Why Malerin is Wrong About Bayes Theorem

[JoeTheJuggler]

I just had a thought... Malerin claims to be able to use subjective spiritual experiences to qualify as evidence for the existence of God, right?

So wouldn't it be fair to say that an atheist could then use subjective spiritual experiences to qualify as evidence against the existence of God? For example, Sam Harris believes this to be the case.

I'd go the other way and ask why if "subjective experience" is sufficient evidence for God's existence is it not sufficient evidence to believe David Copperfield can cause the Statue of Liberty to vanish.

 

[JoeTheJuggler]

Yes, but the problem here is the same. If I invoke the Uncertainty Principle to justify my quack magic water, the problem is not with the Uncertainty Principle. It only makes you look the fool if you deny the Uncertainty Principle as part of your response to my magic water, because the Uncertainty Principle does exist and has a well-defined meaning that any snake-oil salesman can copy out of Wikipedia.

I don't think I was criticising Bayes Theorem (analogous to attacking the Uncertainty Principle) but simply pointing out how silly it is to start with 0.5 prior probability for God's existence. (Also, I was particularly objecting to calling this "maximally uncertain" position "the agnostic" position.)

Would you agree that it would also be a silly and utterly unhelpful approach to calculating your odds of winning the lottery to assert a prior probability of 0.5 (before considering what the lottery is, for example)? In defense you just say this 0.5 is the maximally uncertain position before we consider the "new" evidence of just what the lottery is.

It sounds like you're making basically the same case wrt the life-filled universe.

I think it would be similarly silly to use this argument to try to prove my own existence and start with the prior probability of 0.5 based on my own maximal uncertainty of my own existence. In this case, I'd have to pretend that I don't know whether or not I exist (even though someone is making the argument).

I am uncertain, therefore there is a 0.5 probability that I am.


Or maybe, I, a living being, am uncertain, therefore the existence of a universe with living beings in it is new evidence. OK--that's not quite the same. . . . .

 

[Malerin]

I'd go the other way and ask why if "subjective experience" is sufficient evidence for God's existence is it not sufficient evidence to believe David Copperfield can cause the Statue of Liberty to vanish.

Sufficient evidence for an agnostic position, yes. Ultimately, all evidence is subjective. You cannot get "outside" your mind or senses.

 

[Malerin]

That's a big one, yes.

The idea that life could exist in a universe with different constants would probably require another thread. But even Victor Stenger (staunch atheist that he is) admits, "life as we know it would be impossible" in a universe with different values for the constants (he then speculates on non-molecular life and silicon-based life). The move from "life as we know it would be impossible" to "some form of life is possible" seems awfully similar to what theists always get bashed for- a leap of faith.

 

[drkitten]

I'm not clear on what you're saying.

No, I'm talking about the classic "what is the probability of life existing in the universe, given that someone is alive to ask the question?" issue.

Which is 1. That's not an "old evidence" problem; it's the problem that if the question "is the universe capable of supporting life" were answered "no," no one would pose the question.

Therefore, the question that you are asking --- "what is the probability that a randomly created universe would support life" is irrelevant.

The question you should be asking is "what is the probability that a randomly created universe in which we exist would support life?" And the answer is 1, by definition. If at any point you assume that the probability of life existing, under any conditions, is less than 1, then you are at best lying by omission by ignoring this factor, since it controls everything else.

It's the elephant in the room as far as the fine-tuning argument goes. If you ignore this factor, your calculations are meaningless and deceptive. If you take this factor into account, then everything else works out to be irrelevant because this factor trumps everything else mathematically.

Really, it's just Doug Adams' puddle analogy dressed up in mathematics --- it doesn't matter how unlikely the puddle is to take any particular shape; if the puddle hadn't taken that particular shape, it wouldn't have been able to ask that question.

 

[Malerin]

No, I'm talking about the classic "what is the probability of life existing in the universe, given that someone is alive to ask the question?" issue.

Which is 1. That's not an "old evidence" problem; it's the problem that if the question "is the universe capable of supporting life" were answered "no," no one would pose the question.

