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The Rarity Problem.
Payoff is sparsely distributed in a vast space of
possibilities. In the Klondike metaphor, gold is scarce. In the possi-
bility space of imaginable biological organisms, very few are actually
viable. In the space of possible electronic circuit layouts, few do any-
thing at all, much less anything useful.
As the examples of biological organisms and electronic circuits make
plain, the possibility spaces of biological or human invention are vast
for combinatorial reasons: Proteins or transistors can be assembled in
innumerable configurations. In discussions of heuristic search, this is
often called the problem of "combinatorial explosions," which gen-
erate far too many combinations to be explored by exhaustive search
processes in reasonable periods of time.
The Isolation Problem.
Regions of payoff often lie isolated or semi-
isolated. In the Klondike metaphor, pockets of gold occur here and
there, unconnected with one another. In the possibility space of im-
aginable biological organisms, some imaginable biological organisms,
viable in principle, might be quite unlike anything that exists. In the
world of inventions, a fruitful invention might lack dose precedent.
The Oasis Problem.
This is the flip side of the isolation problem, which
says that some regions are hard to get to. The oasis problem says that
regions of payoff or even promise are hard to leave. In the Klondike
metaphor, even if a rich area becomes nearly mined out, it's tempting
to stay and rework it. After all, when will one really find another?
The Plateau Problem.
In many regions, directions toward greater
promise are not clear. In the Klondike metaphor, a prospector may
find no gold, or traces of gold uniformly across a wide area. In what
direction does the mother lode lie? In the world of biology, a whole
range of biological forms may be more or less equally adaptive with
no natural "direction" for evolution to pursue (although of course
evolution does not really pursue directions, as we shall see). In the
world of inventions, many alternative ideas may seem equally prom-
ising, or do an equally adequate if not ideal job.
(c)Dimensions of Creativity
Payoff is sparsely distributed in a vast space of
possibilities. In the Klondike metaphor, gold is scarce. In the possi-
bility space of imaginable biological organisms, very few are actually
viable. In the space of possible electronic circuit layouts, few do any-
thing at all, much less anything useful.
As the examples of biological organisms and electronic circuits make
plain, the possibility spaces of biological or human invention are vast
for combinatorial reasons: Proteins or transistors can be assembled in
innumerable configurations. In discussions of heuristic search, this is
often called the problem of "combinatorial explosions," which gen-
erate far too many combinations to be explored by exhaustive search
processes in reasonable periods of time.
The Isolation Problem.
Regions of payoff often lie isolated or semi-
isolated. In the Klondike metaphor, pockets of gold occur here and
there, unconnected with one another. In the possibility space of im-
aginable biological organisms, some imaginable biological organisms,
viable in principle, might be quite unlike anything that exists. In the
world of inventions, a fruitful invention might lack dose precedent.
The Oasis Problem.
This is the flip side of the isolation problem, which
says that some regions are hard to get to. The oasis problem says that
regions of payoff or even promise are hard to leave. In the Klondike
metaphor, even if a rich area becomes nearly mined out, it's tempting
to stay and rework it. After all, when will one really find another?
The Plateau Problem.
In many regions, directions toward greater
promise are not clear. In the Klondike metaphor, a prospector may
find no gold, or traces of gold uniformly across a wide area. In what
direction does the mother lode lie? In the world of biology, a whole
range of biological forms may be more or less equally adaptive with
no natural "direction" for evolution to pursue (although of course
evolution does not really pursue directions, as we shall see). In the
world of inventions, many alternative ideas may seem equally prom-
ising, or do an equally adequate if not ideal job.
(c)Dimensions of Creativity
