🚀 go-pugleaf

>>>  Can a part be greater than the whole?
>>>  
>>>  Specifically, can a part have more information than the whole?
>>>  
>>>  but consider this, the whole is a sequence like this: 
>>>  1111111111111111111111111111111111111111111111111111
>>>  and the part is:
>>>  10110110010110101010010111100111110101101011110001000
>
>Bad example. I don't see why the second list of 0's and 1's is a part of the
>first.

Consider instead a volume with a cross section, this could is equivalent.

>>>  Here, the part seems to have a higher informaition content than the whole.

>Why does the second list contain more information than the first. Because
>the 0 to 1 ratio is close to 0.5? But what about the list: 00000...11111. This
>list ``obviously'' have a low informations content. By induction it follow
>that the list that contain most informations is 0101010101010101 :-).

It is not clear what you mean by information at all.  One standard measure
is Kolmogrov complexity, where the information content of a sequence
is equivalent to the minimal description of that sequence on a universal
Turing machine.  From this measure your comments are meaningless.  It is
not obvious in what interpretation you intend, if any.

>Anyway
>this is a old discussion on the net---What is the information content of pi.
>Infinite? Is it bigger than sqrt(2) or 1/3.

Old conversations are obviously the most interesting and most likely to 
yield important ramifications when understood.  The information content
of PI from Kolmogrov complexity is very small.  It is not infinite in
any way whatsoever.

Shannon's measure of information depends on the probability of choosing some
symbol from an ensemble.  It does not appear directly applicable unless on
can assign probabilities to various sequences.