Has anyone done a “shut up and multiply” for Islam (or Christianity)? I would be interested in seeing such a calculation. (I did a Google search and couldn’t find anything directly relevant.) Here’s my own attempt, which doesn’t get very far.
Let H = “Islam is true” and E = everything we’ve observed about the universe so far. According to Bayes:
P(H | E) = P(E | H) P(H) / P(E)
Unfortunately I have no idea how to compute the terms above. Nor do I know how to argue that P(H|E) is as small as 10^-20 without explicitly calculating the terms. One argument might be that P(H) is very small because of the high complexity of Islam, but since E includes “23% of humanity believe in some form of Islam”, the term for the complexity of Islam seems to be present in both the numerator and denominator and therefore cancel each other out.
If someone has done such a calculation/argument before, please post a link?
P(E) includes the convincingness of Islam to people on average, not the complexity of Islam. These things are very different because of the conjunction fallacy. So P(H) can be a lot smaller than P(E).
I don’t understand how P(E) does not include a term for the complexity of Islam, given that E contains Islam, and E is not so large that it takes a huge number of bits to locate Islam inside E.
It doesn’t take a lot of bits to locate “Islam is false” based on “Islam is true”. Does it mean that all complex statements have about 50% probability?
I don’t think that’s true; cousin_it had it right the first time. The complexity of Islam is the complexity of a reality that contains an omnipotent creator, his angels, Paradise, Hell, and so forth. Everything we’ve observed about the universe includes people believing in Islam, but not the beings and places that Islam says exist.
In other words, E contains Islam the religion, not Islam the reality.
The really big problem with such a reality is that it contains a fundamental, non-contingent mind (God’s/Allah’s, etc) - and we all know how much describing one of those takes - and the requirement that God is non-contingent means we can’t use any simpler, underlying ideas like Darwinian evolution. Non-contingency, in theory selection terms, is a god killer: It forces God to incur a huge information penalty—unless the theist refuses even to play by these rules and thinks God is above all that—in which case they aren’t even playing the theory selection game.
I don’t see this. Why assume that the non-contingent, pre-existing God is particularly complex. Why not assume that the current complexity of God (if He actually is complex) developed over time as the universe evolved since the big bang. Or, just as good, assume that God became complex before He created this universe.
It is not as if we know enough about God to actually start writing down that presumptive long bit string. And, after all, we don’t ask the big bang to explain the coastline of Great Britain.
Non-contingency, in theory selection terms, is a god killer
Agreed. It’s why I’m so annoyed when even smart atheists say that God was an ok hypothesis before evolution was discovered. God was always one of the worst possible hypotheses!
unless the theist refuses even to play by these rules and thinks God is above all that—in which case they aren’t even playing the theory selection game.
Or, put more directly: Unless the theist is deluding himself. :)
I’m confused. In the comments to my post you draw a distinction between an “event” and a “huge set of events”, saying that complexity only applies to the former but not the latter. But Islam is also a “huge set of events”—it doesn’t predict just one possible future, but a wide class of them (possibly even including our actual world, ask any Muslim!), so you can’t make an argument against it based on complexity of description alone. Does this mean you tripped on the exact same mine I was trying to defuse with my post?
I’d be very interested in hearing a valid argument about the “right” prior we should assign to Islam being true—how “wide” the set of world-programs corresponding to it actually is—because I tried to solve this problem and failed.
Sorry, I was confused. Just ignore that comment of mine in your thread.
I’m not sure how to answer your question because as far as I can tell you’ve already done so. The complexity of a world-program gives its a priori probability. The a priori probability of a hypothesis is the sum of the probabilities of all the world-programs it contains. What’s the problem?
By reasonable, I mean the hypothesis is worth considering, if there were reasons to entertain it. That is, if someone suspected there was a mind behind reality, I don’t think they should dismiss it out of hand as unreasonable because this mind must be non-contingent.
In fact, we should expect any explanation of our creation to be non-contingent, since physical reality appears to be so.
For example, if it’s reasonable to consider the probability that we’re in a simulation, then we’re considering a non-contingent mind creating the simulation we’re in.
Whoops, you’re right. Sorry. I didn’t quite realize you were talking about the universal prior again :-)
But I think the argument can still be made to work. P(H) doesn’t depend only on the complexity of Islam—we must also take into account the internal structure of Islam. For example, the hypothesis “A and B and C and … and Z” has the same complexity as “A or B or C or … or Z”, but obviously the former is way less probable. So P(H) and P(E) have the same term for complexity, but P(H) also gets a heavy “conjunction penalty” which P(E) doesn’t get because people are susceptible to the conjunction fallacy.
