We live in the Information Age. Some physicists believe that information is a fundamental aspect of nature. All such theories rest on the adequacy of information theory. In this post I shall argue that information theory does not apply, is, in fact, useless, with respect to the evolution of the biosphere.
There are two major approaches to information theory: Shannon's theory and that of Kolmogorov-Chaitin.
In Shannon's theory, he considered an "information source," containing "messages" in a pre-stated alphabet. The binary string 0100101001 is an example of a message. Different messages may occur with different frequencies in the information source. Shannon was able to compute the information transmitted down an "information channel" to a "decoder." The channel might be noisy, so the decoder receives a degraded version of a given message with "mistakes" with respect to some of the symbols in the symbol string.
In the Kolmogorov-Chaitin theory, one does not consider an information source. One considers, in a pre-stated alphabet, a specific symbol string, e.g., 0100101001. The information content of the string is the shortest program on a universal computer that can compute this string as an output. While the information content is itself uncomputable, for one cannot prove that a given program is the shortest one, this definition of information has had wide application.
But neither applies to the evolution of the biosphere.
Evolving cells and organisms are Kantian wholes, in which the parts exist for and by means of the whole and the whole exists for and by means of the parts. A simple example is a "collectively autocatalytic set" of polymers, say small proteins called peptides. Gonen Ashkenasy at the Ben Gurion University has a nine peptide collectively autocatalytic set. Each peptide catalyzes the formation of a second copy of the next peptide by ligating two fragments of that peptide to form the second copy. No peptide catalyzes its own formation. The set as a whole has the property that each reaction requiring catalysis is catalyzed by some peptide in the set. Calling the catalysis of a reaction a "catalytic task," the set as a whole achieves "catalytic task closure." All the parts exist for and by means of the whole collectively autocatalytic set, and the whole exists for and by means of the parts.
Now consider a dividing bacterium, or single celled eukaryote. It achieves a "task closure" in a very much wider set of tasks, including DNA replication, membrane formation, construction of chemosmotic pumps and cell division.
In my post "Are Functions And Doings Real In The Universe," I answered "Yes." More, the function of a part is typically a subset of its causal consequences. The function of the heart is pumping blood, not making heart sounds.
Consider a screwdriver. Can you enumerate all the possible uses of a screwdriver, alone or with other objects or processes? No. The possible uses of a screwdriver is both indefinite in number and can't be ordered. This means that no algorithmic procedure can list all the uses of such a screwdriver alone or with other objects or processes.
Next, consider one use of a screwdriver, say, opening a can of paint. Can you enumerate all the other objects and processes that can open a can of paint, i.e., carry out the "function" of opening a can of paint? Again, no. The objects or processes that might open a can of paint, carry out that function, are, again, indefinite in number and can't be ordered. Again, no algorithm can list all these objects and processes.
Now consider a bacterium evolving to adapt to some new ecological niche comprised of the abiotic environment and other organisms. To reproduce and adapt and be selected in the new niche, the evolving organism must achieve a task closure that, in part, passes via the environmental niche. But just what features of the niche will turn out to be relevant to that task of closure?
We can only know after the fact, when natural selection reveals what features of the niche are the "actual niche" of the selected bacterium. That is, the task closure of the evolving bacterium and the features of its niche are circularly defined. We cannot pre-state them, we can only analyze after the fact what newly relevant features of the organism and environment have succeeded in achieving a task closure that allows the organism to better adapt.
More, in that adaptive evolution of the bacterium in the niche, some molecular screwdrivers, and other molecules or processes, need only find some use, or a new function, that enhances the fitness of the evolving bacterium in the new niche, for natural selection, acting on heritable variations with respect to those molecules' screwdrivers, to select for the newly relevant uses of the molecular screwdrivers, hence new functions in the circularly defined new niche.
But we cannot pre-state those new uses of molecular screwdrivers in the bacterium that selection will, after the fact, reveal to be relevant.
Critically, any feature could be the relevant one, or ones. This may range from the quantum behavior of a single electron, as in photosynthesis in plants, to the precise distances between cilia at the anterior of the bacterium.
This leads to the essential conclusion: Since literally any feature, alone or relational, of the bacterium and its environment can become relevant to survival and selection, there is no pre-stated alphabet of features by which we can construct either Shannon's information theory or Kolmogorov-Chaitins' theory.
With no pre-stated alphabet, information theory, as now available, has no relevance to evolution.