Conservation of information as developed in several articles (see the publications page at www.evoinfo.org) by Robert Marks and me has come in for criticism not only conceptually but also terminologically. None of the conceptual criticisms has in our view succeeded. To be sure, more such criticisms are likely to be forthcoming. But as this work increasingly gets into the peer-reviewed literature, it will be harder and harder to dismiss.
That leaves the terminological criticism. Some have objected that a conservation law requires that the quantity in question remain unchanged. Take conservation of energy, which states that in an isolated system energy may change forms but total energy remains constant. Some have argued that what we are calling conservation of information is more like entropy. But that’s not the case either. Entropy, as characterized by the second law of thermodynamics, says that usable energy will diffuse and thus be guaranteed (with overwhelming probability) to increase. Hence entropy, unless usable energy is in a maximally diffuse state, will change and cannot rightly be regarded as falling under a conservation principle.
Conservation of information, by contrast, falls in a middle-ground between conservation of energy and entropy. Conservation of information says that the information that must be inputted into a search for it to successfully locate a target cannot fall below the information that a search outputs in successfully locating a target. Robert Marks and I show that this characterization of conservation of information is non-tautological. But as stated, it suggests that as we move logically upstream and try to account for successful search, the information cost of success cannot fall below a certain lower bound.
Strictly speaking, what is conserved then is not the actual inputs of information to make a search successful but the minimum information cost required for success. Inefficiencies in information usage may lead to more information being inputted into a search than is outputted. Conservation of information thus characterizes information costs when such inefficiencies are avoided. Thus it seems to Robert Marks and me that the expression “conservation of information” is in fact appropriate.