Probability Question / Proof Needed (a toughie!)

[Schmitty 87]

So I just got back from Thailand after a two month stay. A few things off the top of my head...

I was talking with a couple of Americans, and one of them was planning on getting a flying spaghetti monster tattoo upon arrival back in the US. For those that are unaware, the spaghetti monster logo is an expression of atheism, as the existence of God is seen as analogous to the existence of a flying spaghetti monster. My feelings about that aside, I felt that the tattoo would look terrible, so, in an effort to dissuade her, I simply noted that theists would perhaps not agree with her contention that the existence of God and the flying spaghetti monster could be equally considered. Though I forget the wording, she essentially replied that there's no proof for God and that basic logic proves the aptness of the spaghetti monster analogy. Her friend added that the probability of God existing was rather low and, again, that there was no proof.

Damn. Proof. I sure don't have it. As the desire for proof proof proof is commonly considered intellectual advancement (I agree), it is certain that believers should be careful when taking Biblical (or whatever) stories as historical fact. At the same time however, all the talk about proof made me eager for another set of proofs. One, for instance, would be a proof of the correctness of the probability model used to judge theists. Maybe a proof that the chance of a quarter landing heads is 1 out of 2. Sure, flip the coin a few billion times and report back to me, but for any given trial, how do we know the true probability? Yeah, it's based on observation, but how do we know that we're seeing the right things? I too operate under the assumption that the flip of a coin is a fair shake each and every time (though maybe that's why I'm down so much damn money flipping), but I'm open to the possibility that there could be more out there, even absent proof. To me I think it's wild enough that when I jump I come back down to the ground. I currently spend my time thinking about that and thanking the universe that I do in fact come back down, though my basketball game would surely improve if I had a bit more control over it.

When people talk about their personal relationship with God, I often smirk to myself and think "Ya well why hasn't He come and talked to me?" Well, I imagine that I just have a different set of observations, and if not even that, I certainly have different interpretations of the same observations.

So I guess ship the proof! If anyone has it a PM would be greatly appreciated. Hopefully it's not too long or complicated. Everytime I read SMP I get pissed off and frustrated that if I try to get into an argument with luckyme or MidGe or whoever else I'll assuredly end up feeling like a fool (either that, or just more pissed) and going back to contemplating gravity, so I likely won't post again, but ideally I'd like something enjoyable to read tomorrow, whatever it is. Enlighten me brothers!

PS gibbons are really cool. they look sorta like humans except they have super long arms and are incredibly good at gymnastics (no offense to the olympic team of any human nation).

[ChrisV]

The point is repeatability and falsifiability. If someone doesn't believe that the probability of flipping a coin is 1 in 2, I can instruct them on how to test it to any accuracy they like (it involves flipping a crapload of coins). No theist can tell me how to reproduce their personal religious experiences. The argument of atheists is not that people shouldn't believe ridiculous things (although we certainly reserve the right to make fun of them) but that nobody should impinge on the lives of others based on beliefs they are unable to substantiate to others.

[br.bm]

"(it involves flipping a crapload of coins)"
yeah baby [img]/images/graemlins/laugh.gif[/img]
our math teacher made us roll a dice like 200 times^^

@OP: uhm, could you fit your question in one or two sentences?

[Kimbell175113]

The coin thing, though, doesn't have to rest upon the coin being fair or being 50/50 in the long run. Even if the coin is certain to be biased, it's still 50/50 for us because we don't know which way it's biased and neither heads nor tails is inherently more likely to be so.

I think that may be analogous to the Pascal's wager arguments (this is related to the debate between bluebassman and wtfsvi in the faq thread). Sure it could be that infinite reward awaits believers in Christianity, but it could also be the same for FSMers, and unless you think you have information that makes one more likely...

[jason1990]

[ QUOTE ]
At the same time however, all the talk about proof made me eager for another set of proofs...Maybe a proof that the chance of a quarter landing heads is 1 out of 2. Sure, flip the coin a few billion times and report back to me, but for any given trial, how do we know the true probability?

[/ QUOTE ]
If you want to prove that the area of a rectangle is width times height, you can do this with pure mathematics. But if you want to prove that the area of Colorado is 104185 square miles, you cannot. To prove the latter statement, you must specify what you mean by "the area of Colorado", you must show that this object satisfies (at least approximately) the properties of a rectangle, and then you must take some measurements.

The same is true of probabilistic statements. If you want to prove abstract theorems in probability, such as the law of large numbers or Bayes' theorem, you can do that with pure math. But if you want to prove a probabilistic statement about something outside of mathematics, such as coins or gods, the "proof" must also lie, in part, outside of mathematics.

The first hurdle to overcome is that you must specify exactly what you mean when you say "the probability of a quarter landing heads is 1/2". In this thread alone, you can see the shadow of different interpretations lurking behind some of the responses. (ChrisV seems to be adopting either the frequency or propensity interpretation, while Kimbell is adopting the logical interpretation.) This post explains four of the most common interpretations of statements such as this.

[wtfsvi]

[ QUOTE ]
The coin thing, though, doesn't have to rest upon the coin being fair or being 50/50 in the long run. Even if the coin is certain to be biased, it's still 50/50 for us because we don't know which way it's biased and neither heads nor tails is inherently more likely to be so.

[/ QUOTE ] That's what I thought too. And Sklansky. If you're interested in this and haven't read it, there's been a huge discussion about it in this forum.

[Schmitty 87]

[ QUOTE ]
@OP: uhm, could you fit your question in one or two sentences?

[/ QUOTE ]

No I was just rambling. No specific question really. Just randomly picked a title.


[ QUOTE ]
nobody should impinge on the lives of others based on beliefs they are unable to substantiate to others.

[/ QUOTE ]

Ya they can't substantiate them to others by having them flip a coin a million times, but they can explain to them their personal experiences and how those experiences have affected them. I imagine you wouldn't consider that impinging on others' lives though. I agree that forcing religion onto people in the various ways that it is done is wrong.


jason1990: Ya good point. Different interpretations of the word probability would obviously lead to different answers. I guess that's basically the point I was trying to make, that it's ridiculous for someone to say "the probability of God exisiting is 1 in a billion, so either you're really lucky or God doesn't exist."

I will read about the biased coin thing. For an individual trial it seems quite obvious that it's 50/50 for us regardless of which way it's biased assuming we can pick. I'm interested in what the huge discussion was about.