Therefore, the question that you are asking --- "what is the probability that a randomly created universe would support life" is irrelevant.

The question you should be asking is "what is the probability that a randomly created universe in which we exist would support life?" And the answer is 1, by definition. If at any point you assume that the probability of life existing, under any conditions, is less than 1, then you are at best lying by omission by ignoring this factor, since it controls everything else.

It's the elephant in the room as far as the fine-tuning argument goes. If you ignore this factor, your calculations are meaningless and deceptive. If you take this factor into account, then everything else works out to be irrelevant because this factor trumps everything else mathematically.

Really, it's just Doug Adams' puddle analogy dressed up in mathematics --- it doesn't matter how unlikely the puddle is to take any particular shape; if the puddle hadn't taken that particular shape, it wouldn't have been able to ask that question.

There are ways around that. Do you know the firing squad analogy?

 

[drkitten]

The idea that life could exist in a universe with different constants would probably require another thread. But even Victor Stenger (staunch atheist that he is) admits, "life as we know it would be impossible" in a universe with different values for the constants (he then speculates on non-molecular life and silicon-based life).

Which is irrelevant, I'm afraid. Because for there to be anyone to pose the question at all, then we would need someone to be alive, which means the universe would have to support life, whether or not it is "as we know it."

The move from "life as we know it would be impossible" to "some form of life is possible" seems awfully similar to what theists always get bashed for- a leap of faith.

Not at all. "Some form of life is possible" is true by definition in any observable universe, because the observer must be alive. If life can only be as we know it, then it doesn't matter how fine-tuned the constants are, because if the constants were wrong, we'd never know it. If life can exist in other ways, then the argument from fine-tuning fails because we could easily have been a different sort of life.

 

[rocketdodger]

I'm not clear on what you're saying. Are you talking about the problem of old evidence? Pr(E) is 1 if E is "life exists", but Pr(E) is also 1 if E is "The coin landed heads". Bayes would get nowhere fast if there wasn't a counterfactual way to look at evidence you already know exists.

You can only say P(E) of "a coin landing heads" is 1 if you knew nothing about coins at all and someone told you "we tossed a coin and it landed heads." Do you know nothing about coins?

This would be much easier for you to understand if you focused on the number example Robin or I provided.

You press a button and a 123 appears. You know literally nothing about the process used to generate that 123. Let E = "123 is produced."

What is the probability distribution for E? As Igor pointed out, with only a single sample and no knowledge of the underlying mechanism the distribution is a single point with zero variance. Which means P( 1.0 < p(E) < 1.0) == 1.0.

And as drkitten pointed out, we only have observations from one universe. And that universe harbors life. Since we know nothing of the mechanisms by which a universe's constants are set at "creation time" we can only say P( 1.0 < p( a life giving universe ) < 1.0 ) == 1. It is a situation identical to the mystery number generator.

 

[drkitten]

There are ways around that. Do you know the firing squad analogy?

I do, yes. It completely fails. There's a good response here.

The easiest and simplest response is just to note that we have no evidence for a directed firing squad. We were taken out to a field and heard a lot of gunshots. Until and unless you can prove that there was actually a firing squad or that any of the riflemen were aiming at you, then there's nothing to explain in the fact that you weren't hit.

But more to the point (from the citation above)

Suppose, in the spirit of Leslie's example, that there is only a one in a trillion chance that a particular prisoner can survive his scheduled execution "by accident." But let us also suppose that the firing squad has the overwhelming task of executing a trillion and one prisoners, one after the other. In that case, no one would be surprised if one prisoner was not killed.

While that particular prisoner might justly be astonished at his particular survival (why should he be the one), as outside observers, we know that someone was likely to survive.

Suppose that, as a news reporter, I decide that I will interview the "expected" survivor afterwards. Should I be surprised that I have someone to interview? And while he is probably shocked and elated, I find it rather ho-hum. Is it a miracle that I have interview footage to show? Of course not. And while the fact that any one prisoner survived is unusual, the fact that someone would survive is predictable --- as is the fact that that one person would be astonished at his miraculous escape. But if there is an interview at all, then there must be a survivor.

 

[drkitten]

There are ways around that. Do you know the firing squad analogy?

Further to above. For most of human history, more than 50% of children died in infancy or early childhood.

Do you find it astonishing that neither your father nor your mother died in childhood? Why, that's got less than a 25% chance of happening!

Do you find it astonishing that none of your four grandparents died in childhood? Why, that's got less than a 7% chance of happening!

Do you find it astonishing that none of your great-grandparents died in childhood? Why, that's got less than 2% chance of happening!

... Do you find it astonishing that none of your great-to-the-tenth grandparents died in childhood? Why, that's got less than one chance in ten million of happening!

How, then, do you explain that there are six billion people on this Earth, all of whom can say that none of their great-to-the-tenth grandparents died in childhood?

When you understand why you're not impressed that none of my grandparents died in childhood, you'll understand why I'm not impressed by your assessment of the probability of life existing is an arbitrarily small fraction.

 

[drkitten]

I don't think I was criticising Bayes Theorem (analogous to attacking the Uncertainty Principle) but simply pointing out how silly it is to start with 0.5 prior probability for God's existence.

Well, Bayes' theorem says you need a prior probability to calculate a posterior probability; Bayes' theorem also says that if you have no information, you should use the maximally uncertain prior.

Would you agree that it would also be a silly and utterly unhelpful approach to calculating your odds of winning the lottery to assert a prior probability of 0.5 (before considering what the lottery is, for example)?

How many times do I need to say that it isn't silly before you stop asking me if it is?

In defense you just say this 0.5 is the maximally uncertain position before we consider the "new" evidence of just what the lottery is.

Yes, I do. So why are you asking questions to which you already know the answer?

It sounds like you're making basically the same case wrt the life-filled universe.

I think it would be similarly silly to use this argument to try to prove my own existence and start with the prior probability of 0.5 based on my own maximal uncertainty of my own existence. In this case, I'd have to pretend that I don't know whether or not I exist (even though someone is making the argument).

And then to do the calculations properly, you would need to incorporate the evidence at some point that you do exist since you're the one posing the question, which would end up proving via Bayes' theorem that the probability of you existing is 1.

This isn't a problem. It's only a problem if you stop halfway, before you've considered the single most relevant piece of evidence.

 

[RandFan]

Yes you do. For any property, the negation of that property is also a property.

Thus turning a two headed coin into a three headed coin, four headed coin, five headed coin, etc., etc..

Heads
Tails
Not heads
Not tails
Not not heads
Not not tails
Not not not heads
Not not not tails

It's nonsense. And it is a pointless game. The point isn't how many statements we can invent out of whole cloth. The point is how many statements are true or false and are not redundant or superfluous.

heads = not tails.

Adding the statement doesn't create an additional state of the coin. It's just restating the same truth statement.

 

[GreedyAlgorithm]

Thus turning a two headed coin into a three headed coin, four headed coin, five headed coin, etc., etc..

Heads
Tails
Not heads
Not tails
Not not heads
Not not tails
Not not not heads
Not not not tails

It's nonsense. And it is a pointless game. The point isn't how many statements we can invent out of whole cloth. The point is how many statements are true or false and are not redundant or superfluous.

heads = not tails.

Adding the statement doesn't create an additional state of the coin. It's just restating the same truth statement.

I think I see where we're talking past each other. In any case I agree with everything you just said in that post. "not not heads" (assuming a coin can be only heads or tails) is not a different state than "heads". But notice that in this example, if the coin can be only heads or tails, that there are exactly as many true propositions as false: "coin is heads" and "coin is tails". You cannot name a situation where there are more false propositions than true ones.

 

[Frozenwolf150]

The idea that life could exist in a universe with different constants would probably require another thread. But even Victor Stenger (staunch atheist that he is) admits, "life as we know it would be impossible" in a universe with different values for the constants (he then speculates on non-molecular life and silicon-based life). The move from "life as we know it would be impossible" to "some form of life is possible" seems awfully similar to what theists always get bashed for- a leap of faith.

