On Equations, Art and Information Compression

I imagine that part of the beauty of an equation in physics lies in the sense in which it serves as an algorithmic information compression of the phenomena, system or relationship it describes; that the real world can then in some sense be extracted, extrapolated or successfully modelled from the equation. It seems that this relative simplicity is deceptive and possesses an implicit semantic network-reference or foundational information-system inversion. The extensive education, comprehension, intelligence and knowledge-acquisition required to understand these weighty hieroglyphics indicates an interesting feature of semantic compression as a more broadly-considered component of intelligence, information and communication: that the string/symbols of an equation compresses the material description of reality in what is proportional to the extent of a logical or referential inflation of the significance and contextual, relational system within which these symbols are considered meaningful.

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I am no physicist, nor mathematician, but I would be interested in hearing feedback from those quite literally “in the know” on how they would characterise this relationship between message, equation or theory compression and the extensive intellectual and contextual-knowledge requirements necessary to be able to comprehend those theories. While the short-form description of a material system contained within an equation can be decompressed into effective modelling and predictive descriptions of physical reality, at an information and communications level it seems as though the compression to a narrow set of symbols and mathematical relationships occurs synchronously with the displacement of a proportional, equivalent quantity of required knowledge and expertise external to the equation.

In language: where a complex word or compound phrase most effectively captures or articulates a specific question, solution or description of an actual state of affairs in the world, its effective use in message transmission is dependent upon a variety of factors. The intelligence and vocabulary of the intended receiver of the message generally has to be assumed or taken for granted, albeit true that writing to a more general audience usually implies the use of simple words and many more sentences to convey the same message that complex words and clever idioms or motifs might achieve in less overall message information-complexity and string-length.

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The use of specialist vocabularies and contextual knowledge allows for message compression, but at the apparently mandatory cost of displacing the complexity elsewhere: into assumed knowledge, specialist technical skills, cultural contexts or extensive experience and (again) into an implicit, certain assumed level of intelligence in the message recipient or target audience.

Consider by way of analogy the Minimalist movement in (predominantly American) art of the 1960’s and 1970’s. While the visual aesthetic encoded for the most part significantly less information, there was (simultaneous to this information compression in the artefact) a broad and distributed decompression of complexity and semantics or cultural and specialist vocabularies into the various manifestos and media buzz generated around the art movement. The information was still there, even when attempts were made for diverse reasons of political, ideological or spiritual motivation to simplify and compress the objects, paintings, sculptures and architecture down to their simplest and most reductive forms. Isolating centralised semantic components in this sense required a concomitant specialist vocabulary and cultural context to “unpack”. In a broader cultural context this decompression also produced Minimalism-lite filtered through the art establishment and market as rendered in media and literature for an art-consuming public; generating in this way a self-propagating second-order commercial network of semantics and attributed commercial value. (Popular-science literature serves a similar function in regards to the equations, conceptual vocabularies and theoretical education of a broader-public, although aesthetic equivalency between equations and art-objects is perhaps a unique request of any imagination).

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It seems to the mathematically unitiated that advanced physical equations are a little like this minimalist enigma. That the reduction to short strings of symbols and mathematical relationships inversely displaces vast swathes of assumed or required knowledge elsewhere such that, while I acknowledge and deeply respect the beauty, depth and explanatory power of mathematics in physical theory, the view from here is that the relative simplicity of an equation is always implicitly dependent upon a complex network of assumed or implied information and knowledge external to it, a theoretical context perhaps but not necessarily limited to this as full comprehension clearly requires more than mere generalised insights or intuitions. Information and model or equation compression in this sense is always multiplex and synchronous with decompression and displacement into wider contexts and knowledge systems.

Equations are epistemologically consistent or sensible within theoretical systems and these systems of explanation are probably the location of the first-order context, semantics and vocabulary decompression of those equations. At higher-degrees of comprehension of the complexity and abstraction underlying those equations – the relative simplicity (i.e. string/symbol-compression) of the equation is perhaps always at this implicit cost of complexity displaced elsewhere into knowledge and cultural or technical-semantic contexts.

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Art by Piet Mondrian.

 

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