# Pascal's wager re-examined

post by PhilGoetz · 2011-10-05T08:43:56.508Z · LW · GW · Legacy · 120 comments

Let P(chr) = the probability that the statements attributed to Jesus of Nazareth and Paul of Tarsus regarding salvation and the afterlife are factually mostly correct; and let U(C) be the utility of action C, where C is in {Christianity, Islam, Judaism, atheism}.

Two of the key criticisms of Pascal's wager are that

• limit U(Christianity)→∞, P(chr)→0 P(chr)U(Christianity) is undefined, and
• invoking infinite utilities isn't fair.

If, however, P(chr) is not infinitessimal, and U(Christianity) is merely very large, these counter-arguments fail.

Many poor arguments have been made that P(chr) > .1.  But as far as I know, no one has ever made the best argument in favor of Christianity:

• Let P(sim) be the probability that we are living in a simulation.
• Let P(ent|sim) be the probability that this simulation was created for entertainment purposes, as opposed to purposes including scientific, economic, or governmental reasons.
• Let P(ego|ent, sim) be the probability that the person or organization running our simulation wants to be personally glorified within their simulation, and therefore created an avatar of themselves, or represented themselves in myth, or in some other way put some being into the sim whose status in the sim they identify with.
• Let P(chr0|ego, ent, sim, Earth) be the probability, given the observed history of Earth, that, of the various candidate religions or leaders or possible avatars, this egoist God is using Christianity.  (The same argument applies for Islam.  Judaism has a different payoff matrix.  I'm deliberately ignoring polytheistic religions.)
• Let P(follow-thru | chr0, ego, ent, sim, Earth) be the probability that our simulator God, on Earth, who is representing itself via Christianity, will follow through on promises of implementing Heaven and Hell - if not for an infinite time period, then for a long enough time periods that your utility is at least 99% afterlife.  Heaven and Hell could provide utility/disutility much greater than a human lifespan even if they run only until the end of game.  I imagine that pure torment could provide more than a lifetime's worth of disutility in a few days or weeks.
• Then P(chr) > P(sim)P(ent|sim)P(ego|ent,sim)P(chr0|ego,ent,sim,Earth)P(follow-thru|chr0, ego, ent, sim, Earth).

If you accept the simulation argument, then P(sim) > .99.

If you look at the fraction of computing power used for entertainment, I don't know what it is, but the top 100 supercomputer list for June 2011 lists a total of 4,531,940 cores in the top 100 supercomputers in the world; versus (rough guess) a billion personal computers and video game consoles, and a similar number of ordinary computers used at work.  It would be reasonable to set p(ent|sim) = .5.

If you set P(ego|ent, sim) according to the fraction of entertainment simulations in which the person playing the game has an avatar in the game, then P(ego|ent, sim) is large.  I originally set this at p > .99, but am now setting it to p = .5 in response to Jack's comment below.

We notice there are no obviously immortal world leaders on Earth (but see vi21maobk9vp's comment below).  If we therefore limit the possible avatars that our simulator God is using on Earth to the major monotheistic religions of Christianity, Islam, and Judaism, and consider them all equiprobable; plus a 25% chance that this God is jumping from one avatar to another, or chose to reveal Himself via Jesus but then Paul screwed everything up, or some other minority position; then p(chr0|ego, ent, sim, Earth) = .25.

P(follow-thru) is difficult to estimate; I will set it somewhat arbitrarily as .1.  Given our observations of game-players here on Earth, it is not independent of p(ego), as players of self-glorifying games are likely to be young adolescent males, and so are people who enjoy burning insects with magnifying glasses.

We now have p(chr) > .99 x .5 x .5 x .25 x .1 = .0061875.  As stipulated, your afterlife accounts for at least 99% of your utility if follow-thru (and hence chr) is true.  If we suppose that the length of time for which God rewards us in Heaven or torments us in Hell has an exponential distribution, and we are considering only the part of that distribution where >= 99% of your utility is in the afterlife, then almost certainly p(chr) * U(Christianity | chr) > (1-p(chr)) * U(atheism | not(chr)). It now appears we should accept Pascal's wager.

(The expected utilities for Christianity and Islam are similar, and this argument gives no reason for favoring one over the other.  That is of only minor interest to me unless I accept the wager.  The important point is that they both will have expected utilities similar to, and possibly exceeding, that of atheism.)

You can argue with any of the individual numbers above.  But you would have to make pretty big changes to make p(chr)(U(Christianity|chr)) negligible in your utility calculation.

(IMHO, voting this article up should indicate it passed the threshold, "That's an interesting observation that contributes to the discussion", not, "Omigod you're right, I am going out to get baptized RIGHT NOW!".)

comment by lessdazed · 2011-10-04T07:28:43.693Z · LW(p) · GW(p)

We notice there are no immortal world leaders on Earth.

There's no way you could possibly know that unless...Phil...you...you killed them all! How could you?!

Replies from: PhilGoetz
comment by PhilGoetz · 2011-10-04T14:58:47.114Z · LW(p) · GW(p)

With the legendary item I chose on reaching tenth level, of course - this +5 Sword of Smiting.

Wait... you're not an NPC, are you?

comment by Jack · 2011-10-04T07:52:28.652Z · LW(p) · GW(p)

Two things I haven't seen anyone else point out.

If you set P(ego|ent, sim) according to the fraction of entertainment simulations in which the person playing the game has an avatar in the game, then P(ego|ent, sim) > .99.

The most popular PC games ever are The Sims and The Sims 2. Then World of Warcraft which is a multiplayer game. Single player games with avatars do not make up 99% of the market, not even close. And that says nothing about the non-electronic games people play like sports and dating which are almost all multi-player.

We notice there are no immortal world leaders on Earth.

Quite a few have not died yet. One might infer from history that they will- but once you decide we're in an entertainment simulation that evidence is worth little- the simulation may have just begun. I suggest you seriously consider swearing allegiance to Kim Jong Il. Further, there is no particular reason to assume the player is any good at the game- perhaps she died without saving in 500 BCE.

In general the probabilities are really off and you haven't dealt with the issue of having extreme utilities for competing choices (should I choose Christianity or Islam or trying to extend my life and save the world?). But I upvoted because it is kind of interesting and not deserving of -7, though I predict it will go much lower than that.

Replies from: gwern, PhilGoetz
comment by gwern · 2011-10-04T15:35:51.396Z · LW(p) · GW(p)

But I upvoted because it is kind of interesting and not deserving of -7, though I predict it will go much lower than that.

http://predictionbook.com/predictions/3581

Replies from: gwern
comment by gwern · 2011-11-04T15:42:39.059Z · LW(p) · GW(p)

Prediction marked correct.

comment by PhilGoetz · 2011-10-04T14:44:53.790Z · LW(p) · GW(p)

The most popular PC games ever are The Sims and The Sims 2. Then World of Warcraft which is a multiplayer game.

I didn't know that about the Sims. That's what Wikipedia says also. But the number of video-game console games sold is several times the number of PC games sold. The next-best-selling games appear to be Wii Sports and Tetris. But, Wii sports was bundled with the console and often never played; and tetris is a phone game which has very little CPU power - there are reasons this is important, but I don't have time to explain.

So p(ego|...) needs revision - probably to somewhere between .5 and .9.

p(ego) and p(follow-thru) might not be independent. The demographics of players playing what I call 'ego' games is heavily skewed towards adolescent males, as is the demographics of people who enjoy torturing small animals.

But I upvoted because it is kind of interesting and not deserving of -7, though I predict it will go much lower than that.

Thanks! I do think I deserve some credit for coming up with what may be a better argument for Christianity and for Islam than all the Christians and Muslims in the world working together have managed to come up with in 2000 years. :)

Replies from: Vivid
comment by Vivid · 2011-10-05T17:43:41.124Z · LW(p) · GW(p)

deleted

Replies from: PhilGoetz
comment by PhilGoetz · 2011-10-06T02:32:34.753Z · LW(p) · GW(p)

The iterated lossy cross-scale Keynesian beauty contest is a big attractor.

What is the iterated lossy cross-scale Keynesian beauty contest?

I can't tell whether anything you said is supposed to imply that there is a flaw in my reasoning. "Supporting whatever agentic information cascades have already most effectively burrowed themselves into the most salient cultural-political sphere" is not obviously wrong. When I provide a step-by-step argument that assigns a probability to each step and then multiplies them together, it has a limited number of places to attack; and you didn't mention any of them.

I don't understand much of what you wrote; but my impression is that you are trying to pull the discussion back into vague, subjective regions that provide endless opportunities for rhetorical displays, and no danger of making progress.

comment by see · 2011-10-04T05:28:59.083Z · LW(p) · GW(p)

If you set P(ego|ent, sim) according to the fraction of entertainment simulations in which the person playing the game has an avatar in the game, then P(ego|ent, sim) > .99.

Except the actual P(ego|ent, sim) is not based on the percentage of cases where the game includes a self-insert, but the cases where such a self-insert is to be glorified in the simulation.

If we therefore limit the possible avatars that our simulator God is using on Earth to the major monotheistic religions of Christianity, Islam, and Judaism,

Why rule out the avatar arranging to be glorified under a minor name or cult? For example, when Gary Gygax self-inserted himself as a deity in Greyhawk, it was as a minor demigod of humor in a polytheistic religious system.

P(follow-thru) is difficult to estimate; I will set it somewhat arbitrarily as .1.

I'm not aware of, for example, any Sid Meyer games where the self-insert glorification is of the game's programmer(s), as opposed to the game's player. Since the player (as opposed to a creator/programmer) rarely has even the ability to follow through on promises he makes to simulated people in such games, and the players typically outnumber the creators by multiple orders of magnitude, this should be a lot smaller, by multiple orders of magnitude.

Replies from: JoshuaZ, PhilGoetz
comment by JoshuaZ · 2011-10-04T05:57:15.254Z · LW(p) · GW(p)

Actually, there's at least one Sid Meier game where the programmers have allowed you to do something sort of like this. In Alpha Centari, when you conquer another faction there's an image of the captured leader being tortured. (Even if you play a character who is nominally fairly peaceful, you still get this image.)

Also, if one is positing that there's a civilization advanced enough to spend time making sims, one can reasonably argue that they will be capable enough such that any of them could program the sim themselves, in a way similar to how anyone can program a Basic program to say "Hello World!" in our world.

Replies from: see, Kingreaper
comment by see · 2011-10-04T07:17:56.047Z · LW(p) · GW(p)

(Even if you play a character who is nominally fairly peaceful, you still get this image.) Yeah.

