100128 - injunction

It may be helpful to realize…that the primary form of mathematical communication is not description, but injunction.  In this respect it is comparable to practical art forms like cookery, in which the taste of a cake, although literally indescribable, can be conveyed to the reader in the form of a set of injunctions called a recipe.

- G. Spencer-Brown
Laws of Form, 1969

An injunction is a command or directive.  When working by injunction, a procedure (set of commands or directives) is specified and then carefully implemented.  This mode of working is fundamentally exploratory because outcomes cannot be fully anticipated.  It involves iterative improvement (recipe for baking a cake is followed, results are evaluated, recipe is adjusted to achieve a better outcome, and the cake is baked again).  It is a technique for avoiding pre-figuration and extending beyond the expected. 

Much of the work you are currently doing is by injunction; keep this in mind as models and maps evolve and increase in complexity.

Cluster of tetrahedral origami units

Tomoko Fuse

Cluster of dahlia petals,

Chris Morgan

CLUSTERING – PACK AND CONNECT

A cluster is a number of similar units gathered into a larger organization.  In a cluster, characteristics of individual units are secondary to characteristics of the larger organization.  For example, the origami units above connect in a networked pattern and the dahlia petals incrementally change size and proportion forming a gradient.  Observe that patterns and gradients are not visible in a single unit; they emerge when many units combine.

Develop three unique clusters by packing and connecting five wood units.  One cluster must connect all five unit types in order (1-2-3-4-5).  Another cluster must connect five of the same unit type at one end of the family (1-1-1-1-1).  And another must connect five of the same unit type at the other end of the family (5-5-5-5-5).  In the same way that precisely identified geometries in the molding profiles inform a procedure for producing the unit; precisely identified geometries at the scale of the unit will inform procedures for producing the cluster.

Model the 1-2-3-4-5 cluster in Rhino.  Create a top view, side view and a series of sections from the digital model.  Compose these drawings on 18” x 18” sheet(s).  Drawings must be 1:1 scale.   There will be a Rhino tutorial on Saturday covering tools required to complete this model.

Go here for examples of cluster development.

MAP DEVELOPMENT

Continue developing dunescape maps according to feedback received in class.  Focus on the meta-analysis (comparisons of directly mapped data) and on calibrating notations to form a field without gaps.    

Identify three conditions critical in understanding your maps (two conditions from one map and one from the other).  Name the condition with a new word, or neologism, that compounds two previously unrelated words.  Some examples of this type of neologism from poet Paul Celan:  hungercandle, doorcrack, copperglimmer.