Semiotic analysis of the role of the observer in the theory of relativity and in quantum mechanics shows the semiotic function of basic symmetries, such as symmetries under translation and rotation. How can semiotics be relevant to theories in physics? It is always human beings who form the theories. In the process of theory formation and communication, they rely on semiotic systems. Included among these systems is the semiotics involved in our pre-theoretical human understanding of space, time, and motion. Semiotic systems thereby have an influence on theories in physics. As a result, key concepts in fundamental physical theory have affinities with semiotics. In terms of Kenneth Pike’s tagmemic theory, applied as a theory of theories, all symmetries take the form of distributional constraints. The additional symmetry under Lorentz transformations introduced by the special theory of relativity fits into the same pattern. In addition, constraints introduced by the addition of general relativity suggest the form and limitations that might be taken by a “theory of everything” encompassing general relativity and quantum field theory.
A model of semiotic theory informed by information theory can be adapted to provide a simple theory concerning theories, and to model changes in theories over time. The model appropriates from tagmemic theory the fundamental features of contrast, variation, and distribution that characterize emic units. It then applies these features to second-order theories about theories. The specification of behavior of emic units at this second-order level puts constraints on the expected form of first-order theories and changes in time to first-order theories. A key feature in the constraint on first-order theories is the feature of symmetry. Second-order theory leads to an expectation that shifts in perspective in first-order theories can take three forms: (1) contrastive shifts, due to adding or subtracting emic units; (2) variational shifts, due to changes in probability estimates for co-occurrence; and (3) distributional shifts, due to global change in the system of units. The model for second-order theory is applied specifically to phonology, music, and Newton's laws of motion (treated as a semiotic system).
Information theory indirectly confirms some fundamental structures in semiotics. By offering quantitative criteria for efficient transmission of data, it suggests by analogy ways of thinking about efficient communication in language and other media. The criterion in information theory for maximal capacity for information at the source leads to preference for independent data, which can be generalized to the semiotic principle of approximate independence among many kinds of emic units. This independence is closely related to what Kenneth L. Pike's tagmemic theory has called distribution. The criteria in information theory for faithful transmission of data lead by generalization to the semiotic principles of contrast and variation. Together, the aspects of contrast, variation, and distribution constitute fundamental structures characterizing the whole field of semiotics. They also lead to the development of three interlocking views of communication, the particle, wave and field view, which enable us to explain a number of more complicated phenomena in communication. These tools for semiotics receive confirmation from the quantitatively more specialized concerns of information theory.