[extropy-chat] Coin Flip Paradox

[Jef Allbright]

gts wrote:

>[Jef wrote:] 
>> There is great beauty in principles such as the Principle of
>> Indifference...
> 
> Here is another example of where this "beautiful principle" fails
> miserably:

Gordon, principles cannot "fail miserably".  People can fail miserably
when they try to apply principles out of context.

Principles are statements describing some regularity observable in our
interactions with "reality". The principle of indifference is beautiful
(to some of us) because of its elegance; it's an extremely simple
statement of extremely fundamental applicability to knowing what we can
know.  

The principle of indifference says simply and powerfully that equivalent
states of information yield equivalent probabilities. It is a special
case of the principle of maximum entropy which is even more elegant. 

It seems to me that where you're "failing miserably" is in not realizing
the inherent subjectivity (context dependency) of any such statement.
You persist in demanding the "right answer" without understanding that
you haven't fully specified the question.

Q: Do you think there can be "information" without a subjective
(necessarily context-limited) observer? Think deeply about this and
curtains may fall.

You've shown that you're having trouble understanding the difference
between probability and likelihood; that you haven't grasped the
essential idea behind Bertrand's "paradox" that there's a continuum of
views but only a single actuality; that a string of 11111111111s can
easily be random; that there's a strong argument for thinking of
"randomness" in more general terms as the uncertainty of a necessarily
subjective (context-limited) observer; and how this all relates to the
concept of entropy.  All this information is out there on the web and in
books, along with plenty of misunderstanding and controversy.

It would please me, and perhaps a few others who care about this stuff,
if you would speak from your own point of view, rather than in the
pompous and pedantic style of presenting pieces of the work of others,
claiming to play devils advocate in order to share these "great
mysteries".

One can't tell what point of view you might hold, if any, and this
limits the effectiveness of discussion.

Onward!

- Jef