Not really, because "life as we know it" hasn't always existed even on Earth. For example, the eukaryotes of today are very different from the ones 3 billion years ago when life started. We know life adapts to changing conditions and have seen it happen many times. We have zero evidence that the universe changes itself in accordance to life's requirements. It's more reasonable to speculate that exotic forms of self-replicating molecular systems would appear under different conditions than it is to speculate that a divine engineer changed conditions on the fly to let "life as we know it" develop.

What's your evidence for the fine-tuner anyway? Cheap natural chemical highs that you and your buddies have given yourselves? Accounts from brain damage patients who nearly died and have suffered considerable trauma in the process? Yeah, I'm sure those are reliable unbiased sources.

Would you be open to the idea that the fine-tuner is an impersonal naturalistic cause? At all? That's a serious question, by the way.

 

[Robin]

The appropriate way to change our ideas about X is to use Bayes's theorem to produce a new distribution for X from the old distribution. The old mean alone is not enough to enable us to produce even a new mean, let alone an entire new distribution.

I don't really see your point. I think we all understand about using probability to describe the nature of our uncertainty, but you have to understand what you are uncertain about first.

It seems to me that the example you gave tells us nothing about our uncertainty about the machine, in fact it sets us off on the wrong foot.

If I have in my pocket a coin marked "123" on one side and a die marked on one face with "123" and I am interested in the probability of "123" coming up when I reach into my pocket and throw the first object I find, then the thing I am uncertain about is whether I will first find a coin or a die.

So for my machine it would seem to make more sense to assign a probability to what set the number will be drawn from.

In other words Bayesian reasoning is no substitute for thinking a problem through properly and getting it the right way up.

 

[JoeTheJuggler]

Well, Bayes' theorem says you need a prior probability to calculate a posterior probability; Bayes' theorem also says that if you have no information, you should use the maximally uncertain prior.

It doesn't say that if you have information you can blithely ignore it.

So yes, it is very silly to pretend that the prior probability for my ticket winning a lottery is 0.5.

It's silly and dishonest (and circular) to use Bayes' Theorem the way this argument does.

And frankly, I think it fits a pattern of dishonesty in a certain group of people who try hard to sell faith-based religious beliefs as science.

I suppose "Fine Tuner Science" is the next term in the sequence of Creationism, Creation Science, and Intelligent Design.

 

[Malerin]

Which is irrelevant, I'm afraid. Because for there to be anyone to pose the question at all, then we would need someone to be alive, which means the universe would have to support life, whether or not it is "as we know it."

Not at all. We can make a well-informed judgement about the existence of life in a universe with no stars, or no molecules, or no planets based on our current understading of biology- we don't even have coherent theories how life could exist in a star-less universe, let alone any evidence. All the evidence points away from the possibility of life in a star-less universe. We don't have to be agnostic about the possibility of life in a universe just because we're not there to observe it. For any planet like Pluto in this universe we can safely claim that there's no life, even though we haven't observed any Pluto-type planets. The statement has a high degree of confidence attached to it based on what we know of life so far.

Not at all. "Some form of life is possible" is true by definition in any observable universe, because the observer must be alive.

But that doesn't stop us from making claims about possible universes that may or may not have observers. You're just saying "For any universe with an obersever, by definition, that universe has life". Which is equivalent to saying "This universe has life" because we're observers. We know there's life. The question is, what were the odds that life should arise by chance? We know the die landed 1. What were the odds the die would land 1?

If life can only be as we know it, then it doesn't matter how fine-tuned the constants are, because if the constants were wrong, we'd never know it.

In THIS universe. Again, we can look at changes in the constants and make predictions about how the universe might have gone. A universe where fusion is impossible would almost certainly have no life.

If life can exist in other ways, then the argument from fine-tuning fails because we could easily have been a different sort of life.