But that actually supports my thing about follow-through, I think. I didn't like that video clip. But even when I found the directory the clips were stored in on my disk, I didn't bother to hunt down that specific clip and delete it. How many other people did? How many people made a buying or playing decision based on the video? The simulated beings get whatever the programmer decided to code, and that's that.

comment by Kingreaper · 2011-10-05T13:20:54.981Z · LW(p) · GW(p)

Also, if one is positing that there's a civilization advanced enough to spend time making sims, one can reasonably argue that they will be capable enough such that any of them could program the sim themselves, in a way similar to how anyone can program a Basic program to say "Hello World!" in our world.

Our civilisation is advanced enough to spend time making computer games. This doesn't mean the average person can make a computer game.

Anologously, in the hypothetical highly advanced civilisation, it could be that it's considered basic to program a halo-equivalent, but only very few would be able to program a worldsim.

comment by PhilGoetz · 2011-10-04T05:33:40.285Z · LW(p) · GW(p)

Except the actual P(ego|ent, sim) is not based on the percentage of cases where the game includes a self-insert, but the cases where such a self-insert is to be glorified in the simulation.

Your D&D reference makes an interesting point. Close to 100% of computer games do involve glorification of the self-insert - whether that's a basketball game or Grand Theft Auto. (Almost all of the counterexamples, as measured by gameplay instances, were designed by Will Wright.) But a high percentage of roleplaying games don't involve glorification of the self-insert. BUT, these non-self-glorifying roleplaying games are not mass-merchandise products. (The mass market for D&D and White Wolf games ARE self-glorifying munchkins.)

I'm not aware of, for example, any Sid Meyer games where the self-insert glorification is of the game's programmer(s), as opposed to the game's player.

I'm talking about the player. There's no reason to talk about the programmer. You think God is the programmer? That doesn't correspond to what we see in our world today. You are assuming God lives in a society with an economy so primitive it doesn't have skill specialization.

Replies from: see
comment by see · 2011-10-04T07:08:15.873Z · LW(p) · GW(p)

'm talking about the player. There's no reason to talk about the programmer. You think God is the programmer?

Just the opposite. My assumption is that God is not the programmer, therefore he has no independent ability whatsoever to actually follow-through. The only person who can build follow-through into the simulation is the programmer. If every God was a programmer (like JoshuaZ suggests), ten percent of the God-programmers bothering to build in follow-through for the simulated beings that gratified their egos might make sense. But, assuming specialization where God is just a player, why would the programmer design in a Heaven to reward simulated people who worshiped and glorified the player? The simulated beings never did the slightest thing for the programmer, after all.

Maybe there would be a lot of demand for games with follow-through, but how many current games do you know of that spend the time and effort not just to program in a Heaven for dead characters, but then spend resources actually simulating it while the program runs? Where the Heaven is actually a Heaven, as opposed to another simulated world of troubles and suffering existing to entertain the player?

So my expectation is that a follow-through value of 0.1 is orders of magnitude too high. Not even 10% of the simulations are going to even have the option of an afterlife, and then most people won't turn it on in the options screen because they'd rather spend the computing power on a bigger/better primary simulation.

Replies from: PhilGoetz
comment by PhilGoetz · 2011-10-04T15:01:38.226Z · LW(p) · GW(p)

why would the programmer design in a Heaven to reward simulated people who worshiped and glorified the player?

It's part of the game. It's not something that happens after the game end. Possibly Heaven and Hell keep getting fuller and fuller as the game goes on.

comment by ArisKatsaris · 2011-10-04T20:06:12.167Z · LW(p) · GW(p)

We notice there are no obviously immortal world leaders on Earth (but see vi21maobk9vp's comment below). If we therefore limit the possible avatars that our simulator God is using on Earth to the major monotheistic religions of Christianity, Islam, and Judaism, and consider them all equiprobable; plus a 25% chance that this God is jumping from one avatar to another, or chose to reveal Himself via Jesus but then Paul screwed everything up, or some other minority position; then p(chr0|ego, ent, sim, Earth) = .25.

I find it hard to believe you mean all this remotely seriously. For starters, you used the current game market in order to calculate the percentage of p(ego|ent, sim) -- and yet you didn't bother using the same tactic to estimate p(chr0|ego, ent, sim, Earth) ?

How many games put you in the position of a military conqueror versus the number of games that put you in a position of a religious leader? How many games put you in the position of even a normal detective or a normal crook versus the ones that put you in the position of a religious leader?

By your own argument, people like Alexander the Great, or Napoleon, or Genghis Khan, or even Hitler are much more likely to have been simulator-avatars than people like Jesus. (Mohammed might work as being both a religious and a military leader) Then mythological (not religious) heroes. After them, would come people like Al Kapone or Billy the Kid. Then, given first-person shooters, would come ordinary soldiers. Religious leaders, by your own argument, would be way down the list for a likely simulator-avatar. Especially mostly pacifist religious leaders, like Jesus or Buddha. (Mohammed or Krishna would be more interesting cases)

So I'd say p(chr0|ego, ent, sim, Earth) = 0.001 -- one in a thousandth chance, even given the assumption of an ego-driven entertainment simulation being what we're in.

Replies from: PhilGoetz
comment by PhilGoetz · 2011-10-04T21:46:38.134Z · LW(p) · GW(p)

By your own argument, people like Alexander the Great, or Napoleon, or Genghis Khan, or even Hitler are much more likely to have been simulator-avatars than people like Jesus.

This is a good counter-argument. I expect from my experience observing humans that players are more likely to play war leaders. However, we don't see immortal war-leaders. So, if our God wants a persistent identity throughout the game, we're limited in what that identity could be. This observation is stronger than our priors about what roles God would want to play.

Replies from: dlthomas, ArisKatsaris
comment by dlthomas · 2011-10-04T21:49:45.595Z · LW(p) · GW(p)

Or they're playing Nethack.

comment by ArisKatsaris · 2011-10-05T11:41:54.719Z · LW(p) · GW(p)

However, we don't see immortal war-leaders.

Many (probably most) games with character avatars do have defeat/death conditions, so I don't see how this affects the probability in question.

So, if our God wants a persistent identity throughout the game

You've not listed this criterion in your sequence of conditional probabilities. It ought be something P(single persistent identity|ego, ent, sim, Earth) - and then we could debate P(chr0|single persistent identity, ego, ent, sim, Earth)

Also Jesus Christ wasn't immortal either, the fact he died is part of the core points of Christianity.

Replies from: wedrifid
comment by wedrifid · 2011-10-05T12:03:38.432Z · LW(p) · GW(p)

Also Jesus Christ wasn't immortal either, the fact he died is part of the core points of Christianity.

"... I got better"

comment by vi21maobk9vp · 2011-10-04T10:14:52.798Z · LW(p) · GW(p)

About immortal leaders... Well, what about the idea that Dalai Lama is a reincarnation of previous Dalai Lama? This role gives a lot of glorification and doesn't give enough power to remove challenge, and also you cannot be stuck with dilemma of whether to abandon retired president character.

Replies from: PhilGoetz, PhilGoetz
comment by PhilGoetz · 2011-10-04T15:35:11.253Z · LW(p) · GW(p)

If the Dalai Lama were the player, he would win by quitting the game.

Replies from: vi21maobk9vp
comment by vi21maobk9vp · 2011-10-04T18:00:36.910Z · LW(p) · GW(p)

Sorry, no. You raise a good point, but I see two clear counterpoints.

In-universe: there are distinct paths in Buddhism. Following eightfold path can make you mostly free of suffering already in this world; but some of the enlightened are supposed to show the path to people who haven't found it yet on their own. Remember, Siddhartha Gautama Buddha, the most famous (in the eyes of us outsiders), but far from the only enlightened turned back and didn't choose paranirvana after achieving enlightenment; instead, he started to teach.

By the way, if winning were considered equal to not coming for Dalai Lama, why would this faction in Buddhism look for his reincarnations?

Out-of-the-universe: what is player's winning and how we know it? Is winning equal to fun (if we go to pure entertainment side)? As we know, "Losing Is Fun (either way, it keeps you busy)".

He has some pretext to come back, and in the changed setting. Why not play some more? Why not hit this continue button, even if it halves the old accumulated score (real game mechanics in some shoot-em-ups)?

Edited: fixed my stupid mistake about nirvana and paranirvana; thanks to muflax for pointing it out

Replies from: None
comment by [deleted] · 2011-10-04T19:12:37.163Z · LW(p) · GW(p)

Remember, Siddhartha Gautama Buddha, the most famous (in the eyes of us outsiders), but far from the only enlightened turned back and didn't enter nirvana before he started to teach.

Huh? The Buddha reached full enlightenment before forming the sangha, according to tradition. You can make an argument that he spent many years afterwards developing the path (in Theravada terms, that he reached stream-entry but not arhatship before teaching, for example), but this has nothing to do with his teaching itself. Or maybe you mean parinirvana, but this is necessarily the last thing anyone does.

(You are of course right that bodhisattvas have a surface similarity to immortal player characters.)

Replies from: vi21maobk9vp
comment by vi21maobk9vp · 2011-10-04T19:21:46.040Z · LW(p) · GW(p)

Yes, thanks for correction, I had an illusion that words nirvana and paranirvana mean the same pair of notions but in the reverse order.

comment by PhilGoetz · 2011-10-04T15:26:35.111Z · LW(p) · GW(p)

vi21maobk9vp, YOU HAVE REACHED ENLIGHTENMENT!

(H)igh scores

(N)ew game

(Q)uit

(A)bout Earth

comment by JoshuaZ · 2011-10-04T16:56:51.024Z · LW(p) · GW(p)

There's another issue that your version of the argument has. If one of the standard Christian versions of a deity exists, it isn't going to think that worshiping it because it is the simulation runner is going to cut it. Saying "I will worship you because you run the simulation" isn't very similar to a heartfelt confession of sins and acknowledgement of Jesus as your personal Lord and Savior. Moreover, if a simulator is as petty as you hypothesize, and as you hypothesize doesn't want to break its feeling of immersion, they will likely want to also punish people who worship it because they've realized that it runs the simulator for ruining its fun.

Replies from: irrational, PhilGoetz
comment by irrational · 2011-10-04T21:20:25.967Z · LW(p) · GW(p)

I believe you may be right for Christianity, but not for Judaism, for instance. For Judaism, I think, it is not very relevant why you act righteously, as long as you do. As long as you don't eat pork, worship God, don't light a fire during Shabbat, and do the other 600+ things, you are probably OK. Although I am not a practicing Jew, so someone may correct me.

