 and c2 of the disjunction must already be false; therefore you must believe c3.

But how are the populations mixed. How is it that the real observers are in the bag with the simulated observers?
The populations are mixed in the sense that they all exist in the universe. I don't mean that they all live in the same world/subjective reality.

I think a diagram would be helpful here:
http://img489.imageshack.us/img489/1286/simulationargument0eb.png

In this image, the circles represent differing levels of reality and the red dots represent observers.

As you can see, all observers are a member of the toplevel reality (the universe). However, observers can only interact with other observers in the same circle as themselves. Call this circle their subjective reality. For simplicity we will assume that observers cannot interact with other observers in sub-circles (so the observers in s1 cannot interact with the observers in s1.1), but there is no necessary reason for this. You seem to think it isn't possible so I'll argue as if it isn't.

Since we cannot tell if we are simulated or real, the rational thing is to assume that we're in a simulation since most observers live in a simulation.

Note that every circle has the same number of dots (6). This is not an accident. Every simulation simulates all of human history up until posthuman technology, so each simulator has as many observers as reality.

If we know the total number of simulations then why do we need to calculate it? The total number of simulations is X in X/Z for our frequency. So why don't you just put that in there instead?
Two things:
1) C is a common multiple of both the numerator and denominator, so when we simplify the fraction it will drop out anyway. Bostrom skips straight to the equation after dropping C.

2) In your example it's ok to use X since we're talking about c3. In the full equation, though, the total number of simulations is actually a product of 3 other numbers (f_p, f_i, and N_i), so it is necessary to decompose it in order to draw the other two conclusions.

Average what? There cannot be an average if there is only one civilization.
Um, yes there can. Then the average is exactly equal to the population of that civilization. Averages are well defined for a count of 1.

Do you mean the average number of people per civilization, in other words Civ1 + Civ2 + Civ3....CivN/N?
Yes.

Why do that, why count the old civilizations? Who gives a shit about the old civilizations, if they dont' exist anymore (which they would have to in order to distinguish them from the others) ...
Bostrom is covering his bases here by accounting for the possibility that humans will split into multiple civilizations in the future (if we never develop faster-than-light communication, for example). Thus, there may be multiple civilizations that develop simulator technology. You can view all of them as one big civilization, and set C = 1 if it pleases you; that has no effect on the argument.

Then the N is redundant because. If the number of simulated observers is equal to the number of real observers than they must be the same value, even if you divide them by the same number C. N must therefore equal H and yet you multiply the two for no reason.
N = average number of ancestor simulations run per civilization
H = Average number of individuals that have lived in a civilization before it reaches a posthuman stage

Since each ancestor simulation contains H individuals, the average number of simulated observers is NH.

But they cannot be the same, and what's more the number of simulations cannot be greater than the number of real people if they are based on the number of real observers.
Um, there's no restriction on the number of simulations that can be run. Although each simulation has only H individuals, a civilization can perform many, many simulations. Imagine a giant cluster of computers all running in parallel.

You've only given two variables, so how did you calculate this might I ask?
There are three variables: H, N, and f_sim. I did not write N explicitly, but the phrase "the civilizations run four ancestor simulations" is equivalent to "N = 4."
[Your next math example misconstrues the relationship between N and H, namely that they multiply to give the total number of observers]

Maybe you don't understand reasoning?
I apologize, I was overly rude here.

It requires qualifications, qualifications that algebra doesn't share.
We went from idioms to "qualifications?" :confused: I don't understand what you mean by this.

He's agruing that it is close enough to one to be worth betting on. I'm making what I feel to be the import distinction that it cannot possibly equal one.
No argument here.

I'm aware of that.
Then why do you argue that Y = 0? That makes neither physical sense (Y = 0 implies that there are no real observers) nor logical sense (you can make Y/Z very small by making Z very big instead of Y small).

Except that doesn't follow. You can say there are a lot of simulations, but there is nothing to indicate that we are in fact living in a simulation.

This goes back to the example with the urn and 99 white tokens. Basically, if all you know is f_sim, and you have no information about whether you're real or not, then you should assume that the probability you are simulated is f_sim, by the reasoning I've presented earlier.

There has to be a distinction. The formation of his arugment implies that it is possible for us to be both a simulation and a real observer. It's contradictory. It's like being inside a room and outside of it at the same time.
Huh? I don't know where you got this from.

You could have just posed it as a question, instead of bring out the psuedomath.
My original post didn't have any pseudomath at all. I only referred to it when we started debating the merits of Bostrom's argument. I'm not blaming you for anything though, I think this is still a worthy thing to discuss. :)

Feel free to enlighten me then. I'm saying that your use of probabilities to explain this topic is specious because it attempts to say how existence must function with respect to simulated and real observers
Bostrom's disjunction is descriptive, not prescriptive. Given his arguments, we are forced to conclude that one of three statements about the universe must be true. Arguing so doesn't force the universe to conform.

I'll address this further in my next reply.

i.e. there are only three possibilities and I don't agree that there must be three possibilities. There is nothing to dictate that there must be three possible outcomes.
If you believe Bostrom's equation is correct, then three outcomes is what you get. Read my example with f(n) = an...

Discobird

October 31st, 2005, 05:49 AM

Is that "me" and "everyone else" or is it just "everyone else"? Is it timeless? Is it just me? Does it apply to those who might be running a simulation of "me" or "everyone else" or "me" and "everyone else"?
Referring to the diagram I posted previously, it's everyone in the same subjective reality as you. Really, I don't know why this confuses you so much when the paper is clearly addressing this particular group of homo sapiens in the 21st century that are reading it.

I think it just shows the inadequacies of math to explain everything. Just as we cannot explain with words something that is all powerful i.e. able to do anything including preventing itself from doing everything and still being able to do anything aka the unstoppable force vs the immovable object. These problems are flaws of language, not of reality.
The math is perfectly up to the task here... I think it's pretty obvious that Bostrom is not stretching the limits of mathematical language when he writes his fractions.

What an irrelevant approach to the obvious conclusion.
Huh?

Then we have no more reason to believe in the assertion of "his probability" than we do to not believe it.
Then I'm curious to hear what you consider to be credible assertions... are you a solipsist by any chance?

See above.
QFE :p

Yes it is. You'd be better off to assume one or the other and discuss it's implications than waste your time with this.
Um, what? Would you consider a weather report useless if the forecaster said there was a 90% chance of rain tomorrow, only because the chance is not 100%? Did that report give you literally no information?

For all we know they are the same, regardless of what he says.
Now you're making absurd conjectures. For all we know the entire world exists inside a single atom of a single drop of God's snot and he's about to sneeze, in which case Bostrom is totally wrong. That doesn't make his argument any less sound.

Simulation and reality are different with regards to the physical substrate in which consciousness acts. In the former it's a computer, in the latter it's a brain. I don't know how you would even start saying the two are exactly the same.

Except we don't create the equation f=ma and then say that is how the world must act. We observe how the world acts and discover that f=ma is a good model for explaining the relationship between force, mass and acceleration.
Good, now we're getting somewhere. Bostrom's equation follows mathematically from the definition of frequency. If you don't believe the steps he makes are correct, then we have a disagreement somewhere earlier. If you believe the steps are correct, though, we're left with the question "How do we interpret f_sim?"

I hope you'll agree with me so far that f_sim doesn't dictate how the world must act. It's a statistic, a theoretically measurable quantity in the universe. It doesn't even make any sense to think of f_sim as asserting or setting some fact of the universe.

Bostrom concludes that, by the features of the equation and the established premise that N is large, there are three possibilities.

1) f_sim is near 0 and f_p is near 0
2) f_sim is near 0 and f_i is near 0
3) f_sim is near 1

You might say again, "Why three?" No other remotely likely outcomes are consistent with the equation and the premises. I challenge you to come up with another one. (Note: this last sentence is not intended as a proof of why there aren't more outcomes... that is established by mathematical reasoning).

Bostrom's conclusions c1 and c2 follow directly from (1) and (2) above. His c3 goes one more step, using (3) to argue that P(we are simluated) is near 1. Nowhere does he make a priori prescriptions for the universe. The entire paper is formulated around a posteriori reasoning and observations. I can't prove a negative any more than this.

Ch33zy

October 31st, 2005, 06:35 AM

Wow. This is the mathiest thread ever. Interesting concept though.

marty

October 31st, 2005, 08:28 AM

Is it just me or is this totally not a theory since it apparently isn't falsifiable?

FaKToR

October 31st, 2005, 08:30 AM

Yeah Marty is occurred to me that this might be tautologist too.

Really long post to come.

puke o'hara

October 31st, 2005, 01:46 PM

it apparently isn't falsifiable?How did you reach this conclusion?

Modest Genius

October 31st, 2005, 02:51 PM

I'd just like to make an interjection:

This isnt something im very interested in, since it is essentially a question of philosophy, because as marty implied it is not currently falsifiable or able to be empirically measured. Thats probably because im a scientist, and prefer empirical hypotheses (btw, this WOULD be a hypothesis, not a theory. theyre subtly different things).

Having said all that, I think this is an interesting thread, and its nice to see people applying logic to this sort of question. Its also nice to see Discobird attempting to explain it, although some of the logical reasoning of the other participants leaves something to be desired...

Personally, I'm going to chalk this one up into the 'anthropic principle' box (as in its similar to the anthropic principle, not that its equivalent or governed by it), and say its something we cant really know, despite being a real thing, and thus is unworthy of scientific debate. Mind you, theres an awful lot of philisophical capital to be made here.

Bone_Vulture

October 31st, 2005, 05:32 PM

Discobird, did I understand your diagram correctly - the argument assumes that there could be simulations of civilizations who are running simulations of civilizations?

Discobird

October 31st, 2005, 06:08 PM

Discobird, did I understand your diagram correctly - the argument assumes that there could be simulations of civilizations who are running simulations of civilizations?
No, the argument does not assume this. I added them for the general case when this is possible (i.e. when you yourself are in a posthuman civilization), but the argument works just as well if the nesting depth = 1 and you ignore the sub-simulations.

FaKToR

October 31st, 2005, 06:09 PM

No, not everyone. Almost everyone. And if by chance your definition of "reality" is "where the majority of people live," well, that's not a very good definition.
I direct you to this:

Let's say f_sim = 0.5. This does not mean that 3 billion people in this world are real and 3 billion are simulated. It means that either this entire world is real or this entire world is simulated.
Since there is no way for any group at any level of this tier system to tell if they are a simulation or not because all of our realities mirror each other except for the respect of their existence in "reality". The absurdity of this argument is that you can go to any tier and reach the same conclusions. It's like a slippery slope. What distinguishes a simulation from reality if you're living within a realm if you're always inclined to suppose it is a simulation?

The Elvis example was intended purely to demonstrate the equation for frequency. It has nothing to do with sampling or probability.
Except you miss my point. Unless you have some way of counting those values, you have no way of applying frequency. Then it would make as much sense to suppose a f_sim of 0.1 as it would one of 0.9.

There exists an actual, true number of simulated observers and real observers in the universe. This is a statistic.
Except it can't be known with any certainty, it can't even be approximated. All we have is a formula, you need a number to have a statistic.

It might be impossible for humans to ever know this statistic, but it still means something in this universe.
Only if you can exclude yourself from the point in question. This is only of value to an outside observer, an omniscient onlooker if you will.

By analogy, it might be impossible for humans to ever directly measure the temperature at the core of Alpha Centauri, but it does have some temperature. We may never know the true population of the United States at 11:45 EST on 30 October 2005, but it is some number.
It's of no use if we can't even approximate it, which we cannot here.

There is no mixing of real and simulated people (although, technologically, there's no reason this couldn't happen a la The Matrix).
Except that wouldn't get us any further with in the context of this argument because once outside the matrix (assuming that you got there) you would be no better off than when you were inside the matrix (a la The Thirteenth Floor, which is an underrated movie btw).

They comprise the same population in the sense that they all occupy the universe. However, they do not (necessarily) co-exist in the same subjective reality.
I don't think that serves me a lot of good then. If we know there are distinguishable regions then it doesn't matter what the value is within a region as long as it is exclusive from another. This is similar to the real person who looks at the hive of servers. It doesn't matter how many simulated people are in that server because it has no bearing on the probability that I am a simulation so you would not use those values in your calculation.

I think I should make one thing clear. I'm assuming that there exists a "real" reality, the toplevel element that contains all the nested realities inside it.
Except the thinking mind has to exist somewhere within this universe. If that is the case then this mind has no idea where he falls within this topsy-turvy world, yet the equation is predicated on him having some knowledge.

You would know those simulations are not you, but you still don't know you're not in a simulation.
Which applies at any level, which gets us no where.

If you're speaking from the POV of an advanced civilization that has developed simulator technology, then c1 and c2 of the disjunction must already be false; therefore you must believe c3.
How do you know that Y isn't a really large value? Keep in mind there is nothing dictating that the simulations have to be 1:1 with real people. It might behoove Bostrom to say so, but I there is no reason for it.

The populations are mixed in the sense that they all exist in the universe. I don't mean that they all live in the same world/subjective reality.
And I'm saying I don't think the use of a statistic or probability is any good unless they are, which I don't think is possible. The formula takes into account samples that you might know for a fact shouldn't count because they are simulations in your world.

http://img489.imageshack.us/img489/1286/simulationargument0eb.png

This reminds me of Spinoza...

For simplicity we will assume that observers cannot interact with other observers in sub-circles (so the observers in s1 cannot interact with the observers in s1.1), but there is no necessary reason for this. You seem to think it isn't possible so I'll argue as if it isn't.
The only way I can see that one might apply this idea is if you cannot interact. If you can interact with them (presumptively not consciously aware that you are interacting with them) then you'll have nothing to base this formula on.

Let's say you are in a posthuman society. If you have created simulations, but you do not interact with them, then you know for a fact not to include them in determing the probabilty that you are a simulation because you know for a fact you're not one of them, but this creates a new dilemma, because the only way you can have any idea about the size of N is by the number of simulations you create. There is no way to know the number of simulations created by those outside your own world. S1.1 has no idea how many simulationed observers S1 has made, it could be 1, it could be a billion.

Since we cannot tell if we are simulated or real, the rational thing is to assume that we're in a simulation since most observers live in a simulation.
It's like Pascal's wager, again it suffers from the same flaw. If we accept the assumptions presented, then yes we would conclude that. However we have no more reason to believe that N of our universe is really large as we do that it is small, the same applies to Y. This gets us no where just as Pascal's wager got us no where. You have no more reason to believe god would reward false faith as you would have reason for him to believe he punishes false faith.

Note that every circle has the same number of dots (6). This is not an accident. Every simulation simulates all of human history up until posthuman technology, so each simulator has as many observers as reality.
Why? There is nothing to dictate how many simulationed observers they run. They can run all simulated observers that never existed, or they can run all that never existed and the ones that did, or they could run only one, or five etc.

2) In your example it's ok to use X since we're talking about c3. In the full equation, though, the total number of simulations is actually a product of 3 other numbers (f_p, f_i, and N_i), so it is necessary to decompose it in order to draw the other two conclusions.
Again my problem is that we don't know all these numbers, which is really worthless. There is also the problem of simulations that spawn in our world. In which case we wouldn't count simulations that we can discern, but if we're within a simulation we cannot know what to count.

Um, yes there can. Then the average is exactly equal to the population of that civilization. Averages are well defined for a count of 1.
It wouldn't serve any purpose is what I mean. I'm not aware of any other civilizations (counting the earth as one) are you? In which case saying that there could be more is neither here nor there.

You can view all of them as one big civilization, and set C = 1 if it pleases you; that has no effect on the argument.
I find to do otherwise makes it needlessly more convoluted, especially sense he does a poor job of expressing what his averages are.

N = average number of ancestor simulations run per civilization
Not simulated individuals, but simulations. That solves that confusion.

Um, there's no restriction on the number of simulations that can be run. Although each simulation has only H individuals, a civilization can perform many, many simulations. Imagine a giant cluster of computers all running in parallel.
There's the rub, why restrict it only to H? If we're looking at a particular instance I would ask why that as opposed to any other?

There are three variables: H, N, and f_sim. I did not write N explicitly, but the phrase "the civilizations run four ancestor simulations" is equivalent to "N = 4."
I think you mean f_p, not f_sim, which btw you did not give. You have 100 billion which is H, 4 which is N now and f_P is what?

I apologize, I was overly rude here.
Likewise. I might not be the best at math, but the flaws I see with this don't stop at math.

We went from idioms to "qualifications?" I don't understand what you mean by this.
I was using them to mean the same thing. I thought qualifications might be more explicit.

