Why Malerin is Wrong About Bayes Theorem

Malerin said:
His first point is that the physical constants may be set at their precise values (they couldn't be other than what they are. Here's my response:

...snip...

Are you now assuming multiple firing squads? That is the only way it would be predictable that an entire firing squad should miss the target.
Click to expand...

This is all completely irrelevant.

For you to understand why, let's play a little game.

I am going to choose a rational number. Before I type it here, I will decide which process I am going to use to generate that number.

OK, here is the number: 7/5

Now, can you tell me what the odds of me generating that number were?
 
rocketdodger said:
OK, here is the number: 7/5

Now, can you tell me what the odds of me generating that number were?
Click to expand...

Of course not. We don't have enough information to tell you with certainty what the odds of you generating that number were.

On the other hand, we have enough information to estimate the odds of you generating that number. Like any estimate, it will have an associated margin of error --- and given how little information you've given us, it shouldn't surprise you that the margin of error is rather large.

Given that, your odds of generating that number were 0.5 +/- 0.5.

Notice that that is the best possible estimate under the circumstances, in that the margin of error is the smallest possible.
 
drkitten said:
Of course not. We don't have enough information to tell you with certainty what the odds of you generating that number were.

On the other hand, we have enough information to estimate the odds of you generating that number. Like any estimate, it will have an associated margin of error --- and given how little information you've given us, it shouldn't surprise you that the margin of error is rather large.

Given that, your odds of generating that number were 0.5 +/- 0.5.

Notice that that is the best possible estimate under the circumstances, in that the margin of error is the smallest possible.
Click to expand...

But there are an infinite amount of rational numbers.

So, ignoring the decreasing likelihood that a human would bother to come up with a number that requires a huge amount of digits to type, why wouldn't the odds be infinitessimal?

I mean, I could have conceivably choosen any rational number at all, right?

(note that I am playing devil's advocate here)
 
drkitten said:
<snip>

On the other hand, we have enough information to estimate the odds of you generating that number. Like any estimate, it will have an associated margin of error --- and given how little information you've given us, it shouldn't surprise you that the margin of error is rather large.

Given that, your odds of generating that number were 0.5 +/- 0.5.

Notice that that is the best possible estimate under the circumstances, in that the margin of error is the smallest possible.
Click to expand...

A small nit-pick: The probability of generating a number which has been generated has to be greater than zero.
 
rocketdodger said:
But there are an infinite amount of rational numbers.

So, ignoring the decreasing likelihood that a human would bother to come up with a number that requires a huge amount of digits to type, why wouldn't the odds be infinitessimal?
Click to expand...

That's a different question. I mean, first, you've just informed me that the number is chosen from the set of rational numbers. Second, you've told me that the number was chosen by a human instead of a mechanical process, and third, you've told me (but then, explicitly told me to ignore) that humans have strongly limited attention.

With that information, I could come up with a substantially different probability. There are a lot of magic tricks, for example, that hinge on humans not choosing numbers uniformly (and that allow the magician to "read" the subject's mind for the chosen number.

Do you really expect the same number to result as the answer to two different questions?



I mean, I could have conceivably choosen any rational number at all, right?
Click to expand...

You could have, except that you're a human. So, no.

.... but my estimate still stands (mainly because I'm too lazy to do the revision). I am at least 95% confident that your probability is somewhere in the range [0.0,1.0] or 0.5 +/- 0.5. While you could conceivably have chosen any number at all, you could conceivably have chosen any number at all with any probability distribution you choose -- you could have decided to pick 7/5 with probability 0.99 and sqrt(2) with probability 0.01. Since I have no information to select among the distributions, 0.5 +/- 0.5 is still about the best I can do. Any other distribution would either not give me the necessary confidence or would have at least that large an error bar.
 
Last edited:
drkitten said:
That's a different question. I mean, first, you've just informed me that the number is chosen from the set of rational numbers. Second, you've told me that the number was chosen by a human instead of a mechanical process, and third, you've told me (but then, explicitly told me to ignore) that humans have strongly limited attention.

