WK writes:
In what way is he dealing with structures 'explicitly' designed by intelligent beings? By generalising his formulation Shannon allows it to cover any situation in which a signal is being transmitted over a noisy channel, that he may have been thinking specifically in terms of telecommunications as for applicability doesn't stop his work from being generally applicable.
That's true, but in applying it more broadly, it's vitally important to confirm that assumptions valid for a telecommunications channel are equally valid for the structures to which it is being applied. That's the "division by zero". Would it be valid for a non-Chinese-speaking person to use the same assumptions when examining a Chinese newspaper as when examining chicken tracks in the barnyard -- even if they were
Chinese chickens?
If people are able to successfuly analyse the genome in terms of shannon information why do you feeel it is inapplicable? The transmission of genetic information from one generation to the next seems ideally suited to Shannon's problem of transmitting a signal over a noisy channel.
Well, an erupting volcano may
seem like a violent demonstration of power on the part of an angry god, but a lot depends on your initial assumptions.
My problem is in the circular way "information" is defined:
What is a code? That which contains information.
What is information? That which is represented by a code.
What is DNA? Coded information.
It's an empty tautology -- hence the division by zero.
With some effort, we might analyze the topography of a hillside on the assumption that it represented a coded set of instructions specifying the path a given rock should take while rolling down the hill (we could similarly interpret the rock's topograhpy as the instructions for decoding this message -- or, for that matter, we could do it the other way around). A particular bump might be assigned a value such as "turn left five degrees", etc. We might then take a shovel up on the hill and introduce some "noise" by flattening out that bump. But the only possible basis for regarding the bump in its original form as "signal", and the flat spot as "noise" would be that somebody or something
cared what path the rock took.
Once were done looking at all the charts and graphs and equations, and considering all the nuances of conflating Shannon entropy with Kolmolgorov complexity, and reviewing Kant and Hume, Gitt's argument emerges as a Sunday-school-simple proposition: DNA is a message from God. I can't prove that false, and I won't waste a lot of energy trying. If your initial assumptions make you happy, who am I to screw with that?