Then why do you argue that Y = 0? That makes neither physical sense (Y = 0 implies that there are no real observers) nor logical sense (you can make Y/Z very small by making Z very big instead of Y small).
I wasn't meaning it to be taken literally. Y would approach zero, but I found the only significance being in that it could never reach zero.

This goes back to the example with the urn and 99 white tokens. Basically, if all you know is f_sim, and you have no information about whether you're real or not, then you should assume that the probability you are simulated is f_sim, by the reasoning I've presented earlier.
Which doesn't tell us anything. Sure if we had 99 to work with and we accepted everything else about f_sim that might be so, but why look at this one instance as opposed to any other? Why look at f_sim when N is large?

Huh? I don't know where you got this from.
The way this functions is from the view of an omniscient observer, or someone who is removed from this universe. We do not have this luxury. We can only analyze it from within our subjective context, which excludes significant information that is necessary to formulate any information with regard to f_sim.

My original post didn't have any pseudomath at all. I only referred to it when we started debating the merits of Bostrom's argument. I'm not blaming you for anything though, I think this is still a worthy thing to discuss.
I wouldn't mind discussing the other topic, I just feel this is a futile approach, especially if the conversation instead could have been "given the uncertainty of our own reality, and the possibility of AI and simulations that perfectly recreate our own world, what are the ethical implications?" (a la Ghost in the Shell).

If you believe Bostrom's equation is correct, then three outcomes is what you get.
Not so. N could be very small, or Y could be very large.

FaKToR

October 31st, 2005, 06:29 PM

Referring to the diagram I posted previously, it's everyone in the same subjective reality as you. Really, I don't know why this confuses you so much when the paper is clearly addressing this particular group of homo sapiens in the 21st century that are reading it.
What I'm getting at is what exactly am I to conclude? Am I a simulation or mererly living in a simulated world with fake people (they need not be simulated people in the same sense as being exactly like a real observer). Or am I to conclude that everyone with me is living in a simulated world or simulated? What exactly are we concluding about simulations?

The math is perfectly up to the task here... I think it's pretty obvious that Bostrom is not stretching the limits of mathematical language when he writes his fractions.
Not for these types of questions. When you start playing with reality like this all bets are off. Like the evil demon manipulating our world, the simulation could be instilling us with inaccurate information about math. You may recall that in the Matrix their idea of generating power from humans is contrary to our understanding of thermodynamics. The solution to this problem is that we are being lied to in the simulation about thermodynamics. He is stretching it with these questions because it calls into question mathematics as well.

Huh?
If this gets us no farther then when we started out, and is poor reasoning, then it is an irrelevant approach to an already obvious conclusion.

Then I'm curious to hear what you consider to be credible assertions... are you a solipsist by any chance?
That's close to what I would describe myself. I'd like the term "subjective foundationalist" to catch on because I used Descartes as my starting point.

Um, what? Would you consider a weather report useless if the forecaster said there was a 90% chance of rain tomorrow, only because the chance is not 100%? Did that report give you literally no information?
I would if the weatherman only gave me the formula he uses and said "if variable such and such was this than we can conclude this, but we really don't have anyway of knowing what this variable is."

Now you're making absurd conjectures. For all we know the entire world exists inside a single atom of a single drop of God's snot and he's about to sneeze, in which case Bostrom is totally wrong. That doesn't make his argument any less sound.
As I said, when your dealing with these types of questions in which reality can be totally falsified other doubts start to rise and it seems arbitrary to hold some as being beyond corruptibility.

Simulation and reality are different with regards to the physical substrate in which consciousness acts. In the former it's a computer, in the latter it's a brain. I don't know how you would even start saying the two are exactly the same.
How do we distinguish a computer from a brain? It could simply be an issue of appearances rather than actual differences.

I hope you'll agree with me so far that f_sim doesn't dictate how the world must act. It's a statistic, a theoretically measurable quantity in the universe. It doesn't even make any sense to think of f_sim as asserting or setting some fact of the universe.
But the conclusions do and if we were given that c1 and c2 were not possible we would be forced to accept that the universe is like c3, which I don't agree with.

You might say again, "Why three?" No other remotely likely outcomes are consistent with the equation and the premises. I challenge you to come up with another one. (Note: this last sentence is not intended as a proof of why there aren't more outcomes... that is established by mathematical reasoning).
If you accept all of his arbitrary conditions, yes.

1. Nowhere does he make a priori prescriptions for the universe. The entire paper is formulated around a posteriori reasoning and observations. I can't prove a negative any more than this.
How is it empirical? Math is a priori inherently, and it is based upon mathematics so how can it be empirical in it's approach?

although some of the logical reasoning of the other participants leaves something to be desired...
FO

Discobird

October 31st, 2005, 08:52 PM

This is going to be one of the longest single pages in the forums, but oh well.

Let's think about what falsifiability means in this context. I'll first outline what it means to say that Bostrom's conclusion is false, then I'll talk about what falsifiability means, and finally I'll try to explain whether his conclusion is falsifiable.

This is going to be a complicated post so I'll put my key points in obnoxious boldened yellow. It will sting a little.

----------------------------------
What does it mean to say that Bostrom's conclusion is false?

Bostrom draws his three outcomes from the following three logical propositions:
i) f_p is near zero (humankind will very likely die out before reaching posthuman tech)
ii) f_i is near zero (humankind will choose not to run simulations)
iii) f_sim is near one (we are almost certainly living in a simulation).

As I argued earlier, the variables in these propositions are all grounded in reality (they represent some real quantity in the universe). We can assign a truth value to each proposition. In other words, each of i, ii, and iii must be either true or false. There are naively 2^3 = 8 truth assignments (I say "naively" because some of them are arguably inconsistent), which is small enough that I can list them exhaustively.

T = true, F = false
GREEN lines are in Bostrom's conclusion

i ii iii
1. F F F
2. F F T
3. F T F
4. F T T
5. T F F
6. T F T
7. T T F
8. T T T

Key Point #1: since this table is logically exhaustive, exactly one of these assignments must correspond to the true state of the universe. Call this the "true assignment."

Let the notation S = {x1, x2...xn} mean one of the assignments x1...xn in conclusion S must correspond to the true state of the universe.

We can then compactly express Bostrom's conclusion as B = {2, 3, 5, 7}.*. What does it mean to say that Bostrom's conclusion is false? It means that the universe probably does not match either 2, 3, 5, or 7. Conversely, we say that his conclusion is true if the universe is probably 2, 3, 5, or 7.

This leads us to key points 2 and 3:

Key Point #2: B is false <=> the true assignment is probably not in B. (The symbol <=> means "if and only if").

Key Point #3: B is not a tautology because B is not a priori necessarily true. If B were a tautology we would have B = {1, 2, 3, 4, 5, 6, 7, 8}. This is not the case; Bostrom has used evidence and reasoning to reduce the size of his conclusion.

Question for Faktor: You think that Bostrom's conclusion is false. Which assignment(s) do you believe is correct, and why? You must choose at least one by Key Point #1. In other words, if I use the same notation as for Bostrom, fill in the blanks: F = {_______}

----------------------------------
What does it mean to say that Bostrom's conclusion is falsifiable?

When we say a statement is falsifiable, we mean that there exists a (hypothetical) set of observations that would cause us to believe the statement is false.

Key Point #4: (By Key Point #2) Falsifiable in this case means there exists a set of observations that would make us believe that Assignment 1, 4, 6, or 8 is probably true.

----------------------------------
Is Bostrom's conclusion falsifiable?

At first glance, Assignments 6 and 8 don't make any sense. They say that humankind will die out before reaching simulator technology, yet most human observers are simulated. We can understand these assignments as saying that the entire human race has been simulated by aliens. We could obtain evidence for these Assignments if, for example, a giant window popped up in everyone's vision and played a movie of the aliens explaining that we never really existed, and we are only software in their alien computer. Then we would have very strong reason to believe in Assignment 6 or 8.

At this point I've already demonstrated that Bostrom's conclusion is falsifiable. But hang onto your asses, ass-holders, there's more to come.

Assignment 4 says that zero or nearly zero posthuman civilizations are interested in running ancestor simulations, yet we are almost certainly inside one. We can again imagine a window suddenly popping into our view saying "Congratulations big guy, you're our first and only generation of sims! Now let's make with the disasters." This would support Assignment 4 and falsify Bostrom's conclusion.

You may have noticed in the previous three Assignments that it's possible to find support for us being in a simulation, if our simulators intervene directly with our world. However, it's probably not possible for us to devise our own equipment and methods, and go out and say, "Yes! We're in a simulation." So, while Bostrom's conclusion is weakly falsifiable, the scientists among us are probably not very satisfied (so far).

Assignment 1 is a little more interesting than the other three assignments. It says that humans will survive to posthuman level, there will be interest in making simulators, but we are not almost certainly living in a simulation. One could argue for Assignment 1 from several directions:

1) Attacking p1 or p2, saying that humans will never develop simulation technology because it is beyond our technological reach for all time

2) Attacking p3 by finding evidence we are really in reality.

3) Attacking Bostrom's Bland Indifference Principle by which he argues we should treat P(we are simulated) = f_sim.

Of these possible arguments, (1) is most evidently falsifiable. We might discover new physical laws or reach a hard limit in our engineering abilities that give us good reason to believe we will never be able to run ancestor simulations. Thus it is possible to find empirical support for Assignment 1 and thereby falsify Bostrom's conclusion.

(2) is not really possible.

(3) can be debated in mathematical and philosophical terms, but it's not the sort of thing one finds evidence for.

Key Point #5: Bostrom's conclusion is falsifiable if we find evidence that we're in a simulator and that i or ii is true. Bostrom's conclusion is also falsifiable if we discover that simulator technology is beyond our reach.

Key Point #6: the scientists in the audience want their money back.

*You may notice that there are four assignments in this subset, but Bostrom only gave three outcomes in his conclusion. This is because his conclusion says that at least one of c1, c2, or c3 must be true. Assignment 7 effectively says that both c1 and c2 are true.

For fun, you could also express his conclusion in an equation like this (using C-style notation):

iii = !(i || ii)

Or equivalently by DeMorgan's theorem,

iii = !i && !ii

Degree:N

November 1st, 2005, 11:39 AM

I used this kind of reasoning to prove (with 0.0000001% doubt) that I will never invent a time machine, as I know I would have already seen my future self before now (to give myself exam answers).

I have no trouble believing that if Simulation were possible, it would happen. That is because I have great confidence in humans not reaching that stage of technology.

A question on the Simulation "computer": It can't possibly have infinite memory and processing power so sometime the Simulations of the Simulations will have to stop, and if so, would this have a domino effect to wipe out all Simulations leaving the only real reality in existence?

Discobird

November 2nd, 2005, 08:34 AM

Faktor, I think it'd be in everyone's interest if I condensed your objections instead of replying quote-by-quote since you repeat many of the same arguments. Please correct me if you think I left anything out or made a mistake. Aw hell, I know you'll do that even if I don't ask, but I'm nice like that.

Faktor's fun grab bag o' objections
in approximate order of appearance

(1) Bostrom's argument applies at any level of reality.

(2) You can't count or approximate the variables in Bostrom's equation.

(3) If you've actually built a simulator in your reality, you shouldn't count the observers inside since you know you're not one of them.

(4) An observer has no idea which level of reality he's at, which is bad because the argument is "predicated on him having some knowledge."

(5) Ancestor simulations don't each have to simulate H people. Alternatively, under Faktor's simplified equation, Y/Z can be large and X/Z correspondingly small. (I'll treat these objections together because they merit the same response.)

(6) c3 is analagous to Pascal's Wager and therefore faulty.

(7) Faktor doesn't know of any other human civilizations, so Faktor doesn't understand why Bostrom uses average values and the implicit C.

(8) Bostrom's equation doesn't have enough "qualifications," where "qualifications" is understood to mean something more specific than axioms.

(9) Why look at f_sim when N is large? N could be very small.

(10) Implications of c3 are still vague.

(11) Simulation might be distorting our understanding of math.

(12) Something about an obvious conclusion

(13) How do we distinguish a computer from a brain? Maybe they only appear different.

(14) All of Bostrom's argument is a priori and not empirical.

(15) REI-FUCKING-CATION.

----------------------------------
Replies

1. Bostrom's argument applies at any level of reality.
To be precise, the argument applies to any subjective reality in which, from the observer's point of view, p1, p2, and p3 are true. Do you have a problem with this? Every observer who comes to Bostrom's conclusion is making the best possible guess given the information he has. It is not possible to be more rational than this.

What distinguishes a simulation from reality if you're living within a realm if you're always inclined to suppose it is a simulation?
You're presupposing that the factual distinction between simulation and reality depends on which one you think you're in, which is patently absurd.

Suppose I have a rare eye condition and I can't tell the difference between owls and hawks. Every time I see either bird, I assume it's an owl. Does that mean that there is in fact no difference between owls and hawks? Of course not (YA RLY). These animals have an objective existence beyond my percepts, just as reality and simulation have objectively different qualities (brain vs metal at the toplevel) even if I can't tell which one I am.

If you want to argue that obects only exist insofar as we can sense them, save it for another thread because that is way beyond the scope of this debate, not to mention the practical problems with that philosophy...

2. You can't count or approximate the variables in Bostrom's equation.
By the structure of Bostrom's equation, you don't need to find numbers for the other variables once you establish that N_i is large (which is what Part III of his paper does). If N_i is large you are automatically led to the conclusion that one of three statements must be true, which I will not repeat since I've written them down before.

Look back to my example with f(n) a few posts ago if you don't understand the mathematical reasoning behind this.

In summary: the objection "You can't actually count observers!", or variants thereof, have no impact on the argument.

3. If you've actually built a simulator in your reality, you shouldn't count the observers inside since you know you're not one of them.
Again, you're not actually counting anything in the argument.

4. An observer has no idea which level of reality he's at, which is bad because the argument is "predicated on him having some knowledge."
You'll have to clarify what knowledge you're talking about because I have no idea what you mean. The argument is actually predicated on the observer having no knowledge of which level he's at.

5. Ancestor simulations don't each have to simulate H people. Alternatively, under Faktor's simplified equation, Y/Z can be large and X/Z correspondingly small.
An ancestor simulation is a simulation of the entire mental history of humankind up to posthuman tech-- in other words, a simulation of H minds. If it simulates significantly less than H minds, it isn't an ancestor simulation, by definition. And the equation is concerned only with ancestor simulations.

You can argue two things here:
(1) future humans will choose not to run ancestor simulations (they may run simulators with far less than H observers)

(2) future humans will be incapable of running ancestor simulations

If you argue (1), you're arguing for c2. If you argue (2), you're attacking p2. Either way, you have not shown a problem with Bostrom's equation. The only thing you've shown is that you don't understand it.

Under your simplified equation, Y/Z (the frequency of real observers) cannot be larger than X/Z (the frequency of simulated observers), because X = NY where N is very large (unless humanity dies out or chooses not to run simulations, in which case N is 0 or close to it).

6. c3 is analagous to Pascal's Wager and therefore faulty.
I'll be blunt here and say WTF? to this assertion. Show me the similarities, because I can't think of any nontrivial ones.

7. Faktor doesn't know of any other human civilizations, so Faktor doesn't understand why Bostrom uses average values and the implicit C.
You may not know of any other human civilizations now, but that's irrelevant. Unless we develop superluminal communications technology, future humans are likely to splinter into separate civilizations as we explore the galaxy and grow further and further apart from each other. Bostrom is just covering all his bases.
In which case saying that there could be more [civilizations] is neither here nor there.
What do you think a variable is?

8. Bostrom's equation doesn't have enough "qualifications," where "qualifications" is understood to mean something more specific than axioms.
I still don't understand what you mean by qualifications. If this is supposed to be a unique objection (i.e. not subsumed by any of the other ones), please clarify what you think Bostrom is missing.

9. Why look at f_sim when N is large? N could be very small.
Recall that N = f_i * N_i, where f_i is the fraction of posthuman civilizations interested in running ancestor simulations.

Bostrom argues that N_i must be very large (using current best estimates about the physical limits of computation and advanced construction processes). Therefore N must also be very large unless f_i is very small. So to answer your objection, N could be very small--this is c2 of Bostrom's conclusion. Either way, Bostrom's reasoning is solid.

10. Implications of c3 are still vague.
If you believe c3, you believe that you and everyone else in the world are a simulated observer. I thought this was clear from my first post but I guess not.

11. Simulation might be distorting our understanding of math.
First of all, remember that this argument considers ancestor simulations run by other humans (or other simulated humans), so we can at least assume that our creators reason the same way we do.

