[extropy-chat] Coin Flip Paradox

[gts]

Gordon: "Say there, Jef! Can you help explain something to me? I don't  
know much about probability theory and I was hoping you could help me out."

Jef: "Sure! How can I help you?"

Gordon: "Let's say I have a coin hidden in my pocket. I retrieved this  
coin from my garbage disposal, so I should tell you it might be bent and  
unfair, or it might be normal and fair. Are you justified in believing or  
assuming it is fair?"

Jef: "What a silly question, Gordon! Of course not! I would need to  
inspect your coin or see some other evidence before I would be justified  
in commenting in any way about the fairness or unfairness of that coin in  
your pocket. Until then I have no justification for believing or assuming  
it is fair, and no justification for believing or assuming it is not fair."

Gordon: "Okay, that's what I thought. Just wanted to be sure. Thanks for  
the lesson."

Jef: "You're welcome!"

(The ghost of Pierre-Simon Laplace enters the room and taps Jef on the  
shoulder)

Laplace: "Excuse me, but I couldn't help overhearing that conversation."

Jef: "Huh? Who are you? Borat?"

Laplace: "No, I am the one-and-only Pierre-Simon Laplace, Magnificent High  
Priest of the Glorious Classical School of Probability! I am here to  
enlighten you about the Beautiful Principle!"

Jef: "What Beautiful Principle?"

Laplace: "My devoted followers called it the Principle of Insufficient  
Reason. You moderns call it the Principle of Indifference. The principle  
states that if you have no reason to expect one outcome over another, the  
outcomes are equiprobable."

Jef: "Wow! That really IS beautiful! It's BEAUTIFUL and it's ELEGANT, so  
it must be a TRUE PRINCIPLE OF LOGIC!"

Laplace: "That's what I thought, too. Good luck with it, Jef. I have to go  
now."

(The ghost of Laplace leaves the room.)

Jef: "Say there, Gordon! Come on back here! I have something new to teach  
you!"

Gordon: "Great, what is it?"

Jef: "I was wrong before when I said I have no justification for assuming  
that coin in your pocket is fair. According to the Beautiful Principle of  
Indifference, I am justified in assuming the coin IS fair because I have  
no reason to believe it is NOT fair. I heard this from a very reliable  
source: Pierre-Simon Laplace!"

Gordon: "Laplace? Reliable? But wasn't he wrong about the determinism  
thing?"

Jef: "Maybe, but this isn't about that. It's about The Beautiful  
Principle, Gordon! Don't you see? It's BEAUTIFUL and it's ELEGANT and it's  
TRUE!"

Gordon: "Let me get this straight: a few minutes ago you told me you were  
NOT justified in believing or assuming anything about the fairness of the  
coin in my pocket, and now you're telling me you ARE justified in assuming  
the coin is fair, *despite having obtained no new knowledge about the coin  
itself*. Is that right?

Jef: "Right. It's about the Principle, Gordon. It's BEAUTIFUL. You should  
be glad I told you about it! You need only dwell on its magnificent beauty  
for a few moments, and then you too will have THE POWER."

Gordon: "If you say so..."

-gts