Conclusion

Abstract

The purpose of this chapter is to summarize the new foundations for information theory presented in the book and to point out work yet to be done on the topic. The claim is that logical information theory fills the gap left by the Shannon theory of giving a definition of information as being about distinctions, differences, distinguishability, and diversity (as opposed to “uncertainty” etc.) with logical entropy as its direct measure—and with Shannon entropy as its requantification for the purposes of coding and communications theory. Shannon himself said that the “information theory” bandwagon created by the science press and popularizers had gone far beyond the actual accomplishments of communications theory—so the mathematical theory of logical entropy should not be seen as contrary to Shannon’s claims about his concept of entropy. The linearization methodology showed how to extend the ‘classical’ logical information theory to the quantum version where it was shown that quantum logical entropy is naturally related to ‘measuring’ quantum measurement and to providing a distance measure between quantum states. Finally, it is emphasized that the surface has only been scratched to relate logical entropy to all the fields that touch on information theory.