The Division Number
"There are two types of people in the world ;
Those who divide the world into two parts
and those who do not." .......... Anonymous
is the number into which we most often divide things.
In dealing with abstract logical principles, whenever one is identified, it is also possible to 'find' its "mate".
Examples of such mated principles are:
electric - magnetic|
straight - curved
capitalism - communism
male - female
time - space
Moreover, these are not arbitrary distinctions. Rather they are part of the natural order of things originating from the separation of quantity from quality (1,0) which "initializes" existence itself (see Natex.htm).
In keeping with this rule of "mated principles", we might also expect that things are arranged in another manner (a type of hierarchical structure related to the foregoing).
And it is true. We may divide specific things into categories the members of which do not divide into mated principles. These are unique entities rather than generalized concepts
(things like family trees, types of vegetables, team player rosters, etc.).
We very often divide things into two categories even when it is not strictly indicated in order to take advantage of the simplest divisional possibility. For example:
If you want to estimate the number of people in a crowd you might obtain an aerial photograph of the crowd ... then ... cut it in half ... then cut the half in half again, etc. until you've got a picture with few enough people to count by hand. Then back calculate the total number of people in the crowd by reverse-multiplying the process . (This works great for a big tub of pennies also. And you can get a high/low estimate by asking another disinterested party to pick between the halves - high for one estimate then low.)
I think you can see why it would be less desirable to divide things into 'three' or 'seven' pieces.
I call the division of concepts into mated principles
Scalar and Vector Modes (for want of a better terminology).
This might be objectionable to mathematicians because these terms do not mean exactly what I intend them to mean in this context.