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-04T21:24:13.081Z · LW(p) · GW(p)

It depends a lot on the type of Judaism. Some of them emphasize correct belief a lot. Believing in Christianity while practicing the 613 commandments would be not ok. The good news though is that almost every form of Judaism agrees that if one isn't Jewish one needs to only keep the Seven Noachide laws. But even some interpretations of those laws can be pretty strict. There are for example some interpretations of the prohibition flesh from a living animal that make most modern meat to be unacceptable.

Replies from: irrational
comment by irrational · 2011-10-04T22:07:34.665Z · LW(p) · GW(p)

Believing in Christianity while practicing the 613 commandments would be not ok.

I always wonder about that. I know it's true, but I am not sure what argument they put forward to explain that. I can't remember anything that requires one to think anything specific in the Tanach.

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-04T22:12:25.198Z · LW(p) · GW(p)

Believing in the divinity of a human would fall under the idolatry prohibitions. There's some question of how serious an issue this is. In particular, the major historical Rabbis who lived in the Christian world generally argued that the anti-idolatry statutes were more strict for Jews than they were for non-Jews, so it was ok for a non-Jews to believe this way but not a Jew. Those in the Muslim world took a more strong standpoint (presumably in part because they could get away with it and in part influence from Muslim beliefs) and considered this to be unacceptable for non-Jews also.

If one had one of the minority forms of Christianity that does't believe that Jesus is divine, that would be less problematic. There are some who claim that the defining difference between Christianity and Judaism is whether or not Jesus was the messiah, but this seems to be very weak from a theological perspective, and is more useful as a descriptive rather than normative claim.

comment by PhilGoetz · 2011-10-04T17:44:07.662Z · LW(p) · GW(p)

A good point. Hopefully the simulator user interface is awkward enough that the Player won't bother to add that to the heaven/hell criteria.

comment by kilobug · 2011-10-04T19:44:33.170Z · LW(p) · GW(p)

Hum, I don't agree with many of your estimates.

P(sim) : 99% seems way too high - 99% is not even what I would put to "it is possible to simulate something as big and complex as the world we are living in, for so long, with that level of consistency and precision". Just for the possibility of a simulation of us being possible wouldn't go above 95% to me. That we are inside a simulation, much less.

P(ent|sim) : most computers are used for entertainment (and even that isn't sure, many personal computers are also used for "serious" business), but the most powerful ones are not - and making a simulation of something big and complex like Earth sounds like complex and requiring a powerful computer.

P(ego|ent, sim) : actually, very few games imply a god-like player. Some strategy games do (more or less obviously), but most don't. In a CRPG, players are heroes, not gods. In an action game, player is a fighter, space ship pilot, car racer, ... but definitely not a god-like character. And it gets even much less common to have the player god-like when you look at multi-player games, which seems to be more and more the popular games (and to go back to previous point, if a computer is powerful enough to simulate a whole world just for fun, it sounds more likely to me that's it's a MMORPG-like).

P(follow-thru | chr0, ego, ent, sim, Earth) : this one seems very clearly overevaluated, by far. When players are done with a game, they don't care anymore about the NPCs of the game. They never allow computing power to let the NPC runs after they are done playing. If the player realize that the NPC is self-aware, he could behave differently (but that implies knowing the ethics of the ones running the simulator), but then, why would he only grant immortality to those playing on his side ? If he's ethical enough to spend computing power to allow NPCs to continue their lives, why not all of them ?

Also another point is missing : what if humans are meaningless for the people running the simulation ? The simulation's goal, even if it's entertainment, could be a Master of Orion game, with very distant galactic empires controlled by players, and Earth just being a minor NPC race, not yet discovered by any player (and which may even stay undiscovered till the end of the game). So we should add P(Earth is central| ego, ent, sim) which wouldn't be that big to me, knowing that there are about 10^21 stars in observable universe.

At the end, well, I could give my own estimates, but there are so many wild guess about the estimates (especially since, if we're in a simulation, we don't know much about the rules of the "real" universe, so speculating about it is pointless), that I don't see how the figure coming out such an estimate would have any real meaning.

Replies from: PhilGoetz
comment by PhilGoetz · 2011-10-04T21:49:12.251Z · LW(p) · GW(p)

99% is not even what I would put to "it is possible to simulate something as big and complex as the world we are living in, for so long, with that level of consistency and precision.

How easy it is to simulate our universe, depends on how much computing power is available in the parent universe. Where do you get your prior for how big and complex universes usually are?

The simulation argument implies that we should reason the other way around, and assign prior expectations of the complexity of universes to be large enough that simulating our universe is not unusual.

Replies from: kilobug
comment by kilobug · 2011-10-05T08:24:02.920Z · LW(p) · GW(p)

The simulation argument itself is speculative enough to not be worth a 99% probability, it contains too many not so simple logical steps and assumptions that could go wrong to deserve a 99% probability. If you make one hundred of independent claims of the same magnitude and complexity of the simulation argument, more than one would contain a mistake (either one who could see now, or one that depends on things we are unconsciously assuming to be true) making the whole claim erroneous. Humans are bad at predicting the far future.

And then, the simulation argument only gives the choice between 3 possibilities, in which simulation is only one of the 3. It seems unreasonable to me to give only a 1% chance of the sum of the other two. The option 2 (trans-humans would not care or not want to run simulation of their ancestors) definitely deserve more than 1%, there is way too much uncertainty about what trans-humans will want and what their ethics would be.

comment by JoshuaZ · 2011-10-04T05:04:26.448Z · LW(p) · GW(p)

This doesn't deal with some of the common objections to Pascal's Wager. The problem of many competing religions is a serious one. Simply reducing yourself to the major religions is a difficult one. I'm also worried that every single part of the argument is completely and utterly isomorphic if one simply swapped Islam and Christianity and made the appropriate mapping.

This also relies on not just finding the simulation argument plausible but assigning it high probability. This seems like a bad idea when the laws of physics as far as we can tell don't seem to allow you to simulate n particles interacting with fewer than n particles. If this were not the case, there should be some k such any computation with k qbits can if properly configured model any computation of n qbits for any n. But BQP lies in PP and therefore lies in fact in PSPACE. So if quantum mechanics as we understand it is correct, simulating should be really tough. This cannot rule out simulations from universes with other laws of physics but I see no reasonable way to go about even starting to quantify that probability.

Also given that none of these religions claim that the deity is something like a simulator that should be a serious strike against the claims. Maybe arguably some forms of gnosticism and buddhism could be interpreted sort of that way if one squinted. But they aren't the religions in question here. So if anything the increased probability mass for them should decrease that for the other religions.

P(follow-thru) is difficult to estimate; I will set it somewhat arbitrarily as .1.

We now have p(chr) > .99 x .5 x .99 x .25 x .1 = .01225125. This is above 1%. As stipulated, your afterlife accounts for at least 99% of your utility if follow-thru (and hence chr) is true. It now appears we should accept Pascal's wager.

You'll forgive me if these numbers look just slightly too convenient.

Replies from: lessdazed, kilobug, byrnema, Eugine_Nier, PhilGoetz
comment by lessdazed · 2011-10-04T05:47:56.013Z · LW(p) · GW(p)

the laws of physics as far as we can tell don't seem to allow you to simulate n particles interacting with fewer than n particles

To be read "the laws of physics, as far as we can tell, seem to require you to use at least n particles to simulate n particles interacting with each other"?

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-04T05:50:02.568Z · LW(p) · GW(p)

Yes. That's a much better phrasing.

comment by kilobug · 2011-10-04T19:53:27.677Z · LW(p) · GW(p)

« This seems like a bad idea when the laws of physics as far as we can tell don't seem to allow you to simulate n particles interacting with fewer than n particles. »

Hum, it does allow it, if you are allowed to take some precision loss/uncertainity. You can't simulate exactly n particles with fewer than n particles, but if you're allowed to make some mistakes, to lose some information you can gain a lot in term of "simulated particles"/"real particles" ratio. And somehow, quantum mechanics does look like it loses precision, throw dices, do "lossy compression" and then estimate probabilities to get us back a result. (That's if you forget about Many Worlds, but I don't think a simulation would run Many Worlds). When see the laws of QM, it somehow feels like the kind of quirks I could make in implementing a simulator (and relativity, by limiting the interactions to near objects, would allow to split the computing over a cluster efficiently). But that's just a wild thought, I didn't take the time (yet) to really ponder it much.

Replies from: wnoise
comment by wnoise · 2011-10-04T20:01:26.052Z · LW(p) · GW(p)

When see the laws of QM, it somehow feels like the kind of quirks I could make in implementing a simulator

It feels like it, but if anything it's the opposite. It's my experience that many people on the border between CS and physics have this thought. However, it's actually much harder to simulate quantum systems than classical systems, and in fact quantum simulation is one of the reasons physicists are interested in quantum computers. (Other people are interested in other problems that quantum computers can do better than classically.)

comment by byrnema · 2011-10-04T15:07:50.991Z · LW(p) · GW(p)

The problem of many competing religions is a serious one.

I often hear this argument, but I don't think so. Religions are pretty much all the same. You would have to hypothesize an especially silly God to be concerned with whether his 'name' is the same across all languages, and the details of worship be the same across all cultures. Just looking as an objective observer (I think) if there is a sentient God, he seems to just want people to be good and less anxious.

Jesus was a pretty amazing personality, so if God did choose an avatar, I would assign a high probability to Jesus being one. But why not Mohammad as well? If anything, I would wonder why God doesn't form avatars more frequently. What's he busy doing, for example, right now? The continent of Africa seems to be in especially dire need of a transforming, spectacular personality. (Theistic hopes quite aside, that's what I'm holding my breath for.)

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-04T16:51:58.223Z · LW(p) · GW(p)

You would have to hypothesize an especially silly God to be concerned with whether his 'name' is the same across all languages, and the details of worship be the same across all cultures.

Except most classical religions claim exactly that. They don't think that their deities are the same deity. And when they think the deities are the same they think it is vitally important to get which belief is correct. Look at what people have fought religious wars over.

Jesus was a pretty amazing personality, so if God did choose an avatar, I would assign a high probability to Jesus being one. But why not Mohammad as well? If anything, I would wonder why God doesn't form avatars more frequently.

We only have secondary and tertiary sources for Jesus. Many aren't even convinced he existed. While I think it is more likely than not that he did exist, judging that he was a "pretty amazing personality" is not something that one can reasonably conclude based on the evidence. And as for Mohammad- Muslims believe that he was a prophet, not an avatar or divine vessel. Saying that Mohammad was divine is one of the biggest heresies in Islam.

