[Bio-information-theory] A Question About the Central Paradox in Shannon

[Doug Wedel]

I have never posted in here but have read a great deal from the Chowder 
group.  Now I wish to pose a question.

You use Shannon's definition of information as "decrease in the uncertainty 
of a receiver."  However as you well know this definition contains a nasty 
paradox:  information defined this way is at its maximum in random numbers.

The idea that information is at its maximum in random numbers is not just 
different from our intuition, but more like opposite to it. As Richard 
Feynman put it in his Lectures on Computation, "How can a random string 
contain any information, let alone the maximum amount? Surely we must be 
using the wrong definition of 'information.'"

How do you deal with this paradox in Shannon's definition of information?