Evolution is difficult to define without resorting to anthropocentric assumptions. Many definitions involve the notion that evolution is marked by the emergence of increasingly complex structure or organization.
According to such definitions, the human body with its uncanny nervous system and the intricate web of cultural artifacts created by that nervous system seem obviously to stand at the apex of evolution. Can evolution be defined without falling into those assumptions? Can it be defined in a more abstract and general way without implicitly invoking the notion of progress?
Every process requires a definite amount of time, regardless of how simple the process or how rapidly the process executes. If a large number of states are equally likely to have a particular property, then a search agent that seeks to identify states that have that property will probably have to evaluate many states. The time needed to evaluate each state may be small, but because the interval of time can never be reduced to zero, the search for the particular property will carry an unavoidable cost in terms of time.
Once the states are identified, the time that the agent has spent searching can be represented as a scalar potential. If all agents are equally capable, then the time already invested by one agent obviously gives it an advantage over other agents that face the same journey through state space. To prevent some agents from reaching the equivalent of a higher potential without paying the due cost in time, we should assume that every agent must evaluate all the states.
An agent maintains its time-cost potential only if it has memory. If the agent has no memory, it will slide back down its potential and lose its advantage over other agents.
Suppose that the number of states is much too large for any agent to search, but that certain states can eliminate the need to search other states by identifying some states that do not have the property being sought. Although no state is likelier to have the property sought, certain states would be more desirable because they would narrow the search, eliminating choices and therefore effectively boosting an agent's time-cost potential. The more states that a particular state could eliminate, the more valuable it would be to an agent.
Now suppose that information about other states is itself the particular property that is being sought by the agents. Each state is like a node with one-way connections, or vectors, to other nodes. When an agent lands on the node, that node points to some other node, indicating how much information the other node has about yet other nodes. This information is defined in terms of the number of vectors that each node has. In other words, each vector tells how many vectors the node pointed to has.
In this example, the depth of the nodes will vary. Between zero and some maximum number of vectors will originate in each node. If the number of vectors varies randomly for each node, then it will turn out that some nodes will be rich in pointers to nodes that are also rich in pointers, and so on to an arbitrary depth.
Because a node has information only about the next degree of relationship, each node's depth is unknown to an agent. Shallow nodes may point to much deeper ones, and the various vectors on a given node may point to nodes of various depths. Because of that variation, some paths through state space will give an agent a greater time-cost potential than other paths will.
Evolution is about innovation, but innovation is not the same as mere novelty. Inventions leading to richer trails through pattern space, and indirectly to further innovation, are more innovative than terminal inventions. Evolution is the time-cost advantage gained through the discovery of state-space paths that account for a greater number of possible states in that space. The emergence of the ability to innovate is the crux of evolution.
Just as entropy implies the dispersal of energy, evolution implies an increase in diversity as a greater number of possible states are occupied or accounted for. This increase in diversity is the essence of evolution. Increased diversity may mean increased complexity, but diversity and complexity are not the same.
Michael Webb, 2002
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