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12.5 Aesthetic Reward
=
Change of Subjective Compressibility?
Most people use concepts such as
beauty
and
aesthetic pleasure
in an informal way.
Some say one should not try to nail them down formally; formal definitions should
introduce new, unbiased terminology instead. For historic reasons, however, I will
not heed this advice in the present section. Instead I will consider previous formal
definitions of
pristine
variants of beauty (Schmidhuber
1997c
) and aesthetic value
I(D,O(t))
as in Sect.
12.3.1
.
Pristine
in the sense that they are
not a priori
re-
lated to pleasure derived from external rewards or punishments. To illustrate the
difference: some claim that a hot bath on a cold day feels
beautiful
due to rewards
for achieving prewired target values of external temperature sensors (external in the
sense of: outside the brain which is controlling the actions of its external body). Or
asongmaybecalled
beautiful
for emotional reasons by some who associate it with
memories of external pleasure through their first kiss. This is different from what
we have in mind here—we are focusing only on beauty in the sense of elegance and
simplicity, and on rewards of the intrinsic kind reflecting learning progress, that is,
the discovery of previously unknown types of simplicity, or novel patterns.
According to the
Formal Theory of Beauty
(Schmidhuber
1997c
;
1998
;
2006a
),
among several sub-patterns classified as
comparable
by a given observer, the sub-
jectively most beautiful (in the pristine sense) is the one with the simplest (shortest)
description, given the observer's current particular method for encoding and mem-
orising it. For example, mathematicians find beauty in a simple proof with a short
description in the formal language they are using. Others find beauty in geometri-
cally simple low-complexity drawings of various objects.
According to the
Formal Theory of Creativity
, however, what's beautiful is not
necessarily
interesting or aesthetically rewarding
at a given point in the observer's
life. A beautiful thing is interesting only as long as the algorithmic regularity that
makes it simple has not yet been fully assimilated by the adaptive observer who is
still learning to encode the data more efficiently (many artists agree that pleasing art
does not have to be beautiful).
Following Sect.
12.3
, aesthetic reward or interestingness are related to pristine
beauty as follows:
Aesthetic reward is the first derivative of subjective beauty
.As
the learning agent improves its compression algorithm, formerly apparently ran-
dom data parts become subjectively more regular and beautiful, requiring fewer
and fewer computational resources for their encoding. As long as this process is
not over, the data remains interesting, but eventually it becomes boring even if it
remains beautiful.
Section
12.3
already showed a simple way of calculating subjective interesting-
ness: count how many bits are needed to encode (and decode in constant time) the
data before and after learning; the difference (the number of
saved
bits) corresponds
to the internal joy or intrinsic reward for having found or made a new, previously
unknown regularity—a novel pattern.
