Simplicity theory
Encyclopedia
Simplicity theory is a cognitive theory that seeks to explain the attractiveness of situations or events to human minds. It is
based on work done by scientists like Nick Chater, Paul Vitanyi
, Jean-Louis Dessalles, Jürgen Schmidhuber. It claims that interesting
situations appear simpler than expected to the observer.
, which means that, for an observer, the shortest description
of the situation is shorter than anticipated. For instance, the description of a consecutive lottery draw, such as 22-23-24-25-26-27, is
significantly shorter than a typical one, such as 12-22-27-37-38-42. The former requires only one instantiation (choice of a number
among all possible numbers in the lottery), whereas the latter requires six instantiations.
Simplicity theory makes several quantitative predictions concerning the way distance, recency, prominence (places, individuals), or
atypicality influence interestingness.
In most contexts,
corresponds to generation complexity, which is the smallest description of all parameters
that must be set in the 'world' for the situation to exist. In the lottery example, generation complexity is identical for a consecutive draw
and a typical draw (as long as no cheating is imagined) and amounts to six instantiations.
Simplicity theory avoids most criticisms addressed at Kolmogorov complexity
by considering only descriptions that are available
to a given observer (instead of any imaginable description). This amounts to saying that complexity, and thus unexpectedness, are
observer-dependent. For instance, the typical draw 12-22-27-37-38-42 will appear very simple, even simpler than the consecutive one, to
the person who played that combination.
is linked to subjective probability 
through formula:
The advantage of this formula is that subjective probability can be assessed without necessarily knowing the alternatives. Classical
approaches to probability would consider all situations in the world as having virtually zero probability to have occurred, as each
situation is complex and unique. Simplicity theory avoids this trap by considering that subjective improbability is only due to
complexity drop.
based on work done by scientists like Nick Chater, Paul Vitanyi
Paul Vitanyi
Paul Vitanyi is a Fellow of the Dutch Centrum Wiskunde & Informatica and Professor of Computer Science at the University of Amsterdam.He received his Ph.D...
, Jean-Louis Dessalles, Jürgen Schmidhuber. It claims that interesting
situations appear simpler than expected to the observer.
Overview
Technically, simplicity corresponds in a drop in Kolmogorov complexityKolmogorov complexity
In algorithmic information theory , the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object...
, which means that, for an observer, the shortest description
of the situation is shorter than anticipated. For instance, the description of a consecutive lottery draw, such as 22-23-24-25-26-27, is
significantly shorter than a typical one, such as 12-22-27-37-38-42. The former requires only one instantiation (choice of a number
among all possible numbers in the lottery), whereas the latter requires six instantiations.
Simplicity theory makes several quantitative predictions concerning the way distance, recency, prominence (places, individuals), or
atypicality influence interestingness.
Formalization
The basic concept of simplicity theory is unexpectedness, defined as the difference between expected complexity and observed complexity.In most contexts,
corresponds to generation complexity, which is the smallest description of all parametersthat must be set in the 'world' for the situation to exist. In the lottery example, generation complexity is identical for a consecutive draw
and a typical draw (as long as no cheating is imagined) and amounts to six instantiations.
Simplicity theory avoids most criticisms addressed at Kolmogorov complexity
Kolmogorov complexity
In algorithmic information theory , the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object...
by considering only descriptions that are available
to a given observer (instead of any imaginable description). This amounts to saying that complexity, and thus unexpectedness, are
observer-dependent. For instance, the typical draw 12-22-27-37-38-42 will appear very simple, even simpler than the consecutive one, to
the person who played that combination.
Connection with probability
Unexpectedness is linked to subjective probability through formula:The advantage of this formula is that subjective probability can be assessed without necessarily knowing the alternatives. Classical
approaches to probability would consider all situations in the world as having virtually zero probability to have occurred, as each
situation is complex and unique. Simplicity theory avoids this trap by considering that subjective improbability is only due to
complexity drop.