Tuesday, 1 August 2017

Semiotics and Symmetry

Next week I'm giving a talk about Peirce and Quaternions at the Alternative Natural Philosophy Association. It's a fascinating group which was introduced to me by Peter Rowlands at Liverpool, and I've quite enjoyed getting stuck in to thinking about Peirce long after I'd thought I'd left all that stuff behind.

The thing which has dragged me back to Peirce is his interest in quaternions, which Peter Rowlands introduced me to through his physical theory. It was a coincidence that I discovered that Peirce had been fascinated by Hamilton's work too - largely because of his father who was quite an eminent mathematician. In Peirce's writing, the quaternion tables are quite prominent, and I'm pretty convinced that his obsession with tripartite structures derives from this.

What put me off Peirce is a kind of semiotic dogmatism which analysed the stuff of the world as Symbol, Icon and Index, obsessing about Interpretants, signs and representamens. There didn't seem to be any ground for the dogmatism. But of course, this was the fault of those who jumped onto the Perice bandwaggon, not the man himself. Even within more thoughtful scholarship, and emphasis on semiosis as process  (which it clearly is), the Peircian categories are overlaid as if to say "this sign is produced by this process".

What does it mean to say "this sign" anyway? This has got me thinking about contexts, and whether Peirce's sign theory is really a theory about the context of signs.

A tripartite, anticommutative, symmetrical idea like the quaternions is an interesting way of thinking about contexts. We detect sameness and stability through a continually changing context. To say "this is a sign" is to make a declaration about something remaining the same despite changes in the context of its perception. Peirce's distinction between Sign, Representamen and Interpretant are different dimensions of the context, and within each dimension, there are a further three subdivisions. So "sign" breaks down into Icons, Indexes, and Symbols, for example. His firstness, secondness, thirdness feels like the three dimensions which hold the structure together.

This has significance for the way we think about analogy, sameness and induction (which is dependent on analogy) - Peirce was doing logic after all.

Sameness, counting, induction and analogy are all declarations: we say "this is a chair" because of its sameness with other chairs. We say "there are three chairs" because of the sameness between them. Of course, in making declarations like that, we are producing signs; but the declaration itself is necessitated by the differences between the context of the perceptions of the objects. Nothing is ever really "the same".

However, things may be symmetrical. To make a sign and say "this is a chair" is to respond to the differences of context in which chairs are perceived. Might those changes in context result from an anti-commutative rotational symmetry? I'd like to explore this. What of the anti-commutative rotational symmetry of the statement "this is a chair?" - are the changes in the contexts related? What are their dynamics? How might we investigate it?

The best way we have of investigating a context - or a constraint - is information theory. It's a crude instrument. However, what it does do is allow us to look at the many descriptions of something (the statements people make about something) and see how they relate to one another. The most interesting context to do this is over time-based media like music or video. constraints change over time, and it is possible to explore the dimensions of constraint over time, and particularly the way that changes in one constraint relates to changes in another.

The technique for doing this is known as relative entropy. A similar technique is used for exploring the presence of entanglement in physics. There, the descriptions of charge, mass, space and time seem fixed - and yet, do these properties also change the context for observation?

Questions like this are intriguing because they hint at a closing gap between the physical and the social sciences.

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