Consider the following numbers and concepts (dare I say platonic forms):
1/9 or 0.111111…..
The Book War and Peace by Tolstoy
approximate self-replicating von-Neuman automaton (i.e. living cells)
Omega Number, Chaitin’s Constant
Chaitin’s Super Omega Numbers
I listed the above concepts in terms of which concepts I estimate are more information rich than others, going from lower to higher.
The curious thing is that even though we can’t really say exactly how many bits each concept has, we can rank the concepts in terms of estimated complexity. PI can be represented by an infinite number of digits, and thus be represented with far greater number of bits than contained in Tolstoy’s War and Peace, but PI is conceptually just the circumference of a circle divided by its diameter.
PI can have an infinitely complex representation (infinite number places past the decimal), but this does not make it conceptually more complex than War and Peace provided we have in our conceptual repertoire the notions of circle, circumference, and diameter. Thus I rank PI as more simple than War and Peace. An amusing conjecture is whether somewhere in the digits of PI is a representation of Tolstoy’s War and Peace. 🙂 But from an algorithmic information standpoint, using human math and natural language, most would say PI is more algorithmically simple than War and Peace.
As an aside, the digits of PI can be compactly represented via the Chundovsky algorithm. Notice, the Chudnovsky presumes the concept of infinity to make the representation compact. However the presumption of infinity does not help us express the Chaitin’s Omega number more compactly, because by definition, there is no compact representation of the Omega number, it is incompressible, it is non computable.
The above list can be said to be platonic forms, or concepts, or ideas. ID literature is very friendly to the notion of platonic forms. Whether PI is represented in various ways, there is the sense it is immutable. We can write a hundred textbooks with representations of PI, it doesn’t add or detract from the conceptual amount of information in the number PI. The concept of PI is immutable, hence the concept might be said to be a conserved quantity. Printing more digits of PI on a piece of paper does not increase the information content of the concept of PI. The information content of PI, if we assume platonic worlds are real, is conserved. To me, this illustrates one aspect of conservation of information.
This discussion raises the philosophical issue of whether there can be a platonic world of concepts without minds in the first place, or whether platonic forms are themselves an illusion of human minds. Darwinists and materialist tend to loathe the notion of platonic forms, but ironically if they use math and computers, they succumb to believing in platonic forms in practice if not in philosophy…
The notion of “human” or the classes of species that Linnaeus identified were also considered platonic forms. Even though the world might be filled with 7 billion humans, there is the fundamental platonic form of “human” in the creationist view. Creationists viewed the essentials of the human form as invariant much like the essentials of a rectangle are invariant even though there are infinite varieties of rectangles. In contrast, evolutionists classify species according to some presumed phylogeny. I tried to highlight to folly of classifying organisms according prevailing phylogenetic views versus platonic forms in Two-faced Nick Matzke.
Penrose, when pondering intelligence suggested that when human “produce” information in the form of great works of art, the human consciousness is actually accessing the world of immutable eternal platonic forms. Penrose rightly observed, when a composer composes music, it almost seems that some notes are more right than others, that ideal form just happens to be there. The right notes seemed to pre-exist the composer himself, the composer merely discovered the beautiful forms.
The ID debate centers frequently on the question whether random processes can generate instances of such immutable forms if the immutable forms are sufficiently complex like the approximate Turing machines and information processing systems in biology.
In the question of OOL, a living organism approximates a platonic form we call a Turing machine. Can random process generate such an approximation? If a random process by definition does not have complex platonic form built into it, why should it be expected to create an instance of it (a copy of it) in geological time?
The algorithmic complexity of a self-replicating von-Neumann automaton is substantially greater than what we would expect a random process to generate. If a process manufactured such a system we would presume it was already resident in some form within the process, and that the process is merely decompressing pre-existing conceptual information in order to create such a marvel. Of course, that is exactly what happens when a chicken makes an egg which becomes a chicken. The question then is where did the first chicken come from?
Empirical studies of plausible prebiotic environments suggest it was not information rich enough to make the first cell, much less a chicken. Empirical studies of evolution in real-time and in the field suggest evolution in the wild does not have access to the requisite information to construct a chicken from primitive unicellular organisms. It stands to reason, an information source outside of what we observe in the wild made the first chicken.
ID literature sometime refers to the problem of chicken evolution as the problem posed by conservation of information. Perhaps one might say, it is a problem posed by common sense.
HT: Gpuccio his discussion about PI at UD inspired this thread
HT: Michael Denton who championed the pre-Darwinian conception of platonic forms in biology