The Whole Is Greater Than the Part (Part 1)

One of Euclid’s “Five Common Notions” forming the basis of his geometry is “The whole is greater than the part”.  Euclid sought to develop his account of space based on ideas he could not prove, but seemed so obvious that no proof was needed.  Indeed, a study published by the National Academy of Sciences about an Amazonian tribe suggested that geometric reasoning is innate.

Well almost.  Euclid’s Fifth Postulate, asserts in effect that parallel lines don’t intersect.  (Actually it describes how non-parallel lines do so.)   Euclid’s contemporaries were suspicious of this idea and our Amazonian friends understood more frequently than Westerners that this is not true on curved surfaces.  And of course, spactime does not conform to Euclid’s description which is functional only in local areas where curving spacetime, intense gravitational fields or the curvature of, say, a planet does not come into play.

Why am I writing about this?

I recently finished reading Code/Space by geographers Rob Kitchin and Martin Dodge (MIT Press) which discusses how applied software transduces space. (Their website links to many of their papers leading up to their book and some of the quotes I use will be from these rather than from the book.) This prompted me to meditate on space in general.  Euclid seemed a good place to start.

K&D discuss how Euclidian geometry represents space as mere container of objects and processes.  They write:

This absolute ontology of space is essentialist  in formulation. It effectively reduces space to  its geometric essence and depicts that essence as natural  and given.

Recently, this viewpoint has been challenged by relational  ontologies that understand space as being constituted  and given meaning through human endeavor.  Within these relational ontologies, space is not a given,  neutral, and passive geometry but rather is produced  through social relations. Space, it is posited, is not essential  or objective in nature, but produced: ‘‘constituted  through social relations and material social practices’’   Code and the Transduction of Space  Dodge, Kitchin

They note that this allows one to think of space either as metaphor or container, social or apart from the social, outside of time or fundamentally temporal, always in a state of becoming.  Reformulating this a bit, we can think of each set of these binaries as parallel lines, as local functionalities that apparently never intersect but in fact do.  I find this an interesting way to think about binaries in general. Nature/culture; body/mind; subject/object each as a set of lines seemingly never meeting in a local, functional context, but that inevitably do.

Anyway, D&K explore the way coded objects and process (ie technicity) transduce space.  In general, a transducer converts one form of energy into another.  So as I understand it, D&K discuss how technicity converts one form of space into another.

From this perspective, society, space and time are co-constitutive – processes that are at once social, special and temporal in nature produce diverse spatialities.  Software matters because it alters the conditions through which society, space and time, and thus spatiality, are produced. Code/Space

I hope in subsequent posts to further explore the ideas in this book.


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