[extropy-chat] Coin Flip Paradox

[Jef Allbright]

gts wrote:
> 
> On Wed, 31 Jan 2007 10:32:48 -0500, Mike Dougherty
> <msd001 at gmail.com>
> wrote:
> 
> > So are you saying that I should inspect the coin to determine
> that it
> > is fair?...
> 
> Yes, but I wouldn't get too hung up about the coin in my story.
> It's just
> a convenient prop for the sake of illustration, and maybe not the
> best
> prop at that.
> 
> The point is that the principle of indifference gives one the
> permission
> to assign imaginary probabilities to events when one is actually in
> a
> state of total and complete ignorance about the true probabilities
> of
> those events. Is that logical? I don't think so.
> 
> As I wrote yesterday, the "principle" is in my opinion not really a
> logical principle at all. It is rather a wild-assed conjecture made
> in the
> face of complete ignorance about the true state of nature. Granted
> this
> wild-assed conjecture is less wild than some alternatives one could
> make
> in ignorance, (if one is going to make this unjustified logical
> leap then
> it certainly makes sense to assign the probabilities equally rather
> than
> unequally), but it's a wild-eyed conjecture nonetheless.

I remember clearly one morning walking to school when I was in the
seventh grade (school was about three miles away and I much preferred
walking and thinking to sitting in a bus full of raucous kids.) I was
thinking about randomness, and a part of me kept saying "Yes, a tossed
coin converges on 50% heads, but what *causes* it to do that?"  Then I
made a connection to the idea of logical induction, and the same
question "Yes, but what *makes* the process valid?", and then I further
connected this thinking to Newton's first law of motion, again thinking
"Yes, but what *keeps* an object moving at constant velocity?".

And I realized that it comes down to information.  Any deviation or bias
would require additional information, and I had no reason to think there
was any additional information to be considered.  So it came down to a
pure issue of parsimony, of basic logic and supported by all available
experiencial evidence.  

The elegance and beauty of these ideas fitting into place resonated
noticeably in my mind for days and weeks to come.

FWIW,

- Jef