El principio de proporcionalidad como criterio del juez al momento de implementar

A meme can be defined by its functional ability to sustainably reproduce within a society through social learning. This is similar to how computer viruses are defined as a subset of all possible combinations of code strings. In this view, a meme’s semantic information contains a function definition. This approach to definition has precedent in biology’s definition of life, in which reproduction is a necessary process (Koshland Jr., 2002). Wilkins(1998) expresses this condition for memes in his articleWhat’s in a Meme?

The necessary condition of recursive reproducibility can be expressed explicitly. The following symbols will be defined:

S - The society of agents under analysis. Env - The environment that an agent inhabits. Ω - All possible environments.

Xa - All information stored by an agenta.

xa - Semantic information for a meme, as understood by agenta. xa∈Xa. Ba(Env, Xa) - Behavior function of agent a. Alters and returns Env, returning it as a changed environmentEnv∗.

Ba(Env, xa) - Behavior function of an agentawhen expressing xa.

Pa(Env, Xa) - Perception function of agent a. Alters and returns Xa, returning it as a changed set of stored informationX_a∗.

The term “agent” is used to define members of a society, as it connects this definition to agent based simulation techniques explored later. At this stage, interchanging humans with agents must be discouraged, as significant evidence exists for cultural learning by apes, dolphins, and songbirds (Zentall,2007).

The reproduction process of a meme is defined in Eqn. 2.1. A single reproduction requires three steps, each occurring over some span of time. First, the agent’s relationship to the environment must activate some behavioral expression of the meme, changing their patterns of activity. Second, this behavior

Meme Reproduction Process

Assume a1, a2 ∈S s.t. a1 =6 a2 &xa1 ∈Xa1 &

@(xa2 ∈Xa2) s.t. xa2 ≈xa1

Define R(a1, a2, Env) :

Ba1(Env, x)∈Ba1(Env, Xa1) Env∗ =Ba1(Env, x) X_a∗₂ =Pa(Env∗, Xa2) where∃(xa2 ∈X ∗ a2) s.t. :xa2 ≈xa1 (2.1)

Meme Reproduction Non-Triviality Condition

P{∃xa2 ∈X ∗ a2 :xa2 ≈xa1kBa1(Env, x)∈Ba1(Env, Xa1)} P{∃xa2 ∈X ∗ a2 :xa2 ≈xa1kBa1(Env, x)∈/ Ba1(Env, Xa1)} (2.2)

must alter the environment in some observable way. Finally, a second agent must perceive this environment either during or after the behavior and learn new information similar to the meme. The question of what makes memes similar will be discussed further in Section 4.1 and in further depth in Appendix A. For reproduction (and the meme itself) to be non-trivial then Eqn. 2.2 must hold. Eqn. 2.2 formally states that the probability of learning the semantics would be much lower without observing the expression of the meme. This means that reproduction involves a transmission of semantic, meaningful information as opposed to a coincidental spontaneous learning event that would have been likely without such an observation.

From a certain standpoint, this definition of meme reproduction may seem overly general: any semantic information could be a meme, depending on the population and the environmental context. Indeed, if one makes no assumptions about the society or the environment- any information could be a meme. As a result, any meaningful study of memes must be tied to the society and environment. As the the environment and societal context is constrained, the set of possible memes becomes respectively constrained. As such, this definition of memes uses the society and environmental contexts almost like parameters- one cannot define memes without defining these two.

The society is important on many levels, depending on the level of specification given. The first obvious constraint is the species involved. For instance, humans appear capable of spreading a much different and wider array of memes than songbirds. Within a species, there are semantic requisites to

learning certain information. For example, one cannot learn that an apple is on a dog without also learning about the concept of an apple and a dog. This may be thought of as a zone of proximal development for learning a meme, where knowing necessary concepts allows learning the meaningful information of the meme (Vygotsky,1980). Through more detailed specification of the society, the set of possible memes can be constrained significantly. The environment, of which the communication medium is a part, also defines what memes can theoretically reproduce. In an extremely noisy environment, with no verbal communication possible, there would be significant constraints on the memes that could exist.

Even after maximally constraining the possible semantic information that can be reproduced, humans still have a vast amount of possible semantic information that can be communicated and reproduced. This definition may seem too general, bordering on a “theory of everything.” Indeed, the reproduction process is general with respect to any semantic information. The special quality that differentiates memes from the larger body of semantic information is its ability to reproduce recursively- a significant additional constraint.