Information theory is a new field. It really only dates to my grandfather's era and I'm a child of the 1970s. It came about as big telecommunications systems started spreading around the United States and good mathematical models were needed to engineer them. Information theory is really a statistical model of
symbol transmission. Most modern telecommunication systems use modulators and demodulators plus some encoding method (really very complicated and sparse alphabets) to move strings of bits. Typically the bits are represented by a modulated carrier signal where groups of 1's and 0's are represented as regular perturbations of the carrier; Old timey audio-frequency modems transmitted data in the audible range (e.g. 300 Hz) and you could hear the signal. Information theory describes the probability of the symbols being decoded correctly based on signal-to-noise ratio.
Natural information is different. If you drop a sugar cube in a bathtub, for example, the concentration of sugar in the water will form a
gradient. That is, the concentration will be higher near the cube than further away until a number of hours or minutes elapses. The gradient is information. Is it in any way symbolic in information theory terms?
No. The concept of a symbol is really a formalized expression of human language--really it's a systemic representation of writing--a mark. One of the topics I wanted to get at in the earlier post about
information and scales is that telecom systems are really, really specific and the engineering concepts apply mostly to representing 1's and 0's within specific extremely constrained systems in terms of time (frequency really) and space and method.
Natural information is not constrained, which may be the chief reason it can't be symbolic.
Symbolic really strongly implies space and time constraints that are exemplified by electronic telecommunication systems.
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