So you rebuke Williams, Gitt, Meyers, etc, for pointing out that the statistical aspects of information (i.e. Shannon information) is inadequate to evaluate that which makes information meaningful?
They all make the same mistake - which no big league mathematician would make – they criticize Shannon’s theory for not addressing the meaning of the message and then deign to bring Shannon up-to-date.
Shannon’s theory, the mathematical theory of communications doesn’t care whether the message being transmitted is “The Greatest Story Ever Told” or “Debbie does Dallas” or DNA. It doesn’t matter if the message is Einstein’s theory of General Relativity (very complex by any measure) – or a single binary digit.
Moreover, the meaning of a very simple message could be earth-shattering. What if that single binary digit was the command from Obama's nuclear football to launch a thermonuclear attack on China?
Meaning goes to either or both complex systems theory and philosophy.
If Shannon’s theory included the meaning of the message, it would not be a transportable mathematical model. It would only be applicable to whatever class of message fit the complex systems theory or philosophy he embraced.
Remember there are two types of complex systems theories – least description and least time. How complexity is measured depends on what you are looking for, e.g. functional complexity, algorithmic complexity, Kolmogorov complexity, irreducible complexity.
The measure of complexity in DNA does not ipso facto apply to the measure of complexity in literature, algorithms, images, music and so on.
It is the strength of Shannon’s theory, not the weakness, that he didn’t include the meaning of the message. Criticizing Shannon on that point shows an extreme lack of good judgment and understanding of math theory.
In my view, it is as if these intelligent design or creationism theorists are doing the same thing we criticize Dawkins, Pinker, Lewontin and Singer of doing – pedaling atheism under the color of science. In their case, they are pedaling a complex systems theory under the color of information theory.
My disappointment with Myers and Williams is profound because their complex systems theories have merit on their own right – with Myers the geometry of biological information content and Williams the temporal displacement of metainformation in biological life.
They should have been presented them for what they are. They should have stood on their own two feet.
As it is, I doubt any of the big league mathematicians - who are notoriously open to new theories (e.g. they accepted in peer review for publication in 1994 Statistical Science the equidistant lettering sequence theory, aka Bible Codes) – would give their ideas a second look. If you want to play in their ballpark, you have to know the rules of the game.