A likelihood better than chance
"Information is the currency of life," Christoph Adami recently told Quanta. "One definition of information is the ability to make predictions with a likelihood better than chance."
I've never heard anyone define information in quite that way before—as an "ability" or capacity. It's pithy and catchy as far as it goes, yet I'm not so sure I'd use it to characterize Claude Shannon's position on information (something Adami has done elsewhere).
Adami's "is" complicates the definition, for if information "is" (that is, "equals") an ability to make predictions, some readers might tend to localize this ability, to make it a matter of a singular actor's activity. (Of course, one must then ask: What does it mean "to information"?) And doing this would seriously misconstrue the nature of the problem the concept of information attempts to solve.
Rather, we might say information concerns choice; it simply isn't synonymous with some intentional or rationalistic activity (recall that Shannon's "choice" was a cryptographic term that referred to a certain degree of variability; he typically put the word in scare quotes when writing about it). "Information" names the relative degree of certainty a field affords. That doesn't necessarily roll off the tongue as easily as Adami's little ditty, but it does gesture more squarely to what I think is the most appropriate locus of information's problem-space: the milieu, the more-or-less arranged melange of symbols and/or materials that permit certain degrees of (un)certainty.
Yet for Adami information is "the currency of life"—some kind of possession or medium. The Quanta interview is a fascinating example of the ways "information" takes on various dimensions, referents, and capacities. For example, information performs a symbolic function ("Life is information stored in a symbolic language [...] Our DNA is an encyclopedia about the world we live in and how to survive in it"). It maintains its ethereality ("Information is substrate-independent") while demanding specificity ("A sequence is information in context").
Information inhabits the tension between immateriality and embeddedness in extraordinarily productive ways. It's "substrate-independent" to the extent that it pertains to something "outside" a body's material dimensions, but is irreducibly contextual insofar as it names something about particular material relations. By insisting that information remain contextual, Adami indicates something about its referentiality; information is always about something, and is therefore never entirely divorced from anything. (Roman Jakobson says this is true of any communicative phenomenon, by the way.)
Put another way: If "information" names a fact of repeatability or unrepeatability—if it signals some differentiation between certainty and uncertainty—then it indicates something about an organization of material relations that are always already context-specific. Asking the question of information would be impossible otherwise.