Zenith Grant Awardee

David Wolpert

Santa Fe Institute

Project Title

A Semantic Information-Theory Model of Reality

Project Summary

Ever since Wheeler discussed \'it from bit\', there has been great interest in whether the ultimate nature of reality can be formulated in purely information-theoretic terms, and what insights such a formulation would provide, e.g., as a priori restrictions on the nature of reality. The mathematics of inference devices (ID\'s) – mathematical abstractions of any physical device that can be used for observation, prediction, or control – provides such an information theory. Already ID theory has provided a non-quantum-mechanical \'uncertainty principle\' that restricts the possible nature of reality. This suggests that we formalize reality as the information that a set of ID\'s have about one another and about other physical variables. A challenge with this approach is that the definition of ID\'s is too weak to fully capture the concept of semantic information, and contains no notion of distance. I propose to introduce extra structure into ID theory to overcome both of these shortcomings. This extension to ID theory may allow us to capture all testable aspects of physical reality in terms of ID theory, and the mathematics of this extended ID theory should provide very powerful a priori restrictions on the nature of reality.

Technical Abstract

Can physical reality be formulated in purely information-theoretic terms? Traditionally this question has been addressed using Shannon\'s information theory. But as Shannon emphasized, his theory concerns syntactic information, ignoring the semantic structure of what the variables mean. This suggests we need a semantic information theory to fully describe physical reality. The mathematics of inference devices (ID\'s) – mathematical abstractions of any physical device that can be used for observation, prediction, or control – provides such a theory. Moreover, there are connections between ID theory and physics, e.g., ID theory provides a non-quantum-mechanical \'uncertainty principle\'. This suggests that we formalize reality as the semantic information that a set of ID\'s have about one another and about other physical variables. A challenge with this approach is that the definition of ID\'s is too weak to fully capture the concept of semantic information, and contains no notion of distance measure. I propose to introduce extra structure into ID theory to overcome these shortcomings. This extended ID theory may allow us to capture all testable aspects of physical reality in terms of a semantic information theory, and thereby provide very powerful a priori restrictions on the possible nature of physical reality.