Re: Entropy: sorted=0 unsorted=237

[Leigh Palmer <palmer@SFU.CA>]

> > It shouldn't matter (in my view) whether the cards
> > are all arranged in order or not--they are in some order and that is all
> > that matters.
>
> Well, it depends on what you are told about the deck.
> --) If you are told it is sorted (in the standard order), then there is
> only one ordering that is consistent with that description.  That's zero
> entropy.
> --) In contrast, if you are told that the deck is unsorted, then there are
> something like 54 factorial different orderings that are consistent with
> that description.  That's 237 bits of entropy.
>
> Does that help?

No. The deck has a perfectly well defined entropy whether you are informed
of it or not. Were that not the case the entropy of a deck for which you
know the order and I don't would be different from our respective frames
of reference (frames of relative ignorance?). Barlow Newboldt is exactly
right. The deck is in some determined order regardless of anyone's
possessing knowledge of that order. To hold otherwise is sophistry, or,
more charitably, solipsism.

I will now tread on your territory. Please explain how it can be that less
information is necessary to specify the order of one sequence of 52 cards
than is necessary to specify the order of any other sequence. In my naive
view the amount of information necessary is exactly the same for any given
order. I am unfamiliar with the manner in which quantity of information is
measured beyond the knowledge that it is denominated in bits, but if you
can, please outline the algorith for measuring the information content. I
am simply asking; I have no idea what the answer to my question may be,
and whatever it is I will still maintain that it has nothing to do with
the entropy of the deck if, indeed, there is a difference in the amounts
of information in ordered and disordered decks.

Leigh