It seems to me that “reduction of uncertainty” is not the best way to define information. First, it implies that someone or something is waiting for or otherwise anticipating a message. But if nobody is waiting for a message, how does that reduce uncertaintly? Second, “reduction of uncertainty” does not strike me as an adequate description of what is really happening when successful communication takes place. For instance, how is uncertainty quantified? And even if it can be quantified, it’s not really telling you what’s going on IMHO. Take for example a pile of lumber. Could not the lumber be described as being in a state of uncertainty? Simply describing a reduction of lumber does not describe a house, or a porch, or a fence. It seems to me the definition of information needs to include much more than a simple reduction of uncertainty.
That is what I mean by people should not complain about a farmer when their mouth is full.
The title of Shannon's theory is A Mathematical Theory of Communication.
It is not about the message, it is about the communication of the message no matter what the message "is."
Under Shannon, information (successful communication) is the reduction of uncertainty (Shannon entropy) in the receiver (or molecular machine) in going from a before state to an after state. It is the action, the communication. Not the message much less the "meaning" of the message.
It doesn't matter to me if Gitt and Williams want to come up with a new vocabulary but they have no business trying to do while standing on Shannon's shoulders. It destroys their credibility.
Schneider uses the term "uncertainty" because it is more understandable than the term "Shannon entropy." The Shannon entropy formula is basically the same as thermodynamics, Boltzmann's H-Theorem and thus called "entropy" but the similarity ends there.
Shannon entropy is reduced by successful communication. In thermodynamics, entropy increases..
That is a powerful line of argument in Intelligent Design debate.
Likewise, your lumber is indeed in a state of uncertainty. But it cannot act as a receiver of a message. If it could, as something occurring in nature then we would say it is alive.
And you can talk all day long to a bucket of water but it cannot act as a receiver, if it did then voila there would be hard evidence of abiogenesis.
Instead, the fact that there had to exist a capable receiver before the first biological message was sent stands as a powerful argument in favor of biogenesis.
Likewise, the very point that the message (DNA) survives physical death of the biological organism while as long as the biological organism continues to physically communicate (Shannon) - it is alive stands as a very powerful argument in the Intelligent Design debate.
And certainly the content of the biological message (complexity, semiosis, etc.) is a wonderful Intelligent Design argument. But that argument should never be made while criticizing Shannon as not having gone far enough.