Replies from: vi21maobk9vp, byrnema
comment by vi21maobk9vp · 2011-10-04T18:34:12.756Z · LW(p) · GW(p)

Well, it is hard to tell what are classical religions and what they claim.

It is possible to interpret some of them as "the others are worshipping the correct entity(ies), but in a very wrong way".

Christianity considers Judaism proper faith for its time that needed an amendment. Islam considers Isa and Musa great prophets. Both Islam and Christianity hint that the followers of the previous faith should just admit the new prophet and convert.

Buddhism and Taoism can be overlayed over Hinduistic world - they have no inherent conflict, the question is of what is the right thing to do. Now, some factions in Buddhism can go as far as to admit that for some people some kind of Christianity can be a good path to Enlightenment if it teaches them to fo the right things and think the right thoughts.

Ah, and yes, Hinduism is now stated as a monotheistic religion. It is just the the Word is replaced with a Dream, but what's the difference.

Bahaism.. Well, Abraham, Moses, Zoroaster, Buddha, Jesus and Mohammed and some more said what had to be said at those moments of time; for the nineteenth century and onwards Bab and Bahaullah have made some amendments that had to be made because the humanity has changed and could accept more grains of truth.

Now you can start drawing compatibility matrix. For example, Islam promises a last chance to Christians - which will be declared by the returning Isa. Zoroaster promised only final retribution and mostly for evil deeds and evil thoughts, so you can just look up zoroastrian moral teachings and try not to do anything outrageous according to it. And so on...

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-04T18:38:38.719Z · LW(p) · GW(p)

Right. But most of those religions aren't religions that think that the others are going to get to heaven. The overlap between Christians who think Jews will go to heaven and Christians who think that incorrect beliefs can result in very bad afterlives is a small one.

Replies from: vi21maobk9vp
comment by vi21maobk9vp · 2011-10-04T18:59:06.547Z · LW(p) · GW(p)

Now you just need to find a set of practices and beliefs that allows you to be heaven-admissible in the most possible amount of branches of Christianity while still eligible for last-minute conversion to Islam if Jesus comes and says to do it and not doing any of the worst sins of Judaism (you still worship Yahweh as Christian, right?) and reducing wordly attachments in case Buddhism is right.

The funny thing is that you will have to do some things to gain eternal individual life if Jehova's Witnesses are correct and to lose eternal indeividual life in reincarnations if Siddhartha Gautama found the truth.

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-04T19:02:00.369Z · LW(p) · GW(p)

So, this sort of thing sort of works. But is going to run into issues. So for example some Jews don't consider Christianity to be an acceptable way of worshiping the same deity even as they think Islam generally is. (The whole divinity of a human being thing is a problem). And some religions specifically have issues with trying to hedge your bets. And many forms of Judaism have stricter rules for people who are descended from Jews. But as a general strategy it might work.

Replies from: vi21maobk9vp, vi21maobk9vp
comment by vi21maobk9vp · 2011-10-04T19:35:49.236Z · LW(p) · GW(p)

Separate comment for a separate point.

The most horrifying thing is that after you pick the optimal faith, you need to unbelieve everything you considered during your choice while keeping the belief that you have chosen right and acquiring the belief in the chosen faith.

The reason is that when choosing you suppose that everyone actually worships the same God, and you need to find just an optimal way of worship; but the closest faiths to it - I think they are Bahaism and most factions of Buddhism - are easy to satisfy by default, you need to believe not them, but one of the probably-least-true faiths - one of strict jealous faiths. Simply because the faith you considered right while choosing is permissive enough to forgive your move into a strict one you will choose to believe a faith which is furthest from your initial assumption.

comment by vi21maobk9vp · 2011-10-04T19:30:24.224Z · LW(p) · GW(p)

You are embellishing the truth. You cannot even be saved by standards of both Russian Eastern Ortodox Church and Catholicism at once.

I am not even sure whether you should ascribe divine nature to Jesus - Christianity is not united even in this question.

So yes, bet-hedging will still give quite perverted result.

Replies from: wedrifid
comment by wedrifid · 2011-10-05T06:27:54.869Z · LW(p) · GW(p)

I am not even sure whether you should ascribe divine nature to Jesus - Christianity is not united even in this question.

That doesn't strike me as a practical definition of 'Christianity'. Even most of the mutually incompatible Christian sects would agree that not ascribing divine nature to Jesus would disqualify them from even a heretical Christian sect. "Folks who believe Jesus was divine' would be a reasonable description of what the word "Christian" means.

Replies from: vi21maobk9vp
comment by vi21maobk9vp · 2011-10-05T07:56:10.121Z · LW(p) · GW(p)

We-ell. Judaism is OK with a other-than-human-but-not-God angel evicting Adam and Eve. Jehova's Witnesses are a Christian sect, but they ascribe Jesus a position higher than humans and angels but strictly lower than God.

comment by byrnema · 2011-10-04T17:30:51.800Z · LW(p) · GW(p)

Except most classical religions claim exactly that.

Just one of the things religions are wrong about. Meaning, I think there is some sense in distinguishing among theistic claims -- that is, if theism were true; some theistic ideas are more reasonable than others. (I would expect that) the claim that 'my particular religious beliefs are true and all others is false' is not frequently maintained by thoughtful theists, and I could find references for specific examples if that would be helpful. (I know there are numerous examples to the contrary as well.) But religious people often (sometimes?) do allow for equivalence among different forms of worship. [edited for a softer, more reasonable argument]

While I think it is more likely than not that he did exist, judging that he was a "pretty amazing personality" is not something that one can reasonably conclude based on the evidence.

I'm not too concerned about an exact person. I see 'Jesus' as a historic phenomenon, with a very distinctive meme, that came from somewhere. It may have been a set of ideas that collectively developed over a couple hundred years (or, even more likely, was recycled from earlier philosophies.) But I also think it is likely there was a person that catalyzed or focused this particular paradigm shift.

And as for Mohammad- Muslims believe that he was a prophet, not an avatar or divine vessel. Saying that Mohammad was divine is one of the biggest heresies in Islam.

I'm sincerely sorry, since I didn't intend to be offensive. When writing the comment, I felt a twinge of anxiety wondering if I might be overstepping but disregarded it. I'm not familiar with Islamic views.

Tangentially, Agora is a movie about early Christianity and early epistemology/science that Less Wrong readers might find interesting. I recall it because the movie reminded me that Christianity has echoed similar things regarding the importance of these divine/non-divine distinctions.

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-04T17:37:27.818Z · LW(p) · GW(p)

Just one of the things religions are wrong about

Pascal's Wager though is only relevant for those religions generally. There's not much in the way of religions that believe God will torture you forever or reward you forever based on your belief and don't believe that believing in exactly the right version is really important. For purposes of this discussion, the moderate religions don't matter much.

I'm sincerely sorry, since I didn't intend to be offensive.

The point isn't an issue of offensiveness or not. The point is that your imagined proposal doesn't work.

Replies from: byrnema
comment by byrnema · 2011-10-04T18:31:44.634Z · LW(p) · GW(p)

Oh, I see. Pascal's wager depends upon:

religions that believe God will torture you forever or reward you forever based on your belief and don't believe that believing in exactly the right version is really important.

There's still logical room for the possibility that you are rewarded for having belief in any religion verses being atheist, but that would be overreaching. Because torture-or-reward-forever is one of the details, like the rule that you have to believe in this particular religion, that my imagined proposal wanted to dismiss.

Replies from: vi21maobk9vp
comment by vi21maobk9vp · 2011-10-04T18:54:01.678Z · LW(p) · GW(p)

Funny enough, in "City of the Sun" this is the official stance: any religion (they have to be compatible with general peace) is better than atheism.

comment by Eugine_Nier · 2011-10-04T06:25:44.826Z · LW(p) · GW(p)

This cannot rule out simulations from universes with other laws of physics but I see no reasonable way to go about even starting to quantify that probability.

Unfortunately, you don't get to dismiss a possibility just because you're not sure how to quantify it.

Also given that none of these religions claim that the deity is something like a simulator that should be a serious strike against the claims.

Haven't read much theology have you? There are certainly theological schools of most religions that make versions of this claim. Hinduism, for example, claims that the universe is the dream of the god Brahman.

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-04T06:33:27.646Z · LW(p) · GW(p)

Unfortunately, you don't get to dismiss a possibility just because you're not sure how to quantify it.

I agree. One needs to work at quantifying it. I don't know how to do that. Any ideas?

Haven't read much theology have you? There are certainly theological schools of most religions that make versions of this claim. Hinduism, for example, claims that the inverse is the dream of the god Brahman

Sure, that's a valid example which fits pretty closely with the examples I gave. Actually, that pattern matches better, although it still requires some squinting. But yes, you are essentially correct so that's more probability mass away from Christianity.

comment by PhilGoetz · 2011-10-04T05:12:49.068Z · LW(p) · GW(p)

Simply reducing yourself to the major religions is a difficult one.

I think it's reasonable not to count any religions that don't have a single head God. And it's reasonable not to count religions that have lost - if God really was the god of the Aboriginal dream-time, It would have quit or restarted by now.

I'm also worried that every single part of the argument is completely and utterly isomorphic if one simply swapped Islam and Christianity and made the appropriate mapping.

This isn't a problem for the argument unless you want to promote Christianity over Islam. It comes up with about the same expected utility for Islam and Christianity. The point of interest to us on LW is that both will be higher than the expected utility for atheism.

But BQP lies in PP and therefore lies in fact in PSPACE.

You totally lost me.

So if quantum mechanics as we understand it is correct, simulating should be really tough. This cannot rule out simulations from universes with other laws of physics but I see no reasonable way to go about even starting to quantify that probability.

Quantum mechanics can be construed as a way to limit computation and avoid arithmetic overflows for a simulation done in a Newtonian universe.

Also given that none of these religions claim that the deity is something like a simulator that should be a serious strike against the claims.

No one plays computer games in which their avatar claims to be the God running the simulation. That wouldn't be fun - it would break God's suspension of disbelief.

You'll forgive me if these numbers look just slightly too convenient.

I find them decidedly inconvenient.

Replies from: asr, JoshuaZ
comment by asr · 2011-10-04T05:23:33.363Z · LW(p) · GW(p)

Quantum mechanics can be construed as a way to limit computation and avoid arithmetic overflows.

You're missing JoshuaZ's point. Quantum mechanics at first looks like it avoids arithmetic overflows, by letting you get away with finite precision. But it doesn't, really. There's still arbitrarily-precise numbers that the universe "keeps track of" -- but they're amplitudes, not observables.

