Configurational Formalism - The most powerful in detecting formal and functional regularities in real systems.
The main reasons:
1. The problem of understanding the simultaneous effects of a whole complex of entities on each other through their pattern of relationships, (configuration). This is why formalism often seem to offer mathematical sophistication out of proportion to the empirical results achieved.
With configurational analysis, it leads to a disproportionate success in finding significant formal and form-functional regularities.
2. The representation of the spatial or formal systems that is to be analyzed as to the method of quantification. By doing this we conclude with trying to represent space in terms of the type of function we are interested in. 'j-graphs' creating formally or functional thoughts of informative results.
3. The graphic representation of the results of mathematical analysis. Creating a graphical representation rather than a mathematical understanding. By representing mathematical results graphically, a level of communication is possible that permits large numbers if people to be interested and knowledgeable who would otherwise fall at the first fence of mathematical analysis.
The 'Space Syntax' itself has been researched at UCL University. It has been drive by a remark of Lionel March's: 'The only thing you can apply is good theory'.
The techniques of spatial representation and quantification proposed here are essentially survivors of an intensive program of empirical investigation.
Defining Configuration *relating back to Part 3
1. Simple relation was defined as a relation between any pair of elements in a complex.
2. Configurational relation defined as a relation insofar as it is affected by the simultaneous co-presence of at least a third element, and possibly all other elements in a complex.
In figure one, a and b are two cubes standing on a surface. The relation of a and b is symmetrical in that a being the neighbor of b implies that b is the neighbor of a.
In figure two, a and b are brought together, which again is a symmetrical relation. These two conclude to have a neighbor relation.
However, figure three, does not. The conjoint object formed by a and b in figure one and two is taken and rested on one of its ends, without changing the relation of a and b. B not appears to be above a, and the relation of being above is not symmetrical but asymmetrical, i.e. b being above a implies that a is not above b.
The surface is introduced as a new relation to these three figures, known as c. In figure one and two, the surface to which the cubes are standing on, say the surface of the earth, have a symmetrical relation as to each other. Therefore we can say that a and b are symmetrical with the respect to c.
This is a configurational statement, since it describes a relation of at least a third.
Observing figure three, a and b are asymmetrical with the respect to c.
This is a configurational difference due to figure 1-2 and 3 being totally different, i.e. symmetrical/asymmetrical.
The relation of a and b to each other is changed if we add the 'with the respect to' clause which embed the two cubes in a larger complex which includes c.
The situation clarified by the justified graphs
j-graph:
Nodes are aligned above a root according to their depth from the root of the configurations shown above. The bottom node is the earth itself, with a cross indicating that is the root. In the first two figures, a and b are each independently connected as neighbors to the earth. In figure three, the relation between b and c is broken creating a 'two deep' relation.
The numbers that are attached to each node in the j-graphs, indicate the sum of 'depth'. This is a total of sum from node to another node in the system.
TD also known as Total Depth, is the total sum of all the nodes. The distribution of TD and their overall sum describes at least some configurational characteristics of these composite objects. (less amount of TD, more integrated the system is)
These figures here take this notion of TD into a complex stage. They are all composed of seven identically related cells plus an eighth one which is joined to the original block of seven initially at the top end in the leftmost figure, then progressively more centrally from left to right.
The two principal effects from changing the position of this single element:
1. The total depth values and their distribution all change.
2. The sum total depth for each figure change, reducing from left to right as the eighth element moves to a more central location.
As you can see, the least amount of depth is in the fourth figure, making this system a much more integrated scheme.
The two key principals of configurational analysis:
1. Changing one element in a configuration can change the configurational properties of many others.
2. The overall characteristics of a complex can be changed by changing a single element, that is, changes do not somehow cancel out their relations to different elements and leave the overall properties invariant. Virtually any change will alter the overall properties of the configuration.
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