With that information, I could come up with a substantially different probability. There are a lot of magic tricks, for example, that hinge on humans not choosing numbers uniformly (and that allow the magician to "read" the subject's mind for the chosen number.

Do you really expect the same number to result as the answer to two different questions?
Click to expand...

No, I don't. I didn't want you to revise your estimate.

My question was more along the lines of "you have literally no idea how that number was generated, other than that it must be rational, so why not assume any rational number at all could have been generated?"

You answered that. Because 0.5 +/- 0.5 is statistically the best estimate you can make given the information you have. Estimating "infinitessimal" would be statistically worse -- namely, because it leaves out nearly all of the interval (0,1] where the true distribution might lie.

drkitten said:
You could have, except that you're a human. So, no.

.... but my estimate still stands (mainly because I'm too lazy to do the revision). I am at least 95% confident that your probability is somewhere in the range [0.0,1.0] or 0.5 +/- 0.5. While you could conceivably have chosen any number at all, you could conceivably have chosen any number at all with any probability distribution you choose -- you could have decided to pick 7/5 with probability 0.99 and sqrt(2) with probability 0.01. Since I have no information to select among the distributions, 0.5 +/- 0.5 is still about the best I can do. Any other distribution would either not give me the necessary confidence or would have at least that large an error bar.
Click to expand...

Ok. Let's move on to the next part of the game.

Now, I tell you that the number 7/5 is very special because it was the number generated.

Does this new information change your estimate of the distribution?
 
drkitten said:
Given that, your odds of generating that number were 0.5 +/- 0.5.

Notice that that is the best possible estimate under the circumstances, in that the margin of error is the smallest possible.
Click to expand...
That's technically true, but can you explain how this ever changes?
 
Ivor the Engineer said:
If you have only seen one sample how is it reasonable to assume the process which generated it has a variance greater than zero?
Click to expand...

I didn't say that the process has a variance greater than zero. I said that the probability distribution which summarizes our incomplete knowledge of the process has a variance greater than zero.

The process that I was talking about was a hypothetical machine which, every time its button is pressed, displays "123" with probability p (and something else with probability 1 - p). This process is completely characterized by the single number p. However, we don't know what p is.

The question is, if we press the button once and the machine displays "123", what can we conclude about p?

When I said that a distribution with zero variance is unreasonable, all I meant was this: it is unreasonable to conclude that p is definitely 1. It might be 1, and it's more likely to be 1 now than it was before we saw the "123", but it still could be anything between 0 and 1, except exactly 0.
 
rocketdodger said:
Ok. Let's move on to the next part of the game.

Now, I tell you that the number 7/5 is very special because it was the number generated.

Does this new information change your estimate of the distribution?
Click to expand...

Not really; the information you just told me was implicit in your original statement that 7/5 was the number generated. No new information means no change in the estimate.
 
yy2bggggs said:
That's technically true, but can you explain how this ever changes?
Click to expand...

Because "margin of error" doesn't usually mean the maximum possible variation, but the maximum LIKELY variation; when a pollster, for example, says that the results are 41% +/- 3% positive, that mean that the real value is LIKELY to be between 38% and 44%. (Depending upon your formalism, "likely" can mean 50% probable, about 67% probable, or 90% probable.)
 
Robin said:
Ah yes, I see that you have already cited the paper that has the multiverse fine-tuned for life:


http://home.messiah.edu/~rcollins/finetune/anth.htm.htm

So it seems to me that Theists are claiming that it is evidence for God if there is a single Universe when there might have been many, and also if there is a single Universe when there could not have been many, and also if there is a Multiverse.

Basically then, every possible circumstance that can lead to human life will be claimed equally as evidence for God.

If so, then fine-tuning cannot be regarded as altering the probability of God existing.
Click to expand...