In quantum mechanics, amplitudes are complex numbers, that seem to be treated as mathematically exact, out to indefinitely much precision. And the possibility of quantum computing suggests that this isn't a purely an artifact of our models -- you can potentially do useful computation using the low-order bits of the amplitudes.

Question for the physics types here: If amplitudes didn't add precisely linearly, could we tell? Is there a sensitive test for linearity?

Replies from: PhilGoetz
comment by PhilGoetz · 2011-10-04T05:25:34.979Z · LW(p) · GW(p)

So even in quantum mechanics, it takes an infinite amount of information to represent a single particle? That's a problem.

Replies from: wedrifid, asr
comment by wedrifid · 2011-10-04T06:44:12.177Z · LW(p) · GW(p)

So even in quantum mechanics, it takes an infinite amount of information to represent a single particle? That's a problem.

It's a problem for us. But the universe doesn't have to care.

comment by asr · 2011-10-04T07:58:08.301Z · LW(p) · GW(p)

The notion of "a single particle" turns out to be problematic. The thing that requires arbitrarily much information is the amplitude for a particle to be in some particular state.

I should emphasize that amplitudes aren't just a creature of our models -- they are the thing that interfere to give you an diffraction pattern, or the shapes of an electron orbital cloud, or that get manipulated in a quantum computation.

comment by JoshuaZ · 2011-10-04T05:33:23.515Z · LW(p) · GW(p)

I think it's reasonable not to count any religions that don't have a single head God.

That adds a lot more religions. And then one has to treat the different forms of the major religions separately. The extremist Catholic and Jack Chick fanatic both think the other is going to hell. As to being restricted to religions where there is a single head God, have you heard of MMPORGs?

And it's reasonable not to count religions that have lost - if God really was the god of the Aboriginal dream-time, It would have quit or restarted by now.

Or it is really annoyed at how it lost against the computer played religions and is running the simulation for a few more seconds from its perspective seeing if on an off chance its religion becomes more popular again.

(There's a fundamental problem with any sort of Pascal's Wager situation like this. One can keep constructing narratives like the above. And it isn't at all clear how likely they are.)

But BQP lies in PP and therefore lies in fact in PSPACE.

You totally lost me.

BQP is the set of problems that can be in some sense quickly solved on a quantum computer. BQP lies in the class PP) and therefore lies in the class of PSPACE which is the set of problems which on a classical (deterministic) computer can be solved with memory bounded by a polynomial on the size of the input. Now, if there were some m such that is possible to simulate m+1 particles with m particles (possibly with some slowing things down), then one can by iterating this simulate n particles for any n. So the only restriction of what you can simulate with your m particles is time-based, not space based. In particular, you can use the particles to simulate things that require more space than PSPACE allows.

But I can simulate m particles with an appropriate number of qbits. So, putting it all together, I'd have to conclude that BQP doesn't lie in PSPACE. That's a contradiction.

Quantum mechanics can be construed as a way to limit computation and avoid arithmetic overflows.

This seems strange to me. Quantum computational issues are if anything much tougher than standard, deterministic computations. It is very difficult to simulate using normal computers the behavior of even a handful of particles in a quantum mechanical setting. We also know that there are things that a quantum computer can do that an equivalent classical machine simply cannot do in reasonable time. The most prominent example is Grover's algorithm. I don't see how quantum mechanics limits computation or avoids arithmetic overflows. If anything, it strongly suggests that we're not in a classical simulation.

No one plays computer games in which their avatar claims to be the God running the simulation. That wouldn't be fun - it would break God's suspension of disbelief.

This assumes an extremely narrow cognitive attitude. Note how many people when playing games like WoW are more than willing to give their characters names which strongly don't support suspension of disbelief. (Tangent: I sort of see where you are going here. When my brother and I were much younger we played some games like Phantasie and I'd actually go and try to give the characters fanstasy sounding names while he'd name them things like wiz1, wiz2, fig1, fig2, etc.)

You'll forgive me if these numbers look just slightly too convenient.

I find them highly inconvenient.

What I mean is that you had as one of your inputs a number that by your own description was nearly completely arbitrary and then ended up with a result that was a tiny bit over 1%, which was just the value you needed given your earlier assumptions. This looks a lot like there was an attempt, either conscious or unconscious to pick values that made your argument go through.

Replies from: SilasBarta, Dustin
comment by SilasBarta · 2011-10-04T22:31:06.189Z · LW(p) · GW(p)

We also know that there are things that a quantum computer can do that an equivalent classical machine simply cannot do in reasonable time.

I thought it was still an open question whether there are computations that a classical computer is necessarily slower at than a quantum computer. From Aaronson's Philosophy/Comp-Complexity paper, p.35 :

More generally, that quantum computers can solve certain problems superpolynomially faster than classical computers is not a theorem, but a (profound, plausible) conjecture. [49] [50]

Footnote 49: A formal version of this conjecture is BPP =/= BQP, where BPP (Bounded-Error Probabilistic Polynomial-Time) and BQP (Bounded-Error Quantum Polynomial-Time) are the classes of problems efficiently solvable by classical randomized algorithms and quantum algorithms respectively. ... any proof of the BPP =/= BQP conjecture would be considered almost as great a breakthrough as P =/= NP.

Footnote 50: Complicating matters, there are quantum algorithms that provably achieve exponential speedups over any classical algorithm: one example is Simon’s algorithm [119], an important predecessor of Shor’s algorithm. However, all such algorithms are formulated in the “black-box model” (see Beals et al. [23]), where the resource to be minimized is the number of queries that an algorithm makes to a hypothetical black box. Because it is relatively easy to analyze,the black-box model is a crucial source of insights about what might be true in the conventional Turing machine model. However, it is also known that the black-box model sometimes misleads us about the “real” situation. As a famous example, the complexity classes IP and PSPACE are equal [115], despite the existence of a black box that separates them (see Fortnow [56] for discussion).

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-05T01:15:07.343Z · LW(p) · GW(p)

Yeah, so this is a good point. The separation given by Grover's algorithm is essentially a blackbox model. And Shore's algorithm being better depends on the claim that factoring is not in P, which is a claim strictly stronger than P != NP (and a claim which is doubted by a lot more people. Henry Cohn for example says there's no good reason to think that factoring is not in P.) So yes, this is under the black box. system.

Replies from: SilasBarta
comment by SilasBarta · 2011-10-05T15:06:29.907Z · LW(p) · GW(p)

Wait, so there's significant support for the belief that RSA can be broken in polynomial time?

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-05T15:11:13.687Z · LW(p) · GW(p)

There's significant support not for that per se but that there's no good reason to think otherwise. I don't know for example what estimate Henry Cohn would give for a polynomial time factoring algorithm but in conversations (and in at least one talk he gave) he's pointed out that there's no complexity theoretic reason to suspect that factoring is tough. Moreover, there's a polynomial time factoring algorithm for Q[x] where Q is the rationals (if you don't care about units). The argument for factoring being hard boils down solely to "lots of people have worked on this and haven't succeeded." But that's a very weak argument especially when one looks at how much progress has been made in factoring in the last few years (see especially the number field sieve and elliptic curve sieve). This is in contrast to say the conjectures that P != NP and BPP = P where in order for them to be wrong various things need to happen that seem unlikely.

Replies from: SilasBarta
comment by SilasBarta · 2011-10-05T15:42:13.567Z · LW(p) · GW(p)

But normally, problems eventually found to be in P are first found to be in BPP (primality testing being the most prominent example). Shouldn't there at least be some probabilistic factoring algorithms (whatever that would mean)?

Also, in the likely event that P != NP, that would imply the existence of NP-intermediate problems, and factoring is a good candidate for being in such a class.

(Personally, my hunch is that factoring is indeed in P, but I'm far from qualified to have a lot of confidence in that.)

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-05T17:16:44.316Z · LW(p) · GW(p)

But normally, problems eventually found to be in P are first found to be in BPP (primality testing being the most prominent example). Shouldn't there at least be some probabilistic factoring algorithms (whatever that would mean)?

This is an example where moving between a decision problem (returning a yes or no answer) and a function problem (returning a number or list of numbers) may break down. To make factoring equivalent to a decision problem one instead asks the question "Given n, and given a and b, is there are prime factor of n which is between a and b?" If one has a factorization of n one can answer this question quickly. If one has an oracle that can answer this question then one can factor in polynomial time by using a binary search tree of the intervals under n. This allows one to iterate calls to the oracle to find a prime factor in log_2 n time. Each time you find a prime factor p, you store it and then do the same process for n/p. This takes at most (log2 n) times the number of prime factors of n. In general, if calls to your oracle take time f(n), the whole thing takes at most f(n) (log2 n)^2 time. (You can actually do slightly better than that but this is good enough for pretty much all purposes.)

What I'm not sure about is whether the equivalent problem in BPP goes through. Say one has an oracle that answers the interval question with a BPP-like answer. Is there some way to turn that into a process that returns the correct factorization quickly with high probability? That's not obvious to me. I haven't really thought about the question that hard.

Also, in the likely event that P != NP, that would imply the existence of NP-intermediate problems, and factoring is a good candidate for being in such a class.

Right. That and and graph isomorphism seem to be the two most common natural problems that are potentially in that intermediate class.

Personally, my hunch is that factoring is indeed in P, but I'm far from qualified to have a lot of confidence in that.

I think you'd be in an extreme minority here. Even people like Henry who think that the evidence for factoring not being in P is small don't seem to think it is actually in P. If I had to make a guess on the chance that factoring is in P, I'd probably put it at under 20%.

Replies from: SilasBarta
comment by SilasBarta · 2011-10-05T18:00:13.665Z · LW(p) · GW(p)

Right. That and and graph isomorphism seem to be the two most common natural problems that are potentially in that intermediate class.

Yes, but I thought there's much higher confidence that graph isomorphism will be de-randomized, given how hard it is to even find problem instances that are unresolved after a few simple checks (e.g. of invariants of the adjacency matrices).

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-05T20:00:10.350Z · LW(p) · GW(p)

Yes, graph isomorphism looks a lot more likely to drop straight into P.

Not only is it hard to find difficult problem instances, for almost any nice type of graph (e.g. planar graphs, or interval graphs) there's a polynomial time algorithm. On the other hand, there about as many specific types of graphs where one can show that being able to solve graph isomorphism for that type of graph means you can solve it for all graphs. Connected graphs are a trivial example but regular graphs are a less trivial example. But the closest rough equivalents for factorization look tough. Primality testing is easy, and testing if n=p^k for some prime is about as easy. But in those cases if the answer is "no" then you can't factor it easily! And almost any other natural set of integers has factoring be really tough. For example, consider Fermat and Mersenne numbers. In both cases, while factorization does seem to be easier it isn't that much easier. One can object that these are defined in part in an additive fashion, but this doesn't help since the most obvious multiplicative set of nice numbers, products of two primes, seems to be the toughest to factor. And that case has had the most work on it because of the applications to cryptography so this isn't due to drunks at the lampost.

