Malaclypse the Younger

Satan Oscillate My Metallic Sonatas

You are taking an imprecision that is trivially obvious to (at least to everyone else on this thread) correct and attempting to turn it into an argument. This activity is unproductive.

This analogy is not accurate, because you are presuming it is possible to know a priori that the "fixed" die is fixed in a particular way--you are trying to slide an unwarranted assumption in.

A reformulation of your example would be we have two boxes that are externally indistinguishable from each other. One is truly random (fair), the other is fixed to produce a certain unknown number. We choose a single box, ask it to generate a single number. Regardless of what that number is, we cannot determine whether we have the fair or fixed box.

[ February 24, 2002: Message edited by: Malaclypse the Younger ]</p>

pug846

I think I see your point now. It would be like calculating the number of carbon atoms in the Universe. From there, figuring out how many potential universes would have that many carbon atoms. Let’s say….17 Universes would have that many carbon atoms out of 10^10000. It would be invalid to argue that since the chance of there being this many carbon atoms in the universe is only 17/10^10000, the Universe must have been designed.

*sigh* My life long dream to be a Christian apologetic is crushed once again.

Malaclypse the Younger

The analogy can be further extended by assuming the anthropic principle.

I am an experimenter. I have a box known to be a fair random number generator with a range of 1 to 10^12. I have another box known to be fixed to always produce a certain number; I know also that that number is the range 1 to 10^12. I also know which box is which, but I don't know what number the fixed box is preset to produce, nor do I know (by definition) which number the fair box will produce. I also have a coin known to be fair.

Before doing anything, I document the following protocol:

I decide to flip the coin; if heads, I will choose the fair box; if tails I will choose the fixed box. I will generate a single number from the box that I choose.

If I choose the fair box and it produces the number 1093, I will call the subject on the telephone and have her come in and observe the box and number. If the fair box does not produce the number 1093, I will abandon the experiment and the subject will never even know that the experiment existed.

If I choose the fixed box, I will call the subject and have her observe the box and number regardless of what number the fixed box is preset to produce.

I flip a coin (and hide the results of that flip), pick a box based on the coin flip (and hide whether that box is fixed or fair) and generate a number. That number is "1093". I thus call the subject, explain the protocol, and ask her to determine whether it is more likely that she is looking at the fair or fixed box.

I will leave as an exercise for the student to show the probability that one is looking at the fair or fixed box. Please show your work.

Malaclypse the Younger

There is a trivial alternative to the above protocol.

Suppose, a priori I decide to choose the fair box and generate a number. If that number is 1093, I will call the subject; if not, I will abandon the experiment.

The box shows "1093" and I call the subject. Before she arrives, I flip the coin, If heads, I show the subject the unlabelled fair box showing 1093. If tails, I will take the fixed box, fix it to show 1093, and present that box (also unlabelled) instead.

Again, what is the probability that the subject observes the fair or fixed box?

Malaclypse the Younger

Sorry to disappoint you, pug.

Dr. Retard

You're wrong, but I understand how you could have made that mistake. I just meant a RNG program -- which, as is obvious, cannot be really random. RNG programs aren't random, they're just written in such a way that, from our epistemic viewpoint, they may as well be random. And since we're dealing with epistemic probability here anyway, this feature fits.

If you want, though, you can just replace my RNG with a trillion-sided die. It makes no difference. Then if you get 1093, you can wonder, "What are the odds that I'd get 1093!? A trillion to one! I bet there was a magic troll who loves the number 1093 who interfered with the die somehow to yield that result!"

Tercel

Dr. Retard,
The important relevant different is the differing values taken by P(E|D) and P(E|C), it is the values of these which make the Fine-Tuning argument what it is.
In the fine tuning argument, P(E|D) is found to be so huge compared to P(E|C) that is completely outstrips the difference between P(D) and P(C).
Now you say the probability of an intelligent designer creating the universe, is intuitively, very unlikely. I'm not sure exactly how unlikely you mean. Personally, I'm not convinced that it is that unlikely at all, say 1 in 10. But for the sake of argument (and to show you how the Fine-Tuning argument still works) I'm happy to assume that it's really unlikely: say 1 in a million, million, million, million, million. (Is that unlikely enough for you?)
ie P(D) = 10^-30
And you also say that the universe created by chance seems extremely likely, so P(C) is going to be high, approaching 1. Again for the sake of argument lets say it's so close to one that we can approximate by having P(C) = 1.

But here's where the strength of the Fine-Tuning argument comes, in evaluation P(E|C) and P(E|D):
According to the scientific evidence for Fine-Tuning there are a number of independent properties which need to lies within a range of 10^-50 or so. Thus P(E|C) = 10^-300 say. But I'm being generous, so let's say P(E|C) = 10^-50.

The final question is what is P(E|D)? That is, given that an intelligent designer has chosen to create the universe, what is the probability that that designer will choose to create a universe with intelligent life rather than a universe without life? I would say, an intelligent being would be far more interested in creating a universe with other intelligent life than it would be in creating a boring lifeless universe so I would put P(E|D) at about 90%. But again, being generous to you, lets say our intelligent creator is 100 times more interested in creating a universe without intelligent life[/i] than he is in creating one with intelligent life. So P(E|D) = 1%

Evaluating:
P(E|D) * P(D) = 10^-2 * 10^-30 = 10^-32
P(E|C) * P(C) = 10^-50 * 1 = 10^-50

We see from this that an intelligent designer is 10^18 times (a million, million, million times) a more likely explanation than chance.
Now you can see what the reason was: P(E|D) is greater than P(E|C) by a much larger margin than P(D) is less than P(C).

Compare to your troll analogy in which P(E|D) (the probability of the troll likely the number 1093) was equal to P(E|C) (the probability of random chance selecting 1093). That is where the difference lies between the two.

Tercel

[ February 24, 2002: Message edited by: Tercel ]</p>

Malaclypse the Younger

Tercel

Incorrect. The difference between P(E|D) and P(E|C) is assumed to be (entirely without justification) vastly higher than the difference between P(D) and P(C). All of the numbers in your example (even the probability of this particular universe, which seems to fluxuate somewhere between 10^-24 and 10^-50) are just magically pulled out of a hat--or rather carefully constructed to allow you to "prove" your preexisting bias.

There is simply no justification for assuming that the difference between P(D) and P(C) is anything other than the same as the known difference between P(E|D) and P(E|C).

You are "generously" assuming--entirely without evidence or even argument--that the a priori probability of your designer is now twenty orders of magnitude higher than the chance probability of the universe. If you make this assumption, it is entirely unsurprising that you will arrive at the exact same conclusion.

Bayes theorem (or your approximation of it) is just a formula. Garbage in, garbage out, and garbage is not sanitized by running it through an equation.

Using a 20-OOM difference between the assumed probabilities, one could "prove" it is most plausible to believe that I myself (at the tender age of ~12 weeks) actually assassinated JFK.

[ February 24, 2002: Message edited by: Malaclypse the Younger ]</p>

tronvillain

Ah, how I love the Bayesian Fine Tuning Argument.

Malaclypse the Younger

Indeed--it is innumeracy's finest hour. It seems that the FTA is to mathematics as the Ontological argument is to language.