Addition of Simples
123
Simple rules, acting over and over on each of a large number of objects,
are able to give rise to astonishingly complex collective behavior. In fact, they
often generate repetitive patterns having great regularity and symmetry. This
fact is at the origin of the new science of Complexity, which is striving to work
out the details of how simple laws lead to complex global phenomena. The
perplexing intricacy that we see in the world is actually the cumulative result
of simple laws that have been operating for billions of years, creating patterns
upon patterns.
A computer program known as the Game of Life was devised in 1970 by
the British mathematician John Conway: It is a provocative example of the
way simple elements, manipulated according to simple rules, can give rise to
complex global behavior that looks like the product of careful design. The game
unfolds in successive steps, one step at a time. It consists of a two-dimensional
grid like a chessboard: Each square may be either dark or lit, and there are three
rules whereby each square interacts with its neighbors. (1) Every lit square with
fewer than two—or more than three—lit neighbors goes dark. (2) All the other
lit squares remain lit. (3) Any unlit square with three lit neighbors lights up.
Each step of the game leads to the next step by applying one of these rules.
The game begins with an arbitrary configuration of lit squares, and in one
cycle, the rules are applied to every square. The same is done on every cycle, over
and over. Depending on the initial configuration, all kinds of regular patterns
evolve and dance in unison across the screen as the basic cycle is repeated.
Patterns build on patterns and appear to be purposefully designed, though in
fact the patterns evolve blindly. 1
The fact that the physical world evolves by addition of simples is enormously
significant: It reveals that Gestalt, or wholistic processes, do not play a constitutive
role in the physical world. When global patterns emerge, they are the result of elementary laws. Physical laws are not irreducibly wholistic. In fact, global processes
are alien to the strictly physical side of reality, for they arise in perception only.
For complex objects, their Gestalt unity is a creation of the mind and is
not an aspect of the underlying matter: Their global character is the way they
appear to observers. Their wholeness rests on a material substrate but is not
material—it exists only in perception. The unity seen in complex objects does
not dwell in the physical world but in perceivers.
For instance, Newton’s equations, which apply to pairs of bodies in space,
determine the trajectories of planets around the sun. However, these trajectories
are meaningful only to beings who see and conceive in Gestalts. The shape of
an orbit, though it exists only in the eyes of a Gestalt observer, is a direct
consequence of Newton’s laws, and no further principle is needed to account
for it.
123
Simple rules, acting over and over on each of a large number of objects,
are able to give rise to astonishingly complex collective behavior. In fact, they
often generate repetitive patterns having great regularity and symmetry. This
fact is at the origin of the new science of Complexity, which is striving to work
out the details of how simple laws lead to complex global phenomena. The
perplexing intricacy that we see in the world is actually the cumulative result
of simple laws that have been operating for billions of years, creating patterns
upon patterns.
A computer program known as the Game of Life was devised in 1970 by
the British mathematician John Conway: It is a provocative example of the
way simple elements, manipulated according to simple rules, can give rise to
complex global behavior that looks like the product of careful design. The game
unfolds in successive steps, one step at a time. It consists of a two-dimensional
grid like a chessboard: Each square may be either dark or lit, and there are three
rules whereby each square interacts with its neighbors. (1) Every lit square with
fewer than two—or more than three—lit neighbors goes dark. (2) All the other
lit squares remain lit. (3) Any unlit square with three lit neighbors lights up.
Each step of the game leads to the next step by applying one of these rules.
The game begins with an arbitrary configuration of lit squares, and in one
cycle, the rules are applied to every square. The same is done on every cycle, over
and over. Depending on the initial configuration, all kinds of regular patterns
evolve and dance in unison across the screen as the basic cycle is repeated.
Patterns build on patterns and appear to be purposefully designed, though in
fact the patterns evolve blindly. 1
The fact that the physical world evolves by addition of simples is enormously
significant: It reveals that Gestalt, or wholistic processes, do not play a constitutive
role in the physical world. When global patterns emerge, they are the result of elementary laws. Physical laws are not irreducibly wholistic. In fact, global processes
are alien to the strictly physical side of reality, for they arise in perception only.
For complex objects, their Gestalt unity is a creation of the mind and is
not an aspect of the underlying matter: Their global character is the way they
appear to observers. Their wholeness rests on a material substrate but is not
material—it exists only in perception. The unity seen in complex objects does
not dwell in the physical world but in perceivers.
For instance, Newton’s equations, which apply to pairs of bodies in space,
determine the trajectories of planets around the sun. However, these trajectories
are meaningful only to beings who see and conceive in Gestalts. The shape of
an orbit, though it exists only in the eyes of a Gestalt observer, is a direct
consequence of Newton’s laws, and no further principle is needed to account
for it.