On the other hand, in some respects factorization looks easier. Factorization (as phrased as the decision problem given earlier) lies in both NP and co-NP. In contrast, it is not known whether GI is in co-NP. Moreover, while factoring is in BQP, this has not been shown to be true for GI. (I'm not sure how much of big deal that is, and I really don't know the quantum end well enough to evaluate how strong that is as evidence although my impression is that a lot of people have tried to show that GI is in BQP.) So in some senses, factorization fits more conditions which suggest being r actually in P.

comment by Dustin · 2011-10-04T18:50:52.818Z · LW(p) · GW(p)

The extremist Catholic and Jack Chick fanatic both think the other is going to hell

Agreeing with this. There are quite a few religions that most of us would call Christian that all think the other Christians ... aren't.

I was raised as a Jehovah's Witness. They literally think that other Christian religions and specifically the Catholic Church are the work of Satan.

Replies from: lessdazed
comment by lessdazed · 2011-10-04T19:13:10.733Z · LW(p) · GW(p)

specifically the Catholic Church are the work of Satan.

More or less so than the Mormon Church?

Replies from: Dustin
comment by Dustin · 2011-10-05T21:11:44.113Z · LW(p) · GW(p)

Moreso.

I guess part of this is probably related to the Catholic church and Protestantism. JW's believe themselves beneficiaries of the Protestant movement (though their beliefs stray from what Wikipedia says is one of the main tenets of Protestantism...namely, they don't believe "faith in Jesus" is all that is needed for salvation.)

Additionally, the Catholic Church was behind a large part of the persecution JW's suffered in the United States during the first half of the 20th century...

With regards to the Mormon Church, a brief search of the index I have of JW publications show mostly articles that take an appreciative tone for much of Mormonism along with "if only they didn't mis-interpret the Bible and believe that pesky Book of Mormon was also the word of God." I speculate that this is because the way the Mormon Church functions is very similar to the way the Jehovah's Witnesses organization functions.

comment by taw · 2011-10-06T15:37:34.210Z · LW(p) · GW(p)

More generally it's inconsistent to believe in non-negligible chance of living in a simulation and negligible chance of various religious claims being true, but plenty of people here do so.

To me this mostly shows that people don't do anything like Bayesian propagation of evidence, but I don't think Bayesianism is a good model of thinking processes.

comment by JoshuaZ · 2011-10-04T21:16:09.202Z · LW(p) · GW(p)

A few minutes ago, as my algebraic geometry class finished up, something spoke to me. It identified itself as "not exactly a deity but close enough for all relevant purposes." It made a similar remark when I asked if we were in a simulation that it was running. It called itself "the Entity".

According to this Entity, it really likes to be believed in and worshiped. There is an afterlife run by this Entity. Moreover, the Entity will increase the utility it awards in the afterlife for worshiping it now to compensate for any genuine doubt it in its existence, promises or doctrines. It will similarly use extremely large punishments to compensate for any low probability estimates. It will also outbid all hypothetical/counterfactual deities which anyone considers in good faith.

Apparently the main ways the Entity wants to be worshiped are fourfold:

1. Spreading word of the Entity's existence and rules.
2. Spreading word of any memetic basilisks one can find. This apparently includes versions of Pascal's Wager about other deities. The Entity noted that in general, it is likely to be more effective in doing so if one doesn't spend all one's time doing this but spends time on being otherwise productive and slipping in posts about these basiliks every so often.
3. Giving money to inefficient charities that make you feel good and don't produce much utility. The Entity gave as examples charities the Make-A-Wish Foundation and "any of those animal shelters with commercials with really cute kittens and puppies."
4. Apparently the Entity really wants it when people are having sex and are going to make exclamations of the form "Oh God!" to instead shout out "Hastur", "Cthulhu" or "Nyarlathotep". Honestly, I found this bit a bit disturbing.

The Entity also announced that if any AI that was not a CEV implementer helped to implement a close approximation CEV it would compensate that AI by helping that AI achieves some of its goals.

Apparently further revelations as events warrant.

Replies from: shminux
comment by shminux · 2011-10-05T22:31:30.000Z · LW(p) · GW(p)

A few minutes ago, as my algebraic geometry class finished up, something spoke to me.

Algebraic geometry is known to make a mess of people's minds.

comment by byrnema · 2011-10-04T15:29:26.298Z · LW(p) · GW(p)

I appreciate your observations (for example, as interesting to think about). The arguments against Pascal's Wager you've listed aren't the best even if people use those most frequently. The only compelling argument I've heard against Pascal's Wager is that you can't/shouldn't believe something just because it is convenient to do so.

But suppose your hypothetical scenario, in broad strokes, is true. We are in a simulation that has been tweaked so that we will worship the creator. How is this any different from the beliefs of Christianity? For example, 'creating the universe' is the same thing as building a simulation, and Jesus specifically said he was an avatar. Also regardless of why the simulation was actually created, it might as well be cached as 'entertainment purposes'. Unless the creator is somehow dependent upon the simulation .. but in any case we probably don't have enough insight into this psyche to speculate about the differences between his 'needs' and 'wants'!

But I'll provide the same counter-argument to your sim-creator that I provide against theism and see how it stands. If this simulator is able to induce worship by, for example, occasionally creating miracles and inspiring avatars, then why doesn't he do a better job of it? (Maybe this is a who-can-induce-the-most-vehement-worship tournament and the rules are very strict? For example, only 5 interferences in the first 5000 years?) Also, the Jesus avatar was very keen on human fellowship. If the sim-creator was keen on this, why did he instill such antagonistic human behaviors?

It seems that the sim-creator doesn't have a lot of control of the simulation after all. Regardless of the sim-creator's motives, we're still the product of evolution and the sim-creator still needs to follow the laws of physics. So the hypothesis doesn't explain anything extra or give us any extra hope.

Yet amazing people and wonderful events do indeed leave a little hope. There is an apparent 'force for good' in the universe, which people can deify if they want (or externalize for convenience, as I do) . It just is what it is though, nothing supernatural or omnipotent but possibly prevailing.

Replies from: quentin, PhilGoetz
comment by quentin · 2011-10-04T20:29:12.253Z · LW(p) · GW(p)

the only compelling argument I've heard against Pascal's Wager is that you can't/shouldn't believe something just because it is convenient to do so

As I understand it, that's because our universe has provided no evidence that belief alters reality; but it does seem to suggest that the optimum strategy is relentless pursuit of truth. However, if we had good reason to think otherwise (I don't think this article counts), I see no reason why one shouldn't alter their beliefs to their benefit, apart from aesthetics.

Whether or not this is even possible is unclear to me; but my intuition is that I could intentionally update to false beliefs, contrary to what seems to be the consensus here.

comment by PhilGoetz · 2011-10-04T16:01:02.319Z · LW(p) · GW(p)

But I'll provide the same counter-argument to your sim-creator that I provide against theism and see how it stands. If this simulator is able to induce worship by, for example, occasionally creating miracles and inspiring avatars, then why doesn't he do a better job of it? (Maybe this is a who-can-induce-the-most-vehement-worship tournament and the rules are very strict? For example, only 5 interferences in the first 5000 years?) Also, the Jesus avatar was very keen on human fellowship. If the sim-creator was keen on this, why did he instill such antagonistic human behaviors?

The Player plays in mysterious ways.

Interesting points. Hard, though, to have good priors for. My default assumption would be that the game imposes restrictions, such as the laws of physics and of game theory; and the Player tries to create an interesting world within those restrictions. The Player isn't free to say, "Humans will all be nice to each other all the time!" That isn't an evolutionarily stable strategy.

IMHO, given the laws of physics and what we know about game theory and evolutionary theory, it's pretty amazing that we have creatures who care about each other at all, and art, and music. (It doesn't contradict these theories, but it is counter-intuitive.) I would give the Player a pretty high score.

The advantage of the argument in my post is that it tries to make only simple claims about how a God should be expected to behave. "God made the universe for fun" is much simpler, and therefore has a higher prior, than "God should construct the universe to contain super-happy beings", which embeds many assumptions about God's circumstances, morality, energy budget, etc.

There is an apparent 'force for good' in the universe, which people can deify if they want (or externalize for convenience, as I do).

This is a digression, but: Suppose the universe has no force for good, and has an average goodness of zero. Would we not expect that the creatures that thrived best in that universe would perceive the universe as good?

comment by Desrtopa · 2011-10-04T06:15:35.646Z · LW(p) · GW(p)

Even adjusting for all the arguments provided here, only the probability given the other premises that the simulator would chose to represent itself through Christianity is on the same order of magnitude of what I would assign.

I don't understand at all why you lump entertainment and religious purposes into a single hypothesis and treat evidence for one as evidence for the other. If we accept that our universe is being simulated for entertainment purposes, it would still not give us significant reason to believe that it's being simulated for religious purposes.

If the person running the sim wanted to be personally glorified within it, I would expect them to do a much, much better job of arranging it. I would adjust this one down several orders of magnitude.

The numbers I'd assign would be more like

P(sim) < .001 (I find it doubtful that, should it be possible to simulate a universe such as our own, a civilization capable of doing so would chose to simulate our universe; should we ever gain the capability to do so I suspect it would be regarded as ethically impermissible to simulate a universe with such a degree of suffering.)

P(rel|sim)< .00000001 (I find it much more likely than this that if our universe is being simulated, it's being simulated for entertainment, although the proportion of computing power we devote to entertainment cannot reasonably be substituted for this. How well optimized does the universe look for entertainment for an external witness? But our universe looks much worse optimized for religious veneration of a particular simulating entity than for generalized entertainment value.)

P(ego|rel, sim)<.00001 (All the available candidates simply do such an atrocious job compared to what I would expect of a simulator's lone avatar that I would give over the vast majority of the probability space to the hypotheses that the simulation is either not like a game with player avatars, but a piece of spectator entertainment like a movie, or numerous people have been used as player avatars.)

P(chr0|ego, rel, sim, Earth) = .5 (On the one hand, I would strongly expect that if the simulator wanted veneration from a particular religion and promoted that religion via an avatar, that religion would be the most popular one on Earth. On the other hand, I would expect it to be minimally ambiguous and factionalized. I'd assign most of the remaining probability mass to Islam.)

