This is an interesting use of "manifold".
In mathematics, a manifold has a well-defined
meaning. The structure of a manifold
is encoded by a collection of charts that form
an atlas. A chart is a mapping between the
manifold and a simple (euclidean) space, see
http://en.wikipedia.org/wiki/Manifold
If science is a manifold, then each science -
physics, chemistry, biology, psychology etc. -
is a chart, and all sciences together form the
atlas of the manifold. Sunny Y. Auyang makes
this point in her book "Foundations of
complex-system theories".
If understanding is a manifold, then each analogy
is a chart, and all analogies together form the
atlas of the manifold, see http://is.gd/22u44
Holt uses the term manifold in the sense of
an emergent property: a forest is an emergent
entity made of trees, plants, soil, etc. The
form of plants and trees can be described
by fractal patterns. There are clearings and
trails in the forest which can be described
by patterns as well.
Thus one can perhaps say if an emergent entity
is a manifold, then each pattern is a chart,
and all patterns together form the atlas
of the manifold. This pattern could be a
simple physical pattern, or a basic agent
interaction pattern (http://is.gd/22uZ6)
for an agent based system, for instance.
-J.
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