
topology notions


As a result of the dominance of clocks,
our experience of time has been radically
transformed over the past thousand years. This affects the way we perceive
change, and the speed of change. More recent technologies have started
to enable a similar transformation of our experience of space. Transport
enables us to travel much greater distances than our forebears. News media
give us information about events in distant lands (or even distant planets).
More recently, Virtual Reality and the Internet
have started to introduce more strange experiences. There is a need to
develop evermore complex modes of topological reasoning  what is connected
to what, what is accessible from where, what is protected from whom, how
can this be stretched or squeezed into that. 
Barrier
A barrier may represent a permanent block or obstacle, or it may merely
cause delay and inconvenience.
Boundary
Ceiling
Something above your head, that limits access to what is above the ceiling.
A normal ceiling prevents you seeing what's above your head.
A glass ceiling allows you to see what's there  but you can't
see what's stopping you reaching it. Among other things, this term
is used to denote practices that seem to prevent certain categories of
employee  such as women or members of ethnic minorities  from reaching
high office. These practices cannot be directly seen, but their existence
is inferred (or alleged) from their apparent effects.
Closed, Closure
In simple topological terms, something is closed if it contains
its own boundary, and the boundary of every neighbourhood.
Intersecting
any
number of closed sets together produces a new closed set.
Open and Closed are not opposites. Some sets may
be both open and closed. Some sets may be neither open nor closed.
Cluster, Clustering
Clustering is essentially a topological exercise. Topology can be thought
of as the mathematics of scope, defining the boundaries between outside
and inside. In general, there may be a complex structure of such boundaries,
both nested and overlapping.
A clustering exercise takes a set of entities and positions them in
a topological space, consisting of a set of neighbourhoods. These neighbourhoods
may then be used to define the scope of projects, systems or organizations.
A clustering exercise is successful (relative to a given purpose) if these
neighbourhoods prove stable, efficient and flexible.
Two forms of clustering are commonly identified.

Interaction clustering groups entities into neighbourhoods according
to the quantity and importance of the interactions between them. This is
particularly suitable for software engineering structures, where the success
of clustering is often measured in terms of maximum cohesion and minimum
coupling. 

Affinity clustering groups entities into neighbourhoods according
to the defined similaries (or lack of dissimilarities) between them. This
is particularly suitable for many organization and management structures,
where the success of clustering can largely (although never entirely) be
gauged in terms of the economies of scale and scope. 
The results of clustering can be depicted in two ways. If you show the
interactions or affinities in the form of a matrix (such as a CRUD matrix),
you can then rearrange the rows and columns, and draw boxes along the diagonal
to show the clusters. Alternatively, clustering can be shown in a tree
diagram, known as a dendrogram. Statistical packages are available
to draw dendrograms automatically.
Cohesion
Clustering is often exercised to maximize cohesion
(within each cluster) and minimize coupling (between
clusters).
Coupling
A measure of the linkages between entities: the extent and rapidity with
which changes within one entity impact on another entity, or the requisite
degree of coordination between entities. Tight Coupling is contrasted with
Loose Coupling.
Maturana and Varela introduced
the notion of structual coupling as a essential component of identity.
Clustering is often exercised to maximize cohesion
(within each cluster) and minimize coupling (between clusters).
Encapsulation
The act or preservation of (en)closure around some stuff.
Fold
Folding gives us layers and envelopes, biological and geological form.
Interface
Labyrinth
Change can sometimes be regarded as a labyrinth. There are many logically
possible ways to go, and you can glimpse some interesting paths, but only
a limited number of them are accessible from where you are today.
The role of the consultant may be to help navigate the labyrinth, or
to find ways of altering the topology of the labyrinth itself  reframing
things so that they become possible (or no longer possible).
Security can be viewed in similar terms.
Open
In simple topological terms, something is open if it contains a
neighbourhood
of
every point. Joining any number of open sets together produces a
new open set.
Open and Closed are not opposites. Some sets may
be both open and closed. Some sets may be neither open nor closed.
Skin
Topology
An abstract way of thinking about space, including such notions as closed/open,
boundary, neighbourhood.
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This page last updated on April 9th, 2003
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