There is a paradox in physics that occupies itself with the arcane possibility that black holes destroy information. Basically, Hawking radiation from the surface of a black hole seems to be uncorrelated with the captured material inside which is evaporating away via that Hawking radiation, and so the state pre-evaporation is not recoverable even in principle. I don’t seek to elucidate the paradox in the slightest, except that the holographic principle seems to resolve it, but rather I’d like to copy and paste their definition of “information” for my term “implicit information.” Implicit information is information regarding the configuration of a [physical] system. I’m not satisfied with that definition, but I think it perhaps more useful to contrast it with “explicit information”: explicit information is information that is ready-to-use by an intelligent agent.
As an example: imagine that my total energy bills for 2012, 2013, and 2014 were $431, $392, and $425, respectively. My energy bill for 2012 is explicit information. You can read it off as $431 quite readily. My average expenditure for these three years, however, is not explicit information. It’s nowhere ready-to-use and thus must be found, discovered, perceived, derived, or computed in some way. Quite easily, I can compute the average, and it is $416. This information, though implicitly present in the three original figures, is now explicit, and I can use it to make a budget.
Things get murky when you try distinguishing implicit and explicit information in the context of the biological world. For instance, there is probably some sense in which a squirrel has a concept for <tree>, and it can apply this concept to that oak in your backyard. The property of that tall, woody mass of being a tree is understood explicitly by the squirrel, but how did that happen? No one ever taught the squirrel that it was a tree, and it certainly never read that anywhere. Maybe we can’t pin down exactly what I mean by “explicit information” in all circumstances but perhaps there’s some way to definitively identify some subset of it. For instance, a good start can be made by “any information represented by an arbitrary code (e.g. human language, Morse code) is explicit information.”
But then DNA qualifies. Intuitively, we can ask ourselves whether DNA is explicit or implicit information. We can ponder: what is DNA about? At a first evolutionarily-minded pass, it’s a blueprint for survival. On a second pass, though, all it’s used for is to make RNA and then proteins. Maybe it’s best to say that DNA contains explicit information about biomacromolecules, but merely implicit information about survival. Certainly this has serious implications for Dembski’s intelligent design arguments which I will probably address in a later post.
The distinction between implicit and explicit information is useful in multiple areas. Science, for instance, can be understood as an enterprise that turns implicit information into explicit information. Actually, that can be broadened to research in general. It is clear that the process of turning implicit information into explicit information is difficult and certain humans do it better than other humans. In economics, one could claim that the main advantage of the free market system is that almost no research has to happen in order to set prices, i.e. the information as to efficient distribution of resources implicitly exists, but no explicit extraction of that information has to happen. By individual agents making locally optimal choices, the price-point for no shortage and no surplus is found automatically. In contrast, communist systems must perform research to find that price-point for all goods, and therefore incur an enormous waste of energies, if the price-point is even found at all.
Gödel’s Incompleteness Theorems almost definitely have stern implications for the distinction between these two types of information. The implications would probably be something along the lines of: any rigorous reckoning of implicit and explicit information must either be inconsistent or incomplete. This differs from other attempted distinctions, such as between male and female, where the fundamental problem is that any thin line in the sand is arbitrary. With information, it’s not that the line is arbitrary, but rather that no line can logically exist. Or so at least I suspect.