The mathematical reasoning Bostrom uses is along the lines of, "If we multiply two numbers together, and one is very large, then the product must be large unless the other number is small" (like I said, the math is trivial). I can't begin to understand how it is possible to warp logic such that this statement is in reality false. It is literally beyond human imagination to conceive of a universe that operates on different logical principles.

Note the difference between distorting math and distortinng our understanding of thermodynamics, as was the case in the Matrix. In the latter, the Matrix lies to us about some fact. In the former, our simulators would somehow create a world that is not logically consistent with reality. I honestly don't think this is even possible, and it's certainly not desirable by humans seeking accurate reproductions of their past.

12. Something about an obvious conclusion.
This is less a reply than a plea for further clarification. The original exchange went like this:
Simulation and reality are different in at least the physical sense. Simulations run on computers and reality runs in meatspace. A simulated mind is software while a real mind is flesh and blood.

You may think, "But so what! We can't tell the difference!" And then you will understand the argument.
What an irrelevant approach to the obvious conclusion.
I still don't know what approach and what conclusion you're referring to.

13. How do we distinguish a computer from a brain? Maybe they only appear different.
This goes back to #1. We don't have to be able to tell the difference; in reality there will be a difference, and that's all that matters.

14. All of Bostrom's argument is a priori and not empirical.
Bostrom's justification for saying N_i must be very large is based on empirical observations (read Part III of the paper). The rest follows logically.

15. REI-FUCKING-CATION.
Just kidding, this isn't really an objection. I just thought it would be fun to put down.

Discobird

November 2nd, 2005, 08:40 AM

A question on the Simulation "computer": It can't possibly have infinite memory and processing power so sometime the Simulations of the Simulations will have to stop, and if so, would this have a domino effect to wipe out all Simulations leaving the only real reality in existence?

This is why Bostrom defines ancestor simulations as stopping when humans reach posthuman technology. In practice I'd think the simulator would have some way of knowing it's approaching its resource limits, and shut down the simulation accordingly.

Discobird

November 2nd, 2005, 08:48 AM

I'd like to address a couple random points that didn't quite fit in my previous post.

That's close to what I would describe myself. I'd like the term "subjective foundationalist" to catch on because I used Descartes as my starting point.
I'm actually quite interested in your philosophy but it wouldn't be topical here. Maybe start a new thread? :cool:

But the conclusions do and if we were given that c1 and c2 were not possible we would be forced to accept that the universe is like c3, which I don't agree with.
The conclusions do not set or assert the universe, either. Bostrom believes that one of c1, c2, or c3 accurately describes the universe. He comes to this conclusion after observing the pace of technology and thinking about the consequences. He doesn't say that the universe must a priori fit c1, c2, or c3.

FaKToR

November 2nd, 2005, 08:52 AM

I thought about laying out my objections, but the quoting thing was so much fun. I've been busy with other things so it's gonna take me some time to get back to responding to all of this. I'll also make up all the different problems I see with this approach to the issue.

I'm actually quite interested in your philosophy but it wouldn't be topical here. Maybe start a new thread?
I've actually been working on writing out all about this, I really need to get back to it...

Discobird

November 2nd, 2005, 08:55 AM

I thought about laying out my objections, but the quoting thing was so much fun. I've been busy with other things so it's gonna take me some time to get back to responding to all of this. I'll also make up all the different problems I see with this approach to the issue.
Take your time, I have two midterms to study for and this thread has been stealing all my brain cycles.

marty

November 2nd, 2005, 08:56 AM

Wow, this thread is actually fun to follow.

Actually, couldn't simulations be nested infinitely?

It would take longer to process the extra stuff. but the simulation wouldn't notice the difference anyway.

FaKToR

November 2nd, 2005, 08:59 AM

Discobird

November 2nd, 2005, 09:02 AM

It would take longer to process the extra stuff. but the simulation wouldn't notice the difference anyway.
Actually that's a really interesting idea. If time were the limiting resource, the simulations could slow down as necessary without the observers inside knowing a thing. Veeeeery interesting. I don't know how memory constraints would work out though.

On a related note, check this out: http://en.wikipedia.org/wiki/Omega_point

marty

November 2nd, 2005, 09:05 AM

How about this: At some point in the simulation, there would be so many simulations that one "real" second would equal one "simulated" second. Then the simulation will actually start to get "slower" than "real life". Trippy

Degree:N

November 2nd, 2005, 11:19 AM

This is why Bostrom defines ancestor simulations as stopping when humans reach posthuman technology. In practice I'd think the simulator would have some way of knowing it's approaching its resource limits, and shut down the simulation accordingly.
It would have to shut down all the Simulations is what I'm getting at. That's what you mean though is it not?

How about this: At some point in the simulation, there would be so many simulations that one "real" second would equal one "simulated" second. Then the simulation will actually start to get "slower" than "real life". TrippyYou could pause the Simulation indefinately. It could be 100000000 years since typing my previous post.

Discobird

November 2nd, 2005, 02:44 PM

It would have to shut down all the Simulations is what I'm getting at. That's what you mean though is it not?
Yes. If a simulation shuts down, I don't see how one could avoid shutting down its child simulations as well.

Discobird

November 2nd, 2005, 09:00 PM

I'd like to say real quickly that I find it absurd that the probability that you are a simulation could fluctuate. If we N were not to remain constant but grow to a large number and then back down, maybe reaching zero the probability that I am a simulation would fluctuate. What I am getting at is why would you look at N when it is only large as opposed to when it is any other value is beyond me.
The problem is you're thinking of N as a dynamic statistic that gets updated in real time as people run more or fewer simulations. It's actually static-- you can imagine God sitting down at the end of time and examining the value of N. In other words, the numbers that go into f_sim are meant to be end totals. The numerator is all simulated observers ever (who believe they are in the 21st century), and the denominator is all observers ever (who believe they are in the 21st century).

By way of another crappy analogy, this is like confusing the money in your wallet with your net worth at death. Or confusing the first derivative of a function at a point with the integral over its domain.

We are justified in taking this "long view" because, as well as not knowing which reality we're in, we also don't know what the real time is. We might be located along any point in humanity's timeline after posthuman tech is reached. We should therefore think of ourselves as drawn from the pool of all observers who will ever exist who think they're in the 21st century.

FaKToR

November 4th, 2005, 02:02 PM

The problem is you're thinking of N as a dynamic statistic that gets updated in real time as people run more or fewer simulations. It's actually static-- you can imagine God sitting down at the end of time and examining the value of N. In other words, the numbers that go into f_sim are meant to be end totals. The numerator is all simulated observers ever (who believe they are in the 21st century), and the denominator is all observers ever (who believe they are in the 21st century).
What good exactly is viewing things from this perspective?

We should therefore think of ourselves as drawn from the pool of all observers who will ever exist who think they're in the 21st century.
That would be presupposing what were attempting to determine though.

Key Point #3: B is not a tautology because B is not a priori necessarily true. If B were a tautology we would have B = {1, 2, 3, 4, 5, 6, 7, 8}. This is not the case; Bostrom has used evidence and reasoning to reduce the size of his conclusion.
You're making assumptions about how I'm using tautology. I was thinking more along the lines that there is no distinction between reality or a simulation, so that they are one in the same. If that were the case then his conclusions regarding whether we are in a simulation or not would be redundant.

When we say a statement is falsifiable, we mean that there exists a (hypothetical) set of observations that would cause us to believe the statement is false.
Except it can never (at least with our present understanding) be tested. Sure it can be false, but that doesn't mean that it can be falsified in the practical sense. What good would it do us to use such a loose standard as having the possibility of a false value in its truth table in determining if something is falsifiable?

1) Attacking p1 or p2, saying that humans will never develop simulation technology because it is beyond our technological reach for all time
Our ability to develop simulation technology is completely irrelevant to this being true. We could develop no technology to produce simulations yet there could be a very large number of simulations being run e.g. in the thirteenth floor they simulate the 1930s, there were no simulations developed within that simulation, but it was definitely a simulated world.

If you're saying humans in the broad sense then that still remains untestable because if we are simulated we cannot know what the real humans are capable of and we aren't simulated, well we really can't know that we aren't simulated can we? I mean that's the dillema we're trying to solve isn't it?

2) Attacking p3 by finding evidence we are really in reality.
I'm not sure what evidence we could possibly find. As far as physical evidence that would be impossible as the simulations are designed to perfectly mirror what has actually happened in human civilization. I don't think we could find a priori evidence.

3) Attacking Bostrom's Bland Indifference Principle by which he argues we should treat P(we are simulated) = f_sim.
I'm trying, but personally I think his set up is too loose (which is why I was inclined to say it's a tautology). It acts as sort of a catch all.

Key Point #5: Bostrom's conclusion is falsifiable if we find evidence that we're in a simulator and that i or ii is true. Bostrom's conclusion is also falsifiable if we discover that simulator technology is beyond our reach.
That doesn't mean it can be tested.

I'm gonna reply to your list of my objections and then I'm going to re-outline my objections (categorizing them instead of the buckshot approach so it's easier to follow).

FaKToR

November 4th, 2005, 02:41 PM

(4) An observer has no idea which level of reality he's at, which is bad because the argument is "predicated on him having some knowledge."
I'd clarify, it's predicated on whomever is applying the formula having some knowledge, otherwise there would be no way to apply it.

(7) Faktor doesn't know of any other human civilizations, so Faktor doesn't understand why Bostrom uses average values and the implicit C.
I think this could be improved upon if the POV of whoever/whatever is applying the equation could be established.

(8) Bostrom's equation doesn't have enough "qualifications," where "qualifications" is understood to mean something more specific than axioms.
I was using the two interchangeably, though I guess you could distinguish the qualification of what it means to be "simulated" from the axioms algebra is based upon.

To be precise, the argument applies to any subjective reality in which, from the observer's point of view, p1, p2, and p3 are true. Do you have a problem with this? Every observer who comes to Bostrom's conclusion is making the best possible guess given the information he has. It is not possible to be more rational than this.
I'm saying that the POV which formulates this equation is based on an objective view, with knowledge that no one at the subjective level could poses. I don't see how an observer could know whether p3 is true or not. If he assumes it is then I think there is no reason you couldn't do this at any level of the system.

You're presupposing that the factual distinction between simulation and reality depends on which one you think you're in, which is patently absurd.
From a logical stand point that may be true, from a significance standpoint maybe not. You may liken it to "if a tree falls in the woods and no one is around, does it make a sound?"

If you want to argue that obects only exist insofar as we can sense them, save it for another thread because that is way beyond the scope of this debate, not to mention the practical problems with that philosophy...
I'll touch a little more on this in my next post.

By the structure of Bostrom's equation, you don't need to find numbers for the other variables once you establish that N_i is large (which is what Part III of his paper does). If N_i is large you are automatically led to the conclusion that one of three statements must be true, which I will not repeat since I've written them down before.
But you cannot establish if N_i is large except within the context of your own realm, which you wouldn't count because you would have to know that you are running simulations in which case you would not take them into account for your equation because you would be removed from those simulations i.e. you could see the servers they're hosted on.

Again, you're not actually counting anything in the argument.
How exactly are you supposed to gauge N_i, or more exactly what is the significance of N_i?

The argument is actually predicated on the observer having no knowledge of which level he's at.
If the observer had no knowledge then this equation could never be applied and would lead no where, because one would not be able to determine which of the three conclusions was likely. I clarify this above as well.

And the equation is concerned only with ancestor simulations.
Why?

Under your simplified equation, Y/Z (the frequency of real observers) cannot be larger than X/Z (the frequency of simulated observers), because X = NY where N is very large (unless humanity dies out or chooses not to run simulations, in which case N is 0 or close to it).
Except I'm denying your restriction about only running ancestor simulations because it is arbitrary.

I'll be blunt here and say WTF? to this assertion. Show me the similarities, because I can't think of any nontrivial ones.
It gives us three possible conclusions, but the conclusions don't really get us anywhere. They are totally worthless conclusions because we have no more reason to believe one of them is right over the another.

What do you think a variable is?
It's rather difficult because you seem to be bouncing back and forth from the hypothetical to the practical. From a hypothetical standpoint yes we don't know how many there are in the future. From the practical standpoint I know of one right now. If I wish to do anything with this equation rather than fawn over how it could be any one of three conclusions I would need to actually have values to plug into it. Going with the values I have there would be only one civilization.

I still don't understand what you mean by qualifications. If this is supposed to be a unique objection (i.e. not subsumed by any of the other ones), please clarify what you think Bostrom is missing.
I clarified at the top of this post.

Bostrom argues that N_i must be very large (using current best estimates about the physical limits of computation and advanced construction processes). Therefore N must also be very large unless f_i is very small. So to answer your objection, N could be very small--this is c2 of Bostrom's conclusion. Either way, Bostrom's reasoning is solid.
Fat load of good that does us. If we have no way of measuring these values what exactly are we supposed to be getting out of this equation?

If you believe c3, you believe that you and everyone else in the world are a simulated observer. I thought this was clear from my first post but I guess not.
There's a difference between being simulated and living in a simulation.

First of all, remember that this argument considers ancestor simulations run by other humans (or other simulated humans), so we can at least assume that our creators reason the same way we do.
That assumes that the simulations parallel the ancestors simulations for some arbitrary reason. Nothing dictates that they have to though.

I can't begin to understand how it is possible to warp logic such that this statement is in reality false. It is literally beyond human imagination to conceive of a universe that operates on different logical principles.
Mabye that's because you're living in a simulation? Maybe some demon is tricking you?

Note the difference between distorting math and distortinng our understanding of thermodynamics, as was the case in the Matrix. In the latter, the Matrix lies to us about some fact. In the former, our simulators would somehow create a world that is not logically consistent with reality. I honestly don't think this is even possible, and it's certainly not desirable by humans seeking accurate reproductions of their past.
Actually you could say it's distorting math with regard to how thermodynamics function. If you have systems that are 100> percent efficient then they will only consume energy.

I still don't know what approach and what conclusion you're referring to.
If we reach the same conclusion "But so what! We can't tell the difference!", which is the same conclusion we would have reached without this equation, and the equation is a bad approach to determining whether we are in a simulation or not, then we have an irrelevant approach to an obvious conclusion.

This goes back to #1. We don't have to be able to tell the difference; in reality there will be a difference, and that's all that matters.
That's a matter of opinion, something that should actually be debated at the least.

Bostrom's justification for saying N_i must be very large is based on empirical observations (read Part III of the paper). The rest follows logically.
About the world in which he lives in. Again, I submit to you that N_i can be large and the evidence in our world for it being so small (again think back to the Thirteenth Floor).

I'll put up my organized objections after I go to class.

Discobird

November 5th, 2005, 06:14 AM

What good exactly is viewing things from this perspective?
It's the correct way to view it. I can't reduce it any further than that. It's like if I said, "The average speed of a car on some path can be determined by taking the total distance traveled and dividing by the total time elapsed." Then you ask me what "good" it does to look at the total distance instead of something else. What more do you want from me? At some point I have to simply say that this is the correct definition of frequency as it pertains to the argument.

You're making assumptions about how I'm using tautology. I was thinking more along the lines that there is no distinction between reality or a simulation, so that they are one in the same.
Simulation and reality are definitionally different. I do not understand what you mean when you say they "could" be the same. If you said "Apples and bananas are the same," I could sort of catch your drift: the things that look and taste like apples are actually the same as the things that look and taste like bananas. But the words "simulation" and "reality" are fairly defined without respect to specific phenomena. It's as if you said "Math and failure could be the same thing," it doesn't make any sense.

The closest sensible objection I can think of is that simulations might not in fact exist, in which case I challenge you to find any evidence supporting that assertion. It's not enough to simply say it could be true.

Except it can never (at least with our present understanding) be tested.
Um, I said as much in my post:
However, it's probably not possible for us to devise our own equipment and methods, and go out and say, "Yes! We're in a simulation." So, while Bostrom's conclusion is weakly falsifiable, the scientists among us are probably not very satisfied (so far).

Sure it can be false, but that doesn't mean that it can be falsified in the practical sense. What good would it do us to use such a loose standard as having the possibility of a false value in its truth table in determining if something is falsifiable?
It's not that there exists a false value in the truth table; it's that there exists a hypothetical set of observations that support that false value. This is a very important difference. There exist statements that can be false ("God exists") but not falsified (there is no possible set of observations that would show God does not exist). I'm saying Bostrom's conclusion can be falsified, not just false.