I disagree with Collins here:

"In the absence of alternative explanations, the existence of such an a system suggests design since it seems very unlikely that such a system would have just the right components by chance. Thus, it does not seem that one can escape the conclusion of design merely by hypothesizing some sort of many-universe generator."

This is so highly speculative, that it is possible for a reasonable person to believe in some sort of multiverse that either doesn't depend on a narrow range of constants or is itself a fundamental principle of cosmology. On the other hand, I think it's also reasonable for a person to draw the opposite conclusion, and for that person, who doesn't believe in a multiverse (or believes the multiverse was itself a product of design), theism (or universe-creationism) will be a rational position to take, given the delicate balance of the constants.

In the end, the FT argument confirms to a great degree either the universe was made by something that favors life, or we are part of a large multiverse of universes.
 
Malerin said:
In the end, the FT argument confirms to a great degree either the universe was made by something that favors life, or we are part of a large multiverse of universes.
Click to expand...

No it does not.

What were the odds that 7/5 was the number generated? When you understand why you can't answer my question in any statistically valid way other than what drkitten already said, you will understand why the FT argument utterly fails.

It is pretty clear to everyone here -- other than you. Using your assumptions the odds of generating 7/5 are likely very close to 1 or likely very close to 0. But there is no mathematically valid argument to support such an assumption. In particular, you are quite off in this case because the true odds are neither close to one nor zero.

If you want to know the true odds, I will tell you, but only after you try to estimate them yourself -- like drkitten did.
 
69dodge said:
I didn't say that the process has a variance greater than zero. I said that the probability distribution which summarizes our incomplete knowledge of the process has a variance greater than zero.

The process that I was talking about was a hypothetical machine which, every time its button is pressed, displays "123" with probability p (and something else with probability 1 - p). This process is completely characterized by the single number p. However, we don't know what p is.

The question is, if we press the button once and the machine displays "123", what can we conclude about p?

When I said that a distribution with zero variance is unreasonable, all I meant was this: it is unreasonable to conclude that p is definitely 1. It might be 1, and it's more likely to be 1 now than it was before we saw the "123", but it still could be anything between 0 and 1, except exactly 0.
Click to expand...
Which pretty much demonstrates what I said before, that this is the wrong question.

However we would now know that the device was probably not an electronic coin flipper or electronic dice or a device for generating secure numeric passwords.

So asking the right question in the first place is important - being clear about what exactly it is that you don't know.
 
drkitten said:
Because "margin of error" doesn't usually mean the maximum possible variation, but the maximum LIKELY variation; when a pollster, for example, says that the results are 41% +/- 3% positive, that mean that the real value is LIKELY to be between 38% and 44%. (Depending upon your formalism, "likely" can mean 50% probable, about 67% probable, or 90% probable.)
Click to expand...
Well, doesn't matter... I thought more could be said, but having been caught up, I think that was mentioned.

69dodge said:
But it still could be anything between 0 and 1, except exactly 0.
Click to expand...
Well... it could, though it almost surelyWP isn't.
 
So I was very wrong mathematically in my OP but my head was in the right place conceptually -- I had never heard of the anthropic principle until Dunstan mentioned it, but I guess it is just common sense for some of us.

Is this thread done now? I think the FT argument is pretty well demolished at this point in this thread and I am guessing Malerin will either stop posting on this thread completely or else totally sidestep the relevant issues that have been brought up and keep responding to questions we didn't ask.
 
69dodge said:
Huh? Are we talking about the same thing?

If you flip a coin once and get heads, you're almost sure that it's a two-headed coin?
Click to expand...
No--this was in reference to your caveat "except exactly 0"; that is, a machine that outputs 123 could have a probability of 0 for generating that output (given certain "ontological' freedoms).
 
yy2bggggs said:
No--this was in reference to your caveat "except exactly 0"; that is, a machine that outputs 123 could have a probability of 0 for generating that output (given certain "ontological' freedoms).
Click to expand...

Oh, I see. Yes, I agree.
 
You must log in or register to reply here.

Back
Top Bottom