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explained explorative learning behaviour in children through his informal concepts
of assimilation (new inputs are embedded in old schemes—this may be viewed as a
type of compression) and accommodation (adapting an old schema to a new input—
this may be viewed as a type of compression improvement). Unlike Sect.
12.3
,how-
ever, these ideas did not provide sufficient formal details to permit the construction
of artificial curious agents.
Aesthetic theory is another source of relevant ideas. Why are curious or creative
humans somehow intrinsically motivated to observe or make certain novel patterns,
such as aesthetically pleasing works of art, even when this seems irrelevant for solv-
ing typical frequently recurring problems such as hunger, and even when the action
of observation requires a serious effort, such as spending hours to get to the mu-
seum? Since the days of Plato and Aristotle, many philosophers have written about
aesthetics and taste, trying to explain why some behaviours or objects are more in-
teresting or aesthetically rewarding than others, e.g. Kant (
1781
), Goodman (
1968
),
Collingwood (
1938
), Danto (
1981
), Dutton (
2002
). However, they did not have or
use the mathematical tools necessary to provide formal answers to the questions
above. What about more formal theories of aesthetic perception which emerged in
the 1930s (Birkhoff
1933
) and especially in the 1960s (Moles
1968
, Bense
1969
,
Frank
1964
,Nake
1974
, Franke
1979
)? Some of the previous attempts at explain-
ing aesthetic experience in the context of information theory or complexity theory
(Moles
1968
, Bense
1969
, Frank
1964
,Nake
1974
, Franke
1979
) tried to quantify
the intrinsic aesthetic reward through an “
ideal
” ratio between expected and unex-
pected information conveyed by some aesthetic object (its “
order
” vs its “
complex-
ity
”). The basic idea was that aesthetic objects should neither be too simple nor too
complex, as illustrated by the
Wundt curve
(Wundt
1874
), which assigns maximal
interestingness to data whose complexity is somewhere in between the extremes.
Using certain measures based on information theory (Shannon
1948
), Bense (
1969
)
argued for an ideal ratio of 1
/e
∼
37 %. Generally speaking, however, these ap-
proaches were not detailed and formal enough to construct artificial, intrinsically
motivated agents with a built-in desire to create aesthetically pleasing works of art.
The Formal Theory of Creativity does not postulate any objective ideal ratio of
this kind. Unlike some of the previous works that emphasise the significance of the
subjective observer (Frank
1964
, Franke
1979
, Frank and Franke
2002
), its dynamic
formal definition of fun reflects the
change
in the number of bits required to encode
artistic and other objects, explicitly taking into account the subjective observer's
growing knowledge as well as the limitations of its given learning algorithm (or
compression
improvement
algorithm). For example, random noise is always novel
in the sense that it is unpredictable. But it is not rewarding since it has no pattern. It is
not compressible at all; there is no way of learning to encode it better than by storing
the raw data. On the other hand, a given pattern may not be novel to a given observer
at a given point in his life, because he already perfectly understands it—again there
may be no way of learning to encode it even more efficiently. According to the
Formal Theory of Creativity, surprise and aesthetic reward are possible only where
there is measurable learning progress. The value of an aesthetic experience (the
intrinsic reward of a creative or curious maker or observer of art) is not defined by