Our ability to develop simulation technology is completely irrelevant to this being true. We could develop no technology to produce simulations yet there could be a very large number of simulations being run e.g. in the thirteenth floor they simulate the 1930s, there were no simulations developed within that simulation, but it was definitely a simulated world.
This scenario corresponds to Assignments 6 and 8 in my truth table, in which we are simulated by nonhuman entities (I said "aliens" in my post but it doesn't really matter who's doing the simulating). I'm going to put my response in green because I will refer to it a lot in my future replies:

It is not sufficient for you to simply point out possible universes in which Bostrom's conclusions are wrong, e.g. the 13th Floor scenario or "Maybe demons are tricking us into using bad math!" To make a real objection, you must show that the probability of these scenarios being true is nontrivial and that Bostrom's omission of them is a serious fault. Of course it is always possible to poke holes in someone's theory by saying the universe is a drunken butterfly's dream. But no one should take you seriously unless you can back up your claims.

On a similar note, I'm also bothered by the unlimited scope of your objections. If you believe that evil miseducation demons are a good reason to dismiss Bostrom's argument, you should also dismiss every scientific theory and fact derived from our knowledge of the universe, since they are all susceptible to the same complaint.

If you're saying humans in the broad sense then that still remains untestable because if we are simulated we cannot know what the real humans are capable of and we aren't simulated, well we really can't know that we aren't simulated can we? I mean that's the dillema we're trying to solve isn't it?
There are two possibilities, either we're simulated or not.
If we're not simulated, then p1 and p2 are soundly derived from our current knowledge of physics etc.
If we are simulated, then obviously humans are capable of developing simulator technology and p1 and p2 are definitely true!
I'll ignore for now the possibility that we're being simulated by nonhumans, please refer to the green text.
Note that it doesn't matter whether we can tell we're in reality or not, since I've just shown that p1 and p2 are very likely true in either case.

I'm not sure what evidence we could possibly find. As far as physical evidence that would be impossible as the simulations are designed to perfectly mirror what has actually happened in human civilization. I don't think we could find a priori evidence.
Um, look 3 sentences down from where you quoted me:
(2) is not really possible.

I'm trying, but personally I think his set up is too loose (which is why I was inclined to say it's a tautology). It acts as sort of a catch all.
Now you think Bostrom's indifference principle is a tautology too? I'd like to see you demonstrate this.

That doesn't mean it can be tested.
See earlier responses.

Discobird

November 5th, 2005, 07:15 AM

I'd clarify, it's predicated on whomever is applying the formula having some knowledge, otherwise there would be no way to apply it.
What knowledge are you talking about that depends on the observer knowing which level of reality he's on?

I think this could be improved upon if the POV of whoever/whatever is applying the equation could be established.
The equation is not being "applied" in any meaningful sense. The argument in the paper applies to any observer who believes he is a human living before posthuman technology is achieved.

I was using the two interchangeably, though I guess you could distinguish the qualification of what it means to be "simulated" from the axioms algebra is based upon.
OK, then am I correct in saying this is like objection 10 in my list? If not please explain.

I'm saying that the POV which formulates this equation is based on an objective view, with knowledge that no one at the subjective level could poses.
You're still hung up on treating the equation as a practical thing to be determined by filling in real numbers. It's not. No observer is required to substitute all the variables, and saying this cannot be done is not a good criticism of the argument. All one needs to do is see that, if N_i is very large, then the resulting f_sim must be very close to 1 unless f_p and/or f_i are very close to zero. One does not need to know the values of any other variables to come to this conclusion.

I don't see how an observer could know whether p3 is true or not.
I think it's easy to see that p3 is true, since a sufficiently advanced simulator could directly stimulate our brain into experiencing the sensations we'd feel if we were in reality.

From a logical stand point that may be true, from a significance standpoint maybe not. You may liken it to "if a tree falls in the woods and no one is around, does it make a sound?"
I don't really know what you mean by significance standpoint, but OK.

But you cannot establish if N_i is large except within the context of your own realm, which you wouldn't count because you would have to know that you are running simulations in which case you would not take them into account for your equation because you would be removed from those simulations i.e. you could see the servers they're hosted on.
From this and your next reply I can sense that you're not quite getting what N_i means. N_i is the average number of ancestor simulations that an interested civilization would run. Bostrom does some calculations to show that future civilizations will have massive computational resources, therefore an appropriately motivated civilization would likely run a huge number of ancestor simulations. In other words, we don't have to be in a posthuman civilization to show that N_i is likely to be extremely large-- Bostrom shows it in Part III of his paper.

If the observer had no knowledge then this equation could never be applied and would lead no where, because one would not be able to determine which of the three conclusions was likely. I clarify this above as well.
First, the equation is not "applied" (see response near the beginning of this post). Second, Bostrom's paper doesn't argue for the truth of any specific conclusion. It simply says that one of them must be true. This is still a very interesting result because most people don't believe that any of the conclusions are true.

Why?
Because ancestor simulations are the kinds of simulations that produce the population of interest (observers who believe they are humans living before posthuman tech). We need to account for ancestor simulations in order to have a valid equation for f_sim.

Except I'm denying your restriction about only running ancestor simulations because it is arbitrary.
Go reread this passage from my post:
You can argue two things here:
(1) future humans will choose not to run ancestor simulations (they may run simulators with far less than H observers)

(2) future humans will be incapable of running ancestor simulations

If you argue (1), you're arguing for c2. If you argue (2), you're attacking p2. Either way, you have not shown a problem with Bostrom's equation. The only thing you've shown is that you don't understand it.
I'm not saying that future civilizations will only run ancestor simulations. They can also run animal simulations, or future simulations, or whatever. But the only simulations that are relevant to determining f_sim are ancestor simulations. Thus the choice of ancestor simulations is not arbitrary.

It gives us three possible conclusions, but the conclusions don't really get us anywhere. They are totally worthless conclusions because we have no more reason to believe one of them is right over the another.
Suppose I tell you that you have pirate treasure buried in either your front yard or your back yard, but I don't tell you which. Is my statement "totally worthless" because you don't know which yard is more likely? Of course not.

In a similar vein, Bostrom's conclusion is valuable because it's shocking, it clashes with most people's worldview, and it's not intuitively obvious. Bostrom expresses it clearly in question form: "If there were a substantial chance that our civilization will ever get to the posthuman stage and run many ancestor-simulations, then how come you are not living in such a simulation?" Although he doesn't favor any particular outcome, he still forces us to think.

It's rather difficult because you seem to be bouncing back and forth from the hypothetical to the practical. From a hypothetical standpoint yes we don't know how many there are in the future. From the practical standpoint I know of one right now.
You're using "hypothetical" and "practical" in very strange ways. Suffice it to say that the future is what counts since it will be future civilizations that develop (or don't develop) simulator technology.

If I wish to do anything with this equation rather than fawn over how it could be any one of three conclusions I would need to actually have values to plug into it. Going with the values I have there would be only one civilization.
Argh, once again, get out of the mindset that you need to plug values into the equation in order for it to be useful. It produces the three conclusions-- that's useful enough, as I argue above.

Fat load of good that does us. If we have no way of measuring these values what exactly are we supposed to be getting out of this equation?
See above.

There's a difference between being simulated and living in a simulation.
If you read the paper at all it is extremely clear which one Bostrom means.

That assumes that the simulations parallel the ancestors simulations for some arbitrary reason. Nothing dictates that they have to though.
See my self-quote above, where I addressed the ancestor-simulations.

Mabye that's because you're living in a simulation? Maybe some demon is tricking you?
See the green text of my previous post.

Actually you could say it's distorting math with regard to how thermodynamics function. If you have systems that are 100> percent efficient then they will only consume energy.
Ditto.

If we reach the same conclusion "But so what! We can't tell the difference!", which is the same conclusion we would have reached without this equation, and the equation is a bad approach to determining whether we are in a simulation or not, then we have an irrelevant approach to an obvious conclusion.
The conclusion is not "So what!" In fact, the "So what!" part is p3 of the premises. The conclusion is much stronger than simply "we can't tell the difference."

That's a matter of opinion, something that should actually be debated at the least.
See the part about simulation and reality in my previous post.

About the world in which he lives in. Again, I submit to you that N_i can be large and the evidence in our world for it being so small (again think back to the Thirteenth Floor).
See the green text in my previous post.

I'll put up my organized objections after I go to class.
Looking forward to it! I will be extremely busy next week with schoolwork, so I probably won't post another detailed reply like this until at least next Thursday.

FaKToR

November 7th, 2005, 12:55 PM

Introduction:
I'm going to outline my objections here, because there are multiple objections. First off I want to point out that there are two distinct type of objections, those which fall under practical application objections, and those which fall under what I would term metaphysical dilemmas. Practical issues would be those dealing with the application of Bostrom's ideas in everyday life while keeping it in the same context as we would any other mathematical equation. By metaphysical I am referring to that which we can question for the sake of argument, but would not govern our lives by.

I find the metaphysical problems to be the more pressing because I personally don't buy into using this equation in a practical application and I'm not all that worried about other people doing it. What bothers me is that is meant to be of a philosophical nature and it is based on bad reasoning.

By "realm" or "world" I am referring to one of the tiers in this supposed system of simulations and one reality.

1. Practical: Perspective
The first objection I have with this equation is its perspective. I take it as only being True if viewed from the perspective of an omniscient being that is removed from the system(s) in question. I reach this conclusion because the equation fails to work on the subjective level of a person/simulation within one of the realms. This causes problems because we are certainly not omniscient beings (otherwise we wouldn't have this question to deal with) which precludes us from being to really get anything useful out of this equation. The equation views the bag as a whole, mixing different realms together, but we only have our realm to work with. I'm aware of your example with the pirate treasure buried in the front yard or backyard, but the problem here is that we never get to dig for the treasure to find out, so the point is entirely moot.

2. Practical: Variable Values
Now, from the practical standpoint, if we attempt to apply this equation we run into problems. We have no values to plug in for N, we don't even have qualitative measurements to apply to N, and even if we did they wouldn't matter because "our" value of N is irrelevant. As I pointed out with the 13th Floor, our value of N could be non-existent and we could still be living in a simulation. Likewise our value of N could be extremely large, and we could be the only real thing out there. The values used in this equation must be taken from an omniscient perspective, that is what is the absolute value of N (the sum of all the worlds, simulated or real N values). That would work within the context of an omniscient viewer, but because we part of only this one world we can only take one value or guess at what N is and that is entirely irrelevant.

Likewise we have no way of knowing the number of post human civilizations or the number of people, we can't even express these values qualitatively. Which makes it even harder to discern anything from this equation.

3. Practical: Equation Formulation
From a practical standpoint there is a problem in how he formulates his equation. The equations really should be X/Z, Y/Z, and X + Y = Z, where X is the number of simulated observers and Y is the number of real observers and Z is the total number of observers. Of course if we did it that way we'd have to know in the first place how many of each there are. To get around this problem Bostrom bases the number of simulated observers on the number of real observers by multiplying the computational power and the number of real people. This is a problem because the computational power can be applied to running any simulations. Bostrom is doing it so that his equation is actually useful, but its exclusion of other possibilities means that whatever probability he does calculate or suppose it entirely worthless because it is based upon an untestable assumption about how the simulations are conducted. Bostrom must assume that ancestor simulations will be run. His conclusions should therefore say "assuming ancestor simulations are run then it must be one of the three." Of course if he did that his conclusions would have no use because we have no reason to assume they would run ancestor simulations, at least we have no more reason to believe they would run ancestor simulations than we would to assume they would not. He also assumes that the ancestor simulations they do run are exactly like the real world, only difference is that the simulation is produced by a computer. But there is no restriction dictating that all simulations must perfectly mirror reality, the simulations can be however the designer wants them to be and I see no reason to assume that they would conform to one pattern over another.

I likened this to Pascal's wager because we are being asked to make our bet based on a probability that makes assumptions altering the question at hand. Pascal's mistake was that he made assumptions about the nature of god. Bostrom's mistake is that he makes assumptions about what simulations would be run by those capable of it.

4. Practical: So what?
Another practical problem is that this question doesn't have practical applications, at least not as I would conduct myself. Even if we could measure f_sim and we concluded that we are probably living in a simulation, then what? I personally find this to be the type of decision that one wouldn't gamble on, and as such a probability would mean little to me because there's always that slim chance that I am a real observer. This is similar to how executions work, where it is randomized so that neither executioner knows who actually killed the person and can therefore reassure themselves that they were not the one who did it. Of course if we did accept that we live in a simulation, how should that affect us? Should we alter our behavior? Should we keep doing what we're doing? Should we be outraged?

1. Metaphysical: REIFICATION aka Math
What you have to understand is that when you start calling into question things such as all of reality you're making a metaphysical quagmire. You can only proceed based on assumptions, but you need reasons why you would choose one assumption over another, and by doing so it is questionable what conclusions, if any, can be reached because they are weak conclusions.

Words don't have power, let's get that out. At least we have no reason to assume they do, and I'm personally of the opinion that they do not lest we tempt rather suspect reasoning such as the ontological proof of god. We do not place faith in math because it is inherently right/accurate/true however you wish to describe it. We put faith in math because we know from experience that it is a good reflection of how the world we live in functions, it has reliable applications that we have tested. The problem is that all empirical evidence is gone when all external reality is brought into question such as we have done. Bostrom sides steps this issue by assuming that the simulations are no different from the real world, that is they are mirror copies in all respects, but as I've stated we have no reason to make that assumption.

What this leaves us with is a system (math) that functions in our head, but no evidence to support that it is accurate for determining how the real world functions. One way of expressing this idea is that maybe we are being tricked, maybe the simulations mislead us about how math and logic function, or maybe they mislead us about how the world actually is. In all honesty we don't know whether that is true or not. To make a major conclusion about how reality acts from this would be a weak statement because there is just too much uncertainty. You must remember that as far as we know there is no force that dictates the universe must adhere to the principles of physics, the rules of logic, and the proofs of math. There isn't something out there making it so or else and when we start making such far reaching metaphysical questions we cannot just suppose one way or another and then proclaim we've found truth.

2. Metaphysical: So what?
You may not consider this to be a flaw of the equation, but I feel it is a failure to understand what is important. The issue that he doesn't address and that I've attempted to get you to think about is what difference is there between a simulation and reality? This really is an epistemological question, but it deals with how significance is attached to ideas. To phrase it another way would be to say "what is truth?" I tried to get you to see this with the question of a tree falling in the woods. If you are unfamiliar with this old mental exercise I'll explain:
"If a tree falls in the woods, and no one is around to hear, does it make a sound?"
In the sense that there are vibrations created upon the tree's impact with the ground and these vibrations travel on the air and can enter an ear and be perceived as a sound, then yes it does. I'd imagine your reasoning would be along those lines, "yes you stupid simp it makes a sound." This however fails to correctly understand the question, that being one of significance. If no one is around to here it make a sound, then who cares whether it does or not? One could view it that without the human or intelligent mind to add importance to events there is no significance or "truth". It's rather like a subjective view of the world.

The case of simulation vs. reality is similar. If there is no discernible difference between reality and a simulation, then so what? We can still conclude that simulations are reality and insomuch as we define and create truth we'd be right. AFAIK no one else creates the language we use to communicate. This is rather a subjective view of things though it need not be. If you've read 1984 you may recall a similar argument for 2+2 = 5 being made. What is truth then? Is it consensus? Is it what the individual defines it as? Is it an objective concrete reality? These questions are the inherent underpinnings of what Bostrom is working on and without dealing with these issues his equation doesn't amount to shit. Otherwise he's begging the question.

It is not sufficient for you to simply point out possible universes in which Bostrom's conclusions are wrong, e.g. the 13th Floor scenario or "Maybe demons are tricking us into using bad math!" To make a real objection, you must show that the probability of these scenarios being true is nontrivial and that Bostrom's omission of them is a serious fault. Of course it is always possible to poke holes in someone's theory by saying the universe is a drunken butterfly's dream. But no one should take you seriously unless you can back up your claims.
Except what Bostrom is doing is no better than what I'm doing with my objections. He is saying "ok let's say everything can be a simulation, but put in constraints (assumptions) that people will find acceptable" You may call my objections trivial, but you misunderstand, I am saying his argument is equally trivial.

I think this is a good, clearer start.

puke o'hara

November 7th, 2005, 04:27 PM

From a practical standpoint there is a problem in how he formulates his equation. The equations really should be X/Z, Y/Z, and X + Y = Z, where X is the number of simulated observers and Y is the number of real observers and Z is the total number of observers.Except you're pulling the "fraction" out of your ass. If you want to take a mathematical approach you should have a proof for your equation. It is not sufficient to just deem it so.

