[extropy-chat] Re: monty hall paradox again: reds and green gorfs

[Eliezer Yudkowsky]

Eliezer Yudkowsky wrote:

> Spike wrote:
> 
> Finally, your friend allegedly stated:
> 
>> What puzzles me even more is the reasoning of the gay mathematician, who
>> had no problem with the idea that opening one envelope somehow causes
>> the other one to become "probably the smaller one."  How?  I asked.  "It
>> doesn't matter how," he calmly replied. "Physicists worry about that
>> sort of thing, the crass empiricists.  Mathematicians do not."
>>
>> I must have been wearing a stunned or puzzled countenance. "Well," he
>> continued, "It must do it, right?  There cannot be any inherent profit
>> to swapping.  You can write a quick sim to prove it.  The probability
>> that the other envelope is larger must go to 1/3, it doesn't matter how
>> it gets there."
> 
> 1)  This is not a physics problem.  This is a Bayesian probability 
> problem.  It is squarely the responsibility of mathematicians.

I'd also like to note that this is an instance of what E.T. Jaynes called 
the Mind Projection Fallacy, against which Jaynes often railed:  Your 
mathematician friend seems to suppose that his *estimated probability* of 
the envelope being the larger one is a *physical property* intrinsic to the 
envelope, rather than a way of measuring his own *knowledge about* the 
envelope.  Your friend would delegate the problem to the physicists, no 
less!  A clearer case of Mind Projection Fallacy I have rarely seen.  The 
map is not the territory.

-- 
Eliezer S. Yudkowsky                          http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence