When I saw the site of the Center for the Mathematics of Information, I started to have a somewhat funny feeling : mathematics of information. Is that the same mathematics we use for calculations on for example moneyrelated topics ? I doubt it, because In the past I heard things like :

if you share information with someone it doubles, because now both of you posess the information.
Very unlike sharing money! 
Drowning in information : if you have more than you can handle, and you add still more information, you end up with less. Is also called “information overload“.
With money it is simple : adding money makes you richer, even if you are Bill Gates. 
– Does negative information exists ? : So that when you received it, you know less than before.
(here I do not mean information about nonpleasant situations or the like) I think it is possible : Suppose you are convinced about something (your info is that X is true). Than you receive new info and as a result you are not sure any more, maybe it is not true after all.
But there is a much more serious explanation on negative information : according to physicists Quantum information really can be negative.
Did you liked this post ? Then you might be interested in the following :
Information overload, filters and Web 3.
Howmany inputs do data miners need ?
Simplexity : new word about old situations
The family of PI
Is Google God ?
Information content cannot be negative; the sum (or integral in the continuous case) of p log p is always positive.
However, in Bayesian statistics, it is possible for a particular observation to cause the posterior to be more diffuse than the prior, though on average the opposite is true. In a sense, this is a loss of information. Or maybe a loss of confidence in possible incorrect information. See this post for details.
By: John on July 25, 2009
at 7:38 pm
John,
I get your point. What you mean is that both before and after receiving new information the information content is positive, as well as the information content of the newly received information. Meaning that adding somthing positive to something positive gets you something smaller than before.
Nevertheless : apparently quantum info can be negative
By: zyxo on July 25, 2009
at 7:44 pm