Symmetry , Entropy , Kolmogorov Complexity , Information

I almost finish the book “Asymmetry: The Foundation of Information” by Scott J. Muller .

I like the description of the concept of Entropy , Symmetry , algorithmic Information but the author did not understand what information is .

I report an evidence in the Table 4.1 of page 96

Symmetry Entropy Information
High     Low     Low
Low      High    High

Here there is a big mistake :

Low Entropy = low Information

High Symmetry = low Information

Low Kolmogorov complexity = low Information

High Entropy != High Information

Low Symmetry != High Information

High Kolmogorov complexity = High information

This is the Correct Table

Symmetry Entropy Information
High     Low     Low
Low      High    ?

When we have a low entropy we know a way to reduce the information to describe the informatical object but when we have high entropy this does not give a way to reduce the information but this does not mean there is not a way to reduce the information to describe the object .

Not only but there are also examples where we have high entropy objects with low Kolmogorov complexity and low information to describe the object . An example is again the Rule 30 Cellular automata that produce a high entropy of data but to describe this data you need only to know the rule number plus a log(N) if you want a complete measure .

This mistaken concept emerges along the entire book.

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