It depends on how adapabtle life is. If life needs a fairly narrow range to get a foothold (the existence of stars, water, planets, heavy elements, etc.), then any universes that are lacking those features would have to be considered lifeless. Everything we know of biology tells us that life requires what I just mentioned (plus a lot more specific things).

 

[Robin]

Well, I didn't single you out by name. But if you insist on putting the shoe on and loudly proclaiming that it fits, I will happily agree with you. From your post (#142) :

post #142 in a different universe presumably, because post #142 in this thread doesn't remotely say that you can just walk away.

Certainly you can.

Well you can in the same sense that you can consult the I Ching or examine the entrails of the morning's sacrifice.

or --- and this is what you would do if you understood Bayes theorem properly --- you would codify the idea that the random event generator would be a coin or a die and use that idea in conjunction with your observations to adjust your posterior distribution, not as part of your prior.

But if you know this then why don't you just codify this idea in the first place, instead of pretending you don't know it when creating a prior distribution?

You seem to think that if it's not part of your prior distribution, you don't know about it.

No, I seem to think that if you know about it you shouldn't ignore it when forming the prior distribution.

Which is equivalent to guessing 50/50 and walking away.

No it is equivalent to making your prior distribution meaningful.

 

[rocketdodger]

But that doesn't stop us from making claims about possible universes that may or may not have observers. You're just saying "For any universe with an obersever, by definition, that universe has life". Which is equivalent to saying "This universe has life" because we're observers. We know there's life. The question is, what were the odds that life should arise by chance? We know the die landed 1. What were the odds the die would land 1?

First, you don't know -- and by that I mean nobody can give a logical argument for -- that our universe arised by chance.

Second, if it was by chance, you don't know the relative probabilities of each outcome. In other words, you don't know whether we are rolling a D4, a D6, a D20, a D100, or whatever.

Didn't you read the link drkitten posted?

In THIS universe. Again, we can look at changes in the constants and make predictions about how the universe might have gone. A universe where fusion is impossible would almost certainly have no life.

And a universe like ours almost certainly has life. So the question I ask you is what are the odds a universe will be like ours instead of one with no fusion?

It depends on how adapabtle life is. If life needs a fairly narrow range to get a foothold (the existence of stars, water, planets, heavy elements, etc.), then any universes that are lacking those features would have to be considered lifeless. Everything we know of biology tells us that life requires what I just mentioned (plus a lot more specific things).

First, just because we have only observed terrestrial biological life does not mean life in general must be terrestrial biological.

Second, this is irrelevant because you don't know the odds of a universe without the requirements for life versus the odds for a universe with the requirements.

 

[Frozenwolf150]

And frankly, I think it fits a pattern of dishonesty in a certain group of people who try hard to sell faith-based religious beliefs as science.

I suppose "Fine Tuner Science" is the next term in the sequence of Creationism, Creation Science, and Intelligent Design.

Creationism has a tendency to take refuge in the last frontiers of science, including fields they think are obscure enough that they can fool most people, or fields that creationists themselves do not understand. They can't hide behind the irreducible complexity of the flagellum, the eye, or blood clotting anymore, though there are still a few holdouts. So now they've run off and hidden behind the human consciousness, thinking that because science doesn't have a full understanding of how the brain works, the consciousness must be magical and separate from physiology. They've hidden behind the universal constants, thinking that because science doesn't have a full explanation as to why the values equilibriated the way they did, there must be some magical fine-tuner who keeps everything in check. The problem? These are nothing more than arguments from ignorance derived from the lack of evidence against them.

I'm still waiting for the evidence of a fine-tuner who alters the laws of the universe in order to accomodate life's changing needs. Saying that the fine-tuner could have set everything in motion and let life evolve from that point is ridiculous, because all it does is set an arbitrary cutoff point at which to introduce a divine middleman. Again, possibility is cheap.

If the universe was fine-tuned, who fine-tuned things to suit the fine-tuner? Oh, I get it, the fine-tuner is defined as tuneless and does not require a tuner itself.