Sets of Signals, Information Flow, and Folktales

I apply Barwise and Seligman’s theory of information flow to understand how sets of signals can carry information. More precisely I focus on the case where the information of interest is not present in any individual signal, but rather is carried by correlations between signals. This focus has the virtue of highlighting an oft-neglected process, viz., the different methods that apply categories to raw signals. Different methods result in different information, and the set of available methods provides a way of characterizing relative degrees of intensionality. I illustrate my points with the case of folktales and how they transmit cultural information. Certain sorts of cultural information, such as a grammar of hero stories, are not found in any individual tale but rather in a set of tales. Taken together, these considerations lead to some comments regarding the “information unit” of narratives and other complex signals. 1 A Theory of Information Flow In their book “Information Flow: The Logic of Distributed Systems,” Barwise and Seligman [1] present a mathematically sophisticated theory of how things can carry information about other things. Barwise and Seligman started from Dreske’s seminal work on information flow [2], and expanded and formalized his observations, integrating his approach with related approaches, resulting in a more general formulation. (From here on out I will refer to this general formulation as the “DBS” theory of information flow, short for Dreske-BarwiseSeligman). I observe that the DBS theory is, in fact, even more general than it at first appears, and it is my aim to illustrate how it can be used to frame and describe several important facets of information flow, knowledge, and belief that were left unelaborated in both Barwise and Seligman’s and Dreske’s work. In particular, I will show how the DBS theory, without modification, can be used to conceptualize two important items which Dreske touched upon only tantalizingly: learning and intensionality. I show how this conceptualization brings into relief a part of information channels that is often taken for granted in philosophical analyses, namely, the process by which categories are applied to raw signals. I will then apply these insights to make some comments on the information content of cultural narratives (folktales). I set the stage by reviewing in brief the relevant parts of the DBS theory. The theory involves, at its core, classifications and infomorphisms. These two S.B. Cooper, A. Dawar, and B. Löwe (Eds.): CiE 2012, LNCS 7318, pp. 228–236, 2012. c © Springer-Verlag Berlin Heidelberg 2012 Sets of Signals, Information Flow, and Folktales 229 objects are used to model how information flows across distributed systems, which are systems that can be analyzed in terms of both a whole and constituent parts. In Barwise and Seligman’s terminology, an information channel brings classifications and infomorphisms together into a full model of the information flow of a particular system. We shall lose no generality if we restrict ourselves to discussing a distributed system W comprising only two parts, a proximal part P , to which we have direct access and be thought of as the “receiving” end, and a distal part D, from which information is flowing. There are infomorphisms that map properties of the classifications of the distal and proximal parts to the whole; call these d and p, respectively. To provide a concrete example to discuss, let us take Barwise and Seligman’s example of a nuclear reactor: in this case W is the whole reactor, D will be the reactor core, and P will be a gauge in the reactor control room, and d and p are the regularities that connect the core to the reactor to the gauge. A classification is similar to what one thinks of when considering the standard classification task in cognitive psychology: it is a set of labels or classes that may be applied to some object or phenomenon. Classifications can be, for example, mutually exclusive (e.g., {square,circle}), exhaustive (e.g., {true,false}), or overlapping (e.g., {tall,fat}). They can also be none of those things. Importantly, though, each part, as well as the whole, receives a classification. For our reactor example we might consider the reactor core D to be classified by the exclusive types normal and overheating, the reactor status gauge can show one of green or red, while the reactor overall can be in one of the four states achieved by the cross product of these two classifications. An infomorphism relates classifications on a part to classifications on the whole. It is a way of describing how classifications are transformed as the information they carry moves through the distributed system, from one part to another: they are models of the regularities that allow information flow. In such a system one infomorphism d may be applied to the distal part’s classification to obtain a classification on the whole, and then another infomorphism p may be applied in reverse to the classification on the whole to obtain a classification on the proximal part. We need not say too much about infomorphisms except that, as they are applied in the forward and reverse directions, the resulting classifications loose some of their guarantees and internal relationships and are downgraded to what Barwise and Seligman call local logics. In the reactor example, the combined infomorphisms from reactor core to reactor whole, and then from reactor whole to control room gauge, given a reactor in working order, results in a display of green on the gauge when the core is normal, and a display of red on the gauge when the core is overheating. Thus information flows from the distal part of the system (the reactor core) to the proximal part of the system (the control room gauge). The details are not critical to my argument, but there are two essential points to take away from this description. First is that regularities across the system, modeled by chains of infomorphisms, are what allow information to flow from one part of the system to another. (It is often helpful to think of these