2. The interesting stuff is in the middle
``Beauty,'' i.e., that which makes something interesting, is related
to a mixture of regularity and irregularity. When things are too
regular, we usually find them to be uninteresting because they yield
no surprises for us. Complementary to this, highly irregular things
are often uninteresting because they make no sense. In the middle,
between regularity and irregularity, lies a place where things can be
understood, but not completely.


This idea is best illustrated with an example that appears in the book
(paraphrased from Section 22.6, ``Internal Representations'').
Consider the task of finding a good movie to see. You have at
your disposal several movie reviews and some prior knowledge
concerning the relative tastes of the individual movie reviewers.
Some reviewers seem to like everything ever put on film, so what they
say about any movie is useless, in that it tells you nothing at all
about whether or not you will like a movie. Other movie reviewers
have such complex tastes that you may be hard pressed to ever guess
what kind of movie they would like or dislike. However, if you find
that your taste in science fiction films is similar to one particular
critic's, or that your preferences for comedy films are exactly
opposite to those of another critic, then these are both useful pieces
of information for you to use when picking a movie.
The key point here is that the usefulness of a movie review
depends on the relative complexity of the critic: if he or she is
either too simplistic or too complex, then the information they
provide is negligible.
We can extend the analogy to partially describe what makes a movie
entertaining. Both predictable and random plots or boring. But
something in between, that contains both familiarity and surprise,
makes a movie fun to watch.
Still not convinced? Then consider music. Very few people enjoy
listening to simple scales, no matter how precisely they are played.
Nor do people enjoy listening to random beeps. Interestingly,
analysis of classical music often reveals a fractal representation for
the notes, which gets to the heart of the idea that ``beautiful''
things contain a mixture of regularity and irregularity.
This basic idea, that neat things are at the midpoint between
computability (simplicity) and incomputability (randomness) can be
extended to just about every conceivable domain. The table below
(adapted from a table in Chapter 24) is a partial listing of a broad
range of things that seem to fit with this idea.

Computable 
Partially Computable 
Incomputable 
Sets 
recursive 
RE and CORE 
not RE & not CORE 
Numbers 
rational 
computable irrational 
incomputable 
Programs 
trivially (never) halt 
possibly halt 
 
Proofs 
true or false 
profound statements 
unprovable 
NPComplete Problems 
underconstrained 
critically constrained 
overconstrained 

Deterministic Geometry 
Euclidean 
deterministic fractal 
 
Stochastic Geometry 
 
stochastic fractal 
pure noise 
AC 
compressible 
possibly incompressible 
incompressible 
Mandelbrot Set 
white regions 
border regions 
black regions 

Continuous Dynamics 
fixed point 
chaotic 
highdimensional chaos or stochastic 
Discrete Dynamics 
regular from oversampling 
complex at midsampling 
irregular from undersampling 
Attractors 
integral dimensions 
strange 
infinite dimensional 
Mater 
solid 
liquid 
gas 

Wolfram CA 
class I or II 
class IV 
class III 
Langton's lambda 
lambda < 1/3 
lambda near 1/2 
lambda > 2/3 
Agent Interactions 
globally coordinated or always cooperative 
locally coordinated or cooperative and cooperative 
uncoordinated or always competitive 
NK Nets 
K = 1 
K = 2 
2 < K <= N 
Sandpiles 
flat and stable 
critical 
tall and unstable 
Economics 
communism 
free but regulated 
unrestrained 
Governments 
dictatorial 
democracy 
anarchy 

Patterns 
consistent 
hidden order 
inconsistent 
Models 
not selfreferential 
coadaptive or recurrent 
hopelessly selfreferential 
Search Methods 
local or greedy 
hybrid 
exhaustive 
Search Spaces 
smooth 
complex structured 
pathological 