P(follow-thru) < .01 (Unless a civilization full of people with unmodified human-like psyches lets just anyone simulate universes for their amusement, I think this would probably be regarded as impermissible, and I don't think most people would be quite that capricious even given the opportunity. I would assign a higher probability of a utility dominating afterlife contingent on behavior rather than belief.)

Which gives a probability of < 5x10^-19.

Replies from: PhilGoetz
comment by PhilGoetz · 2011-10-04T15:14:08.957Z · LW(p) · GW(p)

I don't understand at all why you lump entertainment and religious purposes into a single hypothesis and treat evidence for one as evidence for the other. If we accept that our universe is being simulated for entertainment purposes, it would still not give us significant reason to believe that it's being simulated for religious purposes.

Talking about religious purposes was an afterthought. Nobody does that today. It's conceivable that religions in the future could tell people to run simulations. I wasn't really thinking of a player who wanted to be God; I was thinking of religions that might work things out in simulations for some reason, or have some occult beliefs about the relationship between the world and simulations, or believed it was their moral duty to emulate the Creator.

If the person running the sim wanted to be personally glorified within it, I would expect them to do a much, much better job of arranging it. I would adjust this one down several orders of magnitude.

I think you're saying something like, "What is the probability that we are in a simulation whose purpose is for the player to be a religious figure whom we worship and glorify?" Whereas I lumped that case in there as an afterthought, and am more interested in the higher-probability scenario that we are in a simulation that is supposed to be fun for the player, where the player get credit for playing well, but getting credit/glory is not supposed to be easy. It wouldn't be fun then.

Replies from: Desrtopa
comment by Desrtopa · 2011-10-04T15:26:47.970Z · LW(p) · GW(p)

If we imagine this is sim after the style of a game like Civilization, where the player is measured along multiple metrics of success and has competition from multiple other factions, I would substitute P(rel|sim) with P(rel|gamesim), the probability that religious veneration is one of the metrics in the game, but I would assign P(gamesim) a much lower probability than P(sim), because it occupies a very small part of the probability mass that I assign to a simulation. As before, a large part of the improbability would come from locating that particular type of sim in possibility space.

I would also have to revise P(follow-thru) way down, because more than in the other scenario, it seems like it would be a complete waste of time, completely tangential to the purpose of the simulation and not at all worth the computation time it would take.

comment by dlthomas · 2011-10-04T17:21:10.920Z · LW(p) · GW(p)

To what degree can we make inferences about the outside of the simulation from what we observe inside it?

Replies from: vi21maobk9vp
comment by vi21maobk9vp · 2011-10-04T17:35:23.387Z · LW(p) · GW(p)

If we fully rely on the simulation argument, we can assume that we have cognitive processes remotely similar to the cognitive processes of some assumed ancestors of simulation runners.

Not much.

If we don't - all bets are off.

comment by lavalamp · 2011-10-04T13:10:49.958Z · LW(p) · GW(p)

If we therefore limit the possible avatars that our simulator God is using on Earth to the major monotheistic religions of Christianity, Islam, and Judaism, and consider them all equiprobable; plus a 25% chance that this God is jumping from one avatar to another, or chose to reveal Himself via Jesus but then Paul screwed everything up, or some other minority position; then p(chr0|ego, ent, sim, Earth) = .25.

I have a big problem with this step. Why should (have lots of adherents) imply (is point of simulation)? Surely there will be more unskilled play-throughs of "simgod" than skilled ones. I think this number can be made arbitrarily low just by adding in all known religions...

Replies from: PhilGoetz
comment by PhilGoetz · 2011-10-04T14:46:59.420Z · LW(p) · GW(p)

Theologians clearly need to observe people playing a large number of games of Civilization, and record the distribution of fraction of adherents that the player has.

comment by Jonathan_Graehl · 2011-10-04T22:39:07.809Z · LW(p) · GW(p)

I initially rankled at your suggestions on how I should vote, but ultimately I agree. I've never taken the simulation hypothesis seriously, but it's still an interesting argument.

Our actual history is less exciting to me than I expect from a game or a work of fiction. This is only relevant to the extent that we insist on making predictions as if the likely simulators are psychologically like us. I can't even begin to justify the prior (on what kinds of who are likely to be making what kinds of simulation) that would support that, especially with the "given that (something like) us exists" anthropic teaser.

Further, there's a lot more waste (per entertainment value) than I'd expect. There seem to be precise simulation everywhere, where it's not needed. I don't feel important or entertaining, yet I'm computationally expensive. This matters if we presume that the simulators have limited computational resources (why we should expect that, I have no idea - again, completely shaky ground - it seems to me only by laziness that we keep insisting that the containing universe is anything like ours). Still, if I consider simulation at all, I discount entertainment as the purpose.

I consider simulations of universes like ours psychologically plausible for creators like us only as far as the containing universe has vast resources, and the creators like us are incredibly bored and refuse self-modification. I'm skeptical that people like us will ever be able to simulate universes like ours using a universe like ours. I suspect either the simulators or their universe are far different from us or ours. What should I expect now?

I really have to wonder how people can justify any prior at all on the type of universe we're in, other than the trivial "it must be one that can sustain our existence, and consistent with whatever else we can observe now - and MAYBE the physical laws in operation now were always in operation".

comment by timtyler · 2011-10-04T17:51:10.287Z · LW(p) · GW(p)

If you accept the simulation argument, then P(sim) > .99.

That is not the usual conclusion of the simulation argument.

The conclusion of it is this:

at least one of the following propositions is true: (1) The fraction of human-level civilizations that reach a posthuman stage is very close to zero; (2) The fraction of posthuman civilizations that are interested in running ancestor-simulations is very close to zero; (3) The fraction of all people with our kind of experiences that are living in a simulation is very close to one.

Replies from: PhilGoetz
comment by PhilGoetz · 2011-10-04T21:54:24.588Z · LW(p) · GW(p)

Tim, I assume you meant this as a nit-pick rather than as a substantive criticism. Substitute "if you accept option 3 of the simulation argument".

If you think this objection is substantive, I expect you to lower the probability you assign to reaching post-humanity and to posthumans wanting to run simulations. (The "ancestor" part in option 2 should be struck out; ancestors are only a small subset of the kinds of agents posthumans might want to simulate that would be more primitive than posthumans.)

Replies from: CarlShulman
comment by CarlShulman · 2011-10-04T22:00:48.937Z · LW(p) · GW(p)

Aka the "Simulation Hypothesis."

comment by vi21maobk9vp · 2011-10-04T20:11:16.233Z · LW(p) · GW(p)

On games...

If we consider games with a big population of modeled characters (we are obviously in a game with many characters), strategies of various kinds and multiplayer RPGs come forth.

In multiplayer RPGs, logical behaviour for a killed character is either to reincarnate anew (player character, some NPCs), respawn as previously seen (simpler NPCs - not observed in our world? or maybe some amoebas..) or vanish forever. Player characters in games are not supposed to be stuck in a state they cannot change; and emulating NPCs in player-inaccessible afterlife needs some separate reason for programmers to do.

In strategies, player is far from all-powerful, and eternal fixed-state afterlife for in-game creatures is a state where they are modeled but again cannot affect gameplay.

Of course, more complicated game will be invented; but if we consider a game some mixture of entertainment and competition, heaven and especially hell as depicted in some religions make little sense. Maybe Greek-style Hades where heros occasionally descend can make sense from gameplay point of view; but it is still far from hell. Eternal nearly-fixed state of a player character will make player quit; eternal nearly-fixed state of NPC while simulating its cognitive process still seems pointless...

...unless the player gets to play torturer. These kinds of minigames do seem to exist, but are far from being dominant direction. Let's hope they will stay this way.

Replies from: PhilGoetz
comment by PhilGoetz · 2011-10-04T21:41:57.904Z · LW(p) · GW(p)

I think we can take it that we're not in a multiplayer game, since we don't think that we're players. It's possible that players would agree to have their memories wiped before starting the game, but this seems unlikely.

Anyway, the multiplayer game hypothesis is incompatible with the simulation argument. You need only one large multiplayer game for one universe of players, assuming each player can play only one game at a time.

Replies from: vi21maobk9vp, JoshuaZ
comment by vi21maobk9vp · 2011-10-05T07:45:54.214Z · LW(p) · GW(p)

First,in a multiplayer game you still can have more NPCs than players. Players do not show that they are special because it would break the rules / spoil the fun / lead to their player character locked up as insane.

Second, maybe they too find it tedious to control every single muscle of the character body. So they gave some weak - by their standards - AI, and control the character via nudging desires and choices. Have you ever felt that you doubt which of a few decision to chose and then suddenly decide? The player has finally clicked a menu item of a few provided by your intelligence.

Third, for huge number of NPCs relative to number of players you could set up a strategy. Not like a Civilization, but like a Dwarf Fortress or SimCity - some ideas suddenly become commonplace and autonomous agents try to implement them.

Replies from: PhilGoetz
comment by PhilGoetz · 2011-10-05T15:57:36.862Z · LW(p) · GW(p)

The issue is not the ratio of NPCs to players. The issue is the number of players per simulation. If you assume a multiplayer game, you don't need as many simulations, and we no longer assign a high probability to us being in a simulation.

Replies from: vi21maobk9vp
comment by vi21maobk9vp · 2011-10-05T16:09:42.787Z · LW(p) · GW(p)

A multiplayer game may have a reasonable world limit size, and inter-world movement isn't implemented yet (whether it would be inside one universe, as in Eve Online, or between disjunct universes). So the simultaneous simulation count goes somewhat down, but there are still many and new ones are launched as population grows...

comment by JoshuaZ · 2011-10-04T21:49:36.729Z · LW(p) · GW(p)

In the multiplayer game the players might be different deities not different people.

comment by shminux · 2011-10-04T06:41:09.182Z · LW(p) · GW(p)

Thank you for this excellent example of a clever arguer. You clearly want Christianity to have a chance in hell, so you invent all kinds of rationalizations to support it. Maybe this should be added to the therefore god exists list, though #298 is already close. I understand now why EY refuses to engage in any discussion with you. There are plenty of fallacies in your post, many pointed out in the comments, but it is pointless to argue about it with you, since you have already written your bottom line and will not budge.

Replies from: PhilGoetz, Nisan, PhilGoetz
comment by PhilGoetz · 2011-10-04T16:14:06.813Z · LW(p) · GW(p)

It is depressing that, even after all the posts I've written on LessWrong, most readers (judging from the score on this comment) will still assume I am a Christian if I write something that appears pro-Christian. It is also depressing that the key determination of a person's reaction to an argument seems to be their perceptions of the arguer's motives.