It’s slightly distressing that my wrong comment was upvoted.
Whoops, you’re right. Now I’m ashamed that my comment got upvoted.
I think the argument may still be made to work by fleshing out the nonstandard notion of “complexity” that I had in my head when writing it :-) Your prior for a given text being true shouldn’t depend only on the text’s K-complexity. For example, the text “A and B and C and D” has the same complexity as “A or B or C or D”, but the former is way less probable. So P(E) and P(H) may have the same term for complexity, but P(H) also gets a “conjunction penalty” that P(E) doesn’t get because people are prey to the conjunction fallacy.
EDIT: this was yet another mistake. Such an argument cannot work because P(E) is obviously much smaller than P(H), because E is a huge mountain of evidence and H is just a little text. When trying to reach the correct answer, we cannot afford to ignore P(E|H).
For simplicity we may assume P(E|H) to be near-certainty: if there is an attention-seeking god, we’d know about it. This leaves P(E) and P(H), and P(H|E) is tiny exactly for the reason you named: P(H) is much smaller than P(E), because H is optimized for meme-spreading to a great extent, which makes for a given complexity (that translates into P(H)) probability of gaining popularity P(E) comparatively much higher.
Thus, just arguing from complexity indeed misses the point, and the real reason for improbability of cultish claims is that they are highly optimized to be cultish claims.
For example, compare with tossing a coin 50 times: the actual observation, whatever that is, will be a highly improbable event, and theoretical prediction from the model of fair coin will be too. But if the observation is highly optimized to attract attention, for example it’s all 50 tails, then theoretical model crumbles, and not because the event you’ve observed is too improbable according to it, but because other hypotheses win out.
the term for the complexity of Islam seems to be present in both the numerator and denominator and therefore cancel each other out.
Actually it doesn’t, human generated complexity is different from naturally generated complexity (for instance it fits into narratives, apparent holes are filled with the sort of justifications a human is likely to think of etc.). That’s one of the ways you can tell stories from real events. Religious accounts contain much of what looks like human generated complexity.
Here’s a somewhat rough way of estimating probabilities of unlikely events. Let’s say that an event X with P(X) = about 1-in-10 is a “lucky break.” Suppose that there are L(1) ways that Y could occur on account of a single lucky break, L(2) ways that Y could occur on account of a pair of independent lucky breaks, L(3) ways that Y could occur on account of 3 independent lucky breaks, and so on. Then P(Y) is approximately the sum over all n of L(n)/10^n. I have the feeling that arguments about whether P(Y) is small versus extremely small are arguments about the growth rate of L(n).
I discussed the problem of estimating P(“23% of humanity believes...”) here. I’d be grateful for thoughts or criticisms.
This is a small point but “E includes complex claim C” does not imply that the (for instance, Kolmogorov) complexity of E is as large as the Kolmogorov complexity of C. The complexity of the digits of square root of 2 is pretty small, but they contain strings of arbitrarily high complexity.
E includes C implies that K(C) ⇐ K(E) + K(information needed to locate C within E). In this case K(information needed to locate C within E) seems small enough not to matter to the overall argument, which is why I left it out. (Since you said “this is a small point” I guess you probably understand and agree with this.)
Actually no I hadn’t thought of that. But I wonder if the amount of information it takes to locate “lots of people are muslims” within E is as small as you say. My particular E does not even contain that much information about Islam, and how people came to believe it, but it does contain a model of how people come to believe weird things in general. Is that a misleading way of putting things? I can’t tell.
There are some very crude sketches of shutting-up-and-multiplying, from one Christian and a couple of atheists, here (read the comments as well as the post itself), and I think there may be more with a similar flavour in other blog posts there (and their comments) from around the same time.
(The author of the blog has posted a little on LW. The two skeptics responsible for most of the comments on that post have both been quite active here. One of them still is, and is in fact posting this comment right now :-).)
Wei Dai, exactly. The point about about the complexity of the thing is included in the fact that people believe it was the point I have been making all along. Regardless of what you think the resulting probability is, most of the “evidence” for Islam consists in the very fact that some people think it is true—and as you show in your calculation, this is very strong evidence.
It seems to me that komponisto and others are taking it to be known with 100% certainly that Islam and the like were generated by some random process, and then trying to determine what the probability would be.
Now I know that most likely Mohammed was insane and in effect the Koran was in fact generated by a random process. But I certainly don’t know how you can say that the probability that it wasn’t generated randomly is 1 in 10^20 or lower. And in fact if you’re going to assign a probability like this you should have an actual calculation.
