How many properties does a geometric point have? One: its location. Not a lot.
Let's say you have two geometric points. Now you have two properties, right?
No: you have the points themselves and the distance between them.
Where does this "distance" come from if neither point has such a thing? It emerges from the relationship between the two points. It is an emergent property.
If, for each new point or unit, one must factor in the relation between that unit and each of the others, then the complexity of the system is O(n^2). If one must factor in the relation between the unit and all the other emergent properties (e.g.: packing a suitcase), then the potential complexity grows exponentially.
The existence of emergent properties explains how such a complex world can be built from simple components, and related philosophical quandaries. It is the root cause of why the Fallacy Of Division is a Logical Fallacy. It is why water is wet, and why brains think without the requirement that there be a Ghost In The Machine.
A point can be an Emergent Property of a Named Point, as can the connection between it and another point (not necessarily a straight line) and may also pass through other points connected together. The traversal may also have a name (trip), with each of the points and connections being properties. A property can itself have properties as is illustrated by all of the characteristics(properties) which exist in a font used by a computer, each of which may have properties. Objects may have properties, which can also have properties. -- Thinking Out Loud.Donald Noyes.20110922
See also Emergent Systems
See original on c2.com 