(I let this comment sit awhile before responding, to see where it went; but now that I've provided evidence in other places that I'm not a Christian, my cover is blown.)

Even the LessWronger, trained to spot and avoid biases, still makes the same errors as everyone else, even while consciously thinking about these biases. After 3 years of LessWrong, I don't see evidence that we're getting less wrong.

Replies from: Desrtopa, Nornagest, shminux, wedrifid, Eliezer_Yudkowsky, lavalamp, Kingreaper
comment by Desrtopa · 2011-10-04T16:46:41.526Z · LW(p) · GW(p)

Personally, I downvoted the main post for providing an argument, which you said you felt was the best argument for Christianity, which I felt deserved so little probability mass as to be unworthy of being raised for discussion (as far as I can remember this is the first time I've affirmed that I downvoted anything,) but I never assumed that you were Christian.

If I had previously assigned a significant probability to the proposition that you were a Christian, this post would have forced me to revise it downwards, I just thought it was ill considered.

comment by Nornagest · 2011-10-04T21:23:11.360Z · LW(p) · GW(p)

I didn't downvote the OP, but if I had it wouldn't have been for appearing pro-Christian; it reads as thoroughly secular, in fact, like a theological version of the pseudo-proofs of absurd mathematical statements (that 1 = 2, for example) you see occasionally in places where math trivia is considered entertaining. It does strike me as an argument likely to shed more heat than light, though.

comment by shminux · 2011-10-04T17:03:39.868Z · LW(p) · GW(p)

Even the LessWronger, trained to spot and avoid biases, still makes the same errors as everyone else, even while consciously thinking about these biases. After 3 years of LessWrong, I don't see evidence that we're getting less wrong.

I hate to agree with you, but this is actually a valid point. While this site has, on average, a far more civil discourse than your run-of-the-mill internet forum, I am not convinced that the rationality level has perceptibly increased over the years, judging from the comment threads then and now. Even the site's most prominent and respected contributors occasionally succumb to the standard cognitive biases, as has been pointed out. Apparently the phenomenon of "flash downvoting" in response to a post or comment people dislike is also not imagined.

I wish there were a simple cognitive bias detection algorithm or checklist that a conscientious LWer could employ before posting. Or maybe there is one and I am not aware of it.

Replies from: wedrifid
comment by wedrifid · 2011-10-05T09:44:16.475Z · LW(p) · GW(p)

I am not convinced that the rationality level has perceptibly increased over the years, judging from the comment threads then and now

My estimation is a decrease, mostly due to dilution of the seed polulation from Eliezer-era OvercomingBias. This isn't necessarily a bad thing. Remaining a bastion of the already reasonably rational wouldn't have made lesswrong particularly useful. I'm willing to put up with a somewhat lower standard if it benefits others.

Replies from: Bongo
comment by Bongo · 2011-10-07T09:11:00.594Z · LW(p) · GW(p)

My impression is that the level went up and then down:

• During the first year of LW the posts were good.
comment by wedrifid · 2011-10-05T09:41:28.339Z · LW(p) · GW(p)

It is depressing that, even after all the posts I've written on LessWrong, most readers (judging from the score on this comment) will still assume I am a Christian if I write something that appears pro-Christian.

Nobody said you were Christian.

Even the LessWronger, trained to spot and avoid biases, still makes the same errors as everyone else, even while consciously thinking about these biases. After 3 years of LessWrong, I don't see evidence that we're getting less wrong.

The fact that your accusation of irrationality for Shminux is a blatant error of logic and basic comprehension manages to both undermine your point and support it at the same time. I suppose the fact that you are a far more prominent member of lesswrong than Shminux makes the criticism of lesswrong stronger on net. As does the fact that your comment is positive rather than spiraling into the negative. And this last observation is actually quite troubling.

comment by Eliezer Yudkowsky (Eliezer_Yudkowsky) · 2011-10-05T08:46:13.547Z · LW(p) · GW(p)

I don't think you're a Christian. I do think you want Christianity to have a chance in hell, because... well, I'm not going to speculate. Meta-contrarianism would be one reason. Everyone voting down shminux, please note that they never said they thought Goetz was a Christian.

Replies from: Aleksei_Riikonen
comment by Aleksei_Riikonen · 2011-10-05T16:50:58.521Z · LW(p) · GW(p)

Everyone voting down shminux, please also note that they did say:

You clearly want Christianity to have a chance in hell

it is pointless to argue about it with you, since you have already written your bottom line and will not budge

I'll downvote for those. While I don't claim Goetz' treatment of the topic to have been perfect, I don't see evidence of it necessarily having been motivated by anything else than an honest curious interest in the topic. Claims that he clearly wants Christianity to have a chance or that he wouldn't be able to change his mind on the topic seem to me to be just as uncalled for as claims that he would be a Christian.

Replies from: JoshuaZ, shminux
comment by JoshuaZ · 2011-10-05T23:38:38.776Z · LW(p) · GW(p)

There was definite evidence of this. As I pointed out in my reply the specific numbers picked looked a lot like what one would expect if one had a conscious or unconscious desire for the argument to just barely go through.

comment by shminux · 2011-10-05T23:36:10.807Z · LW(p) · GW(p)

You are probably correct that, taken out of the poster's profile context, one might not

see evidence of it necessarily having been motivated by anything else than an honest curious interest in the topic.

I have my doubts, but in retrospect it looks like my emotions got the better of me, and I concede that my original reply was less neutral than called for. Hey, I'm still new to this rationality thing.

comment by lavalamp · 2011-10-04T19:49:33.826Z · LW(p) · GW(p)

I'm not sure that this conclusion is warranted. This post did not cause me to think you were a christian, in fact I really can't imagine a christian putting that argument together in that way. Additionally, the argument clearly applies equally to Islam and Judaism, and you state as much while making it.

As for me: I initially voted the post up, thinking it was rated too low, but after further thought removed my upvote; I really don't think this is a big departure from more normal statements of the wager.

comment by Kingreaper · 2011-10-05T10:11:08.934Z · LW(p) · GW(p)

The question is not whether or not christianity is true, it's whether or not you set out to create an argument that christianity should be followed.

So, did you stumble across this argument as a realisation while thinking on other things?

Or did you deliberately set out to create such an argument?

It looks like a deliberately constructed argument to me.

comment by Nisan · 2011-10-10T07:00:08.772Z · LW(p) · GW(p)

Ooh, #85 is pretty clever.

comment by PhilGoetz · 2011-10-04T15:04:04.738Z · LW(p) · GW(p)

shminux - For my own education, have you read many of my LessWrong posts?

comment by DanielLC · 2011-10-04T05:11:58.830Z · LW(p) · GW(p)
• limit U(1)→∞, P(chr)→0 P(chr)U(1) is undefined, and
• invoking infinite utilities isn't fair.

You can get these problems if you have only finite utility, but infinite expected utility.

It's impossible for a prior with a converging expected utility to result in a posterior with diverging expected utility using only a finite amount of evidence.

While it's correct that just using absurdly low probability and absurdly high utility won't cause that problem, it's not likely to come up without that problem being there in the first place.

comment by Kingreaper · 2011-10-05T10:03:51.195Z · LW(p) · GW(p)

The fact that we do not see continual interference, and obvious evidence of a deity, is very strong evidence against the ego-trip theory of godly existence.

The fact the bible mentions multiple gods, repeatedly, throughout the old testament, is very strong evidence that it is not a book written by an ego-tripping deity.

Moreover, if the universe is being run as an ego-trip heaven is likely to be, as described in some christian sects, praising 'god' for all eternity. Which is worse than most depictions of hell; making the whole pascal's wager thing null and void.

comment by [deleted] · 2011-10-04T06:17:50.692Z · LW(p) · GW(p)

deleted

Replies from: JoshuaZ, PhilGoetz
comment by JoshuaZ · 2011-10-04T06:30:06.503Z · LW(p) · GW(p)

Pascal says:

This isn't helpful. You are criticizing the version of the argument that Pascal originally presented, not the version that Phil gave in his post. This is a classical failure mode when discussion philosophical issues (and disturbingly common among professional philosophers). That there might be flaws in the original form of an argument doesn't mean that a repaired version doesn't work. Pascal almost certainly didn't know about the idea of simulations for example. This sort of thing is similar to creationists who focus on Darwin's original work rather than the modern understanding of evolution.

Replies from: None, None
comment by [deleted] · 2011-10-04T06:43:55.560Z · LW(p) · GW(p)

Actually I don't understand your objection, did you base it only on those two words.. or did you take into account what I said? I still think what I said refutes Phil's argument. Maybe Phil can comment.

Replies from: JoshuaZ
comment by JoshuaZ · 2011-10-04T06:51:24.817Z · LW(p) · GW(p)

I your comment the first time that some of your arguments do deal with some of the issues that Phil raised. But when I read it the first time it seemed parts of your response and primary criticism seem to address the version of Pascal's wager where one ignores the actual probability in question because the reward is infinite. But Phil's version tries to make actual estimates of the probability and essentially deals with the problem of all the unknown hypothetical religions but giving an argument that assigns them a low probability compared to the believed religions.

comment by [deleted] · 2011-10-04T06:36:22.634Z · LW(p) · GW(p)

OK. I thought this was about Pascals Wager.

I was responding to

Two of the key criticisms of Pascal's wager are that

• limit U(1)→∞, P(chr)→0 P(chr)U(1) is undefined, and
• invoking infinite utilities isn't fair.

If, however, P(chr) is not infinitessimal, and U(1) is merely very large, these counter-arguments fail.

by giving a different counter-argument (which does not fail).

comment by PhilGoetz · 2011-10-04T15:24:20.990Z · LW(p) · GW(p)

I don't think it's a reasonable hypothesis that the God of the simulation secretly wants people to flick the lightswitch off and on 17 times before entering every room but has never told anyone. Creating an infinity of possible alternatives and then assigning them all equal probability would cause you difficulties in many more situations than choosing a religion.

In general when there is an infinity of possible hypotheses (and there always is, in any situation) one does not quantify over them: decisions cannot be made in this way.

I didn't quantify over an infinity of possible hypothesis. I considered only hypothesis that were suggested by the data. We aren't dealing with pure prior probabilities here. We have observations; and even without observations, we have priors based on hypothesis complexity.

Since you say there are always an infinity of possible hypotheses, how would you choose between them, in any situation? Your claim implies that Bayesian reasoning is always impossible.