Definition: The complexity of information is its Shannon entropy minus the Shannon entropy for the randomness of the information.
C = H - Hr
Where C is the complexity, H the Shannon entropy for the information and Hr the Shannon entropy for the randomness in the information.
Rationale
Complexity is order while order is not always complexity. Information with simple order has a low complexity value.
Randomness is disorder and is different than complexity. As an example, the complete information model of a human brain is highly complex. Both the Shannon entropy and the Kolmogorov complexity for the model are high.
If the same brain is run through a food processor into a soup of molecules, the information model will still contain a huge amount of information when all the individual molecules are included. The soup will have a high degree of randomness, and just like for the intact brain both the Shannon entropy and Kolmogorov complexity for the model will be high*).
*) While the Kolmogorov complexity value can be brought down if a simple pseudorandom generator is used, it can be impractical for actual measurements.
C = H - Hr
Where C is the complexity, H the Shannon entropy for the information and Hr the Shannon entropy for the randomness in the information.
Rationale
Complexity is order while order is not always complexity. Information with simple order has a low complexity value.
Randomness is disorder and is different than complexity. As an example, the complete information model of a human brain is highly complex. Both the Shannon entropy and the Kolmogorov complexity for the model are high.
If the same brain is run through a food processor into a soup of molecules, the information model will still contain a huge amount of information when all the individual molecules are included. The soup will have a high degree of randomness, and just like for the intact brain both the Shannon entropy and Kolmogorov complexity for the model will be high*).
*) While the Kolmogorov complexity value can be brought down if a simple pseudorandom generator is used, it can be impractical for actual measurements.
via JREF Forum http://ift.tt/1qNegXA
Aucun commentaire:
Enregistrer un commentaire