Has anyone done a “shut up and multiply” for Islam (or Christianity)? I would be interested in seeing such a calculation. (I did a Google search and couldn’t find anything directly relevant.) Here’s my own attempt, which doesn’t get very far.
Let H = “Islam is true” and E = everything we’ve observed about the universe so far. According to Bayes:
P(H | E) = P(E | H) P(H) / P(E)
Unfortunately I have no idea how to compute the terms above. Nor do I know how to argue that P(H|E) is as small as 10^-20 without explicitly calculating the terms. One argument might be that P(H) is very small because of the high complexity of Islam, but since E includes “23% of humanity believe in some form of Islam”, the term for the complexity of Islam seems to be present in both the numerator and denominator and therefore cancel each other out.
If someone has done such a calculation/argument before, please post a link?
P(E) includes the convincingness of Islam to people on average, not the complexity of Islam. These things are very different because of the conjunction fallacy. So P(H) can be a lot smaller than P(E).
I don’t understand how P(E) does not include a term for the complexity of Islam, given that E contains Islam, and E is not so large that it takes a huge number of bits to locate Islam inside E.
It doesn’t take a lot of bits to locate “Islam is false” based on “Islam is true”. Does it mean that all complex statements have about 50% probability?
I just wrote a post about that.
I don’t think that’s true; cousin_it had it right the first time. The complexity of Islam is the complexity of a reality that contains an omnipotent creator, his angels, Paradise, Hell, and so forth. Everything we’ve observed about the universe includes people believing in Islam, but not the beings and places that Islam says exist.
In other words, E contains Islam the religion, not Islam the reality.
The really big problem with such a reality is that it contains a fundamental, non-contingent mind (God’s/Allah’s, etc) - and we all know how much describing one of those takes - and the requirement that God is non-contingent means we can’t use any simpler, underlying ideas like Darwinian evolution. Non-contingency, in theory selection terms, is a god killer: It forces God to incur a huge information penalty—unless the theist refuses even to play by these rules and thinks God is above all that—in which case they aren’t even playing the theory selection game.
I don’t see this. Why assume that the non-contingent, pre-existing God is particularly complex. Why not assume that the current complexity of God (if He actually is complex) developed over time as the universe evolved since the big bang. Or, just as good, assume that God became complex before He created this universe.
It is not as if we know enough about God to actually start writing down that presumptive long bit string. And, after all, we don’t ask the big bang to explain the coastline of Great Britain.
If we do that, should we even call that “less complex earlier version of God” God? Would it deserve the title?
Sure, why not? I refer to the earlier, less complex version of Michael Jackson as “Michael Jackson”.
Agreed. It’s why I’m so annoyed when even smart atheists say that God was an ok hypothesis before evolution was discovered. God was always one of the worst possible hypotheses!
Or, put more directly: Unless the theist is deluding himself. :)
I’m confused. In the comments to my post you draw a distinction between an “event” and a “huge set of events”, saying that complexity only applies to the former but not the latter. But Islam is also a “huge set of events”—it doesn’t predict just one possible future, but a wide class of them (possibly even including our actual world, ask any Muslim!), so you can’t make an argument against it based on complexity of description alone. Does this mean you tripped on the exact same mine I was trying to defuse with my post?
I’d be very interested in hearing a valid argument about the “right” prior we should assign to Islam being true—how “wide” the set of world-programs corresponding to it actually is—because I tried to solve this problem and failed.
Sorry, I was confused. Just ignore that comment of mine in your thread.
I’m not sure how to answer your question because as far as I can tell you’ve already done so. The complexity of a world-program gives its a priori probability. The a priori probability of a hypothesis is the sum of the probabilities of all the world-programs it contains. What’s the problem?
The problem is that reality itself is apparently fundamentally non-contingent. Adding “mind” to all that doesn’t seem so unreasonable.
Do you mean it doesn’t seem so unreasonable to you, or to other people?
By reasonable, I mean the hypothesis is worth considering, if there were reasons to entertain it. That is, if someone suspected there was a mind behind reality, I don’t think they should dismiss it out of hand as unreasonable because this mind must be non-contingent.
In fact, we should expect any explanation of our creation to be non-contingent, since physical reality appears to be so.
For example, if it’s reasonable to consider the probability that we’re in a simulation, then we’re considering a non-contingent mind creating the simulation we’re in.
Whoops, you’re right. Sorry. I didn’t quite realize you were talking about the universal prior again :-)
But I think the argument can still be made to work. P(H) doesn’t depend only on the complexity of Islam—we must also take into account the internal structure of Islam. For example, the hypothesis “A and B and C and … and Z” has the same complexity as “A or B or C or … or Z”, but obviously the former is way less probable. So P(H) and P(E) have the same term for complexity, but P(H) also gets a heavy “conjunction penalty” which P(E) doesn’t get because people are susceptible to the conjunction fallacy.
