Both a wave and a particle
Light, and matter in general, exhibits both particle and wave properties . Depending on its use, light behaves either as a sequence of particles or as a continuous wave of energy.
It occurred to me that there is a similar duality in computer science: the relation between two objects may be treated as an object in itself. This technique which is called reification, can be used when properties need to be added to the relationship. An example of such a property is weight, another is activation. But even an obvious property like the meaning of a relationship, or its label, may be implemented as an object.
This itself isn't much of a problem, until the reified relationships are objects of the same set as the objects they connect. This happens when the objects form an net of concepts. Let me give you an example:
- Some objects: sameness, identity, left, right, successor, middle, direction, left
- Some relationships: successor, opposite, identity
The relationships between the objects can be as simple as
- left opposite right (left is opposed to right)
And more confusing like
- opposite opposite sameness (the concept 'opposite' is the opposite of the concept 'sameness')
It is pretty hard to think of a relation as an object and even harder to think of a relationship as being an object that connects itself to some other object.
Positively hofstadterian gets the situation when identity introduces itself:
- identity identity identity (the concept 'identity' is identical to itself)
Here identity is an object that relates itself to itself. Can you picture a diagram that shows this relationship? You will need to draw identity at least twice, once (or twice) as an object, once as a relationship.
But that doesn't express the relationship very well. It should show 'identity' - the relation - as being the same thing as 'identity' - the concept - and it does just the opposite! What it does express is the dual nature of concepts as being both an object and a relation.