FaKToR

November 7th, 2005, 05:44 PM

Turn about is fair play puke. Besides I'm just going off his work.

Edit: I would point out when I first made that statement I was having more difficulty because it wasn't clear exactly how he was formulating his equation, he just gave it and it wasn't very clear what his variables represented. And before you post I want you to know that this is a bit of a step backward in the conversation, and knowing you like I do it won't bare any fruit so don't count on starting a debate cause you'll be all by yourself.

Bone_Vulture

November 7th, 2005, 05:52 PM

Considering the baffling amount of debate, one would think that either Faktor or Discobird is writing an university graduation paper on the topic.

FaKToR

November 7th, 2005, 05:54 PM

Actually I'm not certain this is much more than when I used to debate Oblivion. I'd actually have to break those posts in half because it would time out when I would go to post it. And I don't know about Discobird, but I'm a philosophy major.

Bone_Vulture

November 7th, 2005, 06:52 PM

And I don't know about Discobird, but I'm a philosophy major.

It shows. ;)

FaKToR

November 7th, 2005, 07:04 PM

You know another movie that has metaphysical underpinnings that might be fitting for this discussion? Last Action Hero.

Modest Genius

November 7th, 2005, 07:57 PM

kudos to faktor for posting all that

some of his points i agree with, and some of them i dont. the only point im going to make is that the lack of concrete ratios isnt a problem for those of us who are familiar with taking mathematical limits of everything

Discobird

November 8th, 2005, 05:16 AM

Considering the baffling amount of debate, one would think that either Faktor or Discobird is writing an university graduation paper on the topic.
Nah, I'm a computer science major. I haven't taken a philosophy class in my life. But at least I will have a job when I graduate :p

Faktor, I'll post a full rebuttal of your objections on Thursday or Friday after I finish my exams. For now, let me quickly say that Practical #1-3 reveal several perplexing, basic misunderstandings of the equation on your part; Practical #4 was stated by me in the very first post; and I'm perfectly content to place Bostrom's argument on metaphysically equivalent grounds with science. If that means that all of science "doesn't amount to shit" as you so diplomatically put it, that's fine with me, but neither of your metaphysical objections bears the precision necessary to distinguish this argument from any other empirically-derived conclusion.

FaKToR

November 8th, 2005, 10:25 AM

and I'm perfectly content to place Bostrom's argument on metaphysically equivalent grounds with science. If that means that all of science "doesn't amount to shit" as you so diplomatically put it, that's fine with me, but neither of your metaphysical objections bears the precision necessary to distinguish this argument from any other empirically-derived conclusion.
This equation is distinctly different from any other scientific equations because it's not actually based on empirical evidence. You call all external reality into question when you start talking about whether we live in a simulation or not. This is not empirically derived, the only way he can say it is empirically derived requires him to assume that the simulation worlds mirror reality exactly, which he has no basis for.

Nah, I'm a computer science major. I haven't taken a philosophy class in my life. But at least I will have a job when I graduate
I considered comp. sci. but I hate math too much (and as I understand it, it's a lot harder to get a job for comp. sci. then say systems managament or whatever the lesser computer major is called). I'm a Poli. Sci./Philosophy/maybe economics major, so I'm not worried about employment.

FaKToR

November 8th, 2005, 11:40 AM

I was taking a look at the doomsday argument...god that's stupid.

I think this his a wayward application of math (my initial objections).

http://en.wikipedia.org/wiki/Doomsday_argument

Edit: I'm gonna have to look into how to set this up more accurately, but if you were to approach this using quantification I think it will end creating a very weak statement, that is an existentially quantified conditional.

Like this: ∃x( (~C1x ^ ~C2x) -> C3x), this would be a very weak statement. We could reach this statement working from the disjunction (C1 v C2) v C3.

1. (C1 v C2) v C3
/ (~C1 ^ ~C2) -> C3
2. (~~C1 v ~~C2) v C3 1, D.N.
3. ~(~C1 ^ ~C2) v C3 2, D.M.
4. (~C1 ^ ~C2) -> C3 3, Imp.

Now I just need to add existential generalization...
I would also point out that this is where I disagree with the conclusions. I think that you can have (~C1 ^ ~C2) and not conclude C3.

This is interesting:
http://en.wikipedia.org/wiki/Simulated_reality#Is_this_a_simulated_reality.3F

God I love having my objections supported instead of looking crazy:
http://en.wikipedia.org/wiki/Epistemic_probability

When I learned statistics I was taught with frequency probability.

Edit: I was just looking at something and I wondered, could a computer perfectly mirror our world? The way in which computers function with number representation is to use floating-point numbers, an approximation. What effect would this limitation have on a simulation? Would it be magnified into an increasing systemic error in the simulated model of the world?

Discobird

November 9th, 2005, 06:22 AM

This equation is distinctly different from any other scientific equations because it's not actually based on empirical evidence. [...]
I was tempted to reply to this right now, but I'll give it a more thorough treatment in a later post.

I considered comp. sci. but I hate math too much (and as I understand it, it's a lot harder to get a job for comp. sci. then say systems managament or whatever the lesser computer major is called).
Not sure which major you're referring to, but we only have computer science here. At any rate I want to pursue some more exciting stuff after graduation (namely AI, as you can see my interest in this argument is more than academic ;)).

I'm a Poli. Sci./Philosophy/maybe economics major, so I'm not worried about employment.
Ec is probably not a good idea if you're averse to math, but I guess it depends on which courses you take.

I was taking a look at the doomsday argument...god that's stupid.
I don't think it's stupid, but it is much harder to defend than the Simulation Argument. It's fun to bring up at parties though.*

Edit: I'm gonna have to look into how to set this up more accurately, but if you were to approach this using quantification I think it will end creating a very weak statement, that is an existentially quantified conditional.
I don't know why you believe Bostrom's conclusion leads to an existential claim. If anything, it's universally qualified, something like:

∀x, x is an observer who believes he lives in the 21st century: x should believe (C1 v C2 v C3)

We could reach this statement working from the disjunction (C1 v C2) v C3.

1. (C1 v C2) v C3
/ (~C1 ^ ~C2) -> C3
2. (~~C1 v ~~C2) v C3 1, D.N.
3. ~(~C1 ^ ~C2) v C3 2, D.M.
4. (~C1 ^ ~C2) -> C3 3, Imp.
Not to belittle your logic, but you can go straight from the original disjunction to step 4 using unit resolution. And I still don't see where the existential comes from.

I think that you can have (~C1 ^ ~C2) and not conclude C3.
Well, clearly! I doubt we'd be having a debate if you agreed with this.

When I learned statistics I was taught with frequency probability.
I learned frequentist probability in my stat classes and Bayesian inference in one of my AI courses (probabilistic reasoning). Whether you're a fan of of it or not, Bayesian inference works very well in practice for designing rational agents and it has descriptive power in explaining how we reason (e.g. what do we really mean we think there's a 90% chance of rain? Usually the 90% is interpreted as a degree of belief in the statement "It will rain today," and not as a belief that 9 out of 10 identical days have rain). I don't see the two approaches as mutually exclusive, they're both useful for describing different things.

In any case, a Bayesian approach to probability is not necessary at all for the argument. In fact Bostrom refers to a credence function and not probability when he expounds on his Bland Indifference Principle:
http://www.simulation-argument.com/simulation_files/image025.gif

As long as you agree with the BIP (which I doubt you do, but you haven't shown a problem with it yet), Bostrom's conclusion has force even if you don't accept Bayesian probability.

Edit: I was just looking at something and I wondered, could a computer perfectly mirror our world? The way in which computers function with number representation is to use floating-point numbers, an approximation. What effect would this limitation have on a simulation?
The world only needs to be modelled accurately enough for us to think it's continuous. Our creators could compress the representation of distant planets and things like that, and approximate microscopic and smaller interactions whenever no one's looking.

Would it be magnified into an increasing systemic error in the simulated model of the world?
Interesting idea, but I think it's safe to say we would never know if we took a left turn instead of a right at some bifurcation point. At any rate, a creator interested in simulating history would surely program the simulation with control logic and a way to transparently correct errors over time.

*I am very fun at parties

FaKToR

November 9th, 2005, 10:45 AM

I was tempted to reply to this right now, but I'll give it a more thorough treatment in a later post.
Yes it would be if you assume the world we live in would be exactly the same as the real world even if it was a simulation, but we have no reason to believe that.

Not sure which major you're referring to, but we only have computer science here. At any rate I want to pursue some more exciting stuff after graduation (namely AI, as you can see my interest in this argument is more than academic ).
It doesn't matter.

Ec is probably not a good idea if you're averse to math, but I guess it depends on which courses you take.
I know what I'm doing.

I don't think it's stupid, but it is much harder to defend than the Simulation Argument. It's fun to bring up at parties though.
So you would actually try to defend it?

I don't know why you believe Bostrom's conclusion leads to an existential claim.
I was still thinking about it.

Not to belittle your logic, but you can go straight from the original disjunction to step 4 using unit resolution. And I still don't see where the existential comes from.
Belittle? What are you talking about? What are accepted steps of logic not allowed to be used or something? I did nothing wrong and I see no reason why you would consider them to be lesser than any equally valid logical technique. It's not as if one form of manipulation is more true than another.

Well, clearly! I doubt we'd be having a debate if you agreed with this.
Numerous times you asked me what other conclusions there could be.

I learned frequentist probability in my stat classes and Bayesian inference in one of my AI courses (probabilistic reasoning). Whether you're a fan of of it or not, Bayesian inference works very well in practice for designing rational agents and it has descriptive power in explaining how we reason (e.g. what do we really mean we think there's a 90% chance of rain? Usually the 90% is interpreted as a degree of belief in the statement "It will rain today," and not as a belief that 9 out of 10 identical days have rain).
And there is a distinct difference between how we reason and what the actual probability of an event occurring is. Someone believing something to be 90 percent isn't a very strong statement because of it's inherit subjectivity.

As long as you agree with the BIP (which I doubt you do, but you haven't shown a problem with it yet), Bostrom's conclusion has force even if you don't accept Bayesian probability.
I think it's pretty obivious that I don't.

Here's a curious snippet:
More generally, if we knew that a fraction x of all observers with human-type experiences live in simulations, and we don’t have any information that indicate that our own particular experiences are any more or less likely than other human-type experiences to have been implemented in vivo rather than in machina, then our credence that we are in a simulation should equal x:
Just because we don't know if it's anymore or less likely does not mean that the two situations are equally likely. I suppose what would one conclude then knowing the fraction of real observers? Would it then make sense for them to conclude that they live in the real world and not a simulation? I'm not so sure he is really avoiding Bertrand's paradox.

The world only needs to be modelled accurately enough for us to think it's continuous. Our creators could compress the representation of distant planets and things like that, and approximate microscopic and smaller interactions whenever no one's looking.
Do you mean they would be tricking us...

Interesting idea, but I think it's safe to say we would never know if we took a left turn instead of a right at some bifurcation point. At any rate, a creator interested in simulating history would surely program the simulation with control logic and a way to transparently correct errors over time.
Is it possible to account for all that? I think this is moving into the realm of chaos theory in which case you're supposing that we can overcome the limitations that by their nature cannot be predicted.

One thing I find interesting in relation to all this is the inverse gamblers fallacy.

Discobird

November 9th, 2005, 01:49 PM

It doesn't matter.
Not much for small talk I see.

Belittle? What are you talking about? What are accepted steps of logic not allowed to be used or something? I did nothing wrong and I see no reason why you would consider them to be lesser than any equally valid logical technique. It's not as if one form of manipulation is more true than another.
Calm down, man. What part of "not to belittle" do you not understand?

Numerous times you asked me what other conclusions there could be.
This is not a novel conclusion, it only expresses a disagreement with Bostrom's. What's your "c4"?

And there is a distinct difference between how we reason and what the actual probability of an event occurring is. Someone believing something to be 90 percent isn't a very strong statement because of it's inherit subjectivity.
Addressed below.

Just because we don't know if it's anymore or less likely does not mean that the two situations are equally likely.
It doesn't mean that that the two are equally likely, but the most rational possible belief is that they are. Consider the betting problem I gave earlier. Bostrom also provides another justification with a thought experiment: if we believed f_sim = 1, we would deductively infer that we were simulated (our credence would be 1). Thus as our estimate of f_sim approaches 1 (98%, 99%, 99.9%, 99.99%...), it makes sense that our credence in being simulated approaches 1 as well.

It is possible that, say, all simulators lack Tyrannosaurus Rex fossils and therefore the probability that we're in a simulation is zero, despite f_sim being close to 1. But we don't have that information, or any other information that would tilt the scales in favor of reality or simulation. Therefore the best we can do is as Bostrom concludes.

This is also why Bayesian probability makes sense here, since the question is not "What is the actual probability we are simulated?", which is intractable, but instead "What should we believe?"

I suppose what would one conclude then knowing the fraction of real observers? Would it then make sense for them to conclude that they live in the real world and not a simulation?
Huh? It depends on what one believes the fraction of real observers is. If you believed f_real were close to 1, then yes, it would be rational to believe you were real. This is in fact what c1 and c2 amount to (a belief that we are real, but that we'll be destroyed or choose not to run ancestor simulations in the future).

Do you mean they would be tricking us...
I've always assumed a level of trickery on the part of the creators, simply because they would have us believe we're real when we're not. But note the difference between this kind of trickery and the kind of trickery you've been claiming in which demons somehow manipulate mathematics such that very large numbers multiplied by numbers near 1 become very small.

Is it possible to account for all that? I think this is moving into the realm of chaos theory in which case you're supposing that we can overcome the limitations that by their nature cannot be predicted.
The short answer is yes, the long answer is take a class on control theory. In any case, both of us overlooked the fact that the simulator program can assert its state to match the reference state without having to go through complicated predictions.

One thing I find interesting in relation to all this is the inverse gamblers fallacy.
I can see how that applies to the Doomsday Argument, but I don't see the connection with this one.

Modest Genius

November 9th, 2005, 02:58 PM

I learned frequentist probability in my stat classes and Bayesian inference in one of my AI courses (probabilistic reasoning). Whether you're a fan of of it or not, Bayesian inference works very well in practice for designing rational agents and it has descriptive power in explaining how we reason (e.g. what do we really mean we think there's a 90% chance of rain? Usually the 90% is interpreted as a degree of belief in the statement "It will rain today," and not as a belief that 9 out of 10 identical days have rain). I don't see the two approaches as mutually exclusive, they're both useful for describing different things.just wondering, is this baysian interference thing like fuzzy logic? only that has interference patterns between logical contructs.

FaKToR

November 9th, 2005, 03:03 PM

I don't think so MG. They don't appear to reject bivariance but instead relative frequency though I could be wrong.

Edit: For MG,

In some applications fuzzy logic is an alternative to Bayesian inference. Fuzzy logic and Bayesian inference, however, are mathematically and semantically not compatible: You cannot, in general, understand the degree of truth in fuzzy logic as probability and vice versa.

FaKToR

November 10th, 2005, 07:34 PM

Not much for small talk I see.
I don't think this thread has room to spare for smalltalk.

Calm down, man. What part of "not to belittle" do you not understand?
I don't know why else you would say "not to belittle". If you felt they were equally worthy manipulations then it shouldn't be an issue of concern. What is unit rule, I'm not familiar with that term and neither was my symbolic logic professor. Is it another term for disjunctive syllogism? A v B, ~B therefore A? Because if so that would not have worked in my proof. I did not have ~C1 and ~C2 therefore I could not apply a disjunctive syllogism.

This is not a novel conclusion, it only expresses a disagreement with Bostrom's. What's your "c4"?
~C3

It doesn't mean that that the two are equally likely, but the most rational possible belief is that they are. Consider the betting problem I gave earlier. Bostrom also provides another justification with a thought experiment: if we believed f_sim = 1, we would deductively infer that we were simulated (our credence would be 1). Thus as our estimate of f_sim approaches 1 (98%, 99%, 99.9%, 99.99%...), it makes sense that our credence in being simulated approaches 1 as well.
Except I don't agree it is rational to believe that they are.

It is possible that, say, all simulators lack Tyrannosaurus Rex fossils and therefore the probability that we're in a simulation is zero, despite f_sim being close to 1. But we don't have that information, or any other information that would tilt the scales in favor of reality or simulation. Therefore the best we can do is as Bostrom concludes.
No the best we can do is accept the only possible conclusion given the evidence, which is that the answer is inconclusive.

