A Calculus of Negation in Communication

Abstract

The paper compares Claude E. Shannon’s mathematical theory of communication to George Spencer-Brown’s calculus of indications. Whereas the former proposes a probabilistic understanding of information and a redundant world of a code shared among sources and destinations of messages, the latter proposes to start with not just binary but general negation and to account for observers either following a call or crossing the distinction being called. Both Shannon’s theory and Spencer-Brown’s calculus share a cybernetic understanding of control and communication that centers around replacing a complex and, therefore, untreatable contingency with a sequence of many “more special” contingencies relating to one another. In Shannon’s theory, that sequence is exogenously given and technically constrained as the set of possible messages, whereas in Spencer-Brown’s calculus, it is a sequence of crosses by first-order and markers by second-order observers concatenated within the form of their distinction. The calculus of Spencer-Brown imagines states of time as the precondition for the resolution of a complex contingency. Information and communication are to be analyzed in time, not in space. They are events that, appearing and vanishing instantaneously, induce their own decay while also calling for new, or the “same,” indications and distinctions to be called and crossed.

Keywords: Communication, Calculus, Negation, Shannon, Spencer-Brown