I have re-posted this from the "Agency in the Physical World - FQXi's Next Research Program" Blog, because it is also relevant to the "Constructing a Theory of Life" Forum:
What is information:
Information = knowledge = subjective experience of one or more relationships between categories, whereby every "higher" category is ultimately related to the most fundamental-level categories like energy and momentum. Every information category, even the most fundamental ones, can be defined as a relationship between other categories. So that information/knowledge is always contextual (i.e. related and categorised): information does not objectively exist without context (i.e. i.e. without relationship and categorisation), as if it were a binary digit in a vacuum.
How do we represent information:
The physical universe exists because of information relationships. But the relationships are not to be equated to the mathematical symbols we human beings use to represent them. We represent relationships symbolically as: (law of nature) equations, algorithms (these mainly exist in living things), and initial-value number assignments (where every measured number can ultimately be traced to simpler relationships between categories in which the "numerator" and "denominator" categories cancel out, leaving a number, which is a thing without a category).
What knows information and what creates information:
The universe itself creates and knows all the types of relationships (represented by human beings as equations, algorithms, numbers). More precisely, parts of the universe create and know relationships: i.e. agent-observers create and know relationships, where agent-observers are "information-integrated": particles, atoms, molecules, and living things. This "creation" and "knowledge" are otherwise known as "free will" and "consciousness".