This is also why Bayesian probability makes sense here, since the question is not "What is the actual probability we are simulated?", which is intractable, but instead "What should we believe?"
I think I can express my problem with Bayesian probability. I was watching TV and there was commercial and it said "2/3 people liked the taste of our product". Does that mean I should believe there is a 66.6% chance that I might like the taste of their product, or that I should believe that there is a strong chance that I might like the taste of their product? Is it rational to think so?

Huh? It depends on what one believes the fraction of real observers is. If you believed f_real were close to 1, then yes, it would be rational to believe you were real. This is in fact what c1 and c2 amount to (a belief that we are real, but that we'll be destroyed or choose not to run ancestor simulations in the future).
I'm saying it's possible to believe that we are real and not buy into C1 or C2.

The short answer is yes, the long answer is take a class on control theory. In any case, both of us overlooked the fact that the simulator program can assert its state to match the reference state without having to go through complicated predictions.
I'm curious how that would work in an ancestor simulation. As I understand it you've have to predict the unpredictable.

I can see how that applies to the Doomsday Argument, but I don't see the connection with this one.
Let me think about this.

Discobird

November 11th, 2005, 08:20 PM

Here's the long rebuttal I promised on Tuesday. I had to break this into two posts because I broke the 15k character limit. This post addresses Faktor's four Practical objections.

Practical 1: Perspective
Faktor believes that Bostrom's equation is only true when viewed from an omniscient perspective.

Let's take a step back here and clarify what it means for an equation to be true. An equation is true if and only if the left side of the equation equals the ride side of the equation. I know this sounds trivial, but I have to spell it out since Faktor seems to think truth means something else.

Bostrom's equation reduces* to this:

fraction of observers = number of simulated observers in the universe
that are simulated ---------------------------------------------
in the universe total number of observers in the universe

Is this equation true? Obviously it is true, since the right hand side proceeds directly from the definition of "fraction." Furthermore, nothing in the equation changes depending on what level of reality you're in. Whether you're in a simulation or the toplevel reality, the number of simulated observers in the universe and the number of total observers in the universe remain the same. Thus the equation is true at every level, including our own. The equation is not dependent on our current context, which it would have to be for Faktor's argument that it fails to work on our subjective level to hold any water.

Where did this confusion come from? The problem lies in Faktor's vague usage of the term "work:"

I reach this conclusion because the equation fails to work on the subjective level of a person/simulation within one of the realms[...] but we only have our realm to work with [...]
Faktor never explains what he means by work (I know that there are two different usages in the above quote; I think both are unclear). In the first sentence, if "work" means "be true," I've already shown that the equation is true at all levels. If "work" means something else, then that sentence does not support his conclusion that the equation is only true from an omniscient perspective.

The second usage is even less clear; what does he mean when he says we only have our own realm to "work" with? The only sensible interpretation I can think of is that we can only observe our own realm, in which case this sentence belongs under Practical 2 (variable values).

I'm aware of your example with the pirate treasure buried in the front yard or backyard, but the problem here is that we never get to dig for the treasure to find out, so the point is entirely moot.
This belongs under Practical 4, concerning the value of Bostrom's conclusion. It doesn't have anything to do with perspective, so I don't know why Faktor put this under Practical 1.

*Bostrom's equation is more complicated than this, but all he does is subsitute equivalent expressions for the top and bottom. He doesn't change the meaning of the equation. Faktor challenges the validity of these substitutions in Practical 3 (which I address in this post), but as an independent objection, Practical 1 fails.

Practical 2: Variable Values
Faktor argues that we can't measure N to plug in values for the equation.
Faktor's entire argument here ignores the fact that we don't need to plug in a value for N to come to Bostrom's conclusion.

First, it is important to note that Bostrom decomposes N as follows:

N = f_i * N_i

In English, this basically means that the number of ancestor-simulations is equal to the fraction of interested civilizations times the number of ancestor-simulations that an interested civilization would run. This is a sensible substitution, since we can safely assume that only interested civilizations will run simulations, and uninterested civilizations will not (and even if they do, our resulting f_sim will be an underestimate, not a bad thing!).

We can't estimate N, since we have no idea how many civilizations will be interested in running simulations. However, we can estimate N_i, the number of ancestor-simulations that an interested civilization would run. Bostrom does some calculations using our current understanding of physics to arrive at an extremely high lower bound for N_i. Future civilizations with the desire to run ancestor-simulations will run a whole lot of them, since they'll have so much computing power available.

As it turns out, knowing N_i is large is sufficient for Bostrom's conclusion. Recall Bostrom's equation (I've grouped f_i and f_p for clarity):

f_sim = (f_i * f_p) * N_i
---------------------
(f_i * f_p) * N_i + 1

f_i and f_p are real numbers in [0, 1]. Since N_i is large, it follows that f_sim must be close to 1 unless f_i or f_p are very close to 0. These are the three possibilities behind c1, c2, and c3.

An example might make this clearer.

Suppose we had the following equation:

ax
y = ------
ax + 1

Now suppose I told you that x is very large, say 1000000000. Then clearly y must be close to 1 unless a is close to zero.

Now what if I substitute a = cd?

cdx
y = -------
cdx + 1

We come to the same conclusion since nothing really changed: y must be close to 1 unless cd is close to zero. And, if cd is close to zero, then either c or d must be close to zero. Now just substitute y = f_sim, c = f_i, d = f_p, and x = N_i, and we get Bostrom's equation.

Faktor believes that our value of N is irrelevant since it's possible that N is very high and we're real, or N could be very low and we're simulated.

Did you know that, although millions of other people buy lottery tickets, it's still possible for you to win? Whoa!

I don't need to say any more about that statement.

Conclusion: the only variable we need to estimate is N_i. The other variables don't matter.

I expect Faktor will object here and say that our estimate of N_i might be wrong since it depends on our knowledge of physics in this world, yet our world might be simulated. It's easy to show this doesn't matter by considering two cases:

(1) We are real. Then Bostrom's calculations are valid and N_i is very large.
(2) We are in an ancestor simulation. Then N_i is still probably large, by virtue of the fact that we are simulated. The alternative is that N_i is extremely small, yet we're one of the few simulated observers, which by the Bland Indifference Principle we should believe to be unlikely.

In either case, we're justified in saying that N_i is very large.

(There is a third case: we are simulated, but we're not in an ancestor simulation, or we're not simulated by humans. I address this possibility in Practical 3 and Metaphysical 1.)

Practical 3: Equation Formulation
To get around this problem Bostrom bases the number of simulated observers on the number of real observers by multiplying the computational power and the number of real people.
Faktor is confused here. Computational power isn't in the equation. I think when he says computational power he means N_i, which I will assume for the rest of this reply since it's the only explanation that makes sense.

Faktor believes that Bostrom must assume only ancestor simulations will be run.
Nope. Bostrom allows for any number of ancestor simulations, including zero. This is encoded in the variable f_i. The statement "Future civilizations won't run ancestor simulations" is equivalent to saying f_i = 0.

In fact, one of Bostrom's conclusions (c2) says that no ancestor simulations will be run. It amazes me that Faktor is still making these basic comprehension errors so late in the debate. This is a straight-up misreading of the text.

Faktor believes that Bostrom assumes simulations must perfectly mirror reality, but we have no reason to think this is the case.

Ancestor-simulations are defined to mirror reality-- they're large-scale mockups of human history. If Faktor believes future civilizations won't run ancestor-simulations, then he should put more credence in c1 and c2 than in c3. However, he's failed to show any problem with Bostrom's reasoning or equation.

You might ask, what if future civilizations run small simulations of exactly this period in history, containing only a few humans? These wouldn't be ancestor-simulations, but they would still contribute to the count of simulated observers in Bostrom's equation. Then we might have the case where f_i is small yet f_sim is large. The answer is: it would take a lot of these small simulations to overwhelm the ancestor-simulations, since ancestor-simulations are so huge. And given how cheap ancestor-simulations will be (Bostrom estimates < 1µs per run), there's no compelling reason to think these micro-simulations would have a significant effect.

You may also ask, why doesn't Bostrom include other off-the-wall simulations like animal simulations, or simulations of a hypothetical Martian race, or simulations of telepathic humans? The answer is: we know we're not in one of those simulations, so we don't include them in our sum (in probability terms, these simulations are outside our reference class). If you're in Las Vegas and you want to figure out the chance of bumping into an Elvis impersonator, you don't include the population of San Francisco.

Finally you might ask, what if we're being simulated by aliens or some other non-human entity? What if humans don't really exist? This is an intriguing question, and Bostrom doesn't account for it in his equation. But we have literally no reason to believe this is the case, whereas we have empirical evidence that N_i would be large and that humans will go on to run ancestor-simulations if we survive long enough. Faktor argues that malevolent demons could trump all our empirical evidence by warping our logic, and this is true, but then everything we believe about reality becomes suspect, least of all this argument. I'll talk about this a little more in Metaphysical 1.

Practical 4: So what?
Faktor believes that Bostrom's conclusion doesn't have any practical applications.
I totally agree, I don't think this paper will make anyone change his or her life. But, seeing how Faktor is a philosophy major, I doubt he has any problems discussing interesting ideas that have no practical relevance. :) I certainly don't mind (I mean, look at this thread...). And, of course, this isn't a fault with Bostrom's reasoning.

Here is a good place to bring back the pirate booty example:
I'm aware of your example with the pirate treasure buried in the front yard or backyard, but the problem here is that we never get to dig for the treasure to find out, so the point is entirely moot.
My point with the pirate example was not so much that this information is valuable (that depends on whether you can dig for the treasure), but that it's, well, informative. In the Simulation Argument, accepting Bostrom's conclusion greatly reduces the size of the belief set you once held about the future. You've learned something. Even if you don't know which of the three conclusions to believe, at least you know there are only three.

Discobird

November 11th, 2005, 08:22 PM

Metaphysical introduction
Faktor's objections in this domain have less to do with the internal logic of Bostrom's paper than with its epistemological foundations. I'm well aware that induction is unsound, that science's assumption of universality is unprovable, and that empirical results are therefore inherently uncertain. I'll even grant that math and logic might be wrong, although I personally believe they are necessarily true. As I said before, I will settle for merely putting Bostrom's argument on metaphysically equivalent grounds with science.

I'm going to make my job easier by asking, do any of Faktor's metaphysical objections apply to Bostrom's argument but not scientific results or science in general? Does Faktor target the Simulation Argument, or is he making general objections that apply to almost everything we know?

Metaphysical 1
What you have to understand is that when you start calling into question things such as all of reality you're making a metaphysical quagmire. You can only proceed based on assumptions, but you need reasons why you would choose one assumption over another, and by doing so it is questionable what conclusions, if any, can be reached because they are weak conclusions.
I'm sure Faktor already knows this (judging by the next quote), but I want to clarify for the rest of the audience: this statement, while valid, is only interesting if Faktor can show that it applies more to the Simulation Argument than to science or even everyday knowledge. You can always question reality in any context. Whenever you hear about another outbreak of avian flu, question reality; whenever you add 2 + 2, question reality; as you're reading these words on your screen, question reality. All of these actions make fundamentally unsound assumptions about our universe. What Faktor needs to show is that Bostrom's conclusion questions its own assumptions such that the conclusion is invalid.

The problem is that all empirical evidence is gone when all external reality is brought into question such as we have done. Bostrom sides steps this issue by assuming that the simulations are no different from the real world, that is they are mirror copies in all respects, but as I've stated we have no reason to make that assumption.
As Faktor correctly observes, Bostrom's conclusion does not invalidate its own logic. In particular, c3 is not unbounded-- it doesn't say we're probably in any kind of simulation, just an ancestor-simulation run by future humans.* The argument is thus immune to itself.

The only way Faktor can argue around this is to say that Bostrom's assumptions are unfounded. I dealt with this argument in Practical 3.

You may call my objections trivial, but you misunderstand, I am saying his argument is equally trivial.
Except the situation isn't symmetric. We have empirical reasons to believe the truth of Bostrom's conclusion, but we can say nothing about the probability of evil miseducation demons screwing with our minds. Faktor's objections are too broad to target the Simulation Argument. He hasn't shown that the Simulation Argument is unusually susceptible to demonic creators, nor has he shown that it rests on metaphysically stronger assumptions than any scientific result. If Faktor believes Bostrom's argument is trivial, he should also believe science is trivial.

This equation is distinctly different from any other scientific equations because it's not actually based on empirical evidence.
Bostrom's estimate of N_i, and his subsequent conclusion, is based on empirical evidence (namely, calculations on the computing power of future civilizations baesd on our current knowledge of physics and nanotech, which is empirical).

*I shortened c3 to say just "simulation" in my original post for brevity, but this is what Bostrom and I mean.

Metaphysical 2: So what?
Faktor believes that Bostrom's equation "doesn't amount to shit" since he never justifies the significance of the difference between simulation and reality.

Faktor imposes an impossibly high standard on Bostrom's paper. Should acoustic physicists qualify all of their articles by defending their definition of "sound?" Of course not. Bostrom assumes the common definitions of "reality" and "simulation," and it is entirely beyond the scope of his paper to argue about epistemology. His conclusion is worth no less than any other conclusion one can make that assumes an objective reality, including scientific results.

Conclusion
I've defended Bostrom's paper against Faktor's six objections:
Practical 1: Faktor is confused about what it means for an equation to be true. The truth of Bostrom's equation does not depend on one's subjective reality.

Practical 2:Faktor mistakenly thinks we have to plug in values for N. In fact, knowing that N_i is large is sufficient to come to Bostrom's conclusion. We can determine N_i is large from empirical analysis without having to count anything.

Practical 3:Faktor mistakenly thinks that Bostrom must assume future humans will only run ancestor simulations. In fact, Bostrom's c2 represents the opposite! Bostrom's assumptions are sound and not arbitrary.

Practical 4:I agree with Faktor that this argument has little practical significance, but that doesn't mean it's wrong.

Metaphysical 1: Faktor fails to show that the Simulation Argument is more susceptible to metaphysical queries than science itself.

Metaphysical 2:Faktor asks an impossibly high standard of metaphysical justification from Bostrom, one that every scientific paper would fail. It is true that Bostrom's paper isn't a scientific paper per se, but it is empirically grounded and makes no stronger assumptions than science.

Thanks for reading this far.

Discobird

November 11th, 2005, 09:42 PM

I don't think this thread has room to spare for smalltalk.
Ah, I get it... so it's alright for you to reply to my small talk, but when I reply to yours we're suddenly out of room? If you don't think something is worth talking about, don't talk about it. Your flippant remarks aren't helping your case.

I don't know why else you would say "not to belittle". If you felt they were equally worthy manipulations then it shouldn't be an issue of concern.
I was simply pointing out a faster way to arrive at the same conclusion. I didn't know you would take offense to that. If you pointed out some place in my argument where I could've saved time, I'd thank you for it.

What is unit rule, I'm not familiar with that term and neither was my symbolic logic professor. Is it another term for disjunctive syllogism? A v B, ~B therefore A? Because if so that would not have worked in my proof. I did not have ~C1 and ~C2 therefore I could not apply a disjunctive syllogism.
Resolution is a generalized form of that. We don't have ~C1 ^ ~C2, but take a closer look at your original argument. What you did was rearrange the disjunction to arrive at this implication:
(~C1 ^ ~C2) -> C3
Then you said, "I think that you can have (~C1 ^ ~C2) and not conclude C3." You made an implicit proof by contradiction. First you rearranged the original statement, then you said "If ~C1 ^ ~C2, then C3, but I don't agree with that, therefore I disagree with the original disjunction." I'm just saying you could have jumped to the conclusion without needing to manipulate the logic.

~C3

OK, this is assignment 1 of my truth table. So you believe (~C1 ^ ~C2 ^ ~C3) is possible, yes?

I agree that this is possible. The question is whether this is as probable as Bostrom's disjunction. You can argue this two ways: (1) Bostrom's disjunction is unlikely because the reasoning is faulty, etc. (2) Assignment 1 is probable, so Bostrom is wrong because he doesn't account for it in his disjunction.

You've been arguing (1) so far. Now I want to know, do you have positive reason to believe (~C1 ^ ~C2 ^ ~C3) is correct?

Except I don't agree it is rational to believe that they are.
Why not? What's wrong with the reasoning I gave?

No the best we can do is accept the only possible conclusion given the evidence, which is that the answer is inconclusive.
You're conflating the BIP with Bostrom's equation. I already know you don't think there's strong evidence f_sim is near 1. But, if someone believed f_sim was near 1, would it be rational for that person to believe he is probably simulated? If you don't think so, I want to hear your reasons.