It’s slightly distressing that my wrong comment was upvoted.
Whoops, you’re right. Now I’m ashamed that my comment got upvoted.
I think the argument may still be made to work by fleshing out the nonstandard notion of “complexity” that I had in my head when writing it :-) Your prior for a given text being true shouldn’t depend only on the text’s K-complexity. For example, the text “A and B and C and D” has the same complexity as “A or B or C or D”, but the former is way less probable. So P(E) and P(H) may have the same term for complexity, but P(H) also gets a “conjunction penalty” that P(E) doesn’t get because people are prey to the conjunction fallacy.
EDIT: this was yet another mistake. Such an argument cannot work because P(E) is obviously much smaller than P(H), because E is a huge mountain of evidence and H is just a little text. When trying to reach the correct answer, we cannot afford to ignore P(E|H).
For simplicity we may assume P(E|H) to be near-certainty: if there is an attention-seeking god, we’d know about it. This leaves P(E) and P(H), and P(H|E) is tiny exactly for the reason you named: P(H) is much smaller than P(E), because H is optimized for meme-spreading to a great extent, which makes for a given complexity (that translates into P(H)) probability of gaining popularity P(E) comparatively much higher.
Thus, just arguing from complexity indeed misses the point, and the real reason for improbability of cultish claims is that they are highly optimized to be cultish claims.
For example, compare with tossing a coin 50 times: the actual observation, whatever that is, will be a highly improbable event, and theoretical prediction from the model of fair coin will be too. But if the observation is highly optimized to attract attention, for example it’s all 50 tails, then theoretical model crumbles, and not because the event you’ve observed is too improbable according to it, but because other hypotheses win out.
Actually it doesn’t, human generated complexity is different from naturally generated complexity (for instance it fits into narratives, apparent holes are filled with the sort of justifications a human is likely to think of etc.). That’s one of the ways you can tell stories from real events. Religious accounts contain much of what looks like human generated complexity.
Here’s a somewhat rough way of estimating probabilities of unlikely events. Let’s say that an event X with P(X) = about 1-in-10 is a “lucky break.” Suppose that there are L(1) ways that Y could occur on account of a single lucky break, L(2) ways that Y could occur on account of a pair of independent lucky breaks, L(3) ways that Y could occur on account of 3 independent lucky breaks, and so on. Then P(Y) is approximately the sum over all n of L(n)/10^n. I have the feeling that arguments about whether P(Y) is small versus extremely small are arguments about the growth rate of L(n).
I discussed the problem of estimating P(“23% of humanity believes...”) here. I’d be grateful for thoughts or criticisms.
This is a small point but “E includes complex claim C” does not imply that the (for instance, Kolmogorov) complexity of E is as large as the Kolmogorov complexity of C. The complexity of the digits of square root of 2 is pretty small, but they contain strings of arbitrarily high complexity.
E includes C implies that K(C) ⇐ K(E) + K(information needed to locate C within E). In this case K(information needed to locate C within E) seems small enough not to matter to the overall argument, which is why I left it out. (Since you said “this is a small point” I guess you probably understand and agree with this.)
Actually no I hadn’t thought of that. But I wonder if the amount of information it takes to locate “lots of people are muslims” within E is as small as you say. My particular E does not even contain that much information about Islam, and how people came to believe it, but it does contain a model of how people come to believe weird things in general. Is that a misleading way of putting things? I can’t tell.
There are some very crude sketches of shutting-up-and-multiplying, from one Christian and a couple of atheists, here (read the comments as well as the post itself), and I think there may be more with a similar flavour in other blog posts there (and their comments) from around the same time.
(The author of the blog has posted a little on LW. The two skeptics responsible for most of the comments on that post have both been quite active here. One of them still is, and is in fact posting this comment right now :-).)
Wei Dai, exactly. The point about about the complexity of the thing is included in the fact that people believe it was the point I have been making all along. Regardless of what you think the resulting probability is, most of the “evidence” for Islam consists in the very fact that some people think it is true—and as you show in your calculation, this is very strong evidence.
It seems to me that komponisto and others are taking it to be known with 100% certainly that Islam and the like were generated by some random process, and then trying to determine what the probability would be.
Now I know that most likely Mohammed was insane and in effect the Koran was in fact generated by a random process. But I certainly don’t know how you can say that the probability that it wasn’t generated randomly is 1 in 10^20 or lower. And in fact if you’re going to assign a probability like this you should have an actual calculation.