transformation of the whole intellectual problem space. The underlying dy-
namic is a struggle over intellectual territory of limited size. Creativity occurs
both as this space opens up and as it closes down; the result is two kinds of
intellectual innovation, by opposition and by synthesis.
The Intellectual Law of Small Numbers
The structure of intellectual life is governed by a principle: the number of
active schools of thought which reproduce themselves for more than one or
two generations in an argumentative community is on the order of three to
six. There is a strong lower limit; creativity can scarcely occur without rival
positions, and almost always in any creative period there are at least three.
There is also an upper limit; whenever there are more than about four to six
distinct positions, most of them are not propagated across subsequent genera-
tions.
The principle is dynamic over time. Positions appear and disappear, grow
stronger and weaker in adherents. The law of small numbers holds sway amid
the flux. Strong positions (those which have dominant external support),
subdivide in subsequent generations into as many as four or five factions. On
the other side, weak positions (those that have a poor or declining external
base) disappear, or amalgamate into others by syncretisms or syntheses. We
may add a corollary: a second reason why positions become weak is that the
entire attention space becomes overcrowded, violating the upper limits of the
law of small numbers. This too is an incentive to reduce the number of
positions by synthesis.
Why should this pattern exist? There are several aspects to the question.
One is structural: Why should the number of self-sustaining groups be from
three to six? There is also the dynamic issue: Why do schools rise and fall?
Combining the two issues, When schools do rise and fall, why do they split or
amalgamate?
The structural question has already been partially answered. There is a
lower limit because intellectual creativity is a conflict process. If there is any
creativity at all, there must be an organizational basis in the intellectual world
such that there are at least two positions, and in fact there are usually at
least three. If there is freedom to have more than one position, a third at least
always seems available; a plague on both houses is always a viable intellectual
strategy.^1
The upper limit also derives from the structure of conflict. Even though
new positions are largely structured by the negation of existing positions, any
individual philosopher needs allies if his or her position is to be transmitted
to anyone else and propagated across generations. Hence, proliferation of new
Partitioning Attention Space: Ancient Greece^ •^81