I think I can express my problem with Bayesian probability. I was watching TV and there was commercial and it said "2/3 people liked the taste of our product". Does that mean I should believe there is a 66.6% chance that I might like the taste of their product, or that I should believe that there is a strong chance that I might like the taste of their product? Is it rational to think so?
Err, the figure in that commercial isn't a probability.

Now here's a problem with frequentist probability... suppose you're a doctor and you want to know, what is the probability that a patient will develop a certain disease? As a frequentist, you'd want to gather statistics on other patients with similar symptoms, physiology, etc. and see what proportion of them developed the disease. The problem is: how do you define your reference class? If you include all of the patient's characteristics, like her maiden name, her weight in grams, her age in seconds, etc., then you'll end up finding no other patients exactly like her. Your reference class wil have size 1. So how are you supposed to determine what characteristics are important and what aren't, and to what precision? (e.g. her body temperature is important, but not out to the 6th decimal place). You have to make these sort of judgements when defining your reference class, so frequentist probability is really no less subjective than Bayesian probability.

A related problem I have with frequentist probability is that, at the macroscopic level, events aren't really random. We say that coin flips are random, but if we actually knew all the physical characteristics of the coin, and the muscles in your thumb, and the air currents in the room, we could determine if the flip was heads or tails. It's not really random; the concept of random events is a little murky in the real world. Bayesian probability doesn't suffer from this problem because it expresses a degree of belief, not an objective reality.

I'm saying it's possible to believe that we are real and not buy into C1 or C2.
See above re: assignment 1.

I'm curious how that would work in an ancestor simulation. As I understand it you've have to predict the unpredictable.
You're forgetting that the machine has perfect information about the state of the simulated world. In our world, the weather appears unpredictable because we don't know the position and velocity of every air molecule, and we don't have perfect models of the weather anyway. This is not a problem for the computer because it has access to all the relevant state. In fact, perfect prediction is equivalent to simulation from the simulator's POV.

If there's a glitch, the simulator could reset the world, fix it, and erase the memory of the glitch from our minds. None of these actions would violate the assumptions of the Simulation Argument.

FaKToR

November 11th, 2005, 10:29 PM

Is that all? I just finished off watching the 13th Floor again (haven't seen it in years) and I'll see how much I feel like posting before I take a nap before work. I would like to reply to one thing though real quick:

Ah, I get it... so it's alright for you to reply to my small talk, but when I reply to yours we're suddenly out of room? If you don't think something is worth talking about, don't talk about it. Your flippant remarks aren't helping your case.
I really didn't think a major I decided not to pursue in a thread about an entirely different topic was all that important to you. I thought I'd do you the courtesy of explaining why I felt it was unimportant instead of just ignoring you. I didn't think there was anything flippant about it, I was merely stating that this was inconsequential and I did not wish to continue a conversation regarding it.

One more thing, could you use some pronouns instead of saying "Faktor" all the time, that bugs the hell out of me.

Discobird

November 11th, 2005, 11:32 PM

One more thing, could you use some pronouns instead of saying "Faktor" all the time, that bugs the hell out of me.
Sorry, didn't mean to annoy you. I wrote my post that way since it wasn't in the quote-and-reply format and I wanted to address a wider audience.

FaKToR

November 11th, 2005, 11:33 PM

Before I post, perhaps you could clarify what exactly does it mean to be random?

Discobird

November 11th, 2005, 11:40 PM

Before I post, perhaps you could clarify what exactly does it mean to be random?
If you're referring to this line:
It's not really random; the concept of random events is a little murky in the real world.
I'll put it like this: a real-world event X is random iff 0 < P(X|complete state of the universe) < 1

FaKToR

November 11th, 2005, 11:41 PM

Could expand on that perhaps?

Edit: This seems to be fudging half way between a probability and a statistic. Like a probability it doesn't represent real world values, but like a statistic we don't know that the events are equally likely. However with a statistic we find credibility in that we actually calculate a value and it can be tested.

Discobird

November 11th, 2005, 11:44 PM

I guess another way to put it is, call a real-world event random if it's nondeterministic. In frequentist terms, if I were to run many experiments, reseting the entire state of the universe each time, then sometimes the event would occur and sometimes it would not.

[EDIT]
I guess I should clarify a few terms first:

Frequentists and Bayesians (or subjectivists) differ in their definitions of "probability." To a frequentist, probability expresses the fraction of times an event would be observed as the limit of trials goes to infinity. So if a frequentist says P(X) = r, he thinks that, as you run more and more experiments, the fraction of them in which X happened will approach r.

From a Bayesian viewpoint, probability expresses the degree of belief an agent has that an outcome will occur.

In a coin-tossing experiment, a frequentist might conclude that P(Heads) = 1/2 after tossing many coins and observing that 1/2 of them land heads. My point is that each trial will not be exactly the same-- the coins are tossed from minutely different heights with different forces and different room conditions-- so the frequentist cannot make an objective conclusion about P(Heads).

From a frequentist perspective, I interpret "random" to mean the opposite of nonrandom. A random event is neither guaranteed to happen nor guaranteed to not happen-- P(X) != 0 and P(X) != 1.

I don't think there are any truly random macroscopic events in our world. I'm deterministic about such events.

[EDIT #2]
As I understand it, frequentists view events as having some objective, intrinsic probability, and we discover these probabilities by running experiments. Subjectivists, on the other hand, are agnostic about the objective reality of probability. They don't make any objective claims.

FaKToR

November 12th, 2005, 01:17 AM

Let's take a step back here and clarify what it means for an equation to be true. An equation is true if and only if the left side of the equation equals the ride side of the equation. I know this sounds trivial, but I have to spell it out since Faktor seems to think truth means something else.
You misunderstood my statement, the problem comes in applying this. Remember that image you had of the worlds within each other? Recall how the averages were calculated? For example the average number of individuals that have lived in a civilization before it reaches a posthuman stage would be a summation of {H1, H2, H3...Hn} (and then divide this by the number of civilizations to get our average). From our perspective we deal only with Hx, with x being one of the H values that comprise the total number of observes used to calculate the average number of individuals that have lived in a civilization before it reaches a posthuman stage. But if you were to take an omniscient view of all this you would have other values accompanying the one we have. The two fractions will yield different values (unless we're the only civilization).

Now then I say it is not sufficient to apply this equation in our world because we would be (possibly) excluding values, however the only way that we can possibly attempt to apply this equation is within the context of our world.

The only sensible interpretation I can think of is that we can only observe our own realm, in which case this sentence belongs under Practical 2 (variable values).
Unlike your simulated world, I'm not perfect. Don't be surprised to find errors.

This belongs under Practical 4, concerning the value of Bostrom's conclusion. It doesn't have anything to do with perspective, so I don't know why Faktor put this under Practical 1.
I didn't want to forget it, so I plugged it in there. I had not written part 4 when I wrote that.

Faktor's entire argument here ignores the fact that we don't need to plug in a value for N to come to Bostrom's conclusion.
I would like to start off by saying I am frustrated by this problem because if this equation doesn't have some applicable use to determining which of the three disjunctions we're living in, then it seems rather useless because the scope of those three disjunctives is very broad.

Faktor believes that our value of N is irrelevant since it's possible that N is very high and we're real, or N could be very low and we're simulated.
Actualy given the disjunction and my translation of it to (~C1 ^ ~C2) -> C3 this shouldn't be possible. This would be ((~C1 ^ ~C2) ^ ~C3) which shouldn't be possible.

Did you know that, although millions of other people buy lottery tickets, it's still possible for you to win? Whoa!
Except the resulting probability that I'll win the lottery isn't a reflection of a believe. I can either win the lottery or I can lose, therefore I have a fifty-fifty chance right?

Recall you said:
Let's say f_sim = 0.5. This does not mean that 3 billion people in this world are real and 3 billion are simulated. It means that either this entire world is real or this entire world is simulated.
Whereas with the lottery if the chance of me losing is 50% (what a lucky lotto that'd be) that doesn't mean I lost.

The alternative is that N_i is extremely small, yet we're one of the few simulated observers, which by the Bland Indifference Principle we should believe to be unlikely.
I must have missed that part, why should we believe it to be unlikely?

Computational power isn't in the equation. I think when he says computational power he means N_i, which I will assume for the rest of this reply since it's the only explanation that makes sense.
You assume correct.

It amazes me that Faktor is still making these basic comprehension errors so late in the debate. This is a straight-up misreading of the text.
I didn't think he could be meaning that, because his conclusions would then be so vague as to be of no value in determining something about our world.

The answer is: it would take a lot of these small simulations to overwhelm the ancestor-simulations, since ancestor-simulations are so huge. And given how cheap ancestor-simulations will be (Bostrom estimates < 1µs per run), there's no compelling reason to think these micro-simulations would have a significant effect.
That's kind of an important thing to make such an assumption on.

If you're in Las Vegas and you want to figure out the chance of bumping into an Elvis impersonator, you don't include the population of San Francisco.
This gets back to my first practical objection regarding POV. Now our simulation (if it's that) might be such that it's the 21st century. But then what if all the other simulations are simulations that exclude humans?

But we have literally no reason to believe this is the case, whereas we have empirical evidence that N_i would be large and that humans will go on to run ancestor-simulations if we survive long enough.
That assumes we're not simulations in the first place though. If we are simulations and we go on to run simulations we can still be the creation of aliens or what have you. I'm not sure I follow why you chose to exclude it when we have no more information regarding the possibility of that than we do that humans do exist?

Also I think this helps bring out two questions. First is it possible that we are in a cicrle of simulations e.g. there are three simulations, S1 creates a simulated world S2. S2 creates a simulated world S3. S3 creates a simulated world S1.

Another possibility is that if a real posthuman civilization does end up running a bunch of simulations, wouldn't it be likely given the size of N that one of the simulations would end up creating simulations? And then given the size of N wouldn't it be likely that the newly simulated civilization will create simulations, some of which will create simulations of their own and so on ad infinitum?

My point with the pirate example was not so much that this information is valuable (that depends on whether you can dig for the treasure), but that it's, well, informative. In the Simulation Argument, accepting Bostrom's conclusion greatly reduces the size of the belief set you once held about the future. You've learned something. Even if you don't know which of the three conclusions to believe, at least you know there are only three.
Actually I disagree that it's philosophically interesting, which I expressed much earlier talking about an irrelevant approach to an obvious conclusion. We start out looking for an answer to the question, are we simulated? And we end up right back were we started. Tell me what is the significant difference between Bostrom's disjunction and the statement "either we're a simulation or we're not" (besides the fact that Bostrom has two disjunctions)?

FaKToR

November 12th, 2005, 01:45 AM

I'm going to make my job easier by asking, do any of Faktor's metaphysical objections apply to Bostrom's argument but not scientific results or science in general? Does Faktor target the Simulation Argument, or is he making general objections that apply to almost everything we know?
Does it change the veracity of the simulation argument if I do call everything into question or only it? Either way it is included. Recall now solipsistm is a close description of my view of the world.

What Faktor needs to show is that Bostrom's conclusion questions its own assumptions such that the conclusion is invalid.
I've said this several times now. F = ma, when we use that we don't say universally, simulated or not, that F = ma. No, we say given our current "reality" F = ma. Bostrom's equation is fundamentally different because it's making an assumption about what it is attempting to determine. If I was trying to determine if I live in a simulation or some other abstraction I could not reliably employ techniques that I've only tested in my possibly simulated/imagined/whatever world. That would be begging the question.

As Faktor correctly observes, Bostrom's conclusion does not invalidate its own logic. In particular, c3 is not unbounded-- it doesn't say we're probably in any kind of simulation, just an ancestor-simulation run by future humans.* The argument is thus immune to itself.
What are you talking about? I look at what I said, and I look at your reply and I don't see a connection.

We have empirical reasons to believe the truth of Bostrom's conclusion, but we can say nothing about the probability of evil miseducation demons screwing with our minds.
We do not have empirical evidence, that would be begging the question. Assuming that the world we live in is an accurate reflection of reality, then Bostrom's disjunctions follow, but if we assume the world we live in is not an accurate reflection of reality e.g. our knowledge of computational power is being manipulated to mislead us, then Bostrom's disjunctions do not follow. You have to recall that simulations are not the only possible abstractions for our existence e.g. we may just be someone's vivid dream.

He hasn't shown that the Simulation Argument is unusually susceptible to demonic creators, nor has he shown that it rests on metaphysically stronger assumptions than any scientific result. If Faktor believes Bostrom's argument is trivial, he should also believe science is trivial.
When it comes to dealing with metaphysical questions I do.

Bostrom's estimate of N_i, and his subsequent conclusion, is based on empirical evidence (namely, calculations on the computing power of future civilizations baesd on our current knowledge of physics and nanotech, which is empirical).
Again these calculations are possibly based on a simulated world. It may very well not be empirical.

Faktor imposes an impossibly high standard on Bostrom's paper. Should acoustic physicists qualify all of their articles by defending their definition of "sound?" Of course not. Bostrom assumes the common definitions of "reality" and "simulation," and it is entirely beyond the scope of his paper to argue about epistemology. His conclusion is worth no less than any other conclusion one can make that assumes an objective reality, including scientific results.
Acoustic physicists have a common standard (AFAIK) with regard to what constitutes sound, philosophers do not have that standard when it comes to metaphysical questions about reality or epistemological questions about knowledge. Though I'm sure if there are issues of contention amongst acoustic physicists they'll definitely go about defining the terms their evidence supports. It is essential to Bostom's paper that he qualify these issues, otherwise he has said nothing of any value, short of "either we're a simulation or we're not" just in a very roundabout way.

Faktor asks an impossibly high standard of metaphysical justification from Bostrom, one that every scientific paper would fail. It is true that Bostrom's paper isn't a scientific paper per se, but it is empirically grounded and makes no stronger assumptions than science.
Is this a scientific discussion or a philosophical one because the primary way I would approach this is through philosophical means. I think it's telling that Bostrom's paper says "Department of Philosophy" at the top.

FaKToR

November 12th, 2005, 02:26 AM

I was simply pointing out a faster way to arrive at the same conclusion. I didn't know you would take offense to that. If you pointed out some place in my argument where I could've saved time, I'd thank you for it...I'm just saying you could have jumped to the conclusion without needing to manipulate the logic.

I thought it would be a good idea to show my work.

OK, this is assignment 1 of my truth table. So you believe (~C1 ^ ~C2 ^ ~C3) is possible, yes?
Yes.

Now I want to know, do you have positive reason to believe (~C1 ^ ~C2 ^ ~C3) is correct?
Nope. I'd phrase it this way, I have as much reason to believe (C1 v C2) v C3 as I do to believe ((~C1 ^ ~C2) ^ ~C3), which is no reason.

Why not? What's wrong with the reasoning I gave?
I view it as we have no evidence one way or the other in which case the two probabilities would be equivalent in the sense that they are both undefined.

You're conflating the BIP with Bostrom's equation. I already know you don't think there's strong evidence f_sim is near 1. But, if someone believed f_sim was near 1, would it be rational for that person to believe he is probably simulated? If you don't think so, I want to hear your reasons.
Tbh, I'm not sure.

Err, the figure in that commercial isn't a probability.
I'm aware of that.

Now here's a problem with frequentist probability... suppose you're a doctor and you want to know, what is the probability that a patient will develop a certain disease?
That's a bit of a trick question because you wouldn't construct a probability for that situation. Instead you would measure a statistic.

A related problem I have with frequentist probability is that, at the macroscopic level, events aren't really random. We say that coin flips are random, but if we actually knew all the physical characteristics of the coin, and the muscles in your thumb, and the air currents in the room, we could determine if the flip was heads or tails. It's not really random; the concept of random events is a little murky in the real world. Bayesian probability doesn't suffer from this problem because it expresses a degree of belief, not an objective reality.
Statistical randomness doesn't imply true randomness though, it merely imlies that there is no patterns.

If there's a glitch, the simulator could reset the world, fix it, and erase the memory of the glitch from our minds. None of these actions would violate the assumptions of the Simulation Argument.
Of course the only way in which the computer can evaluate what is going is through its inexact floating-point number situation. It can fix the errors, but its corrections will also be susceptible to rounding errors and this could manifest itself as an error increasing in severity, correct?

Discobird

November 12th, 2005, 04:46 AM

Nope. I'd phrase it this way, I have as much reason to believe (C1 v C2) v C3 as I do to believe ((~C1 ^ ~C2) ^ ~C3), which is no reason.
OK.

I view it as we have no evidence one way or the other in which case the two probabilities would be equivalent in the sense that they are both undefined.
You can't tell if you're simulated or not, but you believe that 99% of people like you are simulated. How is it not rational to conclude that you are probably simulated?

This is like the situation with the urn and tokens. You don't know what color token you just pulled, but you believe the urn has 99 white tokens and 1 black one. Do you think it's irrational to put 99% credence in your token being white? Or do you require 100% confidence before you begin holding any belief?

Personally I think the BIP is the soundest part of the proof, but that may not mean much to you. :p

[EDIT] Remember that a credence is not a binary true or false... it's a real number in [0, 1] that describes your degree of belief in the statement.

I'm aware of that.
So how does this express a problem with Bayesian probability?

That's a bit of a trick question because you wouldn't construct a probability for that situation. Instead you would measure a statistic.
Can you expand on what you mean here? How would a frequentist answer the patient? Surely you don't mean that P(patient has disease) doesn't exist?

Statistical randomness doesn't imply true randomness though, it merely imlies that there is no patterns.
I don't know if you saw my edit clarifying my position (post #101 (http://forums.worldatwarmod.com/showpost.php?p=110369&postcount=101)), but my understanding of frequentist probability is that it seeks to approximate objective probabilities using experimental data. If it doesn't do this, what exactly are we approximating?

Of course the only way in which the computer can evaluate what is going is through its inexact floating-point number situation. It can fix the errors, but its corrections will also be susceptible to rounding errors and this could manifest itself as an error increasing in severity, correct?
First, let's clarify-- when we say errors, we mean deviation from some reference state, correct?

The computer always knows exactly what is going on inside itself. Suppose some variable b has value 4.998 when it should equal 5. Upon noticing this error, the computer can simply set b to 5. There's no error propagation here.

FaKToR

November 16th, 2005, 12:11 AM

You can't tell if you're simulated or not, but you believe that 99% of people like you are simulated. How is it not rational to conclude that you are probably simulated?
That's not specifically what I was replying to if you'll go back a ways you'll find you said:
It doesn't mean that that the two are equally likely, but the most rational possible belief is that they are.

I don't agree with that, from which follows that the two events are equal in the sense that they are both undefined.

This is like the situation with the urn and tokens. You don't know what color token you just pulled, but you believe the urn has 99 white tokens and 1 black one. Do you think it's irrational to put 99% credence in your token being white? Or do you require 100% confidence before you begin holding any belief?
The tokens just bring us back to an issue of perspective. :(

Personally I think the BIP is the soundest part of the proof, but that may not mean much to you.
You're right it doesn't.

So how does this express a problem with Bayesian probability?
Because I still don't see Bayesian probability as being a probability, even if it was I don't know why I should make a conclusion based upon it. For example you might conclude that the probability of the universe existing is very unlikely and that would be a safe bet to say we most likely wouldn't exist, yet we have the problem of knowing that our universe does exist (in some sense). I think this is where the inverse gamblers fallacy starts to come in, though you're not making conclusions about the universe being the creation of a deity, you're making conclusions about the universe being the creation of a some entity(ies).

Can you expand on what you mean here? How would a frequentist answer the patient? Surely you don't mean that P(patient has disease) doesn't exist?
Why not? Must everything have a probability? Keep in mind we understand this all in case of a random event. Either the randomness of conditions which we cannot take into account such as the all the factors influencing a coin toss or the random sample that is used in calculating a statistic. But as you've observed the world is not random, least not on the macroscopic level given enough information. This creates a dilemma because then probabilities for predicting future events don't really exist, things are what they are and could not have happened any other way.

Now if I was to do a statistic I would attempt to formulate a random sample of the population to which the patient belongs, looking for characteristics that would most likely yield the most significant effects (keep in mind I'm no expert on statistics here, so maybe I'm wrong). Does a probability exist, I'm not sure given my previous paragraph. If it did though we wouldn't know it and the best we could do is approximate it using knowable, similar real world values. Keep in mind this differs from Bostrom in that with a statistic you actually use values. A statistic is not an algorithm itself, but instead is the result of applying that algorithm to a set of data.

I don't know if you saw my edit clarifying my position (post #101), but my understanding of frequentist probability is that it seeks to approximate objective probabilities using experimental data. If it doesn't do this, what exactly are we approximating?
You were saying that things need not be unpredictable. I'm saying that statistics doesn't depend on that level of randomness, pseudorandomness would suffice, so long as there is no pattern at least as I understand it.

First, let's clarify-- when we say errors, we mean deviation from some reference state, correct?
I'm not sure how exactly this ancestor simulation works, but I'm guessing it's an exact iterative model of our world (our world being the 21st century) yes? I don't know what you'd referencer about specific instances beyond the application of the physical laws this world presumptively models. I'm wondering if significant deviations could be created, in the long term, by rounding errors which then go on to effect other calculations.

The computer always knows exactly what is going on inside itself. Suppose some variable b has value 4.998 when it should equal 5. Upon noticing this error, the computer can simply set b to 5. There's no error propagation here.
How does the computer know some number should equal five? What exactly is being referenced? Keep in mind any data stored on the computer would be susceptible to floating-point precision problems as is the inherent flaw of storing unlimited (or significantly large) amounts of data on a finite medium.

Also I would like to take this opportunity to point out that there are flaws in our logic (you seemed to think the idea our logic could be manipulated wasn't very plausible). At least there are shortcomings in the ability of our logic to describe the world just as there are in our natural language to do so. For example I direct you to Russel's paradox, Quine's paradox, the barber paradox, or the statement "nothing is certain".

Discobird

November 16th, 2005, 03:58 AM

Now then I say it is not sufficient to apply this equation in our world because we would be (possibly) excluding values, however the only way that we can possibly attempt to apply this equation is within the context of our world.
I think we're talking past each other here... I agree that the equation cannot be applied in the sense that we can fill in every variable and arrive at a value for f_sim. But this is a non-issue since we can estimate N_i without needing to count H's or anything else, and knowing N_i is sufficient to reach Bostrom's conclusion. Also remember that, in the final form of the equation, H (# of real observers) and C (total # of civilizations) factor out so we wouldn't need them anyway.

Actualy given the disjunction and my translation of it to (~C1 ^ ~C2) -> C3 this shouldn't be possible. This would be ((~C1 ^ ~C2) ^ ~C3) which shouldn't be possible.
I'm not entirely sure how to approach this since it's a reply to my paraphrasing of your objection. But is this what you mean?

(1) Bostrom's disjunction: (C1 v C2 v C3)
(2) It is possible that (~C1 ^ ~C2 ^ ~C3)
(c) (2) is impossible given (1), therefore (1) is false.

If so, we should remember that (1) is phrased probabilistically, not absolutely-- each of C1, C2, and C3 are couched in terms of likeliness ("very likely," "extremely unlikely," and "almost certainly" are the terms Bostrom uses). Thus (1) doesn't preclude (~C1 ^ ~C2 ^ ~C3), it just says that it's very unlikely as far as we can tell. If we could somehow observe that (~C1 ^ ~C2 ^ ~C3) were true, it wouldn't necessarily make Bostrom's conclusion wrong.

By analogy (oh boy, another one), imagine that you were trapped in a burning building with a fire exit directly in front of you. You believe you have a 90% chance of survival if you take the exit and a 1% chance of survival if you stay where you are. So, not having a death wish, you run for the exit. Suddenly Chuck Norris steps out of the shadows and roundhouse kicks you into a burning room. Game over.

Was it rational to run for the exit? Of course it was, since you had no information suggesting that Chuck Norris was waiting for you. I could argue that Chuck Norris is so good at hiding that you can never tell if he's skulking in the shadows, but that doesn't change the fact that a rational person should always choose to run for the exit.

This isn't a perfect analogy, but running for the exit is like believing Bostrom's disjunction while Chuck Norris is all the possible alternate conclusions. Even though alternate conclusions like (~C1 ^ ~C2 ^ ~C3) are possible, it's still rational to believe in the disjunction. It's the best we can do with the information we have, and the quality of that information is at least as good as the information we act upon every day. You will probably argue that it's still inadequate, but that's for the metaphysical objections which I'll address in the next post.

Except the resulting probability that I'll win the lottery isn't a reflection of a believe. I can either win the lottery or I can lose, therefore I have a fifty-fifty chance right?
No, I wasn't talking about the BIP when I used the lottery example. I was making the same argument I've just made above-- even though your chance of winning is very low, it doesn't mean it's impossible for you to win, just like Bostrom's disjunction doesn't mean (~C1 ^ ~C2 ^ ~C3) is impossible. This is my fault for choosing a poor example with inadequate explanation, sorry.

I must have missed that part, why should we believe it to be unlikely?
Let me think about this a bit.

That's kind of an important thing to make such an assumption on.

What assumption? It's true that micro-simulations like I described are much smaller than ancestor simulations, so it's true that a very large number of them must be run to have a significant effect compared to the ancestor-simulations. I think Bostrom's equation is robust even though it doesn't account for micro-simulations.

This gets back to my first practical objection regarding POV. Now our simulation (if it's that) might be such that it's the 21st century. But then what if all the other simulations are simulations that exclude humans?
Simulations without humans aren't part of our reference class so they're not counted in anything. They'll never show up in any of the variables in the equation.

That assumes we're not simulations in the first place though.
I've argued that our large estimate of N_i is resistant to us being in an ancestor-simulation, so this assumption isn't really being made.

If we are simulations and we go on to run simulations we can still be the creation of aliens or what have you. I'm not sure I follow why you chose to exclude it when we have no more information regarding the possibility of that than we do that humans do exist?
I exclude it because Bostrom doesn't attempt to be more metaphysically sound than the science his paper is based upon, and science rejects these possibilities out of parsimony.

Also I think this helps bring out two questions. First is it possible that we are in a cicrle of simulations e.g. there are three simulations, S1 creates a simulated world S2. S2 creates a simulated world S3. S3 creates a simulated world S1.
I can imagine S3 creating something like S1, say S1', but how is it possible that it could create S1 itself? That would be like you giving birth to your grandmother.

Another possibility is that if a real posthuman civilization does end up running a bunch of simulations, wouldn't it be likely given the size of N that one of the simulations would end up creating simulations? And then given the size of N wouldn't it be likely that the newly simulated civilization will create simulations, some of which will create simulations of their own and so on ad infinitum?
The recursion must stop somewhere unless the parent computer somehow has infinite computational resources. Any finite computer would exhaust its memory pretty quickly since a simulation's space complexity is exponential in its nesting depth.

Tell me what is the significant difference between Bostrom's disjunction and the statement "either we're a simulation or we're not" (besides the fact that Bostrom has two disjunctions)?
Because if you think we're not in a simulation, you're forced to choose between apocalypse or a curiously powerful (ethical?) consensus among our descendants to not run ancestor-simulations.

IMO the disjunction is especially significant since I think c2 is unlikely (given the technological means, how could our future civilizations all agree not to run ancestor simulations)? So for me it's more like a choice between apocalypse and simulation, which I hope you'll agree is philosophically interesting.

Even if you give more weight to c2 the disjunction is still interesting when you think about how c2 could come about. A universal moral code? Faster than light communication? These are all interesting consequences of accepting Bostrom's disjunction.

-------------------------
[EDIT]
To illustrate this point, imagine a conversation with Joe Average off the street:

You: "Mr. Average, do you think humans will eventually be able to simulate human minds on computers?"
Mr. Average: "Eventually? Sure, I guess. I mean, when I was born computers were still the size of rooms, and now look how small my iPod is. *waves iPod*."
You: "Do you think humans will wipe each other out before then?"
Mr. Average: "Hmm... maybe, but probably not, if you ask me. I think we're responsible enough not to let that happen."
You: "Then you should believe you're being simulated, RIGHT NOW."
Mr. Average: "wtf h4x"

Discobird

November 18th, 2005, 03:44 AM

I don't agree with that, from which follows that the two events are equal in the sense that they are both undefined.
I think we've reached a cycle in our argument here since I don't have anything to say to this that I haven't already said.

The tokens just bring us back to an issue of perspective. :(
As above.

Because I still don't see Bayesian probability as being a probability, even if it was I don't know why I should make a conclusion based upon it.
Let me ask you this, how do you reason about uncertain events? What qualities must a probability possess before you can make a conclusion based upon it?

Bayesian probability encodes our degree of belief in a given outcome. It's assigning a real number in [0,1] to the outcome where 1 means you're certain it will happen, 0 means you're uncertain, and numbers in between express degrees of certainty corresponding to their position between 0 and 1. It's not probability the same way frequentists see probability. Nevertheless, it's convenient to manipulate Bayesian probabilities the same way we manipulate frequentist probabilities, they offer an intuitive rationale for certain ideas (e..g conditional probability-- what exactly does it mean for a probability to increase given new information?), and they work well in modeling real rational agents. And you very likely use Bayesian probability every day when you talk about uncertainty with other people.

For example you might conclude that the probability of the universe existing is very unlikely and that would be a safe bet to say we most likely wouldn't exist, yet we have the problem of knowing that our universe does exist (in some sense). I think this is where the inverse gamblers fallacy starts to come in, though you're not making conclusions about the universe being the creation of a deity, you're making conclusions about the universe being the creation of a some entity(ies).
That's a problem specific to the fine-tuning argument and not a fault of Bayesian probability. Bostrom's argument has nothing to do with the apparent suitability of the universe for life. Besides which, a lot of the fine-tuning arguments take an implicitly frequentist approach (i.e. assuming that cosmological constants are uniformly drawn from some interval, and that this particular universe must therefore be a priori unlikely given all the possible universes that could have been created).

Why not? Must everything have a probability?
I think it's reasonable to ask about the probability of an outcome like this. If you can't answer that question, what can you answer? Frequentists usually say P(Heads) exists, so what's the fundamental difference between that and this example with the patient?

This creates a dilemma because then probabilities for predicting future events don't really exist, things are what they are and could not have happened any other way.
Yeah, that's the problem I have with applying frequentist probabilities to the real world. On the other hand, frequentist probability makes for nice theoretical results.

Now if I was to do a statistic I would attempt to formulate a random sample of the population to which the patient belongs, looking for characteristics that would most likely yield the most significant effects (keep in mind I'm no expert on statistics here, so maybe I'm wrong). Does a probability exist, I'm not sure given my previous paragraph. If it did though we wouldn't know it and the best we could do is approximate it using knowable, similar real world values.
1) You still have the problem of picking an appropriate reference class. There might be important details about the patient that you can't incorporate because your reference class would be too small, e.g. the patient has a history of working with particular dangerous chemicals in previous jobs.

2) If you accept that frequentist probability is as subjective as Bayesian probability in real world application, then Bayesian probability is strictly more powerful since it can incorporate statistics. The doctor can perform all the same statistical tests, then use his own judgement and detailed knowledge of the patient to adjust his beliefs. Alternatively, if he thinks statistics are sufficient then he can simply go with the statistics.

You were saying that things need not be unpredictable. I'm saying that statistics doesn't depend on that level of randomness, pseudorandomness would suffice, so long as there is no pattern at least as I understand it.
There's a difference between statistics and probability. I was making a statement about how frequentist probability is no more objective than Bayesian probability. I agree that statistics cannot perfectly represent true probabilities, in fact that's the point I was trying to make.

How does the computer know some number should equal five? What exactly is being referenced? Keep in mind any data stored on the computer would be susceptible to floating-point precision problems as is the inherent flaw of storing unlimited (or significantly large) amounts of data on a finite medium.
You confused me because "error" means something very specific in control theory, and that's the definition I proffered in my last post. What you're describing is more accurately called numerical stability. I haven't studied it so I don't know much about it, but a little Googling suggests that judicious choice of algorithms and small time steps will keep floating-point errors predictably low instead of blowing up.

Remember that the simulation doesn't have to be absolutely perfect. It only has to be good enough that our descendants would want to run it and we couldn't tell we're being simulated. Sure, it's possible for media to become corrupted, just like it's possible your CPU will make an erroneous computation when a stray cosmic ray passes through your room (I believe IBM did some experiments with lead-encased computers in the '70s about this...). It doesn't mean our descendants will never run ancestor-simulations, only that they should follow good engineering practice and design their systems as robustly as possible.

Also I would like to take this opportunity to point out that there are flaws in our logic (you seemed to think the idea our logic could be manipulated wasn't very plausible). At least there are shortcomings in the ability of our logic to describe the world just as there are in our natural language to do so. For example I direct you to Russel's paradox, Quine's paradox, the barber paradox, or the statement "nothing is certain".
I recognize that logic is incomplete. That's not the point I'm making. Rather, I'm saying that I don't believe logic can operate